User:Jon Awbrey/Philosophical Notes
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- CROM. Critical Reflection On Method
- DIEP. De In Esse Predication
- HAPA. Hypostatic And Prescisive Abstraction
- JITL. Just In Time Logic
- NEKS. New Elements • Kaina Stoicheia
- OLOD. Quine On The Limits Of Decision
- POLA. Philosophy Of Logical Atomism
- RTOK. Russell's Theory Of Knowledge
- RTOP. Russell's Treatise On Propositions
- SABI. Synthetic/Analytic ≟ Boundary/Interior
- SYNF. Syntactic Fallacy
- TDOE. Quine's Two Dogmas Of Empiricism
- VOLS. Verities Of Likely Stories
- VOOP. Varieties Of Ontology Project
- VORE. Varieties Of Recalcitrant Experience
- Document Histories
CROM. Critical Reflection On Method
|
Two things here are all-important to assure oneself of and to remember. The first is that a person is not absolutely an individual. His thoughts are what he is “saying to himself”, that is, is saying to that other self that is just coming into life in the flow of time. When one reasons, it is that critical self that one is trying to persuade; and all thought whatsoever is a sign, and is mostly of the nature of language. The second thing to remember is that the man's circle of society (however widely or narrowly this phrase may be understood), is a sort of loosely compacted person, in some respects of higher rank than the person of an individual organism. It is these two things alone that render it possible for you — but only in the abstract, and in a Pickwickian sense — to distinguish between absolute truth and what you do not doubt. (Peirce, CP 5.421). |
Charles Sanders Peirce (1905), “What Pragmatism Is”, The Monist 15, 161–181. Reprinted, Collected Papers, CP 5.411–437.
DIEP. De In Esse Predication
DIEP. Note 1
| [A Boolian Algebra With One Constant] | | Every logical notation hitherto proposed has an unnecessary number of signs. | Is is by means of this excess that the calculus is rendered easy to use and | that a symmetrical development of the subject is rendered possible; at the | same time, the number of primary formulae is thus greatly multiplied, those | signifying facts of logic being very few in comparison with those which | merely define the notation. I have thought that it might be curious to | see the notation in which the number of signs should be reduced to a | minimum; and with this view I have constructed the following. The | apparatus of the Boolian calculus consists of the signs, =, > (not | used by Boole, but necessary to express particular propositions), | +, -, x [·], 1, 0. In place of these seven signs, I propose to | use a single one. | | C.S. Peirce, CP 4.12, untitled paper circa 1880.
DIEP. Note 2
| [A Boolian Algebra With One Constant] (cont.) | | I begin with the description of the notation for conditional | or "secondary" propositions. The different letters signify | propositions. Any one proposition written down by itself | is considered to be asserted. Thus, | | A | | means that the proposition A is true. | Two propositions written in a pair are | considered to be both denied. Thus, | | A B | | means that the propositions A and B | are both false; and | | A A | | means that A is false. We may have pairs of pairs of propositions | and higher complications. In this case we shall make use of commas, | semicolons, colons, periods, and parentheses, just as [in] chemical | notation, to separate pairs which are themselves paired. These | punctuation marks can no more count for distinct signs of | algebra, than the parentheses of the ordinary notation. | | C.S. Peirce, CP 4.13, untitled paper circa 1880.
DIEP. Note 3
| [A Boolian Algebra With One Constant] (cont.) | | To express the proposition: "If S then P", | first write: | | A | | for this proposition. But the proposition | is that a certain conceivable state of things | is absent from the universe of possibility. | Hence instead of A we write: | | B B | | Then B expresses the possibility of S being true and | P false. Since, therefore, SS denies S, it follows | that (SS, P) expresses B. Hence we write: | | SS, P; SS, P. | | C.S. Peirce, CP 4.14, untitled paper circa 1880.
DIEP. Note 4
| I have maintained since 1867 that there is but one primary and fundamental | logical relation, that of illation, expressed by 'ergo'. A proposition, | for me, is but an argumentation divested of the assertoriness of its | premiss and conclusion. This makes every proposition a conditional | proposition at bottom. In like manner a "term", or class-name, is | for me nothing but a proposition with its indices or subjects left | blank, or indefinite. The common noun happens to have a very | distinctive character in the Indo-European languages. In most | other tongues it is not sharply discriminated from a verb or | participle. "Man", if it can be said to mean anything by | itself, means "what I am thinking of is a man". This | doctrine, which is in harmony with the above theory | of signs, gives a great unity to logic. | | C.S. Peirce, 'Collected Papers', CP 3.440, |"The Regenerated Logic", 'Monist', vol. 7, | pp. 19-40, 1896.
DIEP. Note 5
| Cicero and other ancient writers mention a great dispute between | two logicians, Diodorus and Philo, in regard to the significance | of conditional propositions. This dispute has continued to our | own day. The Diodoran view seems to be the one which is natural | to the minds of those, at least, who speak the European languages. | How it may be with other languages has not been reported. The | difficulty with this view is that nobody seems to have succeeded | in making any clear statement of it that is not open to doubt as | to its justice, and that is not pretty complicated. The Philonian | view has been preferred by the greatest logicians. Its advantage | is that it is perfectly intelligible and simple. Its disadvantage | is that it produces results which seem offensive to common sense. | | C.S. Peirce, 'Collected Papers', CP 3.441, |"The Regenerated Logic", 'Monist', vol. 7, | pp. 19-40, 1896.
DIEP. Note 6
| In order to explain these positions, it is best | to mention that 'possibility' may be understood | in many senses; but they may all be embraced | under the definition that that is possible | which, in a certain state of information, | is not known to be false. By varying the | supposed state of information all the | varieties of possibility are obtained. | | Thus, 'essential' possibility | is that which supposes nothing | to be known except logical rules. | |'Substantive' possibility, on the other | hand, supposes a state of omniscience. | | Now the Philonian logicians have always insisted | upon beginning the study of conditional propositions | by considering what such a proposition means in a state | of omniscience; and the Diodorans have, perhaps not very | adroitly, commonly assented to this order of procedure. | Duns Scotus* terms such a conditional proposition | a "consequentia simplex de inesse". | | According to the Philonians, "If it is now lightening it will thunder", | understood as a consequence 'de inesse', means "It is either not now | lightening or it will soon thunder". According to Diodorus, and | most of his followers (who seem here to fall into a logical trap), | it means "It is now lightening and it will soon thunder". | |* 'Quaestiones in Octo libror Physicorum Aristotelis', Liber 1, Question 2. | | C.S. Peirce, 'Collected Papers', CP 3.442, |"The Regenerated Logic", 'Monist', vol. 7, | pp. 19-40, 1896.
DIEP. Note 7
| Although the Philonian views lead to such inconveniences as that it | is true, as a consequence 'de inesse', that if the Devil were elected | president of the United States, it would prove highly conducive to the | spiritual welfare of the people (because he will not be elected), yet | both Professor Schroeder and I prefer to build the algebra of relatives | upon this conception of the conditional proposition. The inconvenience, | after all, ceases to seem important, when we reflect that, no matter | what the conditional proposition be understood to mean, it can always | be expressed by a complexus of Philonian conditionals and denials of | conditionals. It may, however, be suspected that the Diodoran view | has suffered from incompetent advocacy, and that if it were modified | somewhat, it might prove the preferable one. | | C.S. Peirce, 'Collected Papers', CP 3.443, |"The Regenerated Logic", 'Monist', vol. 7, | pp. 19-40, 1896.
DIEP. Note 8
| The consequence 'de inesse', "if A is true, then B is true", | is expressed by letting i denote the actual state of things, | A_i mean that in the actual state of things A is true, and | B_i mean that in the actual state of things B is true, and | then saying "If A_i is true then B_i is true", or, what is | the same thing, "Either A_i is not true or B_i is true". | | But an 'ordinary' Philonian conditional is expressed | by saying, "In 'any' possible state of things, i, | either A_i is not true, or B_i is true". | | Now let us express the categorical proposition, | "Every man is wise". Here, we let m_i mean that | the individual object i is a man, and w_i mean that | the individual object i is wise. Then, we assert that, | "taking any individual of the universe, i, no matter | what, either that object, i, is not a man or that | object, i, is wise"; that is, whatever is a man | is wise. That is, "whatever 'i' can indicate, | either m_i is not true or w_i is true". | | The conditional and categorical propositions | are expressed in precisely the same form; | and there is absolutely no difference, | to my mind, between them. The 'form' | of relationship is the same. | | C.S. Peirce, 'Collected Papers', CP 3.444-445, |"The Regenerated Logic", 'The Monist', vol. 7, | pp. 19-40, 1896.
DIEP. Note 9
| The question is what is the sense which is most usefully attached | to the hypothetical proposition in logic? Now, the peculiarity of | the hypothetical proposition is that it goes out beyond the actual | state of things and declares what 'would' happen were things other | than they are or may be. The utility of this is that it puts us in | possession of a rule, say that "if A is true, B is true", such that | should we hereafter learn something of which we are now ignorant, | namely that A is true, then by virtue of this rule, we shall find | that we know something else, namely, that B is true. | | There can be no doubt that the Possible, in its primary meaning, | is that which may be true for aught we know, that whose falsity | we do not know. The purpose is subserved, then, if throughout | the whole range of possibility, in every state of things in | which A is true, B is true too. | | The hypothetical proposition may therefore be falsified | by a single state of things, but only by one in which A | is true while B is false. States of things in which A | is false, as well as those in which B is true, cannot | falsify it. | | If, then, B is a proposition true in every case | throughout the whole range of possibility, the | hypothetical proposition, taken in its logical | sense, ought to be regarded as true, whatever | may be the usage of ordinary speech. | | If, on the other hand, A is in no case true, throughout the | range of possibility, it is a matter of indifference whether | the hypothetical be understood to be true of not, since it is | useless. But it will be more simple to class it among true | propositions, because the cases in which the antecedent is | false do not, in any other case, falsify a hypothetical. | This, at any rate, is the meaning which I shall attach | to the hypothetical proposition in general, in this | paper. | | C.S. Peirce, 'Collected Papers', CP 3.374, |"On the Algebra of Logic: A Contribution to the Philosophy of Notation", |'American Journal of Mathematics', vol. 7, no. 2, pp. 180-202, 1885.
DIEP. Note 10
| Indexical Dicisigns seem to have no important varieties; but propositions are | divisible, generally by dichotomy primarily in various ways. In the first place, | according to 'Modality' or 'Mode', a proposition is either 'de inesse' (the phrase | used in the 'Summulae'*) or 'modal'. A proposition 'de inesse' contemplates only | the existing state of things -- existing, that is, in the logical universe of | discourse. A modal proposition takes account of a whole range of possibility. | According as it asserts something to be true or false throughout the whole | range of possibility, it is 'necessary' or 'impossible'. According as it | asserts something to be true or false within the range of possibility | (not expressly including or excluding the existent state of things), | it is 'possible' or 'contingent'. (The terms are all from Boethius). | |* Petrus Hispanus, 'Summulae Logicales', p. 71B. | | C.S. Peirce, 'Collected Papers', CP 2.323, | from an unpublished "Syllabus", circa 1902.
DIEP. Note 11
| It remains to show in what manner I suppose the ideas of the other forms | of propositions to be evolved; and this will be a chapter of what I have | called "speculative rhetoric". I may begin by remarking that I use the | sign -< for the sign of inclusion. I believe I was the first to show, | in 1867, that Boole's algebra, as he left it, was unfit to express | particular propositions. Following out that idea, I showed, in 1870, | before anybody else, that we needed in logic a sign corresponding to | the sign =<, but that sign is unsatisfactory because it implies that | the relation is a combination of the relations expressed by < and =, | whereas in truth, as I demonstrated, it is more simple than either. ... | | Accordingly, | | h_i -< d_i | | means that on the occasion i, if the idea h is definitively | forced upon the mind, then on the same occasion the idea d | is definitively forced upon the mind. On the Philonian view | this is the same as to say that on the occasion i, either the | idea h is not definitively forced upon the mind or on the same | occasion the idea d is definitively forced upon the mind. From | that hypothesis, the rules of the sign -< may be mathematically | deduced. ... | | C.S. Peirce, 'Collected Papers', CP 2.356, |"That Categorical and Hypothetical Propositions | are one in essence, with some connected matters", | circa 1895.
DIEP. Note 12
| It must be remembered that | possibility and necessity | are relative to the state | of information. | | C.S. Peirce, 'Collected Papers', CP 4.517, |"The Gamma Part of Existential Graphs", |"Lowell Lectures of 1903", Lecture 4.
DIEP. Note 13
| A modal dyadic relation is either a relation between characters | (including qualities and relations of individuals, of characters, | and of concepts), or between symbols, or concepts. | | Dyadic relations between characters mostly correspond to | relations between the subjects of those characters or to | relations between the symbols of them; and such need not | be separately considered. There remain some relations | between characters, especially between qualities, which | do not seem to be derivative. Such are the relations | of "being more intense than", of "being disparate to" | (or in applicability to subjects of the same category, | as multitude and intensity are disparate). But, so | far as appears at present, no particular logical | interest attaches to such relations, and they | will here be passed by. | | Dyadic relations between symbols, or concepts, are matters of logic, | so far as they are not derived from relations between the objects and | the characters to which the symbols refer. Noting that we are limiting | ourselves to modal 'dyadic' relations, it may probably be said that those | of them that are truly and fundamentally dyadic arise from corresponding | relations between propositions. To exemplify what is meant, the dyadic | relations of logical 'breadth' and 'depth', often called denotation and | connotation, have played a great part in logical discussions, but these | take their origin in the triadic relation between a sign, its object, | and its interpretant sign; and furthermore, the distinction appears | as a dichotomy owing to the limitation of the field of thought, which | forgets that concepts grow, and that there is thus a third respect | in which they may differ, depending on the state of knowledge, or | amount of information. To give a good and complete account of | the dyadic relations of concepts would be impossible without | taking into account the triadic relations which, for the | most part, underlie them; and indeed almost a complete | treatise upon the first of the three divisions of logic | would be required.* | |* |[ The three divisions of logic are: | 1. Speculative Grammar (= the theory of signs) | 2. Critical Logic (= denotative semantics) | 3. Speculative Rhetoric (= methodology, methodeutic)] | | C.S. Peirce, 'Collected Papers', CP 3.606-608, |'A Syllabus of Certain Topics of Logic', intended | as a supplement to the "Lowell Lectures of 1903".
DIEP. Note 14
| Introduction to the Logic of Quantity | | The great importance of the idea of quantity in demonstrative reasoning | seems to me not yet sufficiently explained. It appears, however, to be | connected with the circumstance that the relations of being greater | than and of being at least as great as are transitive relations. | Still, a satisfactory evolutionary logic of mathematics remains a | desideratum. I intend to take up that problem in a future paper | ["The Simplest Mathematics", CP 4.227-323, 1902]. Meantime the | development of projective geometry and of geometrical topics has | shown that there are at least two large mathematical theories of | continuity into which the idea of continuous 'quantity', in the | usual sense of that word, does not enter at all. For projective | geometry Schubert has developed an algebraical calculus which has | a most remarkable affinity to the Boolian algebra of logic. It is, | however, imperfect, in that it only gives imaginary points, rays, and | planes, without deciding whether they are real or not. This defect cannot | be remedied until topology -- or, as I prefer to call it, mathematical topics -- | has been further developed and its logic accurately analysed. To do this | ought to be one of the first tasks of exact logicians. But before that | can be accomplished, a perfectly satisfactory logical account of the | conception of continuity is required. This involves the definition | of a certain kind of infinity; and in order to make that quite clear, | it is requisite to begin by developing the logical doctrine of infinite | multitude. This doctrine still remains, after the works of Cantor, Dedekind, | and others, in an inchoate condition. For example, such a question remains | unanswered as the following: Is it, or is it not, logically possible for | two collections to be so multitudinous that neither can be put into a | one-to-one correspondence with a part or the whole of the other? | To resolve this problem demands, not a mere 'application' of | logic, but a further 'development' of the conception of | logical possibility. | | C.S. Peirce, 'Collected Papers', CP 3.526, |"The Logic of Relatives", 'Monist', vol. 7, | pp. 161-217, 1897.
DIEP. Note 15
| Introduction to the Logic of Quantity (cont.) | | I formerly defined the possible as that which in a given | state of information (real or feigned) we do not know not | to be true. But this definition today seems to me only a | twisted phrase which, by means of two negatives, conceals | an anacoluthon. We know in advance of experience that | certain things are not true, because we see they are | impossible. | | Thus, if a chemist tests the contents of a hundred bottles for fluorine, | and finds it present in the majority, and if another chemist tests them | for oxygen and finds it in the majority, and if each of them reports his | results to me, it will be useless for them to come to me together and say | that they know infallibly that fluorine and oxygen cannot be present in the | same bottle; for I see that such infallibility is 'impossible'. I know it | is not true, because I satisfy myself that there is no room for it even in | that ideal world of which the real world is but a fragment. I need no | sensible experimentation, because ideal experimentation establishes | a much broader answer to the question than sensible experimentation | could give. | | It has come about through the agencies of development that man is | endowed with intelligence of such a nature that he can by ideal | experiments ascertain that in a certain universe of logical | possibility certain combinations occur while others do not | occur. Of those which occur in the ideal world some do | and some do not occur in the real world; but all that | occur in the real world occur also in the ideal world. | For the real world is the world of sensible experience, | and it is a part of the process of sensible experience | to locate its facts in the world of ideas. This is what | I mean by saying that the sensible world is but a fragment | of the ideal world. | | C.S. Peirce, 'Collected Papers', CP 3.527, |"The Logic of Relatives", 'Monist', vol. 7, | pp. 161-217, 1897.
DIEP. Note 16
| Introduction to the Logic of Quantity (cont.) | | In respect to the ideal world we are virtually omniscient; that is | to say, there is nothing but lack of time, of perseverance, and of | activity of mind to prevent our making the requisite experiments | to ascertain positively whether a given combination occurs or not. | Thus, every proposition about the ideal world can be ascertained | to be true or false. A description of thing which occurs in that | world is 'possible, in the substantive logical sense'. | | Very many writers assert that everything is logically possible which involves | no contradiction. Let us call that sort of logical possibility, 'essential', | or 'formal', logical possibility. It is not the only logical possibility; | for in this sense, two propositions contradictory of one another may both | be severally possible, although their combination is not possible. | | That is to say each is 'vaguely', not 'distinctly', possible. [note, 1908]. | | But in the 'substantive' sense, the contradictory of a possible proposition | is impossible, because we are virtually omniscient in regard to the ideal | world. For example, there is no contradiction in supposing that only | four, or any other number, of independent atoms exist. But it is | made clear to us by ideal experimentation, that five atoms are | to be found in the ideal world. Whether all five are to be | found in the sensible world or not, to say there are only | four in the ideal world is a proposition absolutely to be | rejected, notwithstanding its involving no contradiction. | | C.S. Peirce, 'Collected Papers', CP 3.527, |"The Logic of Relatives", 'Monist', vol. 7, | pp. 161-217, 1897.
DIEP. Note 17
| A few of the most frequently recurring scholastic phrases follow. ...
|
|'Essential Predication': in which the predicate is wholly contained in the
| essence of the subject. It is, therefore, in Kant's sense, an analytical
| judgment. But neither Kant nor the scholastics provide for the fact that
| an indefinitely complicated proposition, very far from obvious, may often
| be deduced by mathematical reasoning, or necessary deduction, by the logic
| of relatives, from a definition of the utmost simplicity, without assuming
| any hypothesis whatever (indeed, such assumption could only render the
| proposition deduced simpler); and this may contain many notions not
| explicit in the definition.
|
| This may be illustrated by the following:
|
| Man is a rational animal; hence, whatever is not a man is either,
| on the one hand, not rational, while either at the same time being
| an animal or else benefiting nothing except such objects as love
| nothing but fairies, or, on the other hand, is not an animal,
| while either being rational or standing to whatever fairy may
| exist in the relation of benefiting something that loves it.
|
| Now, if it be said that that is an analytical judgment, or essential predication,
| neither the definition of the scholastics nor that of Kant is adequate. But if it
| be said that it is not an essential predication, or analytical judgement, then the
| accidental predication and the synthetical judgment may be a necessary consequence,
| and a very recondite one, of a mere definition, quite contrary to what either Kant
| or the scholastics supposed and built upon. Cf. Scotus ('In Univ. Porph.', 9.12),
| who makes essential predication the predication of genus, species, or difference.
|
| C.S. Peirce, 'Collected Papers', CP 2.361, in dictionary entry for "Predication",
| J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 326-329.
DIEP. Note 18
I need to go back and repair an omission. It occurs at the point in CP 3.527 where Peirce writes this: | It has come about through the agencies of development that man is | endowed with intelligence of such a nature that he can by ideal | experiments ascertain that in a certain universe of logical | possibility certain combinations occur while others do not | occur. Of those which occur in the ideal world some do | and some do not occur in the real world; but all that | occur in the real world occur also in the ideal world. | For the real world is the world of sensible experience, | and it is a part of the process of sensible experience | to locate its facts in the world of ideas. This is what | I mean by saying that the sensible world is but a fragment | of the ideal world. In a marginal note, dating from 1908, Peirce provides us with an important statement about his take on the "end of inquiry": | For the simple reason that the real world is a part of the ideal world, | namely, that part which sufficient experience would tend ultimately (and | therefore definitively), to compel Reason to acknowledge as having a being | independent of what he may arbitrarily, or willfully, create. | | C.S. Peirce, 'Collected Papers', CP 3.527, |"The Logic of Relatives", 'Monist', vol. 7, | pp. 161-217, 1897. Marginal note, 1908.
DIEP. Note 19
| The other divisions of terms, propositions, and arguments | arise from the distinction of extension and comprehension. | I propose to treat this subject in a subsequent paper.* | But I will so far anticipate that as to say that there is, | first, the direct reference of a symbol to its objects, or | its denotation; second, the reference of the symbol to its | ground, through its object, that is, its reference to the | common characters of its objects, or its connotation; and | third, its reference to its interpretants through its object, | that is, its reference to all the synthetical propositions in | which its objects in common are subject or predicate, and this | I term the information it embodies. And as every addition to | what it denotes, or to what it connotes, is effected by means | of a distinct proposition of this kind, it follows that the | extension and comprehension of a term are in an inverse | relation, as long as the information remains the same, | and that every increase of information is accompanied | by an increase of one or other of these two quantities. | It may be observed that extension and comprehension | are very often taken in other senses in which this | last proposition is not true. | |* C.S. Peirce, "Upon Logical Comprehension and Extension", | 'Proceedings of the American Academy of Arts and Sciences', | vol. 7, pp. 416-432, 1867. CP 2.391-430. Online copy at: | http://www.iupui.edu/~peirce/web/writings/v2/w2/w2_06/v2_06.htm | | C.S. Peirce, CP 1.559, "On a New List of Categories", |'Proceedings of the American Academy of Arts and Sciences', | vol. 7, pp. 287-298, 1867.
DIEP. Note 20
- CP 2.418
DIEP. De In Esse Predication • Discussion
DIEP. Discussion Note 1
Re: CP 3.441
GR: given that two paragraphs later, Peirce writes:
| if the Devil were elected president of the United States, it would prove
| highly conducive to the spiritual welfare of the people (because he will
| not be elected), yet both Professor Schröder and I prefer to build the
| algebra of relatives upon this conception of the conditional proposition.
GR: and given the bizarre situation that the devil HAS been
elected President of the United States, what does this
say about Peirce's or Schroder's logic, especially in
its esthetical and ethical presuppositions?
JA: he means that if the name on the ballot were "The Devil",
the people would not thus knowingly elect him. of course,
putting his real name on the ballot would be the last thing
that the Devil would do.
JA: but hey, don't read ahead,
it'll spoil the surprise.
GR: Most interesting interpretation.
GR: Yes, I certainly try not to "spoil the surprise".
JA: of course, none of this applies in california ...
JA: With that last bit (CP 3.442) on the "state of information" (SOI)
in the mix, I guess that I can now follow-up without letting any
more categories out of the bag -- there are only three after all --
Peirce's simplex faith in the democratic process is conditioned,
simplexly or otherwise, on the evidently inessential contingency
of a "liberally informed electorate" (LIE).
DIEP. Discussion Note 2
CSP = C.S. Peirce
JA = Jon Awbrey
BM = Bernard Morand
CSP: | [A Boolian Algebra With One Constant] (cont.)
|
| To express the proposition: "If S then P",
| first write:
|
| A
|
| for this proposition. But the proposition
| is that a certain conceivable state of things
| is absent from the universe of possibility.
| Hence instead of A we write:
|
| B B
BM: All was going right till there for me.
CSP: | Then B expresses the possibility of S being true and P false.
BM: Now, I am stopped. May be there is an intermediary
implicit proposition that I am not seeing? If yes
which one? This could be of interest to Gary too:
I guess that for the whole passage the elements
of the demonstration count more than the
conclusion in itself.
CSP: | Since, therefore, SS denies S, it follows
| that (SS, P) expresses B. Hence we write:
|
| SS, P; SS, P.
|
| C.S. Peirce, CP 4.14, untitled paper circa 1880.
Peirce is working analytically here -- I mean that in the good sense of the word --
in the manner that Bentham calls "paraphrasis", Boole "development", or most math
folks "expansion", if I remember right. But he already knows the answer he wants,
so the whole analysis will have that "pulling a rabbit out of the hat" quality of
such performances.
The basic operation is unmarked, or you could think of the blank space as a symbol
for the logical operation of "joint denial", that Peirce counted as one of the two
possible "amphecks" (cutting both ways), Sheffer called a "stroke", and comp sci
folk call NNOR (neither nor). The punctuation marks are not really operators,
they just group terms, much like the "puncts" or "dots" of Peano that Russell
so butchered to the point of unintelligibility, like so much else.
In saying "S => P" one is saying "that a certain conceivable state of things
is absent from the universe of possibility" -- sounds awfully "intensional",
does it not? -- but anyway, the conceivable states of things that one is
excluding from the universe of possibility are any states of things that
would form a counterexample to "S => P", namely, those states of things
that are described by "S and not P".
That denial would take the form:
S and not P. S and not P.
Let's call that the Lady Macbeth denial.
It remains to analyze the metalanguage phrase "S and not P"
using only "S", "P", and the tacit joint denial connective.
If I wrote "S P", this would be saying "not S and not P",
so all I need to do is change the sign on the S part of it,
which I can do by doubling the S. As we have stipulated,
doubling is a way of putting things in doubt. Therefore,
"SS, P" says "S and not P", which is the thing we want
to deny, and which final denial we can make by writing:
SS, P; SS, P.
Voila!
DIEP. Discussion Note 3
JA = Jon Awbrey
TJ = Tom Johnson
Re: CP 4.517
This started out as an attempt to track down a 30 year old memory,
having to do with the phrase "predication (de?) inesse", which
I thought I saw first in Peirce, supposed that he got from
Leibniz (who I also read a lot of in those days), and had
a "clear and distinct" idea (the worst kind) that it was
an "intensional" account of predication. I used to have
access to the microfilm manuscripts of Peirce's nachlass
at that time, and if it's there I probably won't get back
to it. From what I have uncovered this time around, I seem
to be correct about the significance that Leibniz attached to
the phrase -- will have to check again -- but all I find so far
in the CP is 'conditio/consequentia simplex de inesse' that Peirce
says he got from Scotus and Petrus Hispanus. I'll probably have to
go about the mindless data collection for a while longer before I try
to draw a conclusion, but in the meantime I have become more intrigued
with the connection to Peirce's theory of information as the third quid
between extension and intension, and relative to states of which the
entire spectrum of modalities is refracted before our minds' eyes.
TJ: Is Peirce saying here that [1] there is necessity de dicto, but not de re?
Is he saying [2] that there are no Aristotelian essences?
Is he [3] distinguishing various kinds of necessity?
My partially informed guesses:
1. No
2. No
3. Yes
TJ: For example, one might argue that physical causality is necessity de re, and
is not influenced by how much information we have about physical processes.
In the spirit of an even wilder guess, I think that he would say that there
is a difference between what we are destined to believe, for example, about
the objective referent, if any, of the phrase "physical causality" at the
"end of inquiry" (EOI) and what we are likely to believe in that respect
at the present time -- time being relative, too, of course -- and that
it may form a useful analytic ideal or a "hypostatic independentity",
to coin a phrase, to think of this "physical_causality_EOI" as being
there all along, or not being there all along, waiting for us to
discover the quantum of truth in the sign "physical causality".
DIEP. Discussion Note 4
JA = Jon Awbrey
TJ = Tom Johnston
Re: CP 4.517
JA, amending JA:
I will probably have to go about the mindless data collection
for a while longer before I try to draw a conclusion, but in
the meantime I have become more intrigued with the connection
to Peirce's theory of information as the third quid between
extension and intension, and relative to the states of which
information the entire spectrum of modalities is refracted
before our minds' eyes.
TJ: I like that last sentence, and look
forward to finding out what it means.
Egged on a bit by Gary and John, I am only just starting to return to
the question of modality, as that was never so compelling to me in math,
where one gets by with a "necessary" and a "sufficient" that seem to rank
inane dismissal quotes in other people's ears, and so mood was never before
so compelling to me as the cousin/cozen issues of intentionality, but here
are some links to Peirce's derivation of information from logical grounds,
Peirce's 1865-1866 Lectures at Harvard and the Lowell Institute, where he
introduces his newfangled notion of "information" and the theory thereof:
C.S. Peirce, Harvard Lectures (1865)
23. http://stderr.org/pipermail/inquiry/2003-March/000216.html -- CE 1, 272
24. http://stderr.org/pipermail/inquiry/2003-March/000217.html -- CE 1, 272-274
25. http://stderr.org/pipermail/inquiry/2003-March/000218.html -- CE 1, 274
26. http://stderr.org/pipermail/inquiry/2003-March/000219.html -- CE 1, 274-275
27. http://stderr.org/pipermail/inquiry/2003-March/000220.html -- CE 1, 275-276
28. http://stderr.org/pipermail/inquiry/2003-March/000221.html -- CE 1, 276
29. http://stderr.org/pipermail/inquiry/2003-March/000222.html -- CE 1, 276-277
30. http://stderr.org/pipermail/inquiry/2003-March/000223.html -- CE 1, 277
31. http://stderr.org/pipermail/inquiry/2003-March/000224.html -- CE 1, 278-279
32. http://stderr.org/pipermail/inquiry/2003-March/000225.html -- CE 1, 279-280
33. http://stderr.org/pipermail/inquiry/2003-March/000226.html -- CE 1, 280
34. http://stderr.org/pipermail/inquiry/2003-March/000227.html -- CE 1, 280-281
35. http://stderr.org/pipermail/inquiry/2003-March/000228.html -- CE 1, 281-282
36. http://stderr.org/pipermail/inquiry/2003-March/000229.html -- CE 1, 282-283
37. http://stderr.org/pipermail/inquiry/2003-March/000230.html -- CE 1, 283
38. http://stderr.org/pipermail/inquiry/2003-April/000356.html -- CE 1, 285
39. http://stderr.org/pipermail/inquiry/2003-April/000357.html -- CE 1, 285-286
40. http://stderr.org/pipermail/inquiry/2003-April/000358.html -- CE 1, 286-288
41. http://stderr.org/pipermail/inquiry/2003-April/000359.html -- CE 1, 288
42. http://stderr.org/pipermail/inquiry/2003-April/000361.html -- CE 1, 288-289
43. http://stderr.org/pipermail/inquiry/2003-April/000362.html -- CE 1, 289
44. http://stderr.org/pipermail/inquiry/2003-April/000363.html -- CE 1, 289-290
C.S. Peirce, Lowell Lectures (1866)
11. http://stderr.org/pipermail/inquiry/2003-March/000204.html -- CE 1, 458-459
12. http://stderr.org/pipermail/inquiry/2003-March/000205.html -- CE 1, 459-460
13. http://stderr.org/pipermail/inquiry/2003-March/000206.html -- CE 1, 460
14. http://stderr.org/pipermail/inquiry/2003-March/000207.html -- CE 1, 461
15. http://stderr.org/pipermail/inquiry/2003-March/000208.html -- CE 1, 461
16. http://stderr.org/pipermail/inquiry/2003-March/000209.html -- CE 1, 462
17. http://stderr.org/pipermail/inquiry/2003-March/000210.html -- CE 1, 462
18. http://stderr.org/pipermail/inquiry/2003-March/000211.html -- CE 1, 462-463
19. http://stderr.org/pipermail/inquiry/2003-March/000212.html -- CE 1, 463-464
20. http://stderr.org/pipermail/inquiry/2003-March/000213.html -- CE 1, 464-465
21. http://stderr.org/pipermail/inquiry/2003-March/000214.html -- CE 1, 465
22. http://stderr.org/pipermail/inquiry/2003-March/000215.html -- CE 1, 466-467
02. http://stderr.org/pipermail/inquiry/2003-March/000195.html -- CE 1, 467
03. http://stderr.org/pipermail/inquiry/2003-March/000196.html -- CE 1, 467-468
04. http://stderr.org/pipermail/inquiry/2003-March/000197.html -- CE 1, 468-469
05. http://stderr.org/pipermail/inquiry/2003-March/000198.html -- CE 1, 469
06. http://stderr.org/pipermail/inquiry/2003-March/000199.html -- CE 1, 470
07. http://stderr.org/pipermail/inquiry/2003-March/000200.html -- CE 1, 470-471
JA: In the spirit of an even wilder guess, I think that he would say that there
is a difference between what we are destined to believe about, for example,
the objective referent, if any, of the phrase "physical causality" at the
"end of inquiry" (EOI) and what we are likely to believe in that respect
at the present time -- time being relative, too, off course -- and that
it may form a useful analytic ideal or a "hypostatic independentity",
to coin a phrase, to think of this "physical_causality_EOI" as being
there all along, or not being there all along, waiting for us to
discover the quantum of truth in the sign "physical causality".
TJ: Perhaps I should know better than to ask this, but what the heck:
(a) What marks the EOI? No more disagreements among members of
the relevant community of inquiry (physicists, biologists, etc)?
(b) Assuming we do reach an EOI in some subject area, what accounts
for it? Why have we stopped disagreeing? Is it that, guided by the
pragmatic principle, we have finally arrived at a set of statements
that accurately represent/describe things as they really are?
These are good questions, part of what I tried
to address in my dissertation ever in progress:
http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
Whatever EOI be in the end, how it functions in the
meantime is as a normative ideal. I will round up
the usual Chapter & Peirce, but in the meanwhile
here is a 3-logy of good books on the subject:
Peter Skagestad, 'The Road of Inquiry: [CSP]'s Pragmatic Realism'.
Cheryl Misak, 'Truth and the End of Inquiry: A Peircean Account of Truth'.
C.F. Delaney, 'Science, Knowledge, and Mind: A Study in the Philosophy of [CSP]'.
The Big EOI can be understood on analogy with the
little EOI's that make up the "fixions of belief"
that we reach every day in our everyday inquiries.
The primer canon shot on that score is found here:
http://members.door.net/arisbe/menu/library/bycsp/fixation/fx-frame.htm
DIEP. Discussion Note 5
GR = Gary Richmond
JA = Jon Awbrey
JA: Egged on a bit by Gary and John, I am only just starting to return to
the question of modality, as that was never so compelling to me in math,
where one gets by with a "necessary" and a "sufficient" that seem to rank
inane dismissal quotes in other people's ears, and so mood was never before
so compelling to me as the cousin/cozen issues of intentionality, but here
are some links to Peirce's derivation of information from logical grounds,
Peirce's 1865-1866 Lectures at Harvard and the Lowell Institute, where he
introduces his newfangled notion of "information" and the theory thereof:
GR: This is very good news indeed, jon.
GR: Of course, you've already expressed that third term
(beyond "necessary" and "sufficient"). And truly,
logical breadth x logical depth = information.
GR: But that's not the whole picture by half, right?
Therefore, modality has finally to be taken up
with all that trichotomic semiosis ought imply.
GR: Personally, I'm glad that John and I have been "nudges" here.
GR: I can hardly wait ...
Be careful what you wait for ...
I had been putting off the gamma graphs until I was older.
I am older now. But I don't know if I am old enough yet.
Maybe when I'm aleph plus one ...
I hadn't really been thinking about this much as I gathered the data.
For my part, and I think for Peirce most of the time, 2-valued logic
of the good old-fashioned classical variety is good enough -- in the
beginning, and in the end, there are just two values of significance,
one begins with a distinction, one ends with a decision, and what it
means is that the question of uncertainty is always a meantime thing.
This is what I concluded long ago from my study of Peirce's essays
in 3-valued logics. The possibility of it all occurred to me when
I was first learning topology, and there you have a 3-valued logic
of {interior, boundary, exterior} rather than classing every point
as {in, out}, 2-tomously in relation to a set, no ifs ands or buts.
There was, and probably still is, a whole literature on "topo-logic",
just my pet name for it, that proceeds from basically this very same
intuition. The issue did not force itself on my attention again, so
far as I can recall at the moment, in this mood, until I was writing
my Theme One program, or one of its early precursors. There, in the
middle of a breadth-&-depth search function -- funny how those words
come up again -- what is frequently called a "beam search" algorithm,
I was led, wil-me, nil-me, to interject a "modal variable" of a type:
mode = (null, moot, firm). See here:
http://stderr.org/pipermail/inquiry/2003-March/000115.html
The use of the mode value dubbed "moot" is in the middle of a search,
to register the fact that the absence or presence of the thing being
sought is not yet decided, though in the end you know that it has to
fall out one way or the other, by the very definition of the case.
That's all I can remember at the moment ...
DIEP. Discussion Note 6
JA = Jon Awbrey
TJ = Tom Johnston
I will go back to your earlier questions and
try to work out my own way of answering them.
There are readers of Peirce I know who would
probably give you a significantly different
collection of answers and interpretations,
so this can only be my own sense of it.
Review.
Quiz 1.
CSP: | It must be remembered that
| possibility and necessity
| are relative to the state
| of information.
|
| C.S. Peirce, 'Collected Papers', CP 4.517,
|"The Gamma Part of Existential Graphs",
|"Lowell Lectures of 1903", Lecture 4.
TJ: 1.1. Is Peirce saying here that there is necessity de dicto, but not de re?
1.2. Is he saying that there are no Aristotelian essences?
1.3. Is he distinguishing various kinds of necessity?
JA: My partially informed guesses:
1.1. No
1.2. No
1.3. Yes
It's not Molly Bloom, but 1 out of 3 ain't bad to my way of counting.
TJ: For example, one might argue that physical causality is necessity de re, and
is not influenced by how much information we have about physical processes.
JA: In the spirit of an even wilder guess, I think that he would say that there
is a difference between what we are destined to believe, for example, about
the objective referent, if any, of the phrase "physical causality" at the
"end of inquiry" (EOI) and what we are likely to believe in that respect
at the present time -- time being relative, too, of course -- and that
it may form a useful analytic ideal or a "hypostatic independentity",
to coin a phrase, to think of this "physical_causality_EOI" as being
there all along, or not being there all along, waiting for us to
discover the quantum of truth in the sign "physical causality".
Quiz 2.
TJ: Perhaps I should know better than to ask this, but what the heck:
2.1. What marks the EOI? No more disagreements among members of
the relevant community of inquiry (physicists, biologists, etc)?
2.2.1. Assuming we do reach an EOI in some
subject area, what accounts for it?
2.2.2. Why have we stopped disagreeing?
2.2.3. Is it that, guided by the pragmatic principle,
we have finally arrived at a set of statements
that accurately represent/describe things as
they really are?
JA: These are good questions, part of what I tried
to address in my dissertation ever in progress:
JA: http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
JA: Whatever the EOI might be in the end,
how it functions in the meantime is
effectively as a normative ideal.
JA: The Big EOI can be understood on analogy with the
little EOI's that make up the "fixions of belief"
that we reach every day in our everyday inquiries.
The primer canon shot on that score is found here:
JA: http://members.door.net/arisbe/menu/library/bycsp/fixation/fx-frame.htm
I get a handle on this subject with the following two hands:
On the 1st hand, Peirce's Theory Of Signs (PTOS).
On the 2nd hand, Peirce's Theory Of Inquiry (PTOI).
PTOS.
The following is what I personally consider
to be the clearest and the most complete of
all the definitions of a sign relation that
I've been able to find in Peirce's writings:
| A sign is something, 'A',
| which brings something, 'B',
| its 'interpretant' sign
| determined or created by it,
| into the same sort of correspondence
| with something, 'C', its 'object',
| as that in which itself stands to 'C'.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54, also available here:
| http://members.door.net/arisbe/menu/library/bycsp/L75/L75.htm
It is one of the few where Peirce is intrepid enough
to go boldly forward without any sop to psychologism.
More detail here:
| On the Definition of Logic [Version 1]
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time. Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'. It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized. (CSP, NEM 4, 20-21).
|
| On the Definition of Logic [Version 2]
|
| Logic is 'formal semiotic'. A sign is something,
| 'A', which brings something, 'B', its 'interpretant'
| sign, determined or created by it, into the same
| sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in
| which itself stands to 'C'. This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident. The word "formal" in
| the definition is also defined. (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.
I will pick up from there next time.
DIEP. Discussion Note 7
BM = Bernard Morand
JA = Jon Awbrey
CSP: | It has come about through the agencies of development that man is
| endowed with intelligence of such a nature that he can by ideal
| experiments ascertain that in a certain universe of logical
| possibility certain combinations occur while others do not
| occur. Of those which occur in the ideal world some do
| and some do not occur in the real world; but all that
| occur in the real world occur also in the ideal world.
| For the real world is the world of sensible experience,
| and it is a part of the process of sensible experience
| to locate its facts in the world of ideas. This is what
| I mean by saying that the sensible world is but a fragment
| of the ideal world.*
CSP: * For the simple reason that the real world is a part of the ideal world,
| namely, that part which sufficient experience would tend ultimately (and
| therefore definitively), to compel Reason to acknowledge as having a being
| independent of what he may arbitrarily, or willfully, create.
|
| C.S. Peirce, 'Collected Papers', CP 3.527,
|"The Logic of Relatives", 'Monist', vol. 7,
| pp. 161-217, 1897. * Marginal note, 1908.
BM: Thanks Jon. This marginal note is a very
important one and it deserves slow reflection.
BM: On one side, I was lead start from the beginning of my peircean studies
to think that such point could be a reason for me to differ radically
from Peirce. I thought that such statements were reflecting two bias:
BM: 1. they could support the critic that Peirce was some kind of
"intellectualist" who was ignorant of how things go in the
actual world: there would be an ideal world the knowledge
of which could be attained in the long run by wise people.
2. they were optimistic about the possibility of such
a happy end. I was wondering too if Peirce's thought
was not really representative of the major trends of
XIXth century that believed in an endless progress
of science, economics, welfare and so on. A kind
of belief in some "age d'or" to become.
BM: It is worth noticing that my background has been fed with marxism
for a long time and that I have no reason to think the contrary
today, particularly from the economical standpoint as it was
developped in 'The Capital'. In marxism too there is the
idea of communism as an ultimate stage of evolution where
all would be going fine.
BM: But undoubtly, there are major differences between both,
namely according to the ways as the happy end could take
place (materialism vs pragmatism). So I put the question
in some kind of provocative manner here:
BM: http://www.iutc3.unicaen.fr/~moranb/accueilperso51.htm
BM: But, on the other hand, I am now less sure about all that.
From the Capital itself, there is nothing that states the
necessity of the happy end. We have just two concluding
statements, first the necessity of the capitalism crisis
as a tendency and second, the statement that there are
"causes which go against this law" (Evidently, in his
political and social works, Marx is much less cautious).
BM: If we turn now to Peirce, the marginal note (written in 1908,
so it is not refering to some "young" Peirce) we get the idea
of tendency too. But we get also the idea that it is the growth
of EXPERIENCE in the real world which will lead Reason to overcome.
BM: So, returning to my starting point, may be they were not so far one
of each other, but not for the reasons I had thought. It seems that
they had in common an interest on the problematic of evolution, which
is after all a leading idea of the XIXth century too. The fact that
one of them was revolutionary and the other a strong conservative is
not without interest here.
When Peirce talks this way about the EOI, some people that I know
will reflexively (not too reflectively) label him as an "idealist",
and I take it that they mean this in a dismissive sense of the word.
I have always taken the concept of the EOI to be a "normative idealization",
or a "regulative principle" in Kant's sense, which I imagine that someone so
steeped in Kant as was Peirce must also have had in mind. In this connection
normative idealizations are bound up with the principle of hope, which also
corresponds to abductive reasoning in Peirce's categories. You will be
thinking of the story of a soldier.
Now the normative ideal or regulative principle of the EOI
refers to an intentional objective in the far remote future,
about the actualization of which we can of course know naught,
but the ideal is embodied in those who maintain it and thus it
has a very real action in the present, the "functional meaning"
of the EOI, in the sociological sense of the word "functional".
I think of Peirce's marginal note as the "Venus de Milo" theory of the
relations among the ideal world, the real world, and the sensible world.
The ideal world is the unhewn block of Parian marble, from which
substrate the brute encounter of recalcitrant experience chips away
everything that "does not look like Aphrodite", or some say Amphitrite,
and this is the real that eternally endures, whatever vicissitudes happen
to befall its concrete images, and yet we possess but a fragment of that in
our sensible world, just barely enough to intimate the nature of that reality.
Time to Muse the Facet:
http://www.louvre.fr/img/photos/collec/ager/grande/ma0399.jpg
DIEP. De In Esse Predication • Work Area
01. 1880, CP 4.12 02. 1880, CP 4.13 03. 1880, CP 4.14 04. 1896, CP 3.440 05. 1896, CP 3.441 06. 1896, CP 3.442 07. 1896, CP 3.443 08. 1896, CP 3.444-445 09. 1885, CP 3.374 10. 1902, CP 2.323 11. 1895, CP 2.356 12. 1903, CP 4.517 13. 1903, CP 3.606-608 14. 1897, CP 3.526 15. 1897, CP 3.527 16. 1897, CP 3.527 17. ????, CP 2.361 18. 1908, CP 3.527 note 19. 1867, 1.559 20. o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o 1.559 x 2.323 x 2.347-349 2.356 x 2.361 x 2.382 2.394 2.407-409 2.418 2.546 2. 323 348 349 546 2. 231 250 260 293 364 409 416 418 418n 3.374 x 3.375 3.382 3.384 Peirce's Law 3.440-445 x 3.446-448 3.526-527 x 3.606-608 x 4.12-14 x 4.21 4.49 4.372-376 4.401 4.454 4.514-523 4.517 x 4.520 4.564 6.450
HAPA. Hypostatic And Prescisive Abstraction
HAPA. Note 1
| When we have analyzed a proposition so as to throw into the subject everything | that can be removed from the predicate, all that it remains for the predicate to | represent is the form of connection between the different subjects as expressed in | the propositional 'form'. What I mean by "everything that can be removed from the | predicate" is best explained by giving an example of something not so removable. | But first take something removable. "Cain kills Abel." Here the predicate | appears as "--- kills ---." But we can remove killing from the predicate | and make the latter "--- stands in the relation --- to ---." Suppose we | attempt to remove more from the predicate and put the last into the form | "--- exercises the function of relate of the relation --- to ---" and then | putting "the function of relate to the relation" into a another subject leave | as predicate "--- exercises --- in respect to --- to ---." But this "exercises" | expresses "exercises the function". Nay more, it expresses "exercises the function | of relate", so that we find that though we may put this into a separate subject, it | continues in the predicate just the same. Stating this in another form, to say that | "A is in the relation R to B" is to say that A is in a certain relation to R. Let | us separate this out thus: "A is in the relation R^1 (where R^1 is the relation | of a relate to the relation of which it is the relate) to R to B". But A is | here said to be in a certain relation to the relation R^1. So that we can | expresss the same fact by saying, "A is in the relation R^1 to the relation | R^1 to the relation R to B", and so on 'ad infinitum'. A predicate which | can thus be analyzed into parts all homogeneous with the whole I call | a 'continuous predicate'. It is very important in logical analysis, | because a continuous predicate obviously cannot be a 'compound' | except of continuous predicates, and thus when we have carried | analysis so far as to leave only a continuous predicate, we | have carried it to its ultimate elements. | | Peirce, "Letters to Lady Welby", 14 Dec 1908, 'Selected Writings', pp. 396-397. | | Charles S. Peirce, "Letters to Lady Welby", pp. 380-432 in: |'Charles S. Peirce: Selected Writings (Values in a Universe | of Chance)', Edited with an Introduction and Notes by | Philip P. Wiener, Dover, New York, NY, 1966.
HAPA. Note 2
| Another characteristic of mathematical thought is the extraordinary | use it makes of abstractions. Abstractions have been a favorite | butt of ridicule in modern times. Now it is very easy to laugh | at the old physician who is represented as answering the question, | why opium puts people to sleep, by saying that it is because it | has a dormative virtue. It is an answer that no doubt carries | vagueness to its last extreme. Yet, invented as the story was | to show how little meaning there might be in an abstraction, | nevertheless the physician's answer does contain a truth | that modern philosophy has generally denied: it does | assert that there really is in opium 'something' which | explains its always putting people to sleep. This has, | I say, been denied by modern philosophers generally. | Not, of course, explicitly; but when they say that | the different events of people going to sleep after | taking opium have really nothing in common, but | only that the mind classes them together -- and | this is what they virtually do say in denying | the reality of generals -- they do implicitly | deny that there is any true explanation of | opium's generally putting people to sleep. | | C.S. Peirce, CP 4.234, "The Simplest Mathematics", | Chapter 3 of the "Minute Logic", Jan-Feb 1902.
HAPA. Note 3
| Look through the modern logical treatises, and you will find that they | almost all fall into one or other of two errors, as I hold them to be; | that of setting aside the doctrine of abstraction (in the sense in | which an abstract noun marks an abstraction) as a grammatical topic | with which the logician need not particularly concern himself; and | that of confounding abstraction, in this sense, with that operation | of the mind by which we pay attention to one feature of a percept to | the disregard of others. The two things are entirely disconnected. | | The most ordinary fact of perception, such as "it is light", involves | 'precisive' abstraction, or 'prescission'. But 'hypostatic' abstraction, | the abstraction which transforms "it is light" into "there is light here", | which is the sense which I shall commonly attach to the word abstraction | (since 'prescission' will do for precisive abstraction) is a very special | mode of thought. It consists in taking a feature of a percept or percepts | (after it has already been prescinded from the other elements of the percept), | so as to take propositional form in a judgment (indeed, it may operate upon | any judgment whatsoever), and in conceiving this fact to consist in the | relation between the subject of that judgment and another subject, which | has a mode of being that merely consists in the truth of propositions of | which the corresponding concrete term is the predicate. | | Thus, we transform the proposition, "honey is sweet", | into "honey possesses sweetness". "Sweetness" might be | called a fictitious thing, in one sense. But since the | mode of being attributed to it 'consists' in no more than | the fact that some things are sweet, and it is not pretended, | or imagined, that it has any other mode of being, there is, | after all, no fiction. The only profession made is that we | consider the fact of honey being sweet under the form of a | relation; and so we really can. I have selected sweetness | as an instance of one of the least useful of abstractions. | Yet even this is convenient. It facilitates such thoughts | as that the sweetness of honey is particularly cloying; | that the sweetness of honey is something like the | sweetness of a honeymoon; etc. | | C.S. Peirce, CP 4.235, "The Simplest Mathematics", | Chapter 3 of the "Minute Logic", Jan-Feb 1902.
HAPA. Note 4
| Abstractions are particularly congenial to mathematics. Everyday life | first, for example, found the need of that class of abstractions which | we call 'collections'. Instead of saying that some human beings are | males and all the rest females, it was found convenient to say that | 'mankind' consists of the male 'part' and the female 'part'. The | same thought makes classes of collections, such as pairs, leashes, | quatrains, hands, weeks, dozens, baker's dozens, sonnets, scores, | quires, hundreds, long hundreds, gross, reams, thousands, myriads, | lacs, millions, milliards, milliasses, etc. These have suggested | a great branch of mathematics.* | | Again, a point moves: it is by abstraction that the geometer says that | it "describes a line". This line, though an abstraction, itself moves; | and this is regarded as generating a surface; and so on. | | So likewise, when the analyst treats operations as themselves subjects of | operations, a method whose utility will not be denied, this is another | instance of abstraction. Maxwell's notion of a tension exercised upon | lines of electrical force, transverse to them, is somewhat similar. | | These examples exhibit the great rolling billows of abstraction in the ocean | of mathematical thought; but when we come to a minute examination of it, | we shall find, in every department, incessant ripples of the same form | of thought, of which the examples I have mentioned give no hint. | |* Of course, the moment a collection is recognized as an abstraction we have | to admit that even a percept is an abstraction or represents an abstraction, | if matter has parts. It therefore becomes difficult to maintain that all | abstractions are fictions. | | C.S. Peirce, CP 4.235, "The Simplest Mathematics", | Chapter 3 of the "Minute Logic", Jan-Feb 1902.
HAPA. Note 5
| Hypostasis. Literally the Greek word signifies that which stands under | and serves as a support. In philosophy it means a singular substance, | also called a supposite, 'suppositum', by the Scholastics, especially | if the substance is a completely subsisting one, whether non-living | or living, irrational or rational. However, a rational hypostasis | has the same meaning as the term, 'person'. | | J.J.R. [= J.J. Rolbiecki] in: | | Dagobert D. Runes (ed.), 'Dictionary of Philosophy', | Littlefield, Adams, & Company, Totowa, NJ, 1972.
HAPA. Note 6
| But the highest kind of synthesis is what the mind is compelled to make neither | by the inward attractions of the feelings or representations themselves, nor by | a transcendental force of necessity, but in the interest of intelligibility, | that is, in the interest of the synthesizing "I think" itself; and this | it does by introducing an idea not contained in the data, which gives | connections which they would not otherwise have had. This kind of | synthesis has not been sufficiently studied, and especially the | intimate relationship of its different varieties has not been | duly considered. The work of the poet or novelist is not so | utterly different from that of the scientific man. The artist | introduces a fiction; but it is not an arbitrary one; it exhibits | affinities to which the mind accords a certain approval in pronouncing | them beautiful, which if it is not exactly the same as saying that the | synthesis is true, is something of the same general kind. The geometer | draws a diagram, which if not exactly a fiction, is at least a creation, | and by means of observation of that diagram he is able to synthesize and | show relations between elements which before seemed to have no necessary | connection. The realities compel us to put some things into very close | relation and others less so, in a highly complicated, and in the [true?] | sense itself unintelligible manner; but it is the genius of the mind, | that takes up all these hints of sense, adds immensely to them, makes | them precise, and shows them in intelligible form in the intuitions | of space and time. Intuition is the regarding of the abstract in | a concrete form, by the realistic hypostatization of relations; | that is the one sole method of valuable thought. Very shallow | is the prevalent notion that this is something to be avoided. | You might as well say at once that reasoning is to be avoided | because it has led to so much error; quite in the same philistine | line of thought would that be; and so well in accord with the spirit | of nominalism that I wonder some one does not put it forward. The true | precept is not to abstain from hypostatization, but to do it intelligently ... | | C.S. Peirce, CP 1.383, "A Guess at the Riddle", | circa 1890, 'Collected Papers', CP 1.354-416.
HAPA. Note 7
| Exceedingly important are the relatives signifying "-- is a quality of --" | and "-- is a relation of -- to --". It may be said that mathematical | reasoning (which is the only deductive reasoning, if not absolutely, | at least eminently) almost entirely turns on the consideration of | abstractions as if they were objects. The protest of nominalism | against such hypostatisation, although, if it knew how to formulate | itself, it would be justified as against much of the empty disputation | of the medieval Dunces, yet, as it was and is formulated, is simply a | protest against the only kind of thinking that has ever advanced human | culture. Nobody will work long with the logic of relatives -- unless | he restricts the problems of his studies very much -- without seeing | that this is true. | | C.S. Peirce, CP 3.509, "The Logic of Relatives", |'The Monist', vol. 7, pp. 161-217, 1897. |'Collected Papers', CP 3.456-552.
HAPA. Note 8
| The logical term 'subjectal abstraction' here requires a | word of explanation; for there are few treatises on logic | which notice subjectal abstraction under any name, except so | far as to confuse it with precisive abstraction which is an | entirely different logical function. When we say that the | Columbia library building is 'large', this remark is a result | of precisive abstraction by which the man who makes the remark | leaves out of account all the other features of his image of | the building, and takes the word "large" which is entirely | unlike that image -- and when I say the word is unlike the | image, I mean that the general signification of the word is | utterly disparate from the image, which involves no predicates | at all. Such is 'precisive abstraction'. But now if this man | goes on to remark that the largeness of the building is very | impressive, he converts the applicability of that predicate | from being a way of thinking about the building to being | itself a subject of thought, and that operation is | 'subjectal abstraction'. | | C.S. Peirce, CP 4.332, "Ordinals", circa 1905.
HAPA. Note 9
| Predicate. | | The view which pragmatic logic takes of the predicate, in consequence of | its assuming that the entire purpose of deductive logic is to ascertain | the necessary conditions of the truth of signs, without any regard to | the accidents of Indo-European grammar, will be here briefly stated. | Cf. Negation [CP 2.378-380]. | | In any proposition, i.e., any statement which must be true or false, | let some parts be struck out so that the remnant is not a proposition, | but is such that it becomes a proposition when each blank is filled by | a proper name. The erasures are not to be made in a mechanical way, but | with such modifications as may be necessary to preserve the partial sense | of the fragment. Such a residue is a 'predicate'. The same proposition | may be mutilated in various ways so that different fragments will appear | as predicates. Thus, take the proposition "Every man reveres some woman." | This contains the following predicates, among others: | | ". . . reveres some woman." | | ". . . is either not a man or reveres some woman." | | "Any previously selected man reveres . . ." | | "Any previously selected man is . . ." | | C.S. Peirce, 'Collected Papers', CP 2.358, in dictionary entry for "Predicate", | J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 325-326.
HAPA. Note 10
| Relatives Of Second Intention | | The general method of graphical representation of propositions has now | been given in all its essential elements, except, of course, that we | have not, as yet, studied any truths concerning special relatives; | for to do so would seem, at first, to be "extralogical". Logic in | this stage of its development may be called 'paradisaical logic', | because it represents the state of Man's cognition before the | Fall. For although, with this apparatus, it easy to write | propositions necessarily true, it is absolutely impossible | to write any which is necessarily false, or, in any way | which that stage of logic affords, to find out that | anything is false. The mind has not as yet eaten | of the fruit of the Tree of Knowledge of Truth | and Falsity. | | Probably it will not be doubted that every child in | its mental development necessarily passes through | a stage in which he has some ideas, but yet has | never recognised that an idea may be erroneous; | and a stage that every child necessarily passes | through must have been formerly passed through | by the race in its adult development. It may | be doubted whether many of the lower animals | have any clear and steady conception of | falsehood; for their instincts work | so unerringly that there is little | to force it upon their attention. | Yet plainly without a knowledge | of falsehood no development | of discursive reason can | take place. | | C.S. Peirce, 'Collected Papers', CP 3.488, |"The Logic of Relatives", 'Monist', vol. 7, | pp. 161-217, 1897.
HAPA. Note 11
| Relatives Of Second Intention (cont.) | | This paradisaical logic appears in the study of non-relative formal logic. | But 'there' no possible avenue appears by which the knowledge of falsehood | could be brought into this Garden of Eden except by the arbitrary and | inexplicable introduction of the Serpent in the guise of a proposition | necessarily false. The logic of relatives affords such an avenue, | and 'that', the very avenue by which in actual development, | this stage of logic supervenes. It is the avenue of | experience and logical reflexion. | | By 'logical' reflexion, I mean the observation of thoughts | in their expressions. Aquinas remarked that this sort of | reflexion is requisite to furnish us with those ideas | which, from lack of contrast, ordinary external | experience fails to bring into prominence. | He called such ideas 'second intentions'. | | It is by means of 'relatives of second intention' | that the general method of logical representation | is to find completion. | | C.S. Peirce, 'Collected Papers', CP 3.489-490, |"The Logic of Relatives", 'The Monist', vol. 7, | pp. 161-217, 1897.
HAPA. Note 12
| One branch of deductive logic, of which from the nature of | things ordinary logic could give no satisfactory account, | relates to the vitally important matter of abstraction. | | Indeed, the student of ordinary logic naturally regards abstraction, | or the passage from "the rose smells sweet" to "the rose has perfume", | to be a quasi-grammatical matter, calling for little or no notice from | the logician. The fact is, however, that almost every great step in | mathematical reasoning derives its importance from the fact that it | involves an abstraction. | | For by means of abstraction, the transitory elements of thought, | the 'epea pteroenta' [winged words], are made substantive elements, | as James terms them, 'epea apteroenta' [plucked words].* It thus | becomes possible to study their relations and to apply to these | relations discoveries already made respecting analogous relations. | In this way, for example, operations become themselves the subjects | of operations. | |* William James, 'Principles of Psychology', vol. 1, p. 243. | | C.S. Peirce, 'Collected Papers', CP 3.642, in dictionary entry for "Relatives", | J.M. Baldwin (ed.), 'Dictionary of Philosophy & Psychology', vol. 2, pp. 447-450. Incidental Musement: http://www.perseus.tufts.edu/cgi-bin/ptext?lookup=Hom.+Il.+1.172
HAPA. Hypostatic And Prescisive Abstraction • Discussion
HAPA. Discussion Note 1
Referring to a few of Peirce's standard discussions
of "hypostatic abstraction" (HA), the main thing
about HA is that it turns an adjective or some
part of a predicate into an extra subject,
upping the arity of the main predicate
in the process.
For example, a typical case of HA occurs in the transformation
from "honey is sweet" to "honey possesses sweetness", which we
could choose to represent in several different ways as follows:
Sweet(honey) ~~~> Possesses(honey, sweetness)
S(h) ~~~> P(h, s)
S P
o o
| ~~~> |
o o
h <h,s>
^
[S] ~~~> /P\
| o->-o
| | |
o o o
h h s
The chief thing about this form of grammatical transformation is that we
abstract the adjective "sweet" from the main predicate, thus arriving at
a new, increased-arity predicate "possesses", and as a by-product of the
reaction, as it were, precipitating out the substantive "sweetness" as a
new subject of the new predicate.
HAPA. Discussion Note 2
Abstractions And Their Deciduation Problems I have studied mathematics one way or another most of my life, and mathematics is nothing if not the study of abstract objects, yet I do not believe that I am ready to venture my own definition of "abstract object", not just yet, and I honestly do not know if I ever will be, but what I have been attempting intermittently to do all this while is to transmit the sort of information that the typical backwoodsman in the wild wold of logic and mathematics might regard as being analogous to a botanical key, useful in recognizing various species of abstract objects, with which I can genuinely say that I have some acquaintance, although I would prefer to defer, in my reference, in my reverence, to ones who I know know vastly more. So forgive a quote: | To most otherwise "forest-minded" folk, the approach of autumn | with its showers of many-colored leaves, spells the end of the | season's activities in the indentification [sic] of deciduous | trees and shrubs. Without leaves, the members of the forest | community, unless they be relatively large, seem to lose | much of their summer's identity and may even descend to | the level of "brush". This is in reality not the case, | as may be easily discovered by examining any leafless | twig with a 10-x pocket lens, or even with the naked | eye. A casual glance at Plate 1 will also serve to | show that woody plants in winter are anything but | featureless. | | Harlow, William M., |"Twig Key to the Deciduous Woody Plants of Eastern North America", | 4th ed., reprinted in 'Fruit Key and Twig Key to Trees and Shrubs', | Dover, New York, NY, 1959. Originally published by the author 1954.
HAPA. Discussion Note 3
I think that it would be useful at this time to run back through one of Peirce's best descriptions of the two kinds of abstraction, and try to tackle it line by line. The first and simpler type of abstraction is "prescisive abstraction" -- where here I have taken something like the running average of several different spellings of the term -- that merely extracts or selectively attends to a feature or a property of a more concrete object. In this case one passes from an object to one of its properties, very analogous to the sort of mathematical operation that is usually called "projection". Here, one speaks of "prescinding" the property in question from the object, whereby prescisive abstraction acquires the equivalent name of "prescission". The second, more substantial type of abstraction is "hypostatic abstraction". This is the operation that we regard as bringing the abstract object proper into being, or into the sphere of human thought, or at least into the frame of a particular discussion. In this case one passes from a concrete object or situation, via a selection of properties, to end with an abstract object. | Look through the modern logical treatises, and you will find that they | almost all fall into one or other of two errors, as I hold them to be; | that of setting aside the doctrine of abstraction (in the sense in | which an abstract noun marks an abstraction) as a grammatical topic | with which the logician need not particularly concern himself; and | that of confounding abstraction, in this sense, with that operation | of the mind by which we pay attention to one feature of a percept to | the disregard of others. The two things are entirely disconnected. Here Peirce gives a first description of the two types of abstraction and emphasizes the importance of distinguishing them one from another. | The most ordinary fact of perception, such as "it is light", | involves 'precisive' abstraction, or 'prescission'. In other words, all attention is selective to some degree, so any perception, such as that which we typically express by means of the sentence "It is light" involves prescission, a trimming of the whole experience to crop an observed fact. | But 'hypostatic' abstraction, the abstraction which transforms | "it is light" into "there is light here", which is the sense | which I shall commonly attach to the word abstraction (since | 'prescission' will do for precisive abstraction) is a very | special mode of thought. In the transformation from "It is light" to "There is light here", the spelling "light" is transformed from an adjective into a noun. This is the typical grammatical clue that an underlying operation of "hypostatic" or "subjectal" abstraction has been accomplished. | It consists in taking a feature of a percept or percepts (after it has | already been prescinded from the other elements of the percept), so as | to take propositional form in a judgment (indeed, it may operate upon | any judgment whatsoever), and in conceiving this fact to consist in the | relation between the subject of that judgment and another subject, which | has a mode of being that merely consists in the truth of propositions of | which the corresponding concrete term is the predicate. This is very significant. It marks not just a grammatical transformation that happens to be taking place in a given example of hypostatic abstraction, but describes the very form of a certain transformation that took place all along the frontiers of thought in the formal sciences beginning toward the middle of the Nineteenth Century, a development in which C.S. Peirce was a major force and prime expositor. But I'll need to save the rest of that story for tomorrow. Reference: | C.S. Peirce, CP 4.235, "The Simplest Mathematics", | Chapter 3 of the "Minute Logic", Jan-Feb 1902. | | http://suo.ieee.org/ontology/msg05091.html
HAPA. Discussion Note 4
By way of starting to compile a "key to abstractions and relatives"
in the spirit of an old-fashioned field study key, I have gone back
through our neck of the woulds and gathered these initial specimens:
1. HIROTUFIA. Handy Indexical Rules Of Thumb Used For Identifying Abstractions
1.1. One of the features that points to an abstract object or
a hypostatic abstraction is its being known by description,
in other words, by the predicates that are attributed to it
in remote reports of some variety, or in the various stories
and theories that are spun about it, instead of being known
more concretely and directly by acquaintance. That is one
of the marks of all of the things that I mentioned before:
dormitive virtues, egos, numbers, quarks, sweetness, the
Starship Enterprise, and last not not least, unicorns.
1.2. CSP on HA: "It consists in taking a feature of a percept
or percepts (after it has already been prescinded from the
other elements of the percept), so as to take propositional
form in a judgment (indeed, it may operate upon any judgment
whatsoever), and in conceiving this fact to consist in the
relation between the subject of that judgment and another
subject, which has a mode of being that merely consists
in the truth of propositions of which the corresponding
concrete term is the predicate."
2. HIROTUFIR. Handy Indexical Rules Of Thumb Used For Identifying Relatives
2.1. A practical test of whether a property of a thing
is a relative property of a thing is that one needs
additional information, beyond that which identifies
the thing, in order to make a decision about whether
the thing in question has the property in question.
2.2. Let me just throw out this thought: Words and phrases like
"ego", "number", "quark", "unicorn", "Starship Enterprise",
along with all of the rest of the words and phrases that
we use, have no meaning at all outside of some community,
context, or framework of interpretation, so all of their
meanings and all of their specifications on any semantic
or semiotic feature, like "abstract" or "concrete", are
relative to the given community, context, or framework
of interpretation that gives them those meanings and
those specifications.
HAPA. Discussion Note 5
BM = Bernard Morand
| CSP on HA: "It consists in taking a feature of a percept
| or percepts (after it has already been prescinded from the
| other elements of the percept), so as to take propositional
| form in a judgment (indeed, it may operate upon any judgment
| whatsoever), and in conceiving this fact to consist in the
| relation between the subject of that judgment and another
| subject, which has a mode of being that merely consists
| in the truth of propositions of which the corresponding
| concrete term is the predicate."
BM: Could you give the source of this passage?
This came up in the context of several different threads on the SUO and
Ontology Lists that involved different people's ideas about abstraction:
Cathy Legg mentioned HA a la Cyc and/or Davidson that piqued my interest,
but I am still waiting for clarification of its relation to Peirce's HA;
Matthew West has a distinction between the categories of <abstract_object>
and <possible_individual> in his Lifecycle Integration Schema, a datamodel
and/or ontology that is currently being considered by the SUO working group;
John Sowa dreams of a divine apportionment of every thing between the domain
of Physical Earth and the realm of Abstract Heaven in his Philosophy, Horatio.
Here is the stem cell of the LIS filiation:
LIS. Lifecycle Integration Schema -- Matthew West
01. http://suo.ieee.org/email/msg10712.html
Here are the links to the source materials
and discussion notes that have accumulated
up to this point on HA and PA:
HAPA. Hypostatic And Prescisive Abstraction
01. http://suo.ieee.org/ontology/msg05089.html -- Cain and Abel
02. http://suo.ieee.org/ontology/msg05090.html -- Dormative Virtue
03. http://suo.ieee.org/ontology/msg05091.html -- Honey is Sweet
04. http://suo.ieee.org/ontology/msg05093.html -- Math Abstraction
05. http://suo.ieee.org/ontology/msg05100.html -- Reading Runes
06. http://suo.ieee.org/ontology/msg05101.html -- Hypostatization
07. http://suo.ieee.org/ontology/msg05105.html -- Abstract Objects
08. http://suo.ieee.org/ontology/msg05108.html -- Subjectal Abstraction
D1. http://suo.ieee.org/ontology/msg05092.html -- Metaphormazes
D2. http://suo.ieee.org/ontology/msg05110.html -- Deciduation Problems
D3. http://suo.ieee.org/ontology/msg05111.html -- Recapitulation
D4. http://suo.ieee.org/ontology/msg05112.html -- Key To Abstraction
D5. http://suo.ieee.org/ontology/msg05113.html -- Self Reference?
The passage that you mention is quoted initially at No. 3, and
it is discussed further at D1, D3, D4, and prospectively at D5.
Have to break fast for breakfast as I am still semi-asleep ...
BM = Bernard Morand
BM: I wonder whether Peirce is refering here to second
intention or namely to hypostatic abstraction (HA).
BM: If we take as a starting case:
(1) "Opium puts to sleep",
in order to transform it by HA, we get:
(2) "Opium has a dormitive virtue".
BM: I see it as the transformation of a fact into
a more abstract concept, or say something like
"opium has the general property of putting to sleep".
It is hypostatic in the sense that it requires no further
proposition than (1) and that the transformation relies on
an "ens rationis". But from (2) we can also get for example:
(3) "this discourse has a dormitive virtue",
which requires a second subject (a fact about discourse).
I would be tempted to call this latter transformation
second intention, and it seems to fit with your quote
before. But going from (2) to (3) doesn't seem to be
an hypostatic abstraction stricly speaking.
BM: Thanks for throwing some light on this if possible.
HAPA. Discussion Note 6
BM = Bernard Morand
The genealogy of this circle of thoughts goes a bit like this:
| Bentham's "Theory of Fictions" begat (paraphrastically)
| Schönfinkel's "Bausteine" and this begat (independently)
| Church's "Lambda Calculus" and this begat (in good time)
| McCarthy's "Lisp" and all the rest is AI and IEEE ...
It is no accident, at least not from the right "state of information" (SOI),
how lambda abstraction got its tale, as it is truly most pertinently tagged.
It is said that the lambda came from Russell('s) and Whitehead's employment
of a caret (^) to mark a cousin operation of relational conversion, but let
me try to look that up later. At any rate, the main idea has been stock in
trade of mathematics for as long as anybody can remember, and in philosophy
more generally (or vaguely, I can never remember which) the laurel is often
placed on Bentham for his idea of paraphrasis. Here's a general/vague link:
http://www.utm.edu/research/iep/b/bentham.htm
What we see here is the very same thing going on
in the colloquial homilies that Peirce attempted
to use to adumbrate the spirit of abstraction in
the formal sciences.
BM: I wonder whether Peirce is refering here to second
intention or namely to hypostatic abstraction (HA).
BM: If we take as a starting case:
(1) "Opium puts to sleep",
in order to transform it by HA, we get:
(2) "Opium has a dormitive virtue".
Here is the diagram that I drew for the analogous case
of "virtus dulcitiva", in lay terminology, "sweetness".
Referring to a few of Peirce's standard discussions
of "hypostatic abstraction" (HA), the main thing
about HA is that it turns an adjective or some
part of a predicate into an extra subject,
upping the arity of the main predicate
in the process.
For example, a typical case of HA occurs in the transformation
from "honey is sweet" to "honey possesses sweetness", which we
could choose to represent in several different ways as follows:
Sweet(honey) ~~~> Possesses(honey, sweetness)
S(h) ~~~> P(h, s)
S P
o o
| ~~~> |
o o
h <h,s>
^
[S] ~~~> /P\
| o->-o
| | |
o o o
h h s
Figs. Are Sweet. If served in season. At just the right temps.
The chief thing about this form of grammatical transformation is that we
abstract the adjective "sweet" from the main predicate, thus arriving at
a new, increased-arity predicate "possesses", and as a by-product of the
reaction, as it were, precipitating out the substantive "sweetness" as a
new subject of the new predicate.
BM: I see it as the transformation of a fact into a more abstract concept, or
say something like "opium has the general property of putting to sleep".
Sticking, sweetly, if you will, to the notion that a concept is a mental symbol,
some might say that a sufficently "precise" abstract concept is already present
in the predicate "is_sweet", but HA takes a step beyond that, as some would say,
onto the flypaper of "abstract but substantial objects" like 'virtus dulcitiva'.
BM: It is hypostatic in the sense that it requires no further
proposition than (1) and that the transformation relies on
an "ens rationis".
Yes, this is the critical observation.
BM: But from (2) we can also get for example:
(3) "this discourse has a dormitive virtue",
which requires a second subject (a fact about discourse).
This is known as "application of the abstraction to another argument",
and it is analogous to the other half of the lambda calculus paradigm.
BM: I would be tempted to call this latter transformation
second intention, and it seems to fit with your quote
before. But going from (2) to (3) doesn't seem to be
an hypostatic abstraction stricly speaking.
As for the matter of intentional orders, I foggily peirceive
but the clue that it has something to do with the operations
that I throw together under the name of "reflection", and by
this plurality of reflection to say I abstract some fraction
of my action's contentious tensor that here-to-fore had been
too obsistently refractory to all of my previous reflections.
BM: Thanks for throwing some light on this if possible.
And thank you for a very peirceptive set of questions.
HAPA. Discussion Note 7
I will pick up from where I left off with Peirce's "sweetness and light" example, illustrating the difference between prescisive abstraction and hypostatic abstraction, and articulating the relationship between them, because there are many important things going on all at the same time in this example that I have yet to sort out and explain clearly enough. But Bernard Morand's observation about the link to "second intentional" or "second order" logic is very helpful in drawing out the main ideas. | CSP on HA: "It consists in taking a feature of a percept | or percepts (after it has already been prescinded from the | other elements of the percept), so as to take propositional | form in a judgment (indeed, it may operate upon any judgment | whatsoever), and in conceiving this fact to consist in the | relation between the subject of that judgment and another | subject, which has a mode of being that merely consists | in the truth of propositions of which the corresponding | concrete term is the predicate." | | C.S. Peirce, CP 4.235, "The Simplest Mathematics", | Chapter 3 of the "Minute Logic", Jan-Feb 1902. | | http://suo.ieee.org/ontology/msg05091.html As a thematic development in logic, this might be called the "relational turn". It involves a change of perspective that changes how one describes the same situation, passing from an expression that uses one subject and a monadic predicate to an expression that uses two subjects and a dyadic predicate. You can see a graphic illustration of the same sort of thing occurring in the transition from Euler's circles, that retain a residue of the asymmetric or inhomogeneous syllogistic form of one subject and one predicate, to the more symmetric or homogeneous relational form of the Venn diagram, that expresses a relation between two subjects in the same intentional order or at the same ontological level. In category theory, perspectival changes involve the concepts of "functors" and of "natural transformations" between them.
HAPA. Discussion Note 8
JA = Jon Awbrey
JS = John Sowa
OS = Oliver Sacks
Yes, very true, at least about the rhematic abstraction,
which is more or less the same as what Frege described
by talking of "saturated" and "unsaturated" expressions.
But still, there seems to be a difference between the
prescisive extraction of the predicate "__ is sweet",
and the hypostatic precipitate of the abstract object
"sweetness". I am still trying to clarify the residue
of what remains a cloudy suspension, but it seems like
this has something to do with the interpretation of the
syntactic abstraction as actually denoting an object,
as a lambda abstraction denotes a real-live function,
an 'ens rationis'.
CP 2.358 is Peirce's Baldwin Dictionary definition of "predicate".
CP 3.465 is a short summary of these poly-unsaturated "polyads".
CP 3.469 mentions the chemical analogy with "unsaturated bonds".
JS: I would put Peirce much closer to the beginning of that
process with his writings on relations in the 1870s:
JA: Bentham's "Theory of Fictions" begat (paraphrastically)
Schönfinkel's "Bausteine" and this begat (independently)
Church's "Lambda Calculus" and this begat (in good time)
McCarthy's "Lisp" and all the rest is AI and IEEE ...
JS: Peirce constructed relational abstractions from sentences
simply by replacing any constituent with a blank. He called
the various constituents "logical subjects". For example,
start with an arbitrary sentence that states a proposition:
John gave a book to Mary.
JS: The proposition as a whole is a medad (0-adic relation).
By erasing one logical subject, you get a monad or
monadic relation:
John gave ____ to Mary.
JS: By erasing two sujects, you get a dyad or dyadic relation:
____ gave ____ to Mary.
JS: By erasing three subjects, you get a triad or triadic relation:
____ gave ____ to ____.
JS: Peirce described this process many times in many different places over
the years, but I don't happen to have any quotations handy. He does
allude to this process in his tutorial on existential graphs:
JS: http://www.jfsowa.com/peirce/ms514.htm -- Existential Graphs
JS: As another interesting example, following is an excerpt from the
book 'Seeing Voices' by Oliver Sacks. He reports the case of an
11-year-old deaf boy, who had not had the benefit of sign language
for his first 10 years:
OS: Joseph saw, distinguished, categorized, used; he had no problems with
perceptual categorization or generalization, but he could not, it seemed,
go much beyond this, hold abstract ideas in mind, reflect, play, plan.
He seemed completely literal -— unable to juggle images or hypotheses
or possibilities, unable to enter an imaginative or figurative realm ...
He seemed, like an animal, or an infant, to be stuck in the present,
to be confined to literal and immediate perception, though made
aware of this by a consciousness that no infant could have.
JS: This example highlights the importance of language in abstraction.
HAPA. Discussion Note 9
"Inhomogeneopus", you say? -- That's Greek for "having two left feet". Here's a corrected version: As a thematic development in logic, this might be called the "relational turn". It involves a change of perspective that changes how one describes the same situation, passing from an expression that uses one subject and a monadic predicate to an expression that uses two subjects and a dyadic predicate. You can see a graphic illustration of the same sort of thing occurring in the transition from Euler's circles, that retain a residue of the asymmetric or inhomogeneous syllogistic form of one subject and one predicate, to the more symmetric or homogeneous relational form of the Venn diagram, that expresses a relation between two subjects in the same intentional order or at the same ontological level. In category theory, perspectival changes involve the concepts of "functors" and of "natural transformations" between them. I think I'll while away the morning by copying out the very instructive passages from Peirce that I mentioned last time: | CP 2.358 is Peirce's Baldwin Dictionary definition of "predicate". | CP 3.465 is a short summary of these poly-unsaturated "polyads". | CP 3.469 mentions the chemical analogy with "unsaturated bonds".
HAPA. Discussion Note 10
There are a several things of note that leap to mind
in reading Peirce's dictionary entry for "Predicate":
http://suo.ieee.org/email/msg11239.html
1. It is not so much a definition in the sense of stating logically
necessary and sufficient conditions for a thing to be a predicate
as it is a "key", an operational definition that tells you how to
recognize a predicate if you encounter one in the wild, or better
yet, a "recipe", a sequence of instructions that tells you how to
construct all the examples of predicates that you might ever need.
2. It is clear that we are looking at one of the precursors of what
would in the fullness of time became a standard socket wrench in
the AI toolbox, namely, frame-&-slot-&-filler systems. Peirce's
objection to this precursory distinction would probably take the
form of a long list of proto-precursors from which he would say
that he borrowed the tool, or derived the materials to build it.
3. It is clear, too, that the precursor has already given rather
more thought to the nature of the rhematic construction than
most of his postcursors have yet to do. For example, Peirce
advises "The erasures are not to be made in a mechanical way,
but with such modifications as may be necessary to preserve
the partial sense of the fragment". This means that the
construction of the predicate is not a purely syntactic
operation, whereby one perforates in a perfunctory way
one isolated sentence at a time, but instead a fully
sign-relational (referential, semiotic, or pragmatic)
operation, working on whole equivalence classes of
sentences at a time.
HAPA. Discussion Note 11
"You can't get there from here" Let us recall why we might be interested in Peirce's formulation of "hypostatic abstraction" (HA), a term that he cannot be blamed for coining because he only borrowed it from established traditions of prior use. The concept of an "abstract object" is dreamt of in many of our faniced and our favored ontologies, the theories of what is and the theories of what may be that we strain to snatch from out the thin air into which, so we dream, they were erstwhile disappeared, and by this dream to say we are led to believe that these "abstract objects" can be recognized by their lack of existence in space and time, or so they say. Now, asking for enlightenment about abstract objects and being told that their distinctive characteristic is their failure to exist in space and time, and not just our space and time -- as if to say "they're not from around here" -- but their remove from all space and time -- as if to say "they're not from anywhere" -- is just about as useful as asking for directions and being wrily informed "you can't get there from here". Whatever else you say about this description of abstract objects, for instance, whether it's true or false to its ostensible object -- for who, indeed, could demonstrate the fact one way or the other? -- this is not what is commonly meant by an "operational definition", since there is no hint of a feasible operation that is used in it, no where, no when, no how. So the search continues for a key or a recipe to abstract objects.
HAPA. Hypostatic And Prescisive Abstraction • Work Area
HAPA. Work Area 1
Subj: Re: ification
Date: Mon, 13 Nov 2000 16:16:02 -0500
From: Jon Awbrey <jawbrey@oakland.edu>
To: Stand Up Ontology <standard-upper-ontology@ieee.org>
Just enough time to insert a genealogical note:
http://www.utm.edu/research/iep/b/bentham.htm
Bentham's "Theory of Fictions" begat (paraphrastically)
Schönfinkel's "Bausteine" and this begat (independently)
Church's "Lambda Calculus" and this begat (in good time)
McCarthy's "Lisp" and all the rest is AI and IEEE ...
By way of stuffing the e-lectural ballot boxes just a little bit better
I will attach here some bits of an ongoing dialectric that a few of the
denizens of the Peirce List, most especially Tom Gollier and yours truly,
have been carrying on intermittently for quite some time now, regarding
this most atmospheric of all topics of our current concern, to wit, the
question of hypostatic electricity, of how or whether it can ever stick.
This will also serve to throw a new synonym into the mix: "subjectal abstraction".
Subj: Re: Varieties of Abstraction
Date: Thu, 15 Jun 2000 01:23:31 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: TGollier@aol.com
JA = Jon Awbrey
TG = Tom Gollier
TG: I knew there was no sense getting carried away until you'd had a chance
to straighten out the context, and your mathematical orientation, which
is not foreign to Peirce's either, was clear in our previous exchanges
on the list. But I don't think mathematicians are to be trusted in
this regard; not from any moral flaw in their characters but
because they're treating this subject of generalization
within an abstract realm, and hence they feel no need
or compulsion to make a distinction between the two.
JA: For me, generalization begins in a fairly concrete realm --
I take "concrete" to mean "grown together", suggesting the
concrescence of attributes or the fusion of features that
go to constitute a definite, particulate, and vivid object --
the action passes through a series of mental affections or
cognitive impressions -- the only place where such a passage
is possible without actually destroying the original object --
toward a conceptual symbol that has a more abstract reference,
to wit, a selection of the attributes, characters, features,
marks, or properties that were initially conceived to make up
the object. There is a common form to this general direction
of thought, whether the objects are apples and oranges being
generalized under the nomen of fruits, or whether the objects
are numbers under addition and numbers under multiplication
being generalized under the the nomen of groups.
JA: Generalization is a relative notion, and there is no more need
for an absolute ground here than there is for a non-inferential
perception at the origin of thought. But the distinction between
precisive (or prescindive) abstraction and hypostatic (or subjectal)
abstraction is independent of how abstracted already, how far along
the continuum or the spectrum of abstraction, happens to be the object
of thought with which one begins.
JA: Again, hypostatic abstraction is a two-edged sword -- a "subject"
is now and henceforth "supposed" to "stand its own ground beneath"
the flight of sorcery of the nominal property that is prescinded
by the flightier fancy of generalization.
JA: This occurs in concrete domains and in vivid realms as much as in the
other sort, if there is any other sort. For instance, I do not know
you as a person, in person, and all I know of you are these signs
that issue from my computer under your name. Naturally, I suppose
that there is a person who stands behind them, someone who is indeed
responsible for their generation, as their hypothetical perpetrator --
this is my act of "hypostation", or abstractive hypostasis -- in one of
its senses, and this is no accident, "hypostasis" = "person", and anyone
can look it up! The supposition of a person, an interpretive performer,
who generates the signs that one passively interprets, indeed, the very
supposition that there is a person called onself who affords the medium,
gives a local habitation and a name, and lends a substance to all of the
signs that constitute the experiences that one calls one's own, well,
those are acts of "drawing away to stand under" that are fundamental
to our "under-standing" of ourselves, however fallible, malfeasant,
and self-deceptive this form of understanding often is.
JA: Four short paragraphs and I have already put myself to sleep --
you can supply your own joke about dormitive virtues here --
I pity the person who finds this stuff in his morning post --
warning: do not drive or operate heavy machinery while under
the influence of this philosophy, or any such stuff as these
dreams are made on!
Subj: Re: Varieties of Abstraction
Date: Mon, 19 Jun 2000 23:07:04 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: TGollier@aol.com
CP = Charles Peirce
JA = Jon Awbrey
CP: CP 4.332 [Subjectal Abstraction = Hypostatic Abstraction]
JA: I think that the relation between 'hypostation', that mode of mental operation
that passes from a verb in action to a noun in stasis, that turn or that style
of thoughtful conduct that converts a "way of thinking" (WOT) about some thing
into a "subject of thought" (SOT) itself, and 'reflection', that "bending back"
and "folding over" of thought on itself, is strikingly clear in this depiction.
Subj: Re: Varieties of Abstraction
Date: Thu, 22 Jun 2000 00:24:07 -0400
From: Jon Awbrey <jawbrey@oakland.edu>
To: TGollier@aol.com
JA: Now, this is where I came in -- that is, it is just the point that I had reached
in my thinking at the end of last year when I decided to take a little break from
my day to day mental grind to see what sorts of diversion I might find on the web.
Little did I know how the play would play out! But the place in question, where
a peculiar form of reflexive complication found itself tied and once again begins
to tighten, is the place where one rises from an ongoing activity, whatever it is,
to reflect on what one is doing, perhaps with a critical eye, and this is where the
activity that one was cast into, thrown into, willy nilly, and not entirely awarely,
begins to appear, by virtue of the reflective image that is formed by the reflection,
like an object, that is, an objective form of conduct, like a chess game, that one
can choose to play or not, and even consider how to generalize and how to transform.
JA: Not too coincidentally, this is the place where the mental operations that implement
precisive and subjectal abstraction, namely, selection and reflection, respectively,
begin to highlight the importance that Dewey placed on a favorite couple of words of
his, namely, "activity" and "reflection". An ongoing activity gradually acquires an
activity of reflection as a parallel rider, then the activity of reflection is turned,
chiasmatically, into a reflection on activity. As far as I am concerned, this is the
true significance of hypostatic abstraction, that takes us from a point in medias res,
of an action that engages us, to a stance that is just a little bit outside the action,
a change of attitude or a shift of status toward the activity that is marked by our
ability to name the action or the state of becoming by means of an abstract noun.
JA: In my case, it is the activity of inquiry that I am wondering how and thus beginning
to reflect on, and this reflection is a critical component of the inquiry into inquiry.
That is a very nice description, I think, so far as it goes, but how can I teach this
skill of reflection to a rock, of the sort that we mine from silicon valley?
JA: Like I said, this is where I came in,
and I seem to be leaving by the very
same door by which I entered.
Previously under this skein, a sampler:
http://suo.ieee.org/email/msg00739.html
http://suo.ieee.org/email/msg00792.html
http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00828.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00836.html
http://suo.ieee.org/email/msg00892.html
http://suo.ieee.org/email/msg00893.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg00933.html
http://suo.ieee.org/email/msg00977.html
http://suo.ieee.org/email/msg00979.html
http://suo.ieee.org/email/msg00980.html
http://suo.ieee.org/email/msg01010.html
http://suo.ieee.org/email/msg01011.html
http://suo.ieee.org/email/msg01680.html
http://suo.ieee.org/email/msg01684.html
http://suo.ieee.org/email/msg01687.html
http://suo.ieee.org/email/msg01689.html
http://suo.ieee.org/email/msg01707.html
http://suo.ieee.org/email/msg01791.html
http://suo.ieee.org/email/msg01837.html
http://suo.ieee.org/email/msg01842.html
http://suo.ieee.org/email/msg01845.html
http://suo.ieee.org/email/msg01858.html
http://suo.ieee.org/email/msg01870.html
http://suo.ieee.org/email/msg01890.html
http://suo.ieee.org/email/msg01891.html
http://suo.ieee.org/email/msg01901.html
http://suo.ieee.org/email/msg01902.html
http://suo.ieee.org/email/msg01931.html
http://suo.ieee.org/email/msg01940.html
http://suo.ieee.org/email/msg01955.html
http://suo.ieee.org/email/msg01964.html
http://suo.ieee.org/email/msg01965.html
http://suo.ieee.org/email/msg01968.html
http://pespmc1.vub.ac.be/ASC/
http://pespmc1.vub.ac.be/ASC/Reification.html
http://pespmc1.vub.ac.be/ASC/SYSTEM.html
http://www.bestweb.net/~sowa/ontology/
http://www.bestweb.net/~sowa/ontology/causal.htm
http://www.bestweb.net/~sowa/ontology/mthworld.gif
http://www.iso18876.org/
http://www.nist.gov/sc4/
http://www.iso18876.org/iso18876/
http://www.iso18876.org/architecture/index.html
http://www.pdtsolutions.co.uk/standard/wg10/n307/wg10n307.pdf
http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm
http://www-formal.stanford.edu/jmc/generality/generality.html
http://www-formal.stanford.edu/jmc/generality/node1.html
http://www-formal.stanford.edu/jmc/generality/node2.html
http://www-formal.stanford.edu/jmc/generality/node3.html
http://www-formal.stanford.edu/jmc/generality/node4.html
http://www-formal.stanford.edu/jmc/generality/node5.html
http://www-formal.stanford.edu/jmc/generality/node6.html
http://www-formal.stanford.edu/jmc/generality/node7.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/design.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node1.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node2.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node3.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node4.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node5.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node6.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node15.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node16.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node17.html
http://www.dcc.unicamp.br/~oliva/guarana/docs/design-html/node18.html
http://blather.newdream.net/r/reification.html
http://www.utm.edu/research/iep/b/bentham.htm
HAPA. Work Area 2
CP 3.642 CP 4.463-465 CP 2.358 is Peirce's Baldwin Dictionary definition of "predicate". CP 3.465 is a short summary of these poly-unsaturated "polyads". CP 3.469 mentions the chemical analogy with "unsaturated bonds". | The most ordinary fact of perception, such as "it is light", involves | 'precisive' abstraction, or 'prescission'. But 'hypostatic' abstraction, | the abstraction which transforms "it is light" into "there is light here", | which is the sense which I shall commonly attach to the word abstraction | (since 'prescission' will do for precisive abstraction) is a very special | mode of thought. It consists in taking a feature of a percept or percepts | (after it has already been prescinded from the other elements of the percept), | so as to take propositional form in a judgment (indeed, it may operate upon | any judgment whatsoever), and in conceiving this fact to consist in the | relation between the subject of that judgment and another subject, which | has a mode of being that merely consists in the truth of propositions of | which the corresponding concrete term is the predicate. | | Thus, we transform the proposition, "honey is sweet", | into "honey possesses sweetness". "Sweetness" might be | called a fictitious thing, in one sense. But since the | mode of being attributed to it 'consists' in no more than | the fact that some things are sweet, and it is not pretended, | or imagined, that it has any other mode of being, there is, | after all, no fiction. The only profession made is that we | consider the fact of honey being sweet under the form of a | relation; and so we really can. I have selected sweetness | as an instance of one of the least useful of abstractions. | Yet even this is convenient. It facilitates such thoughts | as that the sweetness of honey is particularly cloying; | that the sweetness of honey is something like the | sweetness of a honeymoon; etc. Reference: | C.S. Peirce, CP 4.235, "The Simplest Mathematics", | Chapter 3 of the "Minute Logic", Jan-Feb 1902. | | http://suo.ieee.org/ontology/msg05091.html
JITL. Just In Time Logic
JITL. Note 1
| [On Time and Thought, MS 215, 08 Mar 1873] | | Every mind which passes from doubt to belief must have ideas which follow | after one another in time. Every mind which reasons must have ideas which | not only follow after others but are caused by them. Every mind which is | capable of logical criticism of its inferences, must be aware of this | determination of its ideas by previous ideas. But is it pre-supposed | in the conception of a logical mind, that the temporal succession in | its ideas is continuous, and not by discrete steps? A continuum such | as we suppose time and space to be, is defined as something any part | of which itself has parts of the same kind. So that the point of time | or the point of space is nothing but the ideal limit towards which we | approach, but which we can never reach in dividing time or space; and | consequently nothing is true of a pointmical which is not true of a space or | a time. A discrete quantum, on the other hand, has ultimate parts which | differ from any other part of the quantum in their absolute separation from | one another. If the succession of images in the mind is by discrete steps, | time for that mind will be made up of indivisible instants. Any one idea | will be absolutely distinguished from every other idea by its being present | only in the passing moment. And the same idea can not exist in two different | moments, however similar the ideas felt in the two different moments may, for | the sake of argument, be allowed to be. Now an idea exists only so far as the | mind thinks it; and only when it is present to the mind. An idea therefore | has no characters or qualities but what the mind thinks of it at the time | when it is present to the mind. It follows from this that if the succession | of time were by separate steps, no idea could resemble another; for these | ideas if they are distinct, are present to the mind at different times. | Therefore at no time when one is present to the mind, is the other present. | Consequently the mind never compares them nor thinks them to be alike; and | consequently they are not alike; since they are only what they are thought | to be at the time when they are present. It may be objected that though the | mind does not directly think them to be alike; yet it may think together | reproductions of them, and thus think them to be alike. This would be a | valid objection were it not necessary, in the first place, in order that | one idea should be the representative of another, that it should resemble | that idea, which it could only do by means of some representation of it | again, and so on to infinity; the link which is to bind the first two | together which are to be pronounced alike, never being found. In short | the resemblance of ideas implies that some two ideas are to be thought | together which are present to the mind at different times. And this | never can be, if instants are separated from one another by absolute | steps. This conception is therefore to be abandoned, and it must be | acknowledged to be already presupposed in the conception of a logical | mind that the flow of time should be continuous. Let us consider then | how we are to conceive what is present to the mind. We are accustomed | to say that nothing is present but a fleeting instant, a point of time. | But this is a wrong view of the matter because a point differs in no | respect from a space of time, except that it is the ideal limit which, | in the division of time, we never reach. It can not therefore be that | it differs from an interval of time in this respect that what is present | is only in a fleeting instant, and does not occupy a whole interval of | time, unless what is present be an ideal something which can never be | reached, and not something real. The true conception is, that ideas | which succeed one another during an interval of time, become present | to the mind through the successive presence of the ideas which occupy | the parts of that time. So that the ideas which are present in each | of these parts are more immediately present, or rather less mediately | present than those of the whole time. And this division may be carried | to any extent. But you never reach an idea which is quite immediately | present to the mind, and is not made present by the ideas which occupy | the parts of the time that it occupies. Accordingly, it takes time | for ideas to be present to the mind. They are present during a time. | And they are present by means of the presence of the ideas which are | in the parts of that time. Nothing is therefore present to the mind | in an instant, but only during a time. The events of a day are less | mediately present to the mind than the events of a year; the events | of a second less mediately present than the events of a day. | | C.S. Peirce, CE 3, pp. 68-70. | | Charles Sanders Peirce, MS 215, 1873, ["On Time and Thought"], pages 68-71 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 2
| [On Time and Thought, MS 215, 08 Mar 1873] (cont.) | | It remains to show that, adopting this conception, the possibility of the | resemblance of two ideas becomes intelligible; and that therefore it is not | inconceivable that one idea should follow after another, according to a general | rule. In the first place, then, it is to be observed that under this conception, | two ideas may be both present to the mind during a longer interval, while they are | separately present in shorter intervals which make up the longer interval. During | this longer interval they are present to the mind as different. They are thought | as different. And this longer interval embraces still shorter intervals than | those hitherto considered, during which there are ideas which agree in the | respects which are defined by each of the two ideas, which are seen to be | different. During the longer interval therefore, the ideas of these shortest | intervals are thought as partly alike and partly different. There is therefore | no difficulty in the conception of the resemblance of ideas. Let us now see what | is necessary in order that ideas should determine one another, and that the mind | should be aware that they determine one another. In order that there should be | any likeness among ideas, it is necessary that during an interval of time there | should be some constant element in thought or feeling. If I imagine something | red, it requires a certain time for me to do so. And if the other elements | of the image vary during that time, in one part it must be invariable, it | must be constantly red. And therefore it is proper to say that the idea | of red is present to the mind at every instant. For we are not now saying | that an idea is present to the mind in an instant in the objectionable sense | which has been referred to above, according to which an instant would differ | from an interval of time; but we are only saying that the idea is present at | an instant, in the sense that it is present in every part of a certain interval | of time; however short that part may be. The first thing that is requisite | therefore to a logical mind, is that there should be elements of thought which | are present at instants in this sense. The second thing that is requisite is, | that what is present one instant should have an effect upon what is present | during the lapse of time which follows that instant. This effect can only be | a reproduction of a part of what was present at the instant; because what is | present at the instant, is present during an interval of time during the whole | of which the effect will be present. And therefore since all that is present | during this interval is present at each instant, it follows that the effect | of what is present at each instant is present at that instant. So that this | effect is a part of the idea which produces it. In other words, it is merely | a reproduction of a part of that idea. This effect is memory, in its most | elementary form. But something more than this is required in order that the | conclusion shall be produced from a premiss; namely, an effect produced by | the succession of one idea upon another. | | C.S. Peirce, CE 3, pp. 70-71. | | Charles Sanders Peirce, MS 215, 1873, ["On Time and Thought"], pages 68-71 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 3
| [On Time and Thought, MS 216, 08 Mar 1873] | | Any mind which has the power of investigation, and which therefore passes from | doubt to belief, must have its ideas follow after one another in time. And if | there is to be any distinction of a right and a wrong method of investigation, | it must have some control over the process. So that there must be such a thing | as the production of one idea from another which was previously in the mind. | This is what takes place in reasoning, where the conclusion is brought into the | mind by the premisses. We may imagine a mind which should reason and never know | that it reasoned; never being aware that its conclusion was a conclusion, or was | derived from anything which went before. For such a mind there might be a right | and a wrong method of thinking; but it could not be aware that there was such | a distinction, nor criticize in any degree its own operations. To be capable of | logical criticism, the mind must be aware that one idea is determined by another. | Now when this happens after the first idea comes the second. There is a process | which can only take place in a space of time; but an idea is not present to the | mind during a space of time -- at least not during a space of time in which this | idea is replaced by another; for when the moment of its being present is passed, | it is no longer in the mind at all. Therefore, the fact that one idea succeeds | another is not a thing which in itself can be present to the mind, any more than | the experiences of a whole day or of a year can be said to be present to the mind. | It is something which can be lived through; but not be present in any one instant; | and therefore, which can not be present to the mind at all; for nothing is present | but the passing moment, and what it contains. The only way therefore in which we can | be aware of a process of inference, or of any other process, is by its producing some | idea in us. Not only therefore is it necessary that one idea should produce another; | but it is also requisite that a mental process should produce an idea. These three | things must be found in every logical mind: First, ideas; second, determinations | of ideas by previous ideas; third, determinations of ideas by previous processes. | And nothing will be found which does not come under one of these three heads. | The determination of one thing by another, implies that the former not only | follows after the latter, but follows after it according to a general rule, | in consequence of which, every such idea would be followed by such a second one. | There can therefore be no determination of one idea by another except so far as | ideas can be distributed into classes, or have some resemblances. But how can | one idea resemble another? An idea can contain nothing but what is present to | the mind in that idea. Two ideas exist at different times; consequently what is | present to the mind in one is present only at that time, and is absent at the time | when the other idea is present. Literally, therefore, one idea contains nothing | of another idea; and in themselves they can have no resemblance. They certainly | do not resemble one another except so far as the mind can detect a resemblance; | for they exist only in the mind, and are nothing but what they are thought to | be. Now when each is present to the mind the other is not in the mind at all. | No reference to it is in the mind, and no idea of it is in the mind. Neither | idea therefore when it is in the mind, is thought to resemble the other which | is not present in the mind. And an idea can not be thought, except when it is | present in the mind. And, therefore, one idea can not be thought to resemble | another, strictly speaking. In order to escape from this paradox, let us see | how we have been led into it. Causation supposes a general rule, and therefore | similarity. Now so long as we suppose that what is present to the mind at one | time is absolutely distinct from what is present to the mind at another time, | our ideas are absolutely individual, and without any similarity. It is necessary, | therefore, that we should conceive a process as present to the mind. And this | process consists of parts existing at different times and absolutely distinct. | And during the time that one part is in the mind, the other is not in the mind. | To unite them, we have to suppose that there is a consciousness running through | the time. So that of the succession of ideas which occur in a second of time, | there is but one consciousness, and of the succession of ideas which occurs in | a minute of time there is another consciousness, and so on, perhaps indefinitely. | So that there may be a consciousness of the events that happened in a whole day or | a whole life time. According to this, two parts of a process separated in time -- | though they are absolutely separate, in so far as there is a consciousness of the | one, from which the other is entirely excluded -- are yet so far not separate, | that there is a more general consciousness of the two together. This conception | of consciousness is something which takes up time. It seems forced upon us to | escape the contradictions which we have just encountered. And if consciousness | has a duration, then there is no such thing as an instantaneous consciousness; | but all consciousness relates to a process. And no thought, however simple, is | at any instant present to the mind in its entirety, but it is something which we | live through or experience as we do the events of a day. And as the experiences | of a day are made up of the experiences of shorter spaces of time so any thought | whatever is made up of more special thoughts which in their turn are themselves | made up by others and so on indefinitely. It may indeed very likely be that there | is some minimum space of time within which in some sense only an indivisible thought | can exist and as we know nothing of such a fact at present we may content ourselves | with the simpler conception of an indefinite continuity in consciousness. ... | | C.S. Peirce, CE 3, pp. 72-74. | | Charles Sanders Peirce, MS 216, 1873, ["On Time and Thought"], pages 72-75 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 4
| [On Time and Thought, MS 216, 08 Mar 1873] (cont.) | | It will easily be seen that when this conception is once grasped the | process of the determination of one idea by another becomes explicable. | What is present to the mind during the whole of an interval of time is | something generally consisting of what there was in common in what was | present to the mind during the parts of that interval. And this may be | the same with what is present to the mind during any interval of time; | or if not the same, at least similar -- that is, the two may be such | that they have much in common. These two thoughts which are similar | may be followed by others that are similar and according to a general | law by which every thought similar to either of these is followed by | another similar to those by which they are followed. If a succession | of thoughts have any thing in common this may belong to every part of | these thoughts however minute, and therefore it may be said to be present | at every instant. This element of consciousness which belongs to a whole | only so far as it belongs to its parts is termed the matter of thought. | There is besides this a causation running through our consciousness by | which the thought of any one moment determines the thought of the next | moment no matter how minute these moments may be. And this causation | is necessarily of the nature of a reproduction; because if a thought | of a certain kind continues for a certain length of time as it must | do to come into consciousness the immediate effect produced by this | causality must also be present during the whole time, so that it is a | part of that thought. Therefore when this thought ceases, that which | continues after it by virtue of this action is a part of the thought | itself. In addition to this there must be an effect produced by the | following of one idea after a different idea otherwise there would be | no process of inference except that of the reproduction of the premisses. | | C.S. Peirce, CE 3, pp. 74-75. | | Charles Sanders Peirce, MS 216, 1873, ["On Time and Thought"], pages 72-75 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 5
| [Lecture on Practical Logic, MS 191, Summer-Fall 1872] | | I suppose that the fundamental proposition from which all metaphysics | takes its rise is that opinions tend to an ultimate settlement & that | a predestinate one. Upon most subjects at least sufficient experience, | discussion, and reasoning will bring men to an agreement; and another | set of men by an independent investigation with sufficient experience, | discussion, and reasoning will be brought to the same agreement as the | first set. | | Hence we infer that there is something which determines | opinions and which does not depend upon them. To this | we give the name of the 'real'. Now this 'real' may | be regarded from two opposite points of view. | | In the first place, to say that thought tends to come to a determinate conclusion, | is to say that it tends to an end or is influenced by a 'final cause'. This final | cause, the ultimate opinion, is independent of how you, I, or any number of men | think. Let whole generations think as perversely as they will; they can only | put off the ultimate opinion but cannot change its character. So the ultimate | conclusion is that which determines opinions and does not depend upon them and | so is the real object of cognition. This is idealism since it supposes the | real to be of the nature of thought. | | But, in the second place, a cause precedes its effect. And moreover the ultimate | conclusion though independent of this or that mind is not independent of mind in | general. The real, therefore, which determines thought but does not depend upon it, | is not the last conclusion but the first premiss or what produces the first premiss,-- | a something out of the mind and incommensurable with thought. | | Since experience proceeds from the less general to the more general, the | last conclusion is general, and so the first view is realistic, while the | second from a like reason is individualistic. In the first view, the real | is in one sense never realized since though opinion may in fact have reached | a settlment in reference to any question, there always remains a possibility | that more experience, discussion, and reasoning would change any given opinion. | In the second view also the real is a species of fiction for that which is | logically singular,-- or is determined with reference to every quality,-- | can from the continual change which is constantly taking place not remain | for any time however short, (Daniel Webster, for example, is a class embracing | Daniel Webster under 50 years of age & Daniel Webster over 50 years of age) and | consequently does not exist as absolutely determinate at all. | | Upon either view therefore the real is something ideal and never actually exists. | But it is true on the one hand that thought tends to a determinate conclusion and | on the other that if anything is true, true determinations without number are true | of it. We ought therefore to discard the conception of the real as something actual | and to say simply that only thought actually exists and it has a law which no more | determines it than it by the mode in which it acts makes the law. Only this law | is such that in a sufficient time it will determine thought to any extent. | | C.S. Peirce, CE 3, pp. 8-9. | | Charles Sanders Peirce, MS 191, 1872, ["Lecture on Practical Logic"], pp. 8-9 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 6
| [Logic, Truth, and the Settlement of Opinion, MS 179, Winter-Spring 1872] | | Logic is the doctrine of truth, its nature and | the manner in which it is to be discovered. | | The first condition of learning is to know that we are ignorant. | A man begins to inquire and to reason with himself as soon as he | really questions anything and when he is convinced he reasons no more. | Elementary geometry produces formal proofs of propositions which nobody | doubts, but that cannot properly be caled reasoning which does not carry us | from the known to the unknown, and the only value in the first demonstrations | of geometry is that they exhibit the dependence of certain theorems on certain | axioms, a thing which is not clear without the demonstrations. When two men | discuss a question, each first endeavors to raise a doubt in the mind of the | other, and that is often half the battle. When the doubt ceases there is no | use in further discussion. Thus real inquiry begins when genuine doubt begins | and ends when this doubt ends. And the premisses of the reasoning are facts | not doubted. It is therefore idle to tell a man to begin by doubting familiar | beliefs, unless you say something which shall cause him really to doubt them. | Again, it is false to say that reasoning must rest either on first principles | or on ultimate facts. For we cannot go behind what we are unable to doubt, | but it would be unphilosophical to suppose that any particular fact will | never be brought into doubt. | | It is easy to see what truth would be for a mind which could not doubt. That mind | could not regard anything as possible except what it believed in. By all existing | things it would mean only what it thought existed, and everything else would be what | it would mean by 'non-existent'. It would, therefore, be omniscient in its universe. | To say that an omniscient being is necessarily destitute of the faculty of reason, | sounds paradoxical; yet if the act of reasoning must be directed to an end, when | that end is attained the act naturally becomes impossible. | | C.S. Peirce, CE 3, pp. 14-15. | | C.S. Peirce, MS 179, 1872, ["Logic, Truth, Settlement of Opinion"], pp. 14-16 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 7
| [Logic, Truth, and the Settlement of Opinion, MS 179, Winter-Spring 1872] (cont.) | | The only justification for reasoning is that it settles doubts, | and when doubt finally ceases, no matter how, the end of reasoning | is attained. Let a man resolve never to change his existing opinions, | let him obstinately shut his eyes to all evidence against them, and if | his will is strong enough so that he actually does not waver in his faith, | he has no motive for reasoning at all, and it would be absurd for him to | do it. That is method number one for attaining the end of reasoning, and | it is a method which has been much practised and highly approved, especially | by people whose experience has been that reasoning only leads from doubt to | doubt. There is no valid objection to this proceedure if it only succeeds. | It is true it is utterly irrational; that is to say it is foolish from the | point of view of those who do reason. But to assume that point of view is | to beg the question. In fact, however, it does not succeed; and the first | cause of failure is that different people have different opinions and the | man who sees this begins to feel uncertain. It is therefore desirable to | produce unanimity of opinion and this gives rise to method number two, which | is to force people by fire and sword to adopt one belief, to massacre all who | dissent from it and burn their books. This way of bringing about a catholic | consent has proved highly successful for centuries in some cases, but it is | not practicable in our days. A modification of this is method number three, | to cultivate a public opinion by oratory and preaching and by fostering | certain sentiments and passions in the minds of the young. This method | is the most generally successful in our day. The fourth and last method | is that of reasoning. It will never be adopted when any of the others will | succeed and it has itself been successful only in certain spheres of thought. | Nevertheless those who reason think that it must be successful in the end, | & so it would if all men could reason. There is this to be said in favor | of it. He who reasons will regard the opinions of the majority of mankind | with contemptuous indifference; they will not in the least disturb his | opinions. He will also neglect the beliefs of those who are not informed, | and among the small residue he may fairly expect some unanimity on many | questions. | | I hope it will now be plain to the reader, that the only rational | ground for preferring the method of reasoning to the other methods | is that it fixes belief more surely. A man who proposes to adopt the | first method may consistently do so simply because he chooses to do so. | But if we are to decide in favor of reasoning, we ought to do so on | rational grounds. Now if belief is fixed, no matter how, doubt has | as a matter of fact ceased, & there is no motive, rational or other, | for reasoning any more. Any settlement of opinion, therefore, if it | is full and perfect, is entirely satisfactory and nothing could be | better. It is the peculiarity of the method of reasoning, that if | a man thinks that it will not burn him to put his hand in the fire, | reasoning will not confirm that belief but will change it. This is | a vast advantage to the mind of a rationalist. But the advocate of | any one of the first three methods, will be able to say (if either | of those methods will yield a fixed belief) either that he 'knows' | by his method that fire will burn, so that reasoning is inferior to | his method in that it may permit a man for a moment to doubt this, or | else that he 'knows' that fire will not burn, so that reasoning leads | all astray. In either case therefore he will conceive that that which | to the rationalist seems the great advantage of reasoning, to be a great | fault. Thus the only ground of a fair decision between the methods must | be that one actually succeeds while the others break up and dissolve. | Bryant expresses the philosophy of the matter perfectly: | | | Truth struck to earth shall rise again | | The eternal years of God are hers | | While error ... writhes in pain | | And dies amidst her worshippers. | | C.S. Peirce, CE 3, pp. 15-16. | | C.S. Peirce, MS 179, 1872, ["Logic, Truth, Settlement of Opinion"], pp. 14-16 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 8
| Chapter 1 (Enlarged Abstract) [MS 182, Winter-Spring 1872] | | The very first of distinctions which logic supposes is between doubt and belief, | a question and a proposition. Doubt and belief are two states of mind which | feel different, so that we can distinguish them by immediate sensation. | We almost always know without any experiment when we are in doubt and | when we are convinced. This is such a difference as there is between | red and blue, or pleasure & pain. Were this the whole distinction, | it would be almost without significance. But in point of fact the | mere sensible distinguishability is attended with an important | practical difference. When we believe there is a proposition | which according to some rule determines our actions, so that | our belief being known, the way in which we shall behave | may be surely deduced, but in the case of doubt we have | such a proposition more or less distinctly in our minds | but do not act from it. There is something further | removed from belief than doubt, that is to say not | to conceive the proposition at all. Nor is doubt | wholly without effect upon our conduct. It makes | us waver. Conviction determines us to act in a | particular way while pure unconscious ignorance | alone which is the true contrary of belief has | no effect at all. | | Belief and doubt may be conceived to be distinguished only in degree. | | C.S. Peirce, CE 3, pp. 20-21. | | C.S. Peirce, MS 182, 1872, "Chapter 1 (Enlarged Abstract)", pages 20-21 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 9
| Chapter 2. Of Inquiry | | The irritation of doubt causes a struggle to attain a state of belief. | This struggle I shall term 'inquiry', though it must be admitted that | this is sometimes not a very apt designation. | | The irritation of doubt is the only immediate motive for the struggle | to attain belief. It is certainly best for us that our beliefs should | be such as may truly guide our actions so as to satisfy our desires; and | this reflection will make us reject any belief which does not seem to have | been so formed as to insure this result. But it will only do so by creating | a doubt in place of that belief. With the doubt therefore the struggle begins | and with the cessation of doubt it ends. Hence, the sole object of inquiry is | the settlement [...] | | C.S. Peirce, CE 3, p. 23. | | C.S. Peirce, "Chapter 2. Of Inquiry", MS 188, May-June 1872, pages 23-24 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 10
| Chapter 3. Four Methods of Settling Opinion | | If the settlement of opinion is the sole object of inquiry, and if belief is | of the nature of a habit, why should we not attain the desired end, by taking | any answer to a question which we may fancy, and constantly reiterating it to | ourselves, by dwelling on all which may conduce to that belief and learning to | turn with contempt and hatred from anything which might disturb it? This simple | and direct method is really pursued by many men. ... | | But this method of fixing belief, which may be called the | method of obstinacy, will be unable to hold its ground in | practice. The social impulse is against it. ... | | Let the will of the state act then, instead of that of the individual. ... | | In judging this method of fixing belief, which may be called | the method of despotism, we must in the first place allow its | immeasurable mental and moral superiority to the method of | obstinacy. ... | | But no institution can undertake to regulate opinions upon every subject. | Only the most important ones can be attended to, and on the rest men's minds | must be left to the action of natural causes. This imperfection [...] may | affect every man. And though these affections are necessarily as various | as are individual conditions yet the method must be such that the ultimate | conclusion of every man shall be the same. This is called the scientific | method. Its fundamental hypothesis stated in more familiar language is this. | There are real things, whose characters are entirely independent of our opinions | about them; those realities affect our senses, according to regular laws, and | though our sensations are as different as our relations to the objects, yet by | taking advantage of the laws which subsist we can ascertain by reasoning how | the things really are, and any man if he have sufficient experience and reason | enough about it, will be led to the one true conclusion. The new conception here | involved is that of reality. It may be asked how I know there are any realities. | If this hypothesis is the sole support of my method of inquiry, my method of | inquiry must not be used to support my hypothesis. The reply is this. 1st, | If investigation cannot be regarded as proving that there are real things, | it at least does not lead to a contrary conclusion; but the method and the | conception on which it is based remain ever in harmony. No doubts of the | method, therefore, necessarily arise from its practice, as is the case | with all the others. 2nd, the feeling which gives rise to any method | of fixing belief, is a dissatisfaction at two repugnant propositions. | But here already is a vague concession that there is some one thing to | which a proposition should conform. Nobody, therefore, can really doubt | that there are realities, or if he did, doubt would not be a source of | dissatisfaction. The hypothesis therefore is one which every mind admits. | So that the social impulse does not cause me to doubt it. 3rd, Everybody | uses the scientific method about a great many things and only ceases to use | it when he does not know how to apply it. 4th, Experience of the method has | not led me to doubt it but on the contrary scientific investigation has had | the most wonderful triumphs in the way of settling opinion. These afford | the explanation of my not doubting either the method or the hypothesis | which it supposes, and not having any doubt nor believing that anybody | else whom I could influence has, it would be the merest babble for me | to say more about it. If there be anybody with a living doubt upon | the subject, let him consider it. | | To describe the method of scientific investigation is the object of this book. | In this chapter, I shall only notice some points of contrast between it and | other methods of inquiry. | | This is the only one of the four methods which presents any distinction of a right | and a wrong way. If I adopt the method of obstinacy and shut myself out from all | influences, no matter what I think necessary to doing this, is necessary according | to that method. So with the method of despotism, the state may try to put down | heresy by means which from a scientific point of view seem very ill-calculated | to accomplish its purpose, but the only test 'on that method' is what the state | thinks, so that it cannot pursue the method wrongly. So with the 'a priori' | method. If I endeavor to lay my susceptibilities of belief perfectly open to | the influences which work upon them, I cannot on those principles go wrong. | But with the scientific method, the case is different. I may start with | known and observed facts to proceed to the unknown; and yet the rules | which I follow in doing so may not be such as investigation would | approve. The test of whether I am truly following the method | is not an immediate appeal to my feelings and purposes, | but on the contrary itself involves the application | of the method. Hence it is that bad reasoning | as well as good reasoning is possible; and | this fact is the foundation of the | practical side of logic. | | C.S. Peirce, CE 3, pp. 24-28. | | C.S. Peirce, "Four Methods of Settling Opinion", MS 189, May-June 1872, pp. 24-28 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 11
| Chapter 4. Of Reality | | Investigation supposes a true and a false, | truth and falsity being independent of all | opinion upon the matter. The name 'real' | is applied to that which is independent | of how you or I or any number of minds | think it to be. | | It is a truism to say that the character of what I think | depends entirely on what I think it to be. The real is | not, therefore, 'per se' an immediate object of thought, | even though my thought may happen to coincide with it. | Yet the real must influence thought or I could not by | following any rules of reasoning arrive at any truth. | | Investigation consists necessarily of two parts, one by which a | belief is generated from other beliefs, which is called 'reasoning'; | and another by which new elements of belief are brought into the mind, | which is called 'observation'. Thus, the conclusions depend entirely | upon the observations. But while the ultimate conclusion is one and | the same in the minds of all who push investigation far enough, the | observations on which it hangs are for every man private and peculiar. | The observations which I made yesterday are not the same that I make today; | nor are simultaneous observations from different situations or with other | different circumstances the same. Two men cannot therefore make the same | observation. We may go further and say that no two observations are in | themselves in any degree alike. The judgment that they are alike is not | contained in either observation (since they do not relate to one another) | but is a belief generated by the two beliefs in which the two observations | immediately result, so that it is an inference of reasoning, as that has just | been defined. Thus our reasonings begin with the most various premisses, which | have not in themselves anything in common, but which so determine our beliefs as | to lead us at last to one destined conclusion. | | Here is the whole statement of facts from which we must infer whatever we can know | of the mode of being of the real. But there is no additional fact which we can | infer from these facts. For these embrace everything which takes place in | thought, and as to anything out of thought we can know nothing. | | C.S. Peirce, CE 3, pp. 60-61. | | Charles Sanders Peirce, "Chapter 4. Of Reality", MS 205, Fall 1872, pp. 60-61 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 12
| Chapter ___. The List of Categories | | In the doctrines which have thus far been developed, are implicitly | involved certain conceptions of such universal applicability and such | importance in logic, that I propose to consider them especially in this | chapter under the name of 'Categories'. | | In the ideal final opinion which would perfectly represent the reality of things, | all possible doubt would be resolved. It follows that the reality is something | entirely definite. 'Ens est unum.' An object may be conceived to have this | character without being real, that is without being in accord with the | opinion to which observations are fated to tend, and I shall call this | the 'being' of things. A griffin 'is' a fabulous animal. That is, | a griffin is supposed to be a definite object. You may ask as many | questions as you please about a griffin and supply answers according | to some rule and if all the questions which could be invented were | thus answered, the animal would possess as perfect a being as if | it were real, and yet be a mere creature of the imagination. | | In every doubt there is one thing fixed and one thing vague; | the thing which we doubt something about is fixed, what we | doubt about it is vague. These two things must equally be | distinguished in the belief in which the doubt is resolved. | Consequently, every being has elements which are distinguished | from it but which belong to it, in short it has 'qualities'. | | C.S. Peirce, CE 3, p. 61. | | Charles S. Peirce, "The List of Categories", MS 207, Winter 1872-73, p. 61 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 13
| On Representations | | A representation is an object which stands for another so that | an experience of the former affords us a knowledge of the latter. | There are three essential conditions to which every representation | must conform. It must in the first place like any other object have | qualities independent of its meaning. It is only through a knowledge | of these that we acquire any information concerning the object it | represents. Thus, the word "man" as printed, has three letters; | these letters have certain shapes, and are black. I term such | characters, the material qualities of the representation. In the | 2nd place a representation must have a real causal connection with | its object. If a weathercock indicates the direction of the wind | it is because the wind really turns it round. If the portrait of | a man of a past generation tells me how he looked it is because | his appearance really determined the appearance of the picture | by a train of causation, acting through the mind of the painter. | If a prediction is trustworthy it is because those antecedents of | which the predicted event is the necessary consequence had a real | effect in producing the prediction. In the third place, every | representation addresses itself to a mind. It is only in so | far as it does this that it is a representation. The idea of | the representation itself excites in the mind another idea and | in order that it may do this it is necessary that some principle | of association between the two ideas should already be established | in that mind. These three conditions serve to define the nature of | a representation. | | C.S. Peirce, CE 3, p. 62. | | Charles S. Peirce, "On Representations", MS 212, Winter-Spring 1873, p. 62 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 14
| I begin with the soul of man. For we first learn that brutes have souls from | the facts of the human soul. What brutes and other men do & suffer would be | quite unintelligible to us, if we had not a standard within ourselves with | which to measure others. | | At the first dawn of cognition we began to compare and consider the objects about us. | Our thought first assigned to things their right places and reduced the wild chaos | of sensuous impressions to a luminous order. But after thought had classified | everything a residuum was left over, which had no place in the classification. | This was thought itself. What is this which is left over? After thought | has considered everything, it is obliged next to think of itself. Here | it is at once means and end. The question is, 'what' is thought, -- | and the question can only be answered 'by means of' thought. | | This is a noticeable circumstance. How can thought think of itself, it is | asked; that would be an insoluble contradiction. It is as though a tone | should be heard of itself, or a beam of light be seen by itself. But this | objection reminds one of the efforts of the man who tried to look at his | own eye. After great difficulty he got so far as to see the end of his | nose, forgetting that it would be much simpler to hold up a looking-glass | to his face. Common sense, which usually hits the nail on the head, has | long ago held that looking-glass up to thought. If I wish to represent to | myself what my thought is, (says common sense) I have only to act as though | my thought were an external object which I can consider as I should consider | something not a part of myself. Thought thus objectively considered common | sense terms the soul. So if we are to investigate in a scientific manner | the nature of thought, we //need/can// do nothing else than consider the | soul as if it were an object of experience. | | Everyone grants that thought is a sort of experience; otherwise, we | could not know that we think. Everyone further sees that we have in | thought a very varied experience, for it changes both with the object | thought of and with mental development which we have attained. Thus, | we bring together all the experiences which thought has in itself & | subject them to the consideration of our thoughts. There are also | other experiences, not properly thoughts, such as sensations and | feelings which we term phenomena of the soul, because we recognize | them as immediate products of an activity within us, which according | to our observation cannot be separated from the activity of thought. | | C.S. Peirce, CE 3, pp. 10-11. | | Charles S. Peirce, "Third Lecture", MS 192, Summer-Fall 1872, pages 10-11 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 15
| Chapter 11. On Logical Breadth and Depth | | As Logic is the study of the laws of signs so far as these denote things -- | those laws of signs which determine what things they denote and what | they do not -- it is necessary in Logic to pay especial attention to | those terms which denote signs. Such terms are genus species &c. | No thing is a genus but as there are terms such as man and tree | which denote some one thing leaving it more or less indeterminate | what one so we may speak of whatever may be denoted by such a general | term as a genus or class. Such terms are called 'terms of second intention'. | The first intention is the mental act by which an object is conceived. The | second intention is the mental act by which the first conception is made an | object of conception in reference to its relation to its object. A term of | second intention does not so much signify the sign itself as it signifies | whatever is denoted by a sign of a certain description. As signs differ | in their logical characters we may define an object by means of the | logical characters of the sign which denotes it and in that case | it is pointed out with a peculiar kind of generality which | requires special attention. Two of the most important | characters of general terms are their logical breadth | and depth. The breadth of a term in general is that of | which the term can be predicated. The depth of a term is | that which can be predicated of it. The breadth therefore | may be considered as a collection of objects -- real things -- | though it can also be considered as consisting of the terms | which may be made subject of a true proposition of which | the given term is the predicate. The depth of a term | cannot be considered as a collection of things but | can only be considered as a complex of terms or of | attributes. The term attribute, character, mark, or | quality is a term of second intention. Two things are | alike in a certain respect that is to say the same predicate | can be applied to either of them. Then the capacity of having that | predicate applied to it with truth is called an attribute that is a thing | to which it can be applied. The attribute is therefore an abstract term. | Terms are divisible into concrete and abstract. The concrete are such | as white virtuous &c. the abstract such as whiteness virtue, etc. | Abstract terms do not denote any real thing but they denote | fictitious things. An object's being white is conceived | as being due to its being in some relation with a certain | fictitious thing whiteness. In point of fact that the object | is white may in a certain sense be said to be due to its connection | with the sign or predicate white that is to say it must be in such a | relation to the name white that this name may be applied to it with | truth or else it cannot be white. There is no falsity in this | statement although it is more natural to state the matter | in the inverse way and to say that its having that | connection with that name is due to the fact | that it is white. One statement is as true | as the other. In the latter more natural mode | of statement the existence of the thing is looked | upon as the ultimate fact but we have seen in the chapter | upon reality that the final information is the ultimate fact, | that final information consisting in applying a certain sign | to certain objects in the predication and therefore it is | perfectly correct to say that the thing's being white | is due to and consists of the applicability of | a certain predicate to a certain thing. | A attribute or quality is not precisely | the same as a predicate inasmuch as when we | use the word predicate we have in mind the fact | that the predicate is something extraneous to the thing | which does not belong to it as it exists but belongs to it as it is | thought whereas an attribute is considered as belonging to a thing whatever | is thought. But upon our view of the nature of reality this is a distinction | of very slight moment because existence is thus not independent of all thought | and what is affirmed in the final judgment is the same as what really exists. | | C.S. Peirce, 'Chronological Edition', CE 3, 98-99 | | C.S. Peirce, "On Logical Breadth and Depth", MS 233, Spring 1873, pp. 98-102 in: |'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
JITL. Note 16
Cf: JITL 15. http://stderr.org/pipermail/inquiry/2003-August/000732.html In: JITL. http://stderr.org/pipermail/inquiry/2003-August/thread.html#712 | Chapter 11. On Logical Breadth and Depth (cont.) | | Thus in considering the breadth and depth of terms | it is desirable to make a number of distinctions. | | By the "informed breadth" of a term I shall mean all the | real objects of which it is predicable with logical truth | in the supposed state of information as our knowledge is | never absolute but consists only of probabilities that | all the information at hand must be taken into account | and those things of which there is not on the whole | reason to believe that the term is truly predicable | are not to be reckoned as part of its breadth. | | If T be a term which is predicable only of S_1, S_2, and S_3 | then the S_1's, S_2's, and S_3's will constitute the informed | breadth of T. | | If there be a second term T' which is predicable only of S_1 and S_2 | and if it is not known that S_3 is entirely included under S_1 and S_2 | then T is considered to have a greater informed breadth than T'. | | If it is known that the S_3's are not all among the S_1's and S_2's the | excess of breadth is certain but if it is not known whether or not this | is the case it is "doubtful". | | If certain S_3's are known to exist which are not known to be either | S_1's or S_2's, T is said to have a greater actual breadth than T' | but if all the S_3's which are known to exist are also known to | be S_1's and S_2's though there are other S_3's which are not | S_1 or S_2 then T is said to have greater potential breadth | than T'. | | If T and T' are conceptions in different minds | or in different states of the same mind then T | may have a doubtful excess of breadth in one | mind and no excess at all in the other mind. | In that case the conception is said to be | more extensively distinct to the latter | mind. | | C.S. Peirce, 'Chronological Edition', CE 3, 99-100 | | C.S. Peirce, "On Logical Breadth and Depth", MS 233, Spring 1873, | Chapter 11 from ["Toward a Logic Book, 1872-1873"], pp. 14-108 in: |'Writings of Charles S. Peirce: A Chronological Edition, Vol. 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986. NB. I have substituted S_1, S_2, S_3 for Peirce's S', S'', S''', respectively.
JITL. Note 17
| Chapter 11. On Logical Breadth and Depth (cont.) | | By the "informed depth" of a term I mean all the real characters in | contradistinction to mere synonimous names which can be predicated of | it with logical truth in the supposed state of information no character | being counted twice over knowingly. The depth like the breadth will be | certainly doubtful and there is a comprehensive distinctness corresponding | to extensive distinctness. | | The informed breadth and depth suppose a state of information which lies | somewhere between two imaginary extremes. There are first the state of | knowledge in which no fact should be known but only the meanings of terms | and, second, the state of information in which every fact should be known. | This suggests two other sorts of breadth and depth corresponding to the two | essential states of information which I shall term accordingly the essential | and the substantial breadth and depth. | | The essential depth of a term which is sometimes called | its essence consists of the really conceivable qualities | predicated of it in its definition. This is one of the | most important features of logic. | | Suppose the definition of the term T be this: "In T is at once | P_1, P_2, and P_3". This sums up the whole meaning of T. It may | not be known that there is no such thing as P_1 and therefore the | meaning of T does not imply its existence. On the other hand we | must know that P_1, P_2, and P_3 are neither of them coextensive | with the whole conception of being for we know the qualities of | things only by comparison with their opposites hence we must | know that there is something which is not P_1 and that this | is not T, that there is something which is not P_2 and that | this is not T, and that there is something which is not P_3 | and that this is not T. | | Accordingly if we define the essential breadth of a term as "those real things | of which according to its every meaning a term is predicable" then "not T" has | an essential breadth that is to say its very meaning implies that there are | things of which it is predicable. Thus T is a term which has essential depth | but no essential breadth -- "not T" is a term which has essential breadth | but not essential depth and all terms may be divided into two classes, | the "essential positive" and "essential negative", the former having | essential depth but not essential breadth, the latter having essential | breadth but not essential depth. There are some terms which are | affirmative in form but which according to this definition are | essentially negative and vice versa. As examples of this we | may allude particularly to the terms "being" and "nothing" | both of which are terms of second intention. | | As every term has breadth and the breadth of one term is greater | than that of another we may conceive of a term the breadth of | which includes that of every other other term so that it is | predicable of anything whatever. This is the definition | of the term "being". Its definition therefore gives it | breadth but not depth and accordingly it is essentially | negative. | | We may also conceive of a term whose depth includes the depth of all | other terms so that anything whatever may be predicated of it without | any falsity and this is the definition of the term "nothing". For you | may say what you please of nothing and if it is clearly understood that | what you speak of has no existence there is no falsity in what you assert | because you have not made any assertion whatever. "Nothing" therefore is | a term which has essential depth without any breadth and is according to | our definition essentially affirmative. | | C.S. Peirce, 'Chronological Edition', CE 3, 100-101 | | C.S. Peirce, "On Logical Breadth and Depth", MS 233, Spring 1873, | Chapter 11 from ["Toward a Logic Book, 1872-1873"], pp. 14-108 in: |'Writings of Charles S. Peirce: A Chronological Edition, Vol. 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986. NB. I have substituted P_1, P_2, P_3 for Peirce's P', P'', P''', respectively.
JITL. Note 18
| Chapter 11. On Logical Breadth and Depth (concl.) | | If two terms have the same essential breadth or the same essential depth | logic recognizes no distinction between them. They are synonimous. They | may differ rhetorically. One of these words may be associated in our minds | with certain feelings with which the other is not associated but logic has | nothing to do with such distinctions. But two terms may be indistinctly | conceived so that it is not known whether they have the same essential | breadth and depth or not and in this case the distinction must be | admitted even in logic. | | We now come to the "substantial breadth and depth". | The substantial breadth is the aggregate of real | substance of which alone a term is predicable | with absolute truth. Substantial depth is | the real character as it exists in the | object, which belongs to every thing | of which a term is predicable with | absolute truth. | | C.S. Peirce, 'Chronological Edition', CE 3, 101-102 | | C.S. Peirce, "On Logical Breadth and Depth", MS 233, Spring 1873, | Chapter 11 from ["Toward a Logic Book, 1872-1873"], pp. 14-108 in: |'Writings of Charles S. Peirce: A Chronological Edition, Vol. 3, 1872-1878', | Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
NEKS. New Elements • Kaina Stoicheia
NEKS. Note 1
| I now proceed to explain the difference between a theoretical | and a practical proposition, together with the two important | parallel distinctions between 'definite' and 'vague', and | 'individual' and 'general', noting, at the same time, | some other distinctions connected with these. | | A 'sign' is connected with the "Truth", i.e. the entire Universe | of being, or, as some say, the Absolute, in three distinct ways. | | In the first place, a sign is not a real thing. | It is of such a nature as to exist in 'replicas'. | Look down a printed page, and every 'the' you see | is the same word, every 'e' the same letter. A real | thing does not so exist in replica. The being of a | sign is merely 'being represented'. Now 'really being' | and 'being represented' are very different. Giving to | the word 'sign' the full scope that reasonably belongs | to it for logical purposes, a whole book is a sign; and | a translation of it is a replica of the same sign. A whole | literature is a sign. The sentence "Roxana was the queen of | Alexander" is a sign of Roxana and of Alexander, and though | there is a grammatical emphasis on the former, logically the | name "Alexander" is as much 'a subject' as is the name "Roxana"; | and the real persons Roxana and Alexander are 'real objects' of | the sign. | | Every sign that is sufficiently complete refers refers to sundry | real objects. All these objects, even if we are talking of Hamlet's | madness, are parts of one and the same Universe of being, the "Truth". | But so far as the "Truth" is merely the 'object' of a sign, it is merely | the Aristotelian 'Matter' of it that is so. | | In addition however to 'denoting' objects every | sign sufficiently complete 'signifies characters', | or qualities. | | We have a direct knowledge of real objects in every | experiential reaction, whether of 'Perception' or of | 'Exertion' (the one theoretical, the other practical). | These are directly 'hic et nunc'. But we extend the | category, and speak of numberless real objects with | which we are not in direct reaction. | | We have also direct knowledge of qualities in feeling, | peripheral and visceral. But we extend this category | to numberless characters of which we have no immediate | consciousness. | | All these characters are elements of the "Truth". | Every sign signifies the "Truth". But it is only | the Aristotelian 'Form' of the universe that it | signifies. | | The logician is not concerned with any metaphysical | theory; still less, if possible, is the mathematician. | But it is highly convenient to express ourselves in terms | of a metaphysical theory; and we no more bind ourselves to | an acceptance of it than we do when we use substantives such | as "humanity", "variety", etc. and speak of them as if they | were substances, in the metaphysical sense. | | But, in the third place, every sign is intended to determine a | sign of the same object with the same signification or 'meaning'. | Any sign, 'B', which a sign, 'A', is fitted so to determine, without | violation of its, 'A's, purpose, that is, in accordance with the "Truth", | even though it, 'B', denotes but a part of the objects of the sign, 'A', and | signifies but a part of its, 'A's, characters, I call an 'interpretant' of 'A'. | | What we call a "fact" is something having the structure of a proposition, | but supposed to be an element of the very universe itself. The purpose | of every sign is to express "fact", and by being joined with other signs, | to approach as nearly as possible to determining an interpretant which | would be the 'perfect Truth', the absolute Truth, and as such (at least, | we may use this language) would be the very Universe. | | Aristotle gropes for a conception of perfection, or 'entelechy', | which he never succeeds in making clear. We may adopt the word | to mean the very fact, that is, the ideal sign which should be | quite perfect, and so identical, -- in such identity as a sign | may have, -- with the very matter denoted united with the very | form signified by it. The entelechy of the Universe of being, | then, the Universe 'qua' fact, will be that Universe in its | aspect as a sign, the "Truth" of being. The "Truth", the | fact that is not abstracted but complete, is the ultimate | interpretant of every sign. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 238-240 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 2
| Of the two great tasks of humanity, 'Theory' and 'Practice', the former sets out | from a sign of a real object with which it is 'acquainted', passing from this, | as its 'matter', to successive interpretants embodying more and more fully its | 'form', wishing ultimately to reach a direct 'perception' of the entelechy; | while the latter, setting out from a sign signifying a character of which it | 'has an idea', passes from this, as its 'form', to successive interpretants | realizing more and more precisely its 'matter', hoping ultimately to be able | to make a direct 'effort', producing the entelechy. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 240 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 3
| But of these two movements, logic very properly | prefers to take that of Theory as the primary one. | | It speaks of an 'antecedent' as that which being known something else, | the 'consequent' may 'also' be known. In our vernacular, the latter | is inaccurately called a 'consequence', a word that the precise | terminology of logic reserves for the proposition expressing | the relation of any consequent to its antecedent, or for | the fact which this proposition expresses. | | The conception of the relation of antecedent and consequent amounts, | therefore, to a confusion of thought between the reference of a sign | to its 'meaning', the character which it attributes to its object, | and its appeal to an interpretant. But it is the former of these | which is the more essential. | | The knowledge that the sun has always risen about once in each | 24 hours (sidereal time) is a sign whose object is the sun, and | (rightly understood) a part of its signification is the rising of | the sun tomorrow morning. | | The relation of an antecedent to its consequent, in its confusion of | the signification with the interpretent, is nothing but a special case | of what occurs in all action of one thing upon another, modified so as to | be merely an affair of being represented instead of really being. It is the | representative action of the sign upon its object. For whenever one thing acts | upon another it determines in that other a quality that would not otherwise have | been there. | | In the vernacular we often call an effect a "consequence", | because that which really is may correctly be represented; | but we should refuse to call a mere logical consequent | an "effect", because that which is merely represented, | however legitimately, cannot be said really to be. | | If we speak of an argumentation as "producing a great effect", | it is not the interpretant itself, by any means, to which we | refer, but only the particular replica of it which is made | in the minds of those addressed. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 240 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 4
| If a sign, 'B', only signifies characters that
| are elements (or the whole) of the meaning of
| another sign, 'A', then 'B' is said to be a
| 'predicate' (or 'essential part') of 'A'.
|
| If a sign 'A', only denotes real objects that
| are a part or the whole of the objects denoted
| by another sign, 'B', then 'A' is said to be a
| 'subject' (or 'substantial part') of 'B'.
|
| The totality of the predicates of a sign, and also the totality of the
| characters it signifies, are indifferently each called its logical 'depth'.
| This is the oldest and most convenient term. Synonyms are the 'comprehension'
| of the Port-Royalists, the 'content' ('Inhalt') of the Germans, the 'force'
| of DeMorgan, the 'connotation' of J.S. Mill. (The last is objectionable.)
|
| The totality of the subjects, and also, indifferently, the totality of the
| real objects of a sign is called the logical 'breadth'. This is the oldest
| and most convenient term. Synonyms are the 'extension' of the Port-Royalists
| (ill-called 'extent' by some modern French logicians), the 'sphere' ('Umfang')
| of translators from the German, the 'scope' of DeMorgan, the 'denotation' of
| J.S. Mill.
|
| Besides the logical depth and breadth, I have proposed (in 1867) the terms
| 'information' and 'area' to denote the total of fact (true or false) that
| in a given state of knowledge a sign embodies.
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 241
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)',
| Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 5
In our reading of the parts of the "Kaina Stoicheia" that take up -- or take off from -- the subject of "Theory and Practice", we have covered this much: KS 1. http://stderr.org/pipermail/inquiry/2005-September/003063.html -- NEM 4, 238-240 KS 2. http://stderr.org/pipermail/inquiry/2005-September/003065.html -- NEM 4, 240 KS 3. http://stderr.org/pipermail/inquiry/2005-October/003075.html -- NEM 4, 240 KS 4. http://stderr.org/pipermail/inquiry/2005-October/003090.html -- NEM 4, 241 We continue with that reading here: | Other distinctions depend upon those that we have drawn. | | I have spoken of real relations as reactions. It may be asked how far I | mean to say that all real relations are reactions. It is seldom that one | falls upon so fascinating a subject for a train of thought [as] the analysis | of that problem in all its ramifications, mathematical, physical, biological, | sociological, psychological, logical, and so round to the mathematical again. | | The answer cannot be satisfactorily given in a few words; but it lies hidden | beneath the obvious truth that any exact necessity is expressible by a general | equation; and nothing can be added to one side of a general equation without | an equal addition to the other. Logical necessity is the necessity that a sign | should be true to a 'real' object; and therefore there is 'logical' reaction in | every real dyadic relation. If 'A' is in a real relation to 'B', 'B' stands in | a logically contrary relation to 'A', that is, in a relation at once converse to | and inconsistent with the direct relation. For here we speak [not] of a vague | sign of the relation but of the relation between two individuals, 'A' and 'B'. | | This very relation is one in which 'A' alone stands to any individual, | and it to 'B' only. There are, however, 'degenerate' dyadic relations, -- | 'degenerate' in the sense in which two coplanar lines form a 'degenerate' | conic, -- where this is not true. Namely, they are individual relations | of identity, such as the relation of 'A' to 'A'. All mere resemblances | and relations of reason are of this sort. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 241 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 6
| Of signs there are two different degenerate forms. | But though I give them this disparaging name, they | are of the greatest utility, and serve purposes that | genuine signs could not. | | The more degenerate of the two forms (as I look upon it) | is the 'icon'. This is defined as a sign of which the | character that fits it to become a sign of the sort | that it is, is simply inherent in it as a quality | of it. | | For example, a geometrical figure drawn on paper may | be an 'icon' of a triangle or other geometrical form. | | If one meets a man whose language one does not know | and resorts to imitative sounds and gestures, these | approach the character of an icon. The reason they | are not pure icons is that the purpose of them is | emphasized. | | A pure icon is independent of any purpose. It serves as a sign | solely and simply by exhibiting the quality it serves to signify. | The relation to its object is a degenerate relation. It asserts | nothing. If it conveys information, it is only in the sense in | which the object that it is used to represent may be said to | convey information. An 'icon' can only be a fragment of | a completer sign. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 241-242 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 7
| The other form of degenerate sign is to be termed an 'index'. | It is defined as a sign which is fit to serve as such by | virtue of being in a real reaction with its object. | | For example, a weather-cock is such a sign. It is fit to | be taken as an index of the wind for the reason that it is | physically connected with the wind. A weather-cock conveys | information; but this it does because in facing the very | quarter from which the wind blows, it resembles the wind | in this respect, and thus has an icon connected with it. | In this respect it is not a pure index. | | A pure index simply forces attention to the object | with which it reacts and puts the interpreter into | mediate reaction with that object, but conveys no | information. | | As an example, take an exclamation "Oh!" | | The letters attached to a geometrical figure are another case. | | Absolutely unexceptionable examples of degenerate forms must not be expected. | All that is possible is to give examples which tend sufficiently in towards | those forms to make the mean suggest what is meant. | | It is remarkable that while neither a pure icon nor a pure index | can assert anything, an index which forces something to be an 'icon', | as a weather-cock does, or which forces us to regard it as an 'icon', | as the legend under a portrait does, does make an assertion, and forms | a 'proposition'. This suggests the true definition of a proposition, | which is a question in much dispute at this moment. A proposition | is a sign which separately, or independently, indicates its object. | | No 'index', however, can be an 'argumentation'. It may be what many | writers call an 'argument; that is, a basis of argumentation; but an | argument in the sense of a sign which separately shows what interpretant | it is intended to determine it cannot be. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 242 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 8
| It will be observed that the icon is very perfect in respect | to signification, bringing its interpreter face to face with | the very character signified. For this reason, it is the | mathematical sign 'par excellence'. But in denotation it | is wanting. It gives no assurance that any such object | as it represents really exists. | | The index on the other hand does this most perfectly, | actually bringing to the interpreter the experience | of the very object denoted. But it is quite wanting | in signification unless it involves an iconic part. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 242-243 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 9
| We now come to the genuine sign for which I propose the | technical designation 'symbol', following a use of that | word not infrequent among logicians including Aristotle. | | A symbol is defined as a sign which is fit to serve | as such simply because it will be so interpreted. | | To recapitulate: | | ) ( it possesses | An icon } ( the quality | ) ( signified. | ) ( | ) ( it is in real | ) ( reaction | An index > is a sign fit to be used as such because < with the | ) ( object | ) ( denoted. | ) ( | ) ( it determines | A symbol ) ( the interpretant | ) ( sign. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 243 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 10
| Language and all abstracted thinking, such as belongs | to minds who think in words, is of the symbolic nature. | | Many words, though strictly symbols, are so far iconic that they are apt | to determine iconic interpretants, or as we say, to call up lively images. | Such, for example, are those that have a fancied resemblance to sounds | associated with their objects; that are 'onomatopoetic', as they say. | | There are words, which although symbols, act very much like indices. | Such are personal, demonstrative, and relative pronouns, for which | 'A', 'B', 'C', etc. are often substituted. | | A 'Proper Name', also, which denotes a single individual well known | to exist by the utterer and interpreter, differs from an index only | in that it is a conventional sign. | | Other words refer indirectly to indices. Such is "yard" | which refers to a certain bar in Westminster, and has no | meaning unless the interpreter is, directly or indirectly, | in physical reaction with that bar. | | Symbols are particularly remote from the Truth itself. They are abstracted. | They neither exhibit the very characters signified as icons do, nor assure us | of the reality of their objects, as indices do. Many proverbial sayings express | a sense of this weakness; as "Words prove nothing", and the like. Nevertheless, | they have a great power of which the degenerate signs are quite destitute. They | alone express laws. Nor are they limited to this theoretical use. They serve | to bring about reasonableness and law. The words 'justice' and 'truth', amid | a world that habitually neglects these things and utterly derides the words, | are nevertheless among the very greatest powers the world contains. They | create defenders and animate them with their strength. This is not rhetoric | or metaphor: it is a great and solid fact of which it behooves a logician to | take account. | | A symbol is the only kind of sign which can be an argumentation.* | |* I commonly call this an argument; for nothing is more false historically | than to say that this word has not at all times been used in this sense. | Still, the longer word is a little more definite. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 243-244 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 11
| I have already defined an argument as a sign which separately monstrates | what its intended interpretant is, and a proposition as a sign which | separately indicates [what] its object is, and we have seen that | the icon alone cannot be a proposition while the symbol alone | can be an argument. | | That a sign cannot be an argument without being a proposition is shown | by attempting to form such an argument. "Tully, c'est-a-dire a Roman", | evidently asserts that Tully is a Roman. Why this is so is plain. The | interpretant is a sign which denotes that which the sign of which it is | interpretant denotes. But, being a symbol, or genuine sign, it has a | signification and therefore it represents the object of the principal | sign as possessing the characters that it, the interpretant, signifies. | | It will be observed that an argument is a symbol which separately | monstrates (in any way) its 'purposed' interpretant. Owing to | a symbol being essentially a sign only by virtue of its being | interpretable as such, the idea of a purpose is not entirely | separable from it. The symbol, by the very definition of it, | has an interpretant in view. Its very meaning is intended. | Indeed, a purpose is precisely the interpretant of a symbol. | | But the conclusion of an argument is a specially | monstrated interpretant, singled out from among | the possible interpretants. It is, therefore, | of its nature single, although not necessarily | simple. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 244 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 12
| If we erase from an argument every monstration of its special purpose, | it becomes a proposition; usually a copulate proposition, composed of | several members whose mode of conjunction is of the kind expressed by | "and", which the grammarians call a "copulative conjunction". | | If from a propositional symbol we erase one or more of the parts which | separately denote its objects, the remainder is what is called a 'rhema'; | but I shall take the liberty of calling it a 'term'. | | Thus, from the proposition "Every man is mortal", we erase "Every man", | which is shown to be denotative of an object by the circumstance that if | it be replaced by an indexical symbol, such as "That" or "Socrates", the | symbol is reconverted into a proposition, we get the 'rhema' or 'term': | | " ___ is mortal". | | Most logicians will say that this is not a term. The term, | they will say, is "mortal", while I have left the copula "is" | standing with it. Now while it is true that one of Aristotle's | memoirs dissects a proposition into subject, predicate, and verb, | yet as long as Greek was the language which logicians had in view, | no importance was attached to the substantive verb, "is", because | the Greek permits it to be omitted. It was not until the time of | Abelard, when Greek was forgotten, and logicians had Latin in mind, | that the copula was recognized as a constituent part of the logical | proposition. | | I do not, for my part, regard the usages of language | as forming a satisfactory basis for logical doctrine. | Logic, for me, is the study of the essential conditions | to which signs must conform in order to function as such. | How the constitution of the human mind may compel men to | think is not the question; and the appeal to language | appears to me to be no better than an unsatisfactory | method of ascertaining psychological facts that are | of no relevancy to logic. | | But if such appeal is to be made (and logicians generally | do make it; in particular their doctrine of the copula | appears to rest solely upon this), it would seem that | they ought to survey human languages generally and | not confine themselves to the small and extremely | peculiar group of Aryan speech. | | Without pretending, myself, to an extensive acquaintance with languages, | I am confident that the majority of non-Aryan languages do not ordinarily | employ any substantive verb equivalent to "is". Some place a demonstrative | or relative pronoun; as if one should say: | | " ___ is a man 'that' is translated" | | for "A man is translated". Others have a word, syllable, or letter, to show | that an assertion is intended. I have been led to believe that in very few | languages outside the Aryan group is the common noun a well-developed and | independent part of speech. Even in the Shemitic languages, which are | remarkably similar to the Aryan, common nouns are treated as verbal | forms and are quite separated from proper names. | | The ordinary view of a term, however, supposes it to be a common noun in | the fullest sense of the term. It is rather odd that of all the languages | which I have examined in a search for some support of this ordinary view, so | outlandish a speech as the Basque is the only one I have found that seems to | be constructed thoroughly in the manner in which the logicians teach us that | every rational being must think.* | |* While I am on the subject of languages I may take occasion to remark | with reference to my treatment of the direct and indirect "objects" | of a verb as so many subjects of the proposition, that about nine out | of every ten languages regularly emphasize one of the subjects, and | make it the principal one, by putting it in a special nominative case, | or by some equivalent device. The ordinary logicians seem to think | that this, too, is a necessity of thought, although one of the living | Aryan languages of Europe habitually puts that subject in the genetive | which the Latin puts in the nominative. This practice was very likely | borrowed from a language similar to the Basque spoken by some progenitors | of the Gaels. Some languages employ what is, in effect, an ablative for | this purpose. It no doubt is a rhetorical enrichment of a language to | have a form "B is loved by A" in addition to "A loves B". The language | will be still richer if it has a third form in which A and B are treated | as equally the subjects of what is said. But logically, the three are | identical. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 244-246 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 13
| What is the difference between " ___ is a man" and "man"? | The logicians hold that the essence of the latter lies in | a definition describing its characters; which doctrine | virtually makes "man" equivalent to "what is a man". | It thus differs from " ___ is a man" by the addition* | of the badly named "indefinite pronoun", 'what'. | The rhema " ___ is a man" is a fragmentary sign. | But "man" is never used alone, and would have no | meaning by itself. It is sometimes written upon | an object to show the nature of that object; but | in such case, the appearance of the object is an | index of that object; and the two taken together | form a proposition. In respect to being fragmentary, | therefore, the two signs are alike. It may be said | that "Socrates wise" does not make a sentence in the | language at present used in logic, although in Greek | it would. But it is important not to forget that no | more do "Socrates" and "is wise" make a proposition | unless there is something to indicate that they are | to be taken as signs of the same object. On the | whole, it appears to me that the only difference | between my rhema and the "term" of other logicians | is that the latter contains no explicit recognition | of its own fragmentary nature. But this is as much | as to say that logically their meaning is the same; | and it is for that reason that I venture to use the | old, familiar word "term" to denote the rhema. | |* [Missing lines in NEM supplied from EP 2 at this point. -- JA] | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 246 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 14
| It may be asked what is the nature of the sign which joins "Socrates" | to " ___ is wise", so as to make the proposition "Socrates is wise". | I reply that it is an index. But, it may be objected, an index | has for its object a thing 'hic et nunc', while a sign is not | such a thing. This is true, if under "thing" we include | singular events, which are the only things that are | strictly 'hic et nunc'. | | But it is not the two signs "Socrates" and "wise" that are | connected, but the 'replicas' of them used in the sentence. | We do not say that " ___ is wise", as a general sign, is | connected specially with Socrates, but only that it is so | as here used. The two replicas of the words "Socrates" | and "wise" are 'hic et nunc', and their junction is a | part of their occurrence 'hic et nunc'. They form a | pair of reacting things which the index of connection | denotes in their present reaction, and not in a general | way; although it is possible to generalize the mode of | this reaction like any other. | | There will be no objection to a generalization which shall call the mark | of junction a 'copula', provided it be recognized that, in itself, it is | not general, but is an 'index'. No other kind of sign would answer the | purpose; no general verb "is" can express it. For something would have | to bring the general sense of that general verb down to the case in hand. | An index alone can do this. | | But how is this index to signify* the connection? | In the only way in which any index can ever | signify* anything; by involving an 'icon'. | The sign itself is a connection. | | I shall be asked how this applies to Latin, where the parts of the sentence are | arranged solely with a view to rhetorical effect. I reply that, nevertheless, | it is obvious that in Latin, as in every language, it is the juxtaposition | which connects words. Otherwise they might be left in their places in the | dictionary. Inflexion does a little; but the main work of construction, | the whole work of connexion, is performed by putting the words together. | | In Latin much is left to the good sense of the interpreter. | | That is to say, the common stock of knowledge of utterer and interpreter, | called to mind by the words, is a part of the sign. That is more or less | the case in all conversation, oral and scriptal. It is, thus, clear that | the vital spark of every proposition, the peculiar propositional element | of the proposition, is an indexical proposition; an index involving an | icon. The rhema, say " ___ loves ___ ", has blanks which suggest filling; | and a concrete actual connection of a subject with each blank monstrates | the connection of ideas. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 246-247 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998. * [NB by JA. Recall that "signify" has a "connotative" connotation here:] | In addition however to 'denoting' objects every | sign sufficiently complete 'signifies characters', | or qualities. | | NEM 4, 239. | Cf: KS 1. http://stderr.org/pipermail/inquiry/2005-September/003063.html | In: KS. http://stderr.org/pipermail/inquiry/2005-September/thread.html#3063
NEKS. Note 15
| It is the Proposition which forms the main subject
| of this whole scholium; for the distinctions of
| 'vague' and 'distinct', 'general' and 'individual'
| are propositional distinctions.
|
| I have endeavored to restrain myself from long discussions of terminology.
| But here we reach a point where a very common terminology overlaps an
| erroneous conception. Namely those logicians who follow the lead of
| Germans, instead of treating of propositions, speak of "judgments"
| ('Urtheile'). They regard a proposition as merely an expression in
| speech or writing of a judgment. More than one error is involved in
| this practice. In the first place, a judgment, as they very correctly
| teach, is a subject of psychology. Since psychologists, now-a-days,
| not only renounce all pretension to knowledge of the 'soul', but also
| take pains to avoid talking of the 'mind', the latter is at present not
| a scientific term, at all; and therefore I am not prepared to say that
| logic does not, as such, treat of the mind. I should like to take mind
| in such a sense that this could be affirmed; but in any sense in which
| psychology, -- the scientific psychology now recognized, -- treats of
| mind, logic, I maintain, has no concern with it.
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 247-248
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)',
| Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 16
| Without stopping here to discuss this large question, | I will say that psychology is a science which makes | special observations; and its whole business is | to make the phenomena so observed (along with | familiar facts allied to those things), | definite and comprehensible. | | Logic is a science little removed from pure mathematics. | It cannot be said to make any positive phenomena known, | although it takes account and rests upon phenomena of | daily and hourly experience, which it so analyzes as | to bring out recondite truths about them. | | One might think that a pure mathematician might assume these | things as an initial hypothesis and deduce logic from these; | but this turns out, upon trial, not to be the case. | | The logician has to be recurring to reexamination of the | phenomena all along the course of his investigations. | But logic is all but as far remote from psychology | as is pure mathematics. | | Logic is the study of the essential nature of signs. | | A sign is something that exists in replicas. Whether the sign "it is raining" | or "all pairs of particles of matter have component accelerations toward one | another inversely proportional to the square of the distance" happens to have | a replica in writing, in oral speech, or in silent thought, is a distinction | of the very minutest interest to logic, which is a study, not of replicas, | but of signs. | | But this is not the only, nor the most serious error involved in making logic | treat of "judgments" in place of propositions. It involves confounding two | things which must be distinguished if a real comprehension of logic is to | be attained. | | A 'proposition', as I have just intimated, is not to be understood as the | lingual expression of a judgment. It is, on the contrary, that sign of | which the judgment is one replica and the lingual expression another. | But a judgment is distinctly 'more' than the mere mental replica of | a proposition. It not merely 'expresses' the proposition, but it | goes further and 'accepts' it. | | I grant that the normal use of a proposition is to affirm it; and its | chief logical properties relate to what would result in reference to its | affirmation. It is, therefore, convenient in logic to express propositions | in most cases in the indicative mood. But the proposition in the sentence, | "Socrates est sapiens", strictly expressed, is "Socratem sapientum esse". | The defence of this position is that in this way we distinguish between | a proposition and the assertion of it; and without such distinction it | is impossible to get a distinct notion of the nature of the proposition. | | One and the same proposition may be affirmed, denied, judged, | doubted, inwardly inquired into, put as a question, wished, | asked for, effectively commanded, taught, or merely expressed, | and does not thereby become a different proposition. What is | the nature of these operations? The only one that need detain | us is affirmation, including judgment, or affirmation to oneself. | | As an aid in dissecting the constitution of affirmation I shall employ | a certain logical magnifying-glass that I have often found efficient | in such business. Imagine, then, that I write a proposition on a | piece of paper, perhaps a number of times, simply as a calligraphic | exercise. It is not likely to prove a dangerous amusement. But | suppose I afterwards carry the paper before a notary public and | make affidavit to its contents. That may prove to be a horse | of another color. The reason is that this affidavit may be | used to determine an assent to the proposition it contains | in the minds of judge and jury; -- an effect that the paper | would not have had if I had not sworn to it. For certain | penalties here and hereafter are attached to swearing to | a false proposition; and consequently the fact that | I have sworn to it will be taken as a negative index | that it is not false. This assent in judge and jury's | minds may effect in the minds of sheriff and posse a | determination to an act of force to the detriment of | some innocent man's liberty or property. Now certain | ideas of justice and good order are so powerful that | the ultimate result may be very bad for me. | | This is the way that affirmation looks under the microscope; for the only | difference between swearing to a proposition and an ordinary affirmation of | it, such as logic contemplates, is that in the latter case the penalties | are less and even less certain than those of the law. The reason there | are any penalties is, as before, that the affirmation may determine a | judgment to the same effect in the mind of the interpreter to his cost. | It cannot be that the sole cause of his believing it is that there are | such penalties, since two events cannot cause one another, unless they | are simultaneous. There must have been, and we well know that there is, | a sort of hypnotic disposition to believe what one is told with an air [of] | command. It is Grimes's credenciveness, which is the essence of hypnotism. | This disposition produced belief; belief produced the penalties; and the | knowledge of these strengthens the disposition to believe. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 248-249 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 17
| I have discussed the nature of belief | in the 'Popular Science Monthly' for | November 1877. On the whole, we may | set down the following definitions: | | A 'belief' in a proposition is a controlled and contented habit of | acting in ways that will be productive of desired results only if | the proposition is true. | | An 'affirmation' is an act of an utterer of a proposition to an interpreter, | and consists, in the first place, in the deliberate exercise, in uttering | the proposition, of a force tending to determine a belief in it in the | mind of the interpreter. Perhaps that is a sufficient definition of it; | but it involves also a voluntary self-subjection to penalties in the | event of the interpreter's mind (and still more the general mind of | society) subsequently becoming decidedly determined to the belief | at once in the falsity of the proposition and in the additional | proposition that the utterer believed the proposition to be | false at that time he uttered it. | | A 'judgment' is a mental act deliberately exercising a force tending to | determine in the mind of the agent a belief in the proposition: to which | should perhaps be added that the agent must be aware of his being liable | to inconvenience in the event of the proposition's proving false in any | practical aspect. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 249-250 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 18
| In order fully to understand the distinction between a proposition and an argument, | it will be found important to class these acts, affirmation, etc. and ascertain | their precise nature. The question is a purely logical one; but it happens | that a false metaphysics is generally current, especially among men who | are influenced by physics but yet are not physicists enough fully to | comprehend physics, which metaphysics would disincline those who | believe in it from readily accepting the purely logical statement | of the nature of affirmation. I shall therefore be forced to | touch upon metaphysics. Yet I refuse to enter here upon | a metaphysical discussion; I shall merely hint at what | ground it is necessary to take in opposition to | a common doctrine of that kind. | | Affirmation is of the nature of a symbol. | It will be thought that this cannot be | the case since an affirmation, as the | above analysis shows, produces real | effects, physical effects. No sign, | however, is a real thing. It has no | real being, but only being represented. | | I might more easily persuade readers to think that affirmation was | an index, since an index is, perhaps, a real thing. Its replica, | at any rate, is in real reaction with its object, and it forces | a reference to that object upon the mind. But a symbol, a word, | certainly exists only in replica, contrary to the nature of | a real thing; and indeed the symbol only becomes a sign | because because its interpreter happens to be prepared | to represent it as such. Hence, I must and do admit | that a symbol cannot exert any real force. Still, | I maintain that every sufficiently complete symbol | governs things, and that symbols alone do this. | I mean that though it is not a force, it is | a law. | | Now those who regard the false metaphysics | of which I speak as the only clear opinion | on its subject are in the habit of calling | laws "uniformities", meaning that what we | call laws are, in fact, nothing but common | characters of classes of events. It is | true that they hold that they are symbols, | as I shall endeavor to show that they are; | but this is to their minds equivalent to | saying that they are common characters | of events; for they entertain a very | different conception of the nature of | a symbol from mine. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 250 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 19
| I begin, then, by showing that a law is | not a mere common character of events. | | Suppose that a man throwing a pair of dice, which were | all that honest dice are supposed to be, were to throw | sixes a hundred times running. Every mathematician will | admit that that would be no ground for expecting the next | throw to turn up sixes. It is true that in any actual case | in which we should see sixes thrown a hundred times running we | should very rightly be confident that the next throw would turn up | sixes likewise. But why should we do so? Can anybody sincerely deny | that it would be because we should think the throwing of a hundred | successive sixes was an almost infallible indication of there | being some real connection between those throws, so that the | series not merely a uniformity in the common character of | turning up sixes, but something more, a result of a real | circumstance about the dice connecting the throws? | | This example illustrates the logical principle that mere community of | character between the members of a collection is no argument, however | slender, tending to show that the same character belongs to another | object not a member of that collection and not (as far as we have | any reason to think) having any real connection with it, unless | perchance it be in having the character in question. For the | usual supposition that we make about honest dice is that there | will be no real connection (or none of the least significance) | between their different throws. I know that writer has copied | writer in the feeble analysis of chance as consisting in our | ignorance. But the calculus of probabilities is pure nonsense | unless it affords assurance in the long run. Now what assurance | could there be concerning a long run of throws of a pair of dice, | if, instead of knowing they were honest dice, we merely did not | know whether they were or not, or if, instead of knowing that | there would be no important connection between the throws, | we merely did not know that there would be. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 250-251 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 20
| That certain objects 'A', 'B', 'C', etc. are known to have | a certain character is not the slightest reason for supposing | that another object [Xi], quite unconnected with the others so | far as we know, has that character. Nor has this self evident | proposition ever been denied. A "law", however, is taken very | rightly by everybody to be a reason for predicting that an event | will have a certain character although the events known to have | that character have no other real connection with it than the law. | | This shows that the law is not a mere uniformity but involves a real connection. | It is true that those metaphysicians say that if 'A', 'B', 'C', etc. are known | to have two common characters and [Xi] is known to have one of these, this is | a reason for believing that it has the other. But this is quite untenable. | Merely having a common character does not constitute a real connection; | and those very writers virtually acknowledge this, in reducing law to | uniformity, that is, to the possession of a common character, as a | way of denying that "law" implies any real connection. | | What is a law, then? It is a formula to which real events truly conform. | By "conform", I mean that, taking the formula as a general principle, | if experience shows that the formula applies to a given event, then | the result will be confirmed by experience. But that such a general | formula is a symbol, and more particularly, an asserted symbolical | proposition, is evident. Whether or not this symbol is a reality, | even if not recognized by you or me or any generations of men, and | whether, if so, it implies an Utterer, are metaphysical questions | into which I will not now enter. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 251-252 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 21
| One distinguished writer seems to hold that, although events | conform to the formula, or rather, although it conforms to the | Truth of facts, yet it does not influence the facts. This comes | perilously near to being pure verbiage; for, seeing that nobody | pretends that the formula exerts a compulsive force on the events, | what definite meaning can attach to this emphatic denial of the | law's influencing the facts? The law had such mode of being as | it ever has before all the facts had come into existence, for it | might already be experientially known; and then the law existing, | when the facts happen there is agreement between them and the law. | | What is it, then, that this writer has in mind? If it were not | for the extraordinary misconception of the word "cause" by Mill, | I should say that the idea of metaphysical sequence implied in that | word, in "influence", and in other similar words was perfectly clear. | Mill's singularity is that he speaks of the cause of a singular event. | Everybody else speaks of the cause of a "fact", which is an element of | the event. But, with Mill, it is the event in its entirety which is | caused. The consequence is that Mill is obliged to define the cause | as the totality of all the circumstances attending the event. This is, | strictly speaking, the Universe of being in its totality. But any event, | just as it exists, in its entirety, is nothing else but the same Universe | of being in its totality. It strictly follows, therefore, from Mill's use | of the words, that the only 'causatum' is the entire Universe of being and | that its only cause is itself. He thus deprives the word of all utility. | | As everybody else but Mill and his school more or less clearly | understands the word, it is a highly useful one. That which | is caused, the 'causatum', is, not the entire event, but | such abstracted element of an event as is expressible | in a proposition, or what we call a "fact". The cause | is another "fact". Namely, it is, in the first place, | a fact which could, within the range of possibility, | have its being without the being of the 'causatum'; | but, secondly, it could not be a real fact while | a certain third complementary fact, expressed | or understood, was realized, without the being | of the causatum; and thirdly, although the | actually realized causatum might perhaps be | realized by other causes or by accident, | yet the existence of the entire possible | causatum could not be realized without | the cause in question. | | It may be added that a part of a cause, if a part in | that respect in which the cause is a cause, is also | called a 'cause'. In other respects, too, the scope | of the word will be somewhat widened in the sequel. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 252 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 22
| If the cause so defined is a part of the causatum, in the sense that | the causatum could not logically be without the cause, it is called | an 'internal cause'; otherwise, it is called an 'external cause'. | | If the cause is of the nature of an individual thing or fact, | and the other factor requisite to the necessitation of the | 'causatum' is a general principle, I would call the cause | a 'minor', or 'individuating', or perhaps a 'physical cause'. | | If, on the other hand, it is the general principle which is | regarded as the cause and the individual fact to which it is | applied is taken as the understood factor, I would call the | cause a 'major', or 'defining', or perhaps a 'psychical cause'. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 252-253 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 23
| The individuating internal cause is called the 'material cause'. | Thus the integrant parts of a subject or fact form its 'matter', | or material cause. | | The individuating external cause is called the 'efficient', | or 'efficient cause'; and the causatum is called the 'effect'. | | The defining internal cause is called the 'formal' cause, | or 'form'. All those facts which constitute the definition | of a subject or fact make up its form. | | The defining external cause is called the 'final cause', | or 'end'. | | It is hoped that these statements will be found to hit | a little more squarely than did those of Aristotle and | the scholastics the same bull's eye at which they aimed. | From scholasticism and the medieval universities, these | conceptions passed in vaguer form into the common mind | and vernacular of Western Europe, and especially so in | England. | | Consequently by the aid of these definitions I think | I can make out what it is that the writer mentioned | has in mind in saying that it is not the law which | influences, or is the final cause of, the facts, | but the facts that make up the cause of the law. | | He means that the general fact which the law of gravitation | expresses is composed of the special facts that this stone at | such a time fell to the ground as soon as it was free to do so | and its upward velocity was exhausted, that each other stone did | the same, that each planet at each moment was describing an ellipse | having the centre of mass of the solar system at a focus, etc. etc.; | so that the individual facts are the material cause of the general fact | expressed by the law; while the propositions expressing those facts are | the efficient cause of the law itself. | | This is a possible meaning in harmony with the writer's sect of thought; | and I believe it is his intended meaning. But this is easily seen not | to be true. For the formula relates to all possible events of a given | description; which is the same as to say that it relates to all possible | events. Now no collection of actual individual events or other objects of | any general description can amount to all possible events or objects of that | description; for it is possible that an addition should be made to that | collection. The individuals do not constitute the matter of a general; | those who with Kant, or long before him, said that they do were wanting in | the keen edge of thought requisite for such discussions. On the contrary, | the truth of the formula, its really being a sign of the indicated object, | is the defining cause of the agreement of the individual facts with it. | | Namely, this truth fulfills the first condition, which is that it might | logically be although there were no such agreement. For it might be true, | that is, contains no falsity, that whatever stone there might be on earth | would have a real downward component [of] acceleration even although no stone | actually existed on earth. It fulfills the second condition, that as soon as the | other factor (in this case the actual existence of each stone on earth) was present, | the result of the formula, the real downward component of acceleration would exist. | Finally, it fulfills the third condition, that while all existing stones might | be accelerated downwards by other causes or by an accidental concurrence of | circumstances, yet the downward acceleration of every possible stone would | involve the truth of the formula. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 253-254 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. Note 24
... | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 254 | | C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in: | Carolyn Eisele (ed.), 'The New Elements of Mathematics by | Charles S. Peirce, Volume 4, Mathematical Philosophy', | Mouton, The Hague, 1976. | | Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)', | Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
NEKS. New Elements • Kaina Stoicheia • Commentary
NEKS. Commentary Note 1
Here's one for all you Neo-Plots out there. Rummaging about the web I find that the phrase "Utter Indetermination" appears in the Enneads: | Everything the Soul engenders down to this point comes into being shapeless, | and takes form by orientation towards its author and supporter: therefore | the thing engendered on the further side can be no image of the Soul, | since it is not even alive; it must be an utter Indetermination. | | http://www.sacred-texts.com/cla/plotenn/enn214.htm Pretty scary ... As I suspected, we'll probably end up hashing out the whole KS/NE paper before we can get a clue what it's talking about. Here's a sample of some previous encounters: QUAGS. Questions About Genuine Signs 00. http://stderr.org/pipermail/inquiry/2005-May/thread.html#268 00. http://stderr.org/pipermail/inquiry/2005-August/thread.html#2926 01. http://stderr.org/pipermail/inquiry/2005-May/002658.html 02. http://stderr.org/pipermail/inquiry/2005-May/002659.html 03. http://stderr.org/pipermail/inquiry/2005-May/002662.html 04. http://stderr.org/pipermail/inquiry/2005-August/002926.html QUAGS. Questions About Genuine Signs -- Commentary 00. http://stderr.org/pipermail/inquiry/2005-August/thread.html#2923 01. http://stderr.org/pipermail/inquiry/2005-August/002923.html 02. http://stderr.org/pipermail/inquiry/2005-August/002929.html 03. http://stderr.org/pipermail/inquiry/2005-August/002930.html 04. http://stderr.org/pipermail/inquiry/2005-August/002931.html 05. http://stderr.org/pipermail/inquiry/2005-August/002932.html QUAGS. Questions About Genuine Signs -- Discussion 00. http://stderr.org/pipermail/inquiry/2005-May/thread.html#2663 01. http://stderr.org/pipermail/inquiry/2005-May/002663.html 02. http://stderr.org/pipermail/inquiry/2005-May/002664.html 03. http://stderr.org/pipermail/inquiry/2005-May/002665.html 04. http://stderr.org/pipermail/inquiry/2005-May/002666.html 05. http://stderr.org/pipermail/inquiry/2005-May/002668.html 06. http://stderr.org/pipermail/inquiry/2005-May/002669.html 07. http://stderr.org/pipermail/inquiry/2005-May/002670.html QUIPS. Questions Involving Pure Symbols -- Discussion 00. http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602 00. http://stderr.org/pipermail/inquiry/2005-June/thread.html#2766 00. http://stderr.org/pipermail/inquiry/2005-July/thread.html#2866 00. http://stderr.org/pipermail/inquiry/2005-August/thread.html#2927 24. http://stderr.org/pipermail/inquiry/2005-May/002690.html 74. http://stderr.org/pipermail/inquiry/2005-August/002927.html It looks like this'll be one of those "eternal return" type questions. I just hope it won't be one of those "eternal repetition" type issues.
NEKS. Commentary Note 2
Let me try to bring some measure of concreteness to this discussion of "various orders of determination or information" (VOODOI) and its possible relation to "higher order propositional expressions" (HOPE's). To keep things simple let's consider a discrete order of determinations and put off worrying about a continuous order of determinations until we have understood the discrete case well enough to deal with anything more. Again for the sake of simplicity, let's start with a universe of discourse that is constructed on the basis of just two predicates, let's say p and q. Anything in this universe is determined with respect to these predicates by saying whether p is true or false of it and whether q is true or false of it. Thus we have the following four propositions of maximal determination: 0. (p)(q), meaning "not p and not q" 1. (p) q , meaning "not p and q" 2. p (q), meaning "p and not q" 3. p q , meaning "p and q" It's customary to refer to these 4 propositions as the "cells" of the universe of discourse that is built on the predicates p and q. If we don't know enough to determine a thing to the full extent that's permitted by the predicates in this universe of discourse, then other propositions, of less than maximal determination, may serve to say how much we know about the thing in question. For example, if we know that a thing is either p or q, but don't know any more than that, then the proposition "p or q" pins it down to the best of our knowledge. Using only negation and conjunction, we have: ((p)(q)) As we know, there are 16 distinct propositions that we can make about any given thing, relative to the given frame of reference. These 16 propositions exhaust the variety of things that can be said in the language that we will call the "zeroth order logic" based on p and q. Thus we can express an order of determination, or a lack thereof, that hesitates or vacillates among any number of the four "cells" of the universe of discourse in view. That is all well and good, but what if the order of our indetermination is not exactly that, not to be measured by our vacillation among a subset of the above four cells, but more like a state of indecision among some subset of the 16 propositions, as if a hesitation among actual universes? Next time we'll explore a way to express the next higher order of indetermination, or the next lower order of determination.
NEKS. Commentary Note 3
Re: KS 1. http://stderr.org/pipermail/inquiry/2005-September/003063.html In: KS. http://stderr.org/pipermail/inquiry/2005-September/thread.html#3063 In the matter of Theory and Practice, Peirce begins by explaining the difference between theoretical propositions and practical propositions, which he couches in the terms of a semiotic or sign relational framework. We come almost immediately to several problems of interpretation, coming to a head in the following passage: | In the first place, a sign is not a real thing. | It is of such a nature as to exist in 'replicas'. | Look down a printed page, and every 'the' you see | is the same word, every 'e' the same letter. A real | thing does not so exist in replica. The being of a | sign is merely 'being represented'. Now 'really being' | and 'being represented' are very different. Giving to | the word 'sign' the full scope that reasonably belongs | to it for logical purposes, a whole book is a sign; and | a translation of it is a replica of the same sign. A whole | literature is a sign. The sentence "Roxana was the queen of | Alexander" is a sign of Roxana and of Alexander, and though | there is a grammatical emphasis on the former, logically the | name "Alexander" is as much 'a subject' as is the name "Roxana"; | and the real persons Roxana and Alexander are 'real objects' of | the sign. | | Every sign that is sufficiently complete refers refers to sundry | real objects. All these objects, even if we are talking of Hamlet's | madness, are parts of one and the same Universe of being, the "Truth". | But so far as the "Truth" is merely the 'object' of a sign, it is merely | the Aristotelian 'Matter' of it that is so. | | C.S. Peirce, "Kaina Stoicheia", NEM 4, 238-239 | Also appears in "New Elements", EP 2, 303-304 At first it seems obvious enough that the Peirce who says "a sign is not a real thing" is not the Peirce who speaks as a Platonic or Scholastic realist, but one is using the phrases "real thing" and "real object" in accord with the more streetwise values that they bear in mundane parlance, however pre-reflective and pre-critical those uses may be. We may have some difficulty extending this street meaning to the case of Hamlet's madness, but the problem does not seem insurmountable in itself, as all the groundlings wot. Read this way, Peirce is simply pointing out the familiar dual use of the word "sign" to refer to a very concrete thing and also to a very abstract thing, the relationship between the two being more or less well treated in terms of the token/type relation. Here the tokens or replicas are awarded the titular honor of a cave-internal sort of reality, whereas in other lights, more cave-external, it'd be the types or the equivalence classes of tokens that are said to be the real realities. I think most folks know the variations on this theme, all independently of the particular words that are used to play it out, so I think it's safe to proceed on the grounds of that prior understanding.
NEKS. Commentary Note 4
Re: KS-COM 2. http://stderr.org/pipermail/inquiry/2005-September/003067.html
In: KS-COM. http://stderr.org/pipermail/inquiry/2005-September/thread.html#3066
To save a few words in the remainder of this discussion, let's notate
the "universe of discourse based on the predicates p and q" as [p, q].
The universe [p, q] is layed down in two layers:
1. There is the set of 4 cells, that may be enumerated in terms of the
basic propositions that describe them as {(p)(q), (p) q, p (q), p q},
a set that it will be convenient to notate as <<p, q>>. Considered
in regard to its abstract type, <<p, q>> has the type of B^2 = B x B.
2. There is the set of 16 propositions on <<p, q>>, notated as <<p, q>>^.
Each of these propositions is a function of the form f : <<p, q>> -> B.
Thus the space of propositions <<p, q>>^ has the abstract type B^2 -> B.
In the notation just introduced we can say that [p, q] = {<<p, q>>, <<p, q>>^}.
It is important to note that each of the 4 cells in <<p, q>> corresponds so
uniquely to a proposition in <<p, q>>^ = <<p, q>> -> B that we shall seldom
bother to distinguish between them.
The most that we can pin down a thing in the universe [p, q] is by
giving one of the basic propositions, cells, or points in <<p, q>>.
When we find ourselves less certain than that, we can describe our
state of information about a thing by stating any one of the other
propositions in <<p, q>>^.
The thing to notice here is that the step to a lower order of determination
is associated with a passage from a space of points X, in this case <<p, q>>,
to a space of functions X -> B, in the present case <<p, q>>^ = <<p, q>> -> B.
This is the sort of step that we will iterate in order to reach
ever lower orders of determination, or to put it the other way,
ever higher orders of vacillation.
NEKS. Commentary Note 5
The venn diagram shown below presents a familiar way of picturing the universe of discourse [p, q]. The propositional expressions inscribed in the cells represent the four elements of <<p, q>>. The 16 propositions of the form <<p, q>> -> B can be pictured as all the ways of shading the cells of the diagram, given the two colors that correspond to the boolean values in B. One observes that 4 cells shaded in 2 colors produces 2^4 = 16 different patterns altogether. o-------------------------------------------------o | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` `o-----------o` `o-----------o` ` ` ` ` | | ` ` ` ` / ` ` ` ` ` ` \ / ` ` ` ` ` ` \ ` ` ` ` | | ` ` ` `/` ` ` ` ` ` ` `o` ` ` ` ` ` ` `\` ` ` ` | | ` ` ` / ` ` ` ` ` ` ` / \ ` ` ` ` ` ` ` \ ` ` ` | | ` ` `/` ` ` ` ` ` ` `/` `\` ` ` ` ` ` ` `\` ` ` | | ` ` o ` ` ` ` ` ` ` o ` ` o ` ` ` ` ` ` ` o ` ` | | ` ` | ` ` ` ` ` ` ` | ` ` | ` ` ` ` ` ` ` | ` ` | | ` ` | ` ` p (q) ` ` | p q | ` ` (p) q ` ` | ` ` | | ` ` | ` ` ` ` ` ` ` | ` ` | ` ` ` ` ` ` ` | ` ` | | ` ` o ` ` ` ` ` ` ` o ` ` o ` ` ` ` ` ` ` o ` ` | | ` ` `\` ` ` ` ` ` ` `\` `/` ` ` ` ` ` ` `/` ` ` | | ` ` ` \ ` ` ` ` ` ` ` \ / ` ` ` ` ` ` ` / ` ` ` | | ` ` ` `\` ` ` ` ` ` ` `o` ` ` ` ` ` ` `/` ` ` ` | | ` ` ` ` \ ` ` ` ` ` ` / \ ` ` ` ` ` ` / ` ` ` ` | | ` ` ` ` `o-----------o` `o-----------o` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` (p) (q) ` ` ` ` ` ` ` ` ` ` | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | o-------------------------------------------------o Each way of coloring the universe of discourse [p, q] may be thought of as an actual state of that universe or a contingent realization of its inherent potential. This is just another way of interpreting the abstract elements of <<p, q>> -> B, which can now be conceived as "possible universes" of type [p, q]. Suppose we walk into the gallery of possible universes of type [p, q] and find ourselves in a condition of indeterminate choice that ranges over a particular subset of the 16 possible pictures. There are just 2^16 subsets of 16 things, in this case corresponding to the space of propositions of type (<<p, q>> -> B) -> B, which are naturally enough referred to as "higher order propositions" since they can be regarded as propositions about propositions. This brings us to the verge of the next higher order of indetermination.
NEKS. Commentary Note 6
When Peirce starts talking about Aristotle's concept of entelechy it brings to mind some of the issues that I was wrestling with in my work on "Inquiry Driven Systems" or the "Inquiry Into Inquiry", some of which is recorded at the Arisbe website, and some further explorations of which are serialized at my Inquiry Archive. Here is a pertinent selection: Cf: IDS 114. http://stderr.org/pipermail/inquiry/2004-May/001553.html Cf: IDS 115. http://stderr.org/pipermail/inquiry/2004-May/001554.html Cf: IDS 116. http://stderr.org/pipermail/inquiry/2004-May/001555.html In: IDS. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434 I'll copy this much of it below, as it may do some of us some good to consider these issues again in this setting. 1.3.9.3. The Formative Tension The incidental arena or the informal context is presently described in casual, derivative, and negative terms, simply as the "not yet formal", and so this admittedly unruly region is currently depicted in ways that suggest a purely unformed and a wholly formless chaos, which it is not. But increasing experience with the formalization process can help one to develop a better appreciation of the informal context, and in time one can argue for a more positive characterization of this realm as a truly "formative context". The formal domain is where risks are contemplated, but the formative context is where risks are taken. In this view, the informal context is more clearly seen as the off-stage staging ground where everything that appears on the formal scene is first assembled for a formal presentation. In taking this view, one steps back a bit in one's imagination from the scene that presses on one's attention, gets a sense of its frame and its stage, and becomes accustomed to see what appears in ever dimmer lights, in effect, one is learning to reflect on the more obvious actions, to read their pretexts, and to detect the motives that end in them. It is fair to assume that an agent of inquiry possesses a faculty of inquiry that is available for exercise in the informal context, that is, without the agent being required to formalize its properties prior to their initial use. If this faculty of inquiry is a unity, then it appears as a whole on both sides of the "glass", that is, on both sides of the imaginary line that one pretends to draw between a formal arena and its informal context. 1.3.9.3. The Formative Tension (cont.) Recognizing the positive value of an informal context as an open forum or a formative space, it is possible to form the alignments of capacities that are indicated in Table 5. Table 5. Alignments of Capacities o-------------------o-----------------------------o | Formal | Formative | o-------------------o-----------------------------o | Objective | Instrumental | | Passive | Active | o-------------------o--------------o--------------o | Afforded | Possessed | Exercised | o-------------------o--------------o--------------o This arrangement of capacities, based on the distinction between possession and exercise that arises so naturally in this context, stems from a root that is old indeed. In this connection, it is instructive to compare these alignments with those that we find in Aristotle's treatise 'On the Soul', a germinal textbook of psychology that ventures to analyze the concept of the mind, psyche, or soul to the point of arriving at a definition. The alignments of capacites, analogous correspondences, and illustrative materials outlined by Aristotle are summarized in Table 6. Table 6. Alignments of Capacities in Aristotle o-------------------o-----------------------------o | Matter | Form | o-------------------o-----------------------------o | Potentiality | Actuality | | Receptivity | Possession | Exercise | | Life | Sleep | Waking | | Wax | Impression | | Axe | Edge | Cutting | | Eye | Vision | Seeing | | Body | Soul | o-------------------o-----------------------------o | Ship? | Sailor? | o-------------------o-----------------------------o An attempt to synthesize the materials and the schemes that are given in Tables 5 and 6 leads to the alignments of capacities that are shown in Table 7. I do not pretend that the resulting alignments are perfect, since there is clearly some sort of twist taking place between the top and the bottom of this synthetic arrangement. Perhaps this is due to the modifications of case, tense, and grammatical category that occur throughout the paradigm, or perhaps it has to do with the fact that the relations through the middle of the Table are more analogical than categorical. For the moment I am content to leave all of these paradoxes intact, taking the pattern of tensions and torsions as a puzzle for future study. Table 7. Synthesis of Alignments o-------------------o-----------------------------o | Formal | Formative | o-------------------o-----------------------------o | Objective | Instrumental | | Passive | Active | | Afforded | Possessed | Exercised | | To Hold | To Have | To Use | | Receptivity | Possession | Exercise | | Potentiality | Actuality | | Matter | Form | o-------------------o-----------------------------o 1.3.9.3. The Formative Tension (concl.) Due to the importance of Aristotle's account for every discussion that follows it, not to mention for those that follow it without knowing it, and because the issues that it raises arise repeatedly throughout this project, I am going to cite an extended extract from the relevant text (Aristotle, 'Peri Psyche', 2.1), breaking up the argument into a number of individual premisses, stages, and examples. Aristotle wrote (W.S. Hett translation): | a. The theories of the soul (psyche) | handed down by our predecessors have | been sufficiently discussed; now let | us start afresh, as it were, and try to | determine (diorisai) what the soul is, | and what definition (logos) of it will | be most comprehensive (koinotatos). | | b. We describe one class of existing things as | substance (ousia), and this we subdivide into | three: (1) matter (hyle), which in itself is | not an individual thing, (2) shape (morphe) or | form (eidos), in virtue of which individuality | is directly attributed, and (3) the compound | of the two. | | c. Matter is potentiality (dynamis), while form is | realization or actuality (entelecheia), and the | word actuality is used in two senses, illustrated | by the possession of knowledge (episteme) and the | exercise of it (theorein). | | d. Bodies (somata) seem to be pre-eminently | substances, and most particularly those | which are of natural origin (physica), | for these are the sources (archai) | from which the rest are derived. | | e. But of natural bodies some have life (zoe) | and some have not; by life we mean the | capacity for self-sustenance, growth, | and decay. | | f. Every natural body (soma physikon), then, | which possesses life must be substance, and | substance of the compound type (synthete). | | g. But since it is a body of a definite kind, viz., | having life, the body (soma) cannot be soul (psyche), | for the body is not something predicated of a subject, | but rather is itself to be regarded as a subject, | i.e., as matter. | | h. So the soul must be substance in the sense of being | the form of a natural body, which potentially has life. | And substance in this sense is actuality. | | i. The soul, then, is the actuality of the kind of body we | have described. But actuality has two senses, analogous | to the possession of knowledge and the exercise of it. | | j. Clearly (phaneron), actuality in our present sense | is analogous to the possession of knowledge; for both | sleep (hypnos) and waking (egregorsis) depend upon the | presence of the soul, and waking is analogous to the | exercise of knowledge, sleep to its possession (echein) | but not its exercise (energein). | | k. Now in one and the same person the | possession of knowledge comes first. | | l. The soul may therefore be defined as the first actuality | of a natural body potentially possessing life; and such | will be any body which possesses organs (organikon). | | m. The parts of plants are organs too, though very | simple ones: e.g., the leaf protects the pericarp, | and the pericarp protects the seed; the roots are | analogous to the mouth, for both these absorb food. | | n. If then one is to find a definition which will apply | to every soul, it will be "the first actuality of | a natural body possessed of organs". | | o. So one need no more ask (zetein) whether body and | soul are one than whether the wax (keros) and the | impression (schema) it receives are one, or in | general whether the matter of each thing is | the same as that of which it is the matter; | for admitting that the terms unity and being | are used in many senses, the paramount (kyrios) | sense is that of actuality. | | p. We have, then, given a general definition | of what the soul is: it is substance in | the sense of formula (logos), i.e., the | essence of such-and-such a body. | | q. Suppose that an implement (organon), e.g. an axe, | were a natural body; the substance of the axe | would be that which makes it an axe, and this | would be its soul; suppose this removed, and | it would no longer be an axe, except equivocally. | As it is, it remains an axe, because it is not of | this kind of body that the soul is the essence or | formula, but only of a certain kind of natural body | which has in itself a principle of movement and rest. | | r. We must, however, investigate our definition | in relation to the parts of the body. | | s. If the eye were a living creature, its soul would be | its vision; for this is the substance in the sense | of formula of the eye. But the eye is the matter | of vision, and if vision fails there is no eye, | except in an equivocal sense, as for instance | a stone or painted eye. | | t. Now we must apply what we have found true of the part | to the whole living body. For the same relation must | hold good of the whole of sensation to the whole sentient | body qua sentient as obtains between their respective parts. | | u. That which has the capacity to live is not the body | which has lost its soul, but that which possesses | its soul; so seed and fruit are potentially bodies | of this kind. | | v. The waking state is actuality in the same sense | as the cutting of the axe or the seeing of the eye, | while the soul is actuality in the same sense as the | faculty of the eye for seeing, or of the implement for | doing its work. | | w. The body is that which exists potentially; but just as | the pupil and the faculty of seeing make an eye, so in | the other case the soul and body make a living creature. | | x. It is quite clear, then, that neither the soul nor | certain parts of it, if it has parts, can be separated | from the body; for in some cases the actuality belongs | to the parts themselves. Not but what there is nothing | to prevent some parts being separated, because they are | not actualities of any body. | | y. It is also uncertain (adelon) whether the soul as an | actuality bears the same relation to the body as the | sailor (ploter) to the ship (ploion). | | z. This must suffice as an attempt to determine | in rough outline the nature of the soul.
NEKS. Commentary Note 7
Re: KS 3. http://stderr.org/pipermail/inquiry/2005-October/003075.html In: KS-Oct. http://stderr.org/pipermail/inquiry/2005-October/thread.html#3075 Cf: KS-Sep. http://stderr.org/pipermail/inquiry/2005-September/thread.html#3063 In part: | But of these two movements, logic very properly | prefers to take that of Theory as the primary one. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 240 I confess to being a little puzzled by this emphasis. Does Peirce forget that logic is a normative science? Does a normative science not work to know what ought to be done in actual practice to achieve our objects? Well, I'll leave my puzzlement in suspension for now, and continue with the reading in hopes of resolution.
NEKS. Commentary Note 8
Re: KS-COM 5. http://stderr.org/pipermail/inquiry/2005-October/003073.html
In: KS-COM. http://stderr.org/pipermail/inquiry/2005-October/thread.html#3070
Cf: QUIPS-DIS 24. http://stderr.org/pipermail/inquiry/2005-May/002690.html
Cf: QUAGS 4. http://stderr.org/pipermail/inquiry/2005-August/002926.html
The use of "higher order propositional expressions" (HOPE's) is one way
to bring some order of concrete modeling -- concreteness being relative,
of course -- to bear on the following species of statements from Peirce:
| If we are to explain the universe, we must assume that there was in the
| beginning a state of things in which there was nothing, no reaction and no
| quality, no matter, no consciousness, no space and no time, but just nothing
| at all. Not determinately nothing. For that which is determinately not 'A'
| supposes the being of 'A' in some mode. Utter indetermination. But a symbol
| alone is indeterminate. Therefore Nothing, the indeterminate of the absolute
| beginning is a symbol.
|
| That is the way in which the beginning of things can alone be understood.
|
| What logically follows?
|
| We are not to content ourselves with our instinctive sense of logicality.
| That is logical which comes from the essential nature of a symbol. Now it
| is of the essential nature of a symbol that it determines an interpretant,
| which is itself a symbol. A symbol, therefore, produces an endless series
| of interpretants.
|
| Does anybody suspect all this of being sheer nonsense. 'Distinguo.'
| There can, it is true, be no positive information about what antedated
| the entire Universe of being; because, to begin with, there was nothing
| to have information about. But the universe is intelligible; and therefore
| it is possible to give a general account of it and its origin. This general
| account is a symbol; and from the nature of a symbol, it must begin with the
| formal assertion that there was an indeterminate nothing of the nature of a
| symbol. This would be false if it conveyed any information. But it is
| the correct and logical manner of beginning an account of the universe.
|
| As a symbol it produced its infinite series of interpretants, which in the
| beginning were absolutely vague like itself. But the direct interpretant
| of any symbol must in the first stage of it be merely the 'tabula rasa'
| for an interpretant. Hence the immediate interpretant of this vague
| Nothing was not even determinately vague, but only vaguely hovering
| between determinacy and vagueness; and 'its' immediate interpretant
| was vaguely hovering between vaguely hovering between vagueness and
| determinacy and determinate vagueness or determinacy, and so on,
| 'ad infinitum'. But every endless series must logically have a
| limit.
|
| C.S. Peirce, "Kaina Stoicheia", NEM 4, 260-261
| Also appears in "New Elements", EP 2, 322-323
Very roughly speaking, we can model the condition of "vaguely hovering"
over a set F = {f_1, ..., f_m} of "states of (in)determination" f_j by
modeling each f_j as a proposition in a suitable universe of discourse,
and then by modeling the set F as a proposition one level higher than
the highest of the f_j in F. It will be best if we start with a few
simple examples, going back to our base camp in the universe [p, q],
just to see if everything works out in a moderately reasonable way.
NEKS. Commentary Note 9
It appears that many misunderstandings of what's being said at the end of Peirce's "Kaina Stoicheia"/"New Elements" essay arise from a failure to keep in mind what was being said at the beginning, especially with regard to the original model on which Peirce's innovation is designed, to wit, the "Old Elements" of the eponymous Euclid that motivated Peirce's own attempts at emulation. Thus, as I have always suspected, it will be necessary to return to the beginning in order to place the end, that is to say, the object, in its proper perspective. What the editors of the version in 'The Essential Peirce' say by way of orientation is apt enough to bear repeating at this point: | New Elements [Kaina Stoicheia] | | MS 517. [First published in NEM 4:235-63. This document was most | probably written in early 1904, as a preface to an intended book on | the foundations of mathematics.] Peirce begins with a discussion of | "the Euclidean style" he planned to follow in his book. Euclid's | 'Elements' presuppose an understanding of the logical structure | of mathematics (geometry) that Peirce, in his "New Elements", | wants to explicate. | | Headnote to Selection 22, "New Elements", p. 300 in: | Peirce Edition Project (eds.), 'The Essential Peirce, | Selected Philosophical Writings, Volume 2 (1893-1913)', | Indiana University Press, Bloomington, IN, 1998. Da capo, al fine ...
NEKS. Commentary Note 10
We can now complete the following syllogism: Peirce's "Kaina Stoicheia" is a Preface. (NEM 4, 235 & EP 2, Headnote) This very same Preface is a Scholium. (NEM 4, 238 & EP 2, 303) The main Subject of this Scholium is the Proposition. (NEM 4, 247 & EP 2, 311) ------------------------------------------------------------------------------------- The main Subject of Peirce's "Kaina Stoicheia" is the Proposition. QED. The pure symbol remains pure until proven otherwise. The defense rests.
NEKS. Commentary Note 11
Re: KS 16. http://stderr.org/pipermail/inquiry/2005-November/003265.html In: KS. http://stderr.org/pipermail/inquiry/2005-November/thread.html#3183 It is only that untoward bent of reading, that reads Peirce just barely in impatient anticipation of Frege, that could manage to warp Peirce's avowedly "non-psychological" view of logic into a supposed doctrine of "anti-psychologism". Still, it's important to notice that Peirce employs his "logical microscope" -- the magnifying-glasses of the consulting detective, sheriff, posse comitatus, judge, jury, the many long arms of conscientious, divine, and social sanction -- primarily in the service to distinguish the logical matter of the proposition from a motley array of psycho-litigious-socio-politico-eschatological matters: acceptance, acknowledgment, affidavit, affirmation, assent, assertion, avowal, belief, certainty, certification, cognition, conation, consensus, credence, denial, didaction, disposition, doubt, execution, expression, indication, injunction, inquisition, judgment, knowledge, recognizance, salvation, and so on and so forth, if not necessarily in that order, of course. This has consequences that we must needs explore.
NEKS. Commentary Note 12
Re: KS 17. http://stderr.org/pipermail/inquiry/2005-December/003274.html In: KS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3274 For context: KS-Sep. http://stderr.org/pipermail/inquiry/2005-September/thread.html#3063 KS-Oct. http://stderr.org/pipermail/inquiry/2005-October/thread.html#3075 KS-Nov. http://stderr.org/pipermail/inquiry/2005-November/thread.html#3183 I call attention to the fact that Peirce here defines "belief", "affirmation", and "judgment" -- as a habit of acting, an act of uttering, and a mental act, respectively, and thus as what can only be called pragmatic-psychological concepts -- partly with reference to the logical concepts of proposition, proof, and truth, partly in terms of the partly formal partly material concept of determination, and partly in terms of the broadly pragmatic, psychological, sociological, semiotic, and linguistic concepts, not all of them yet defined, of action, affect (contentedness), agency, awareness, conation (desire), control, (in-)convenience, decision, deliberation, disposition (tendency), event, exercise, force, habit, interpretation, mind, pain (penalty), probability (liability), product, result, simultaneity, society, time, utterance, and volition. I think that it requires further examination to sort out the relation of logic, that is, formal (normative or quasi-necessary) semiotics, to this more broadly conceived wildwood of descriptive semiotics. | I have discussed the nature of belief | in the 'Popular Science Monthly' for | November 1877. On the whole, we may | set down the following definitions: | | A 'belief' in a proposition is a controlled and contented habit of | acting in ways that will be productive of desired results only if | the proposition is true. | | An 'affirmation' is an act of an utterer of a proposition to an interpreter, | and consists, in the first place, in the deliberate exercise, in uttering | the proposition, of a force tending to determine a belief in it in the | mind of the interpreter. Perhaps that is a sufficient definition of it; | but it involves also a voluntary self-subjection to penalties in the | event of the interpreter's mind (and still more the general mind of | society) subsequently becoming decidedly determined to the belief | at once in the falsity of the proposition and in the additional | proposition that the utterer believed the proposition to be | false at that time he uttered it. | | A 'judgment' is a mental act deliberately exercising a force tending to | determine in the mind of the agent a belief in the proposition: to which | should perhaps be added that the agent must be aware of his being liable | to inconvenience in the event of the proposition's proving false in any | practical aspect. | | C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 249-250
NEKS. Commentary Note 13
Rummaging about our Polis with Perseus, I find these glosses: | arithmos, as etym. of Stoichadeus, Sch.D.T.p.192 H. | Stoicha^deus , eôs, ho, title of Zeus at Sicyon, Sch.D.T. p.192 H. | Stoicheia , hê, epith. of Athena at Epidaurus, IG42(1).487. | | Perseus at Tufts: http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus:text:1999.04.0057:entry=%2396930
NEKS. Commentary Note 14
| Incidental Muse ~~~ Loreena McKennitt, ''Elemental'' ~~~ | http://www.quinlanroad.com/explorethemusic/elemental.asp
NEKS. Commentary Work Area
NEKS. Commentary Work Area 1
Some folks have yet to discover the basic fact of life that conception is an action.
NEKS. Commentary Work Area 2
Re: KS 15. http://stderr.org/pipermail/inquiry/2005-November/003264.html In: KS. http://stderr.org/pipermail/inquiry/2005-November/thread.html#3183 In light of ever-renewed evidence that icons of argument and indices of reason, the xylem and phloem of those hyloid lumberings that we log as syllogism, make for a roughage that's vegetatively insufficient in its own rick to animate the aimed for sign of interpretant entelechy, I'll pile more wood on the bael-fire.
NEKS. New Elements • Kaina Stoicheia • Discussion
NEKS. Discussion Note 1
SL = Søren Lund
Re: KS-COM 11. http://stderr.org/pipermail/inquiry/2005-November/003269.html
In: KS-COM. http://stderr.org/pipermail/inquiry/2005-November/thread.html#3263
Recall that we are working in the context of Peirce's theory of sign relations,
where a proposition is a type of symbol, a symbol is a type of sign, a sign is
defined by its participation in a specified role of a particular sign relation,
and a sign relation in general is defined as a 3-adic relation that satisfies
a particular definition, for instance, this one:
| A sign is something, A, which brings something, B,
| its interpretant sign determined or created by it,
| into the same sort of correspondence with something,
| C, its object, as that in which itself stands to C.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54 (1902).
|
| C.S. Peirce, [Application to the Carnegie Institution], L 75, pp. 13-73 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by Charles S. Peirce,
| Volume 4, Mathematical Philosophy', Mouton, The Hague, 1976. Available here:
| Arisbe Website, http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm
You give us an able summary of a host of classical and modern aporias
that affect various attempts to say what a proposition is, but all of
those stagmas, so far as I can tell, appear to arise from the attempt
to form a particular order of "wholly useless abstractions" (WUA'a).
Given the obvious utility of many abstractions, that leaves us the
task of saying what exactly pushes an abstraction over the edge
of use. This can be difficult to diagnose, but it's easier to
diagnose than it is to identify the underlying causes thereof.
One factor that strikes me at present is the fact that some
abstractions are "absolutized" or "decontextualized" past
the point of usefulness, and the inclination to do that
appears to arise from a habit of "essentializing" that
may indeed be innate to our evolutionary inheritance,
or at least built into our most familiar languages.
Essentialism is the tendency of thought that tends to seek an explanation
of everything in "categories of unstructured things" (COUT's). In effect,
it tends to think that the end of explanation has been reached once we've
nominated the monadic predicate that classifies the thing to be explained.
This is such a persistent tendency of the human mind that it can be observed
to influence the thinking even of those who more reflectively might know better --
who might know better from reading Peirce, who might know better from being Peirce --
but it is not overall the thrust of Peirce's efforts in logic and semiotics, which
are indeed partly intended as a remedy for the condition of overweaned essentialism.
SL: Speaking of the proposition and Peirce's conception of it.
I think there is good reasons for attacking this curious
logical unit and even better to abandon it.
SL: If "proposition" is not a fancy term for "sentence", what is it? One suggestion
is that the proposition is the meaning of the sentence, or at least of the type
of sentence that grammarians call "declarative". But this will hardly do, for
the reasons already pointed out by the author of the 'Dissoi Logoi'. (The
author of the ancient text known as the 'Dissoi Logoi' points out that the
words "I am an initiate" may be uttered both by an initiate and by one who
is not (W. Kneale and M. Kneale, 'The Development of Logic', rev. ed.,
Oxford Clarendon, 1984, p. 16). If this is accepted, it seems that
we have to conclude either that one and the same form of words may
be both true and false, or else that what is true or false is not
the form of words itself. If the former is the case, it frustrates
any enterprise of formulating the principles of valid inference on
the basis of relations between sentences. If the latter is the case,
then the metalinguistic terms "true" and "false" cannot properly apply
to sentences at all, but must be deemed to apply to something else.
Western logic chose the latter option, and thereby conjured into
existence what was later called the "proposition".) That is to say,
if the grounds for rejecting the sentence are valid (i.e. that the
same sentence can be uttered on one occasion to express a truth, but
on another occasion to express a falsehood), then the objection must
carry over to the meaning of the sentence, unless we are prepared to
divorce the meaning from the sentence. But if we do that, we have in
effect ushered in two even more mysterious metalinguistic entities, i.e.
sentences without (permanent) meanings, and sentence-meaning that float
free of their sentences. It is difficult to see where the explanatory
gain lies, let alone how the two cohere.
SL: Another suggestion is that the proposition is the use
made of the (declarative) sentence. Thus if A and B both
utter the sentence I am an initiate, they may be said to be
putting it to different uses; viz in one case to claim that A
is an initiate, and in the other to claim that B is an initiate.
But this does not get us much further either. For all that has
been achieved here is the proposal of an arbitrarily restricted
employment of the term use. When we investigate the nature of
the restriction, the "use" of the sentence turns out to be
whatever it is that results in something true or false --
e.g. A's claim or B's claim. Here one metalinguistic
term (use) simply hides behind another (claim).
SL: Is the "proposition", then, more plausibly regarded as what it is
that is claimed when a claim is made, asserted when an assertion is
made, stated when a statement is made, etc.? But here we start another
metalinguistic wild goose chase. For claim, assertion and statement are
all metalinguistic terms with no better credentials than proposition itself.
To define the proposition as the "object" or "content" of claims, assertions,
statements, etc. is simply to substitute one obscurity for another.
SL: Why do these and similar attempts to rescue the proposition all come to grief
in this way? Because what is being attempted is a metalinguistic impossibility.
The source of the trouble can be traced back to the original culprit, i.e. the
sentence, deemed to be unsuitable as the basis for logic. The trouble is that
the sentences belong to particular languages (English, Greek, Latin, etc.).
What the logician seeks to substitute for the sentence is an entity which will
afford the same scope for identification, reidentification, generalization and
classification, but independently of the particular languages or words used.
The trouble is that this cannot be done -- or at least, not within the
Western metalinguistic framework. For that framework only allows us
to identify propositions, statements, assertions, etc. by citing
some sentence or part of a sentence.
SL: The moment this strategy fails, any formalization of logic collapses.
In other words, the logician cannot, under pain of undermining the
whole professional enterprise, claim that there are propositions
that cannot be unambiguously expressed in words.
SL: Herculean efforts to move this obstacle merely show how immovable it is.
For instance, some theorists have conjured up an entity which is supposed
to be what there is in common between an English declarative sentence and
its correct translation into any (or all) other language(s). This proposal
is either vacuous or circular. For then either there are no propositions at
all or else we are off after another metalinguistic will-o'-the wisp, namely
the criteria for "correct translation".
NEKS. Discussion Note 2
BM = Bernard Morand
BM: I think I have been unable to understand clearly
what is really at stake in the dispute between
Jon and Joe on the matter of pure symbols,
despite the large exchange of messages
on the topic.
Aside from the focal issue, which I will reserve until I can get focussed on it again,
I believe that there are most likely constitutionally different attitudes as to what
constitutes a definition, a theory, and a science. If logic is a normative science,
or, as Peirce says, "formal semiotics", and if there is to be a part of semiotics
that is a science, then it's very likely to undergo the sort of development that
other sciences have enjoyed. In other sciences, there is a division of labor
where mathematical models are developed in a speculative fashion, taking off
from and being brought home again to practical application. In that world,
definitions are equivalent explications of a concept, that is, necessary
and sufficient conditions for falling under a concept. Definitions of
this sort, once a good portion of the research community accepts them,
have a character of "standing on their own feet". This means that
they serve as a platform for generating all sorts of never-before
suspected consequences, that can be explored by deductive means,
and also evaluated for empirical adequacy, uberty, and truth.
Measured against that scientific standard, which is well understood in
all of the developed sciences, only a few of the so-called "definitions"
of signs are real definitions, the sorts of formulations that are clear
and explicit enough to draw any necessary conclusions from. Most of the
rest are more properly called "descriptions", and they fall into the dual
classes of (1) sufficient descriptions, that say things which are true of
special classes of signs, and (2) necessary descriptions, that say things
which are true of all signs, but which are also true of many things that
are not signs. But only those descriptions which are both necessary and
sufficient count as real definitions. Of course, a good definition must
also have many other virtues in order to support a consistent, effective,
and empirically adequate scientific theory.
This definition of definition will tend to be dismissed in undeveloped sciences,
and by many brands of philosophies -- and of course there are many domains where
we are still mainly arguing 'toward' definitions rather than mainly 'from' them --
so it's a matter of opinion where we are in semiotics today. For my part I am
content with a few of Peirce's more genuine definitions of signs, and I have
been busy reasoning on their basis ever since I first came to notice them.
On that basis, my main reason for thinking that there are sign relations
that do not involve icons or indices is simply that I can see no way to
deduce the involvement of icons or indices by necessary reasoning from
Peirce's most genuine and most general definitions of sign relations,
and so far nobody has even suggested a plausible way of doing this.
NEKS. Discussion Note 3
JP = Jim Piat
Re: KS-DIS 2. http://stderr.org/pipermail/inquiry/2005-December/003282.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
Replies interspersed.
JP: Would you give me an example of one of Peirce's genuine, necessary and sufficient,
descriptions of a sign, and perhaps for the purpose of contrast one of his
non-genuine definitions that fails to meet these criteria. Also would
you give me the necessary and sufficient conditions for discerning
which is which.
Yes, if you Google(TM) -- or Transcendental Meditate (TM) if you prefer --
on +Awbrey "Sign Relation" and its pluralization (Google has taken lately
to using fuzzy conjunctions, so you now have to put in the "+" to force the
old-fangled logical conjunction), you'll get my e-tire e-lected e-corpus of
writings on the subject, but to make a long story clear I can do no better
than recommend the standards of clarity demanded by my co-author in this
'Hermeneutics and Human Science' conference paper from 1992, revised for
the journal 'Inquiry: Critical Thinking Across the Disciplines' in 1995:
| Jon Awbrey & Susan Awbrey, "Interpretation as Action: The Risk of Inquiry"
| http://www.chss.montclair.edu/inquiry/fall95/awbrey.html
| NB. The reference to "Habermas" should be "Gadamer".
In most of those places I will probably allude to the dynamic duo of variants of
the definition in NEM 4 as being my pets for adequacy, clarity, and completeness.
One of the reasons that I remember those so fondly is that it wasn't until rather
late, when I chanced on a copy of the NEM volumes in a used book store in the mid
80's and was actually fortunate enough to have the spare cash on hand to buy them.
I have to tell you that up until that time I had always wondered why Peirce never
bothered to define this most important concept of a sign -- I know, but only now,
that this will sound shocking to many people, but they would need to understand
that the only definition of definition that had been engrained into my engrams
was the one that I knew from logic and math courses, and since it's so common
in loose speech and writing for all of us to say "definition" when we really
mean "something that's more or less true of a special case of the thing",
I had probably developed the automatic habit of reading the looser uses
as "descriptions", not true "definitions". That was my consciousness.
I made the mistake of going to bed early last night,
which only led to my waking up at 3 AM, and so I'll
need to break fast for coffee before I can continue.
NEKS. Discussion Note 4
JP = Jim Piat
Re: KS-DIS 3. http://stderr.org/pipermail/inquiry/2005-December/003296.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
Replies interspersed.
JP: Would you give me an example of one of Peirce's genuine, necessary and sufficient,
descriptions of a sign, and perhaps for the purpose of contrast one of his
non-genuine definitions that fails to meet these criteria. Also would
you give me the necessary and sufficient conditions for discerning
which is which.
So let me haul out the "Carnegie" definitions of a sign relation one more time
and try to tell you why I think they ought to win friends and influence people.
Here's the first link that came up on Google:
SR. Sign Relations
SR. http://forum.wolframscience.com/showthread.php?threadid=647
| A sign is something, 'A',
| which brings something, 'B',
| its 'interpretant' sign
| determined or created by it,
| into the same sort of correspondence
| with something, 'C', its 'object',
| as that in which itself stands to 'C'.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54, also available here:
| http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm
More details on how the definition of a sign relation bears on
the definition of logic are given in the contexts of this text:
| On the Definition of Logic [Version 1]
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time. Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'. It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized. (CSP, NEM 4, 20-21).
|
| On the Definition of Logic [Version 2]
|
| Logic is 'formal semiotic'. A sign is something,
| 'A', which brings something, 'B', its 'interpretant'
| sign, determined or created by it, into the same
| sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in
| which itself stands to 'C'. This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident. The word "formal" in
| the definition is also defined. (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.
Partly I like these statements because they place the
matter of defining "sign" within its due contexts of
defining "formal" and defining "logic", which helps
to "comprehend", in both senses of that term, some
of the purposes and utilities of the definition.
With respect to the question of contrast, Peirce in this instance
explictly contrasts this definition with the most popular host of
sufficient but not necessary descriptions, namely, those that use
some of our common but typically unexamined introspections and/or
intuitions about our own psychological processes in order to fill
in a motley assortment of intuitive blind spots and logical holes
in the description. This affords a significant correction to the
psychologically-biased descriptions, for instance, those deriving
from the "New List" account.
But probably the most important feature of this definition is that
it does not invoke too large a variety of undefined terms as a part
of its try at definition, and the few significant terms that it does
pass the buck to, like "correspondence" and "determination", are ones
for which we find fairly fast definitions elsewhere in Peirce's works.
The reason why these criteria are important is that they give us what we need
in order to carry out any measure of deductive or necessary reasoning on the
basis of the definition alone -- the "standing on its own feet" character
of a genuine definition.
NEKS. Discussion Note 5
JP = Jim Piat
Re: KS-DIS 4. http://stderr.org/pipermail/inquiry/2005-December/003297.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
Replies interspersed.
JP: Would you give me an example of one of Peirce's genuine, necessary and sufficient,
descriptions of a sign, and perhaps for the purpose of contrast one of his
non-genuine definitions that fails to meet these criteria. Also would
you give me the necessary and sufficient conditions for discerning
which is which.
I've given what I think is one of Peirce's better definitions of a sign relation.
It is by no means perfect, but it does provide enough of a basis to start up the
business of drawing necessary conclusions. The nice thing about a good-enough
definition, if you catch my object-relational drift, is that it affords us
the ontological security to begin thinking for ourselves, as we may hope
to do in scientific inquiry, instead of constantly needing to run back
to our primal source for the assurance of some scriptural quotation
that we have not strayed from the path of right-group-thinking and
remain in conformity with the established doctrine, in that most
likely exaggerated caricature of the medieval seminary scholar,
but just as likely a graphic icon with a hint of truth to it.
As I've indicated, some of the descriptions that fall short of this standard
are those that rely on undefined psychological or sociological notions, for
all the possibility of their still being useful in application to specific
subjects, when taken with the due grain of salt. Other descriptions that
tend to lead us astray are those that are afflicted with the residual
biases of essentialism, in spite of all the work that Peirce did to
make clear that the minimal unit of description is a sign relation,
not the isolated sign in itself, which is a meaningless concept.
With respect to the last part of your question, yes, we can give
a logically necessary and sufficient definition of "definition".
For instance, the following from Peirce will do as well as any:
| A 'definition' is the logical analysis of a predicate in general terms.
He immediately elaborates this definition of definition as follows:
| It has two branches, the one asserting that the definitum is
| applicable to whatever there may be to which the definition is
| applicable; the other (which ordinarily has several clauses),
| that the definition is applicable to whatever there may be to
| which the definitum is applicable. 'A definition does not
| assert that anything exists.'
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 237
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)',
| Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.
What we cannot provide so easily is a definition of a 'good' definition,
because that is more properly an applied, empirical, pragmatic matter,
not just a logical or a mathematical question. Here we are "reduced"
to "holism", whereby only models as a whole of theories as a whole
can be judged by their empirical fertility and logical integrity.
NEKS. Discussion Note 6
JA = Jon Awbrey
JP = Jim Piat
Re: KS-DIS 5. http://stderr.org/pipermail/inquiry/2005-December/003298.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
Supplying a missing article:
JA: What we cannot provide so easily is a definition of a 'good' definition,
because that is more properly an applied, empirical, pragmatic matter,
not just a logical or a mathematical question. Here we are "reduced"
to "holism", whereby only models as a whole of theories as a whole
can be judged by their empirical fertility and logical integrity.
Replies interspersed.
JP: I don't mean to sound so confrontational or abrupt. Fact is I seem to recall
you have already posted (maybe a number of times) some of what you felt were
Peirce's most useful sign definitions. So what I'm really trying to ask is
how can we separate our sign selection criteria from our preconceptions of
what a sign is. My concern is that our definitions may beg the questions
we hope they will help us answer. Just as every question presupposes an
assertion that is being doubted, it seems to me that every definition
presupposes a question that is being answered.
I just now notice that I had posted one at the top of this discussion thread,
and had already forgotten it, partly because I did not get my copy back from
the Peirce List -- I sure hope this isn't what made Soren so irate that time --
anyway here's a link to an archive copy:
KS-DIS 1. http://stderr.org/pipermail/inquiry/2005-December/003272.html
I'm not quite sure what you're asking, where the emphasis is meant to be
when you say: "how can we separate our sign selection criteria from our
preconceptions of what a sign is". If by "begging the question" you are
saying that a definition evades the question by assuming what's supposed
to be proved, I don't see how that is, as definitions aren't supposed to
prove anything, only supply a potential clarification of one thing meant
by a term. But if you are emphasizing the difference between unexamined
preconception and clarifying "logical analysis of a predicate in general
terms", in Peirce's phrase, then that again is just what a definition is
supposed to be doing.
JP: Sitting here writing this, Jon, I've come up with what is perhaps a more helpful
question for me -- would you explain a bit more (in so far as possible in layman's
terms for me) why you are trying to translate Peirce's definitions into some sort
of graphic formalization. I don't really understand your goal. I guess in part
what I don't understand is what is meant by a formal definition if in fact that
is part of your goal. I realize you are putting a lot of care into what you
are doing and are trying to move in careful well considered small steps.
That much I think I understand and appreciate. But I don't understand
your methodological goal. My sense is you are attempting some sort
of formalization but I don't really know what constitutes a formal
definition -- what it achieves and what it avoids. I'm not trying
to trap you into some premature formulations -- I just want to get
a better understanding in very informal terms for starters of what
your general methodological goal is so that maybe I can better
understand the steps you are taking. Even off line if you
don't want to be held accountable for some very quick and
dirty, off hand, rough translation of your methodological
goals designed solely for a friend who is largely clueless.
For this one I will have to hunt up that old thinking cap and get back to you ...
P.S. I don't know why the Internet has been so funky the
last couple of weeks -- Sue said there was some kind of
major D.O.S. attack that had their servers bogged down
for a while, or maybe it's just the traffic from the
<insert your denominational festivity>'s holiday
online shopping frenzy -- but if I don't answer
you or anybody for a day or so I won't mind if
you send me a copy by my own email address.
NEKS. Discussion Note 7
JA = Jon Awbrey
JP = Jim Piat
Re: KS-DIS 4. http://stderr.org/pipermail/inquiry/2005-December/003297.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
In substance:
| A sign is something, A, which brings something, B,
| its interpretant sign determined or created by it,
| into the same sort of correspondence with something,
| C, its object, as that in which itself stands to C.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54 (1902).
|
| C.S. Peirce, [Application to the Carnegie Institution], L 75, pp. 13-73 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by Charles S. Peirce,
| Volume 4, Mathematical Philosophy', Mouton, The Hague, 1976. Available here:
| Arisbe Website, http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm
JA: More details on how the definition of a sign relation bears on
the definition of logic are given in the contexts of this text:
| On the Definition of Logic [Version 1]
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time. Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'. It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized. (CSP, NEM 4, 20-21).
|
| On the Definition of Logic [Version 2]
|
| Logic is 'formal semiotic'. A sign is something,
| 'A', which brings something, 'B', its 'interpretant'
| sign, determined or created by it, into the same
| sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in
| which itself stands to 'C'. This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident. The word "formal" in
| the definition is also defined. (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.
JP: I don't want to lose the moment so I'm risking accuracy/depth etc. for haste --
JP: In immediately above definition I notice particularly two comments.
One is the remark about correspondence "(or a lower implied sort)"
and the other is the reference to a definition of "formal". I'm
thinking that correspondence is either iconic or indexical and
that a lower implied sort of correspondence has at least the
same function. And I'm also wondering if you might have
off hand a reference to Peirce's definition of formal
ref in his comment.
Here is the relevant part of the second variant:
| Logic is 'formal semiotic'. A sign is something, 'A',
| which brings something, 'B', its 'interpretant' sign,
| determined or created by it, into the same sort of
| correspondence (or a lower implied sort) with
| something, 'C', its 'object', as that in
| which itself stands to 'C'.
I took the "lower implied sort" as modifying the "same"
in "the same sort of correspondence", and I further took
the word "implied" as intended to generalize the definition
by weakening the condition in question, much in the way that
we would weaken the "sameness" of the equivalence "<=>" into
the lower implied sort of the implication "=>". I will think
about the reading of "lower" as "degenerate" as in the castes
of icons and indices, but the "implied" seems to rule that out,
just off hand, as being as sign does not imply being either one.
The "correspondence" I take in the sense of the phrase "triple correspondence"
that he uses elsewhere for a 3-adic relation, but definitely not anything like
a one-to-one correspondence, which is a 2-adic relation, and thus not intended
to suggest any hint of a "correspondence theory" of meaning or truth. In this
way of reading it, the "correspondence" is just a rhetorical alternate for the
sign relation itself. This interpretation also comports with that "recursive"
definition of the sign relation that Peirce often gives.
A little bit under the weather today --
we've been in the deep freeze for
a couple of weeks hereabouts --
so I'll need to take a rest.
NEKS. Discussion Note 8
JA = Jon Awbrey
JP = Jim Piat
Re: KS-DIS 7. http://stderr.org/pipermail/inquiry/2005-December/003300.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
JA: Partly I like these statements because they place the
matter of defining "sign" within its due contexts of
defining "formal" and defining "logic", which helps
to "comprehend", in both senses of that term, some
of the purposes and utilities of the definition.
JA: With respect to the question of contrast, Peirce in this instance
explictly contrasts this definition with the most popular host of
sufficient but not necessary descriptions, namely, those that use
some of our common but typically unexamined introspections and/or
intuitions about our own psychological processes in order to fill
in a motley assortment of intuitive blind spots and logical holes
in the description. This affords a significant correction to the
psychologically-biased descriptions, for instance, those deriving
from the "New List" account.
JP: Ha! Yes, I've always thought that the New List relied a bit on unexamined
psychological notions such as "attention" but then again I wonder if any
human endeavor (inquiry, defintion, thought or whatever) can completely
escape this sort of reliance. Being a psychologist (whatever that is)
this has never bothered me. In fact it just now occurs to me that that
for me is a good account of what I mean when I say I am a psychologist --
that for me what is left undefined or the starting point if you will --
is what in common parlance people mostly call psychological.
I have no brief against psychology -- it is a fascinating study, one of those
that I passed through several times in the "cycle of majors" that I had as an
undergrad and even spent a parallel life during the 80's taking a Master's in.
And I do not confound "psychological" or even "introspective" with "unexamind" --
it's merely that many of our most intuitive concepts remain as yet "primitive" --
in both the "logical undefind" and the "savage mind" senses of the word. And
it's entirely appropriate to use the concepts that we have until we arrive at
clearer and distincter ideas, as the saying goes -- like you say, there is no
escaping that, not at the outset anyways.
JP: It's always struct me that Peirce's eschewing of psychologogism
was no big deal -- mostly just a reaction to the excesses of the
psychologizing in vogue at the time he was writing. Something
psychologists of the time eventually reacted against (to the
point of excesses in the other direction) themselves.
"Struct" -- a sly alusion to Aristotle's 'pathemeta'
and the classical theory of being tutored by nature,
the mode of instruction via hard knocks impressions.
I like it, ergo, I think I'll steal it.
JA: But probably the most important feature of this definition is that
it does not invoke too large a variety of undefined terms as a part
of its try at definition, and the few significant terms that it does
pass the buck to, like "correspondence" and "determination", are ones
for which we find fairly fast definitions elsewhere in Peirce's works.
JA: The reason why these criteria are important is that they give us what we need
in order to carry out any measure of deductive or necessary reasoning on the
basis of the definition alone -- the "standing on its own feet" character
of a genuine definition.
JA: To be continued ...
JP: Looking forward to that!
WOWYWF, somebody may be keeping a list ...
NEKS. Discussion Note 9
JP = Jim Piat
Re: KS-DIS 4. http://stderr.org/pipermail/inquiry/2005-December/003297.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
I see that the following query fell to
the cutting room floor of my "attention"
somewhere in the process of cut and haste.
JP: And I'm also wondering if you might have
off hand a reference to Peirce's definition
of formal ref[erred to?] in his comment.
The one that comes to mind, the way that I'm forced to recall most
things these days, by Googling on +Awbrey +Peirce "Quasi-Necessary"
is this one:
Cf: SR 3. http://forum.wolframscience.com/showthread.php?postid=2395#post2395
In: SR. http://forum.wolframscience.com/showthread.php?threadid=647
| Logic, in its general sense, is, as I believe I have shown, only another
| name for 'semiotic' [Greek: 'semeiotike'], the quasi-necessary, or formal,
| doctrine of signs. By describing the doctrine as "quasi-necessary", or
| formal, I mean that we observe the characters of such signs as we know,
| and from such an observation, by a process which I will not object to
| naming Abstraction, we are led to statements, eminently fallible, and
| therefore in one sense by no means necessary, as to what 'must be' the
| characters of all signs used by a "scientific" intelligence, that is to say,
| by an intelligence capable of learning by experience. As to that process of
| abstraction, it is itself a sort of observation. The faculty which I call
| abstractive observation is one which ordinary people perfectly recognize,
| but for which the theories of philosophers sometimes hardly leave room.
| It is a familiar experience to every human being to wish for something
| quite beyond his present means, and to follow that wish by the question,
| "Should I wish for that thing just the same, if I had ample means to gratify it?"
| To answer that question, he searches his heart, and in doing so makes what I term
| an abstractive observation. He makes in his imagination a sort of skeleton diagram,
| or outline sketch, of himself, considers what modifications the hypothetical state
| of things would require to be made in that picture, and then examines it, that is,
| 'observes' what he has imagined, to see whether the same ardent desire is there to
| be discerned. By such a process, which is at bottom very much like mathematical
| reasoning, we can reach conclusions as to what 'would be' true of signs in all
| cases, so long as the intelligence using them was scientific. (CP 2.227).
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.227,
| Editor Data: From An Unidentified Fragment, c. 1897.
P.S. I just now got your message from 7:59
this morning, but will save it for tomorrow.
NEKS. Discussion Note 10
JP = Jim Piat
Re: KS-DIS 3. http://stderr.org/pipermail/inquiry/2005-December/003296.html
In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
JP: An early response to an early response. Ah yes, of course, I've read your paper
on interpretation as action before -- but apparently now I'm ready to read it
with more understanding and profit. Strange how some things that I just
glossed over before (thinking them unnecessary filler) now jump out at
me as key concepts! Reminds me of Joe's recent comments about how
successive iterations of philosophical inquiry (in this case my
own) legitimately must keep revisiting old "settled" issues in
the light of new understandings. So I'm going to give your
paper a fresh slow read -- and thanks for the re-minder!
I look forward to any further comments you may wish
to add.
A random response to a random distribution.
Thanks for the once or thrice over. And I
will not reguard it a hermeneutic violence
if you look beneath the subtitles and risk
the wine-dark see-change of look-out-world
that every old grit of your hermenaut wits.
But serially, folks, things take care of themselves as far as raising new doubts.
It's what we do to after that that makes all the difference in styles of inquiry.
Does our peerage into the skies open eyes, or refuse to peer through the 'scopes?
Does our revistation of old friends and familiars bring about a truly new vision,
or merely the sort of apologetic revisal that led Henry Ford to say that History
is post hoc revisionary casuistry of a specious quo, or something to that effect?
Think of a real example, say Galileo, Bellarmine, Descartes. In what sense were
they peers, in what sense not? More to the point, how would it have been viewed
at the time, how sundry and variously, by who? Now let's imagine in our darkest
imaginings that the "Continuous Young Creation" (CYC) theory of the universe can
win out in the next "Tribunal Of The Inquisition" (TOTI), and prevail over minds
for the remains of the Third Millennium. Will not-now people not then look back
on a wholly different "Topology Of Peers" (TOP) than what now transits sic, what
the Scientism of the future will chastise as our benighted age of seculahilarity?
These dim reflections make it clear that the notion of peerage is no explanation,
but concocted after the fact to rationalize whatever fashion or fascism preveils.
NEKS. Discussion Note 11
JP = Jim Piat Re: KS-DIS 3. http://stderr.org/pipermail/inquiry/2005-December/003296.html In: KS-DIS. http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272 I see that some idiom from another language -- Algol or Forth I think -- has muffed my text for the English ear, so speaking of revision, like speaking of the devil, I guess, here is the revised, extended edition: But serially, folks, things take care of themselves as far as raising new doubts. It's what we do to after that that makes all the difference in styles of inquiry. Does our peerage into the skies open eyes, or refuse to peer through the 'scopes? Does our revistation of old friends and familiars bring about a truly new vision, or merely the sort of apologetic revisal that led Henry Ford to say that History is post hoc revisionary casuistry of a specious quo, or something to that effect? Think of a real example, say Galileo, Bellarmine, Descartes. In what sense were they peers, in what sense not? More to the point, how would it have been viewed at the time, how sundry and variously, by who? Now let's imagine in our darkest imaginings that the "Continuous Young Creation" (CYC) theory of the universe can win out in the next "Tribunal Of The Inquisition" (TOTI), and prevail over minds for the remains of the Third Millennium. Will not-now people not then look back on a wholly different "Topology Of Peers" (TOP) than what now transits sic, what the Scientism of the future will chastise as our benighted age of seculahilarity? These dim reflections make it clear that the notion of peerage is no explanation, but concocted after the fact to rationalize whatever fashion or fascism preveils. The spirit of inquiry comes from the heart. Where it lives there's no need to force it. Where it's dead there's no way to argue it into being -- it demands an external shock or an internal quake, a sense of anharmony to kick-start it back to the realm of life. But don't underestimate the persistence of a static status quo to insulate its static atmospherics from all hope of resuscitance, by all the available routines of authority, parochial isolation, not to say xenophobia.
OLOD. Quine On The Limits Of Decision
OLOD. Note 1
| On the Limits of Decision | | Because these congresses occur at intervals of five years, they make | for retrospection. I find myself thinking back over a century of logic. | A hundred years ago George Boole's algebra of classes was at hand. Like | so many inventions, it had been needlessly clumsy when it first appeared; | but meanwhile, in 1864, W.S. Jevons had taken the kinks out of it. It was | only in that same year, 1864, that DeMorgan published his crude algebra of | relations. Then, around a century ago, C.S. Peirce published three papers | refining and extending these two algebras -- Boole's of classes and DeMorgan's | of relations. These papers of Peirce's appeared in 1867 and 1870. Even our | conception of truth-function logic in terms of truth tables, which is so clear | and obvious as to seem inevitable today, was not yet explicit in the writings | of that time. As for the logic of quantification, it remained unknown until | 1879, when Frege published his 'Begriffsschrift'; and it was around three | years later still that Peirce began to become aware of this idea, through | independent efforts. And even down to litle more than a half century ago | we were weak on decision procedures. It was only in 1915 that Löwenheim | published a decision procedure for the Boolean algebra of classes, or, | what is equivalent, monadic quantification theory. It was a clumsy | procedure, and obscure in the presentation -- the way, again, with | new inventions. And it was less than a third of a century ago that | we were at last forced, by results of Gödel, Turing, and Church, to | despair of a decision procedure for the rest of quantification theory. | | Quine, "Limits of Decision", pp. 156-157. | | W.V. Quine, "On the Limits of Decision", pp. 156-163 in |'Theories and Things, Harvard University Press, Cambridge, | MA, 1981. A shorter version of this paper appeared in the |'Akten des XIV. internationalen Kongresses für Philosophie', | vol. 3, 1969.
OLOD. Note 2
| On the Limits of Decision (cont.) | | It is hard now to imagine not seeing truth-function logic | as a trivial matter of truth tables, and it is becoming hard | even to imagine the decidability of monadic quantification theory | as other than obvious. For monadic quantification theory in a modern | perspective is essentially just an elaboration of truth-function logic. | I want now to spend a few minutes developing this connection. | | What makes truth-function logic decidable by truth tables | is that the truth value of a truth function can be computed | from the truth values of the arguments. But is a formula of | quantification theory not a truth-function of quantifications? | Its truth vaue can be computed from whatever truth values may be | assigned to its component quantifications. Why does this not make | quantification theory decidable by truth tables? Why not test a | formula of quantification theory for validity by assigning all | combinations of truth values to its component quantifications | and seeing whether the whole comes out true every time? | | Quine, "Limits of Decision", p. 157. | | W.V. Quine, "On the Limits of Decision", pp. 156-163 in |'Theories and Things, Harvard University Press, Cambridge, | MA, 1981. A shorter version of this paper appeared in the |'Akten des XIV. internationalen Kongresses für Philosophie', | vol. 3, 1969.
OLOD. Note 3
| On the Limits of Decision (cont.) | | The answer obviously is that this criterion is too | severe, because the component quantifications are | not always independent of one another. A formula | of quantification theory might be valid in spite | of failing this truth-table test. It might fail | the test by turning out false for some assignment | of truth values to its component quantifications, | but that assignment might be undeserving of notice | because incompatible with certain interdependences | of the component quantifications. | | If, on the other hand, we can put a formula of quantification | theory into the form of a truth function of quantifications | which are independent of one another, then the truth table | will indeed serve as a validity test. And this is just | what we can do for monadic formulas of quantification | theory. Herbrand showed this in 1930. | | Quine, "Limits of Decision", p. 157. | | W.V. Quine, "On the Limits of Decision", pp. 156-163 in |'Theories and Things, Harvard University Press, Cambridge, | MA, 1981. A shorter version of this paper appeared in the |'Akten des XIV. internationalen Kongresses für Philosophie', | vol. 3, 1969.
OLOD. Note 4
| On the Limits of Decision (cont.) | | ... | | Quine, "Limits of Decision", pp. 157-158. | | W.V. Quine, "On the Limits of Decision", pp. 156-163 in |'Theories and Things, Harvard University Press, Cambridge, | MA, 1981. A shorter version of this paper appeared in the |'Akten des XIV. internationalen Kongresses für Philosophie', | vol. 3, 1969.
POLA. Philosophy Of Logical Atomism
I am going to collect here a number of excerpts from the papers that Bertrand Russell wrote in the years 1910–1920, my interest being focused on the logical characters of belief and knowledge. I will take the liberty of breaking up some of Russell's longer paragraphs in whatever fashion serves to facilitate their study.
POLA. Note 1
|
The Philosophy of Logical Atomism (1918) The following [is the text] of a course of eight lectures delivered in [Gordon Square] London, in the first months of 1918, [which] are very largely concerned with explaining certain ideas which I learnt from my friend and former pupil Ludwig Wittgenstein. I have had no opportunity of knowing his views since August 1914, and I do not even know whether he is alive or dead. He has therefore no responsibility for what is said in these lectures beyond that of having originally supplied many of the theories contained in them. (Russell, POLA, p. 35). |
Bertrand Russell, “The Philosophy of Logical Atomism”, pp. 35–155 in The Philosophy of Logical Atomism, edited with an introduction by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 2
| 1. Facts and Propositions | | This course of lectures which I am now beginning I have called | the Philosophy of Logical Atomism. Perhaps I had better begin | by saying a word or two as to what I understand by that title. | The kind of philosophy that I wish to advocate, which I call | Logical Atomism, is one which has forced itself upon me in the | course of thinking about the philosophy of mathematics, although | I should find it hard to say exactly how far there is a definite | logical connection between the two. The things I am going to say | in these lectures are mainly my own personal opinions and I do not | claim that they are more than that. | | As I have attempted to prove in 'The Principles of Mathematics', when | we analyse mathematics we bring it all back to logic. It all comes back | to logic in the strictest and most formal sense. In the present lectures, | I shall try to set forth in a sort of outline, rather briefly and rather | unsatisfactorily, a kind of logical doctrine which seems to me to result | from the philosophy of mathematics -- not exactly logically, but as what | emerges as one reflects: a certain kind of logical doctrine, and on the | basis of this a certain kind of metaphysic. | | The logic which I shall advocate is atomistic, as opposed to | the monistic logic of the people who more or less follow Hegel. | When I say that my logic is atomistic, I mean that I share the | common-sense belief that there are many separate things; I do | not regard the apparent multiplicity of the world as consisting | merely in phases and unreal divisions of a single indivisible | Reality. It results from that, that a considerable part of | what one would have to do to justify the sort of philosophy | I wish to advocate would consist in justifying the process | of analysis. | | One is often told that the process of analysis is falsification, that | when you analyse any given concrete whole you falsify it and that the | results of analysis are not true. I do not think that is a right view. | I do not mean to say, of course, and nobody would maintain, that when you | have analysed you keep everything that you had before you analysed. If you | did, you would never attain anything in analysing. I do not propose to meet | the views that I disagree with by controversy, by arguing against those views, | but rather by positively setting forth what I believe to be the truth about the | matter, and endeavouring all the way through to make the views that I advocate | result inevitably from absolutely undeniable data. | | When I talk of "undeniable data" that is not to be regarded as synonymous | with "true data", because "undeniable" is a psychological term and "true" | is not. When I say that something is "undeniable", I mean that it is not | the sort of thing that anybody is going to deny; it does not follow from | that that it is true, though it does follow that we shall all think it true -- | and that is as near to truth as we seem able to get. | | When you are considering any sort of theory of knowledge, you are more or less | tied to a certain unavoidable subjectivity, because you are not concerned simply | with the question what is true of the world, but "What can I know of the world?" | You always have to start any kind of argument from something which appears to | you to be true; if it appears to you to be true, there is no more to be done. | You cannot go outside yourself and consider abstractly whether the things that | appear to you to be true are true; you may do this in a particular case, where | one of your beliefs is changed in consequence of others among your beliefs. | | Russell, POLA, pp. 35-37. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 3
| 1. Facts and Propositions (cont.) | | The reason that I call my doctrine 'logical' atomism is because | the atoms that I wish to arrive at as the sort of last residue | in analysis are logical atoms and not physical atoms. Some of | them will be what I call "particulars" -- such things as little | patches of colour or sounds, momentary things -- and some of them | will be predicates or relations and so on. The point is that the | atom I wish to arrive at is the atom of logical analysis, not the | atom of physical analysis. | | Russell, POLA, p. 37. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 4
| 1. Facts and Propositions (cont.) | | It is a rather curious fact in philosophy that the data which are | undeniable to start with are always rather vague and ambiguous. | You can, for instance, say: "There are a number of people in | this room at this moment". That is obviously in some sense | undeniable. But when you come to try and define what this | room is, and what it is for a person to be in a room, and | how you are going to distinguish one person from another, | and so forth, you find that what you have said is most | fearfully vague and that you really do not know what | you meant. That is a rather singular fact, that | everything you are really sure of, right off is | something that you do not know the meaning of, | and the moment you get a precise statement | you will not be sure whether it is true | or false, at least right off. | | The process of sound philosophizing, to my mind, consists mainly | in passing from those obvious, vague, ambiguous things, that we | feel quite sure of, to something precise, clear, definite, which | by reflection and analysis we find is involved in the vague thing | that we start from, and is, so to speak, the real truth of which | that vague thing is a sort of shadow. | | I should like, if time were longer and if I knew more than I do, | to spend a whole lecture on the conception of vagueness. I think | vagueness is very much more important in the theory of knowledge | than you would judge it to be from the writings of most people. | Everything is vague to a degree you do not realize till you | have tried to make it precise, and everything precise is | so remote from everything that we normally think, that | you cannot for a moment suppose that is what we really | mean when we say what we think. | | Russell, POLA, pp. 37-38. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 5
| 1. Facts and Propositions (cont.) | | The first truism to which I wish to draw your attention -- and I hope | you will agree with me that these things that I call truisms are so | obvious that it is almost laughable to mention them -- is that the | world contains 'facts', which are what they are whatever we may | choose to think about them, and that there are also 'beliefs', | which have reference to facts, and by reference to facts are | either true or false. | | I will try first of all to give you a preliminary explanation of what | I mean by a "fact". When I speak of a fact -- I do not propose to | attempt an exact definition, but an explanation, so that you will | know what I am talking about -- I mean the kind of thing that | makes a proposition true or false. | | If I say "It is raining", what I say is true in a certain condition of | weather and is false in other conditions of weather. The condition of | weather that makes my statement true (or false as the case may be), is | what I should call a "fact". | | If I say, "Socrates is dead", my statement will be true owing to a | certain physiological occurrence which happened in Athens long ago. | | If I say, "Gravitation varies inversely as the square of the distance", | my statement is rendered true by astronomical fact. | | If I say, "Two and two are four", it is arithmetical fact that makes | my statement true. | | On the other hand, if I say, "Socrates is alive", | or "Gravitation varies directly as the distance", | or "Two and two are five", the very same facts | which made my previous statements true show | that these new statements are false. | | Russell, POLA, pp. 40-41. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 6
| 1. Facts and Propositions (cont.) | | I want you to realize that when I speak of a fact I do not mean a | particular existing thing, such as Socrates or the rain or the sun. | Socrates himself does not render any statement true of false. You | might be inclined to suppose that all by himself he would give truth | to the statement "Socrates existed", but as a matter of fact that is a | mistake. It is due to a confusion which I shall try to explain in the | sixth lecture of this course, when I come to deal with the notion of | existence. Socrates himself, or any particular thing just by itself, | does not make any proposition true or false. "Socrates is dead" and | "Socrates is alive" are both of them statements about Socrates. One is | true and the other false. What I call a fact is the sort of thing that | is expressed by a whole sentence, not by a single name like "Socrates". | When a single word does come to express a fact, like "fire" or "wolf", | it is always due to an unexpressed context, and the full expression of | a fact will always involve a sentence. We express a fact, for example, | when we say that a certain thing has a certain property, or that it | has a certain relation to another thing; but the thing which has | the property or the relation is not what I call a "fact". | | Russell, POLA, p. 41. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 7
| 1. Facts and Propositions (cont.) | | It is important to observe that facts belong to the objective world. | They are not created by our thought or beliefs except in special cases. | That is one of the sort of things which I should set up as an obvious truism, | but, of course, one is aware, the moment one has read any philosophy at all, | how very much there is to be said before such a statement as that can become | the kind of position that you want. The first thing I want to emphasize is | that the outer world -- the world, so to speak, which knowledge is aiming | at knowing -- is not completely described by a lot of "particulars", but | that you must also take account of these things that I call facts, which | are the sort of things that you express by a sentence, and that these, | just as much as particular chairs and tables, are part of the real world. | | Except in psychology, most of our statements are not intended merely to | express our condition of mind, though that is often all that they succeed | in doing. They are intended to express facts, which (except when they are | psychological facts) will be about the outer world. There are such facts | involved, equally when we speak truly and when we speak falsely. When we | speak falsely it is an objective fact that makes what we say false, and | it is an objective fact which makes what we say true when we speak truly. | | Russell, POLA, pp. 41-42. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 8
| 1. Facts and Propositions (cont.) | | There are a great many different kinds of facts, and we shall be | concerned in later lectures with a certain amount of classification | of facts. I will just point out a few kinds of facts to begin with, | so that you may not imagine that facts are all very much alike. | | There are 'particular facts', such as "This is white"; then there | are 'general facts', such as "All men are mortal". Of course, the | distinction between particular and general facts is one of the most | important. | | There again it would be a very great mistake to suppose that | you could describe the world completely by means of particular | facts alone. Suppose that you had succeeded in chronicling every | single particular fact throughout the universe, and that there did | not exist a single particular fact of any sort anywhere that you had | not chronicled, you still would not have got a complete description of | the universe unless you also added: "These that I have chronicled are | all the particular facts there are". So you cannot hope to describe the | world completely without having general facts as well as particular facts. | | Another distinction, which is perhaps a little more difficult to make, is | between positive facts and negative facts, such as "Socrates was alive" -- | a positive fact -- and "Socrates is not alive" -- you might say a negative | fact. But the distinction is difficult to make precise. | | Then there are facts concerning particular things or particular qualities | or relations, and, apart from them, the completely general facts of the sort | that you have in logic, where there is no mention of any constituent whatever | of the actual world, no mention of any particular thing or particular quality | or particular relation, indeed strictly you may say no mention of anything. | | That is one of the characteristics | of logical propositions, that they | mention nothing. | | Such a proposition is: "If one class is | part of another, a term which is a member | of the one is also a member of the other". | | All those words that come in the statement of a pure logical proposition | are words really belonging to syntax. They are words merely expressing | form or connection, not mentioning any particular constituent of the | proposition in which they occur. This is, of course, a thing that | wants to be proved; I am not laying it down as self-evident. | | Then there are facts about the properties of single things; and facts | about the relations between two things, three things, and so on; and | any number of different classifications of some of the facts in the | world, which are important for different purposes. | | Russell, POLA, pp. 42-43. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 9
| 1. Facts and Propositions (cont.) | | It is obvious that there is not a dualism of true and false facts; | there are only just facts. It would be a mistake, of course, to | say that all facts are true. That would be a mistake because | true and false are correlatives, and you would only say of | a thing that it was true if it was the sort of thing that | 'might' be false. A fact cannot be either true or false. | | That brings us on to the question of statements or propositions or | judgments, all those things that do have the quality of truth and | falsehood. For the purposes of logic, though not, I think, for the | purposes of theory of knowledge, it is natural to concentrate upon | the proposition as the thing which is going to be our typical vehicle | on the duality of truth and falsehood. | | A proposition, one may say, is a sentence in the indicative, | a sentence asserting something, not questioning or commanding | or wishing. It may also be a sentence of that sort preceded | by the word "that". For example, "That Socrates is alive", | "That two and two are four", "That two and two are five", | anything of that sort will be a proposition. | | Russell, POLA, pp. 43-44. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 10
| 1. Facts and Propositions (cont.) | | A proposition is just a symbol. It is a complex symbol in the | sense that it has parts which are also symbols: a symbol may | be defined as complex when it has parts that are symbols. | | In a sentence containing several words, the several words are each symbols, | and the sentence comprising them is therefore a complex symbol in that sense. | | There is a good deal of importance to philosophy in the theory of symbolism, | a good deal more than one time I thought. I think the importance is almost | entirely negative, i.e., the importance lies in the fact that unless you | are fairly self-conscious about symbols, unless you are fairly aware of | the relation of the symbol to what it symbolizes, you will find yourself | attributing to the thing properties which only belong to the symbol. | | That, of course, is especially likely in very abstract studies such as | philosophical logic, because the subject-matter that you are supposed | to be thinking of is so exceedingly difficult and elusive that any | person who has ever tried to think about it knows you do not think | about it except perhaps once in six months for half a minute. | The rest of the time you think about the symbols, because | they are tangible, but the thing you are supposed to be | thinking about is fearfully difficult and one does not | often manage to think about it. | | The really good philosopher is the one who does | once in six months think about it for a minute. | Bad philosophers never do. That is why the | theory of symbolism has a certain importance, | because otherwise you are so certain to | mistake the properties of the symbolism | for the properties of the thing. | | It has other interesting sides to it too. | There are different kinds of symbols, | different kinds of relation between | symbol and what is symbolized, and | very important fallacies arise | from not realizing this. | | The sort of contradictions about which | I shall be speaking in connection with | types in a later lecture all arise from | mistakes in symbolism, from putting one | sort of symbol in the place where another | sort of symbol ought to be. | | Some of the notions that have been thought absolutely fundamental in philosophy | have arisen, I believe, entirely through mistakes as to symbolism -- e.g. the | notion of existence, or, if you like, reality. Those two words stand for a | great deal that has been discussed in philosophy. There has been the theory | about every proposition being really a description of reality as a whole and | so on, and altogther these notions of reality and existence have played a | very prominent part in philosophy. Now my own belief is that as they have | occurred in philosophy, they have been entirely the outcome of a muddle | about symbolism, and that when you have cleared up that muddle, you find | that practically everything that has been said about existence is sheer | and simple mistake, and that is all you can say about it. I shall go | into that in a later lecture, but it is an example of the way in which | symbolism is important. | | Russell, POLA, pp. 44-45. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 11
| 1. Facts and Propositions (cont.) | | Perhaps I ought to say a word or two about what I am | understanding by symbolism, because I think some people | think you only mean mathematical symbols when you talk | about symbolism. I am using it in a sense to include | all language of every sort and kind, so that every | word is a symbol, and every sentence, and so forth. | | When I speak of a symbol I simply mean something that "means" something else, | and as to what I mean by "meaning" I am not prepared to tell you. I will in | the course of time enumerate a strictly infinite number of different things | that "meaning" may mean but I shall not consider that I have exhausted the | discussion by doing that. I think that the notion of meaning is always | more or less psychological, and that it is not possible to get a pure | logical theory of meaning, nor therefore of symbolism. I think that | it is of the very essence of the explanation of what you mean by a | symbol to take account of such things as knowing, of cognitive | relations, and probably also of association. At any rate | I am pretty clear that the theory of symbolism and the | use of symbolism is not a thing that can be explained | in pure logic without taking account of the various | cognitive relations that you may have to things. | | Russell, POLA, p. 45. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 12
| 1. Facts and Propositions (cont.) | | As to what one means by "meaning", I will give a few illustrations. | For instance, the word "Socrates", you will say, means a certain man; | the word "mortal" means a certain quality; and the sentence "Socrates | is mortal" means a certain fact. But these three sorts of meaning are | entirely distinct, and you will get into the most hopeless contradictions | if you think the word "meaning" has the same meaning in each of these three | cases. It is very important not to suppose that there is just one thing which | is meant by "meaning", and that therefore there is just one sort of relation of | the symbol to what is symbolized. A name would be a proper symbol to use for | a person; a sentence (or a proposition) is the proper symbol for a fact. | | A belief or a statement has duality of truth and falsehood, which the | fact does not have. A belief or a statement always involves a proposition. | You say that a man believes that so and so is the case. A man believes that | Socrates is dead. What he believes is a proposition on the face of it, and | for formal purposes it is convenient to take the proposition as the essential | thing having the duality of truth and falsehood. | | It is very important to realize such things, for instance, | as that 'propositions are not names for facts'. It is quite | obvious as soon as it is pointed out to you, but as a matter | of fact I never had realized it until it was pointed out to | me by a former pupil of mine, Wittgenstein. It is perfectly | evident as soon as you think of it, that a proposition is not | a name for a fact, from the mere circumstance that there are | 'two' propositions corresponding to each fact. Suppose it | is a fact that Socrates is dead. You have two propositions: | "Socrates is dead" and "Socrates is not dead". And those two | propositions corresponding to the same fact; there is one fact | in the world which makes one true and one false. That is not | accidental, and illustrates how the relation of proposition | to fact is a totally different one from the relation of name | to the thing named. For each fact there are two propositions, | one true and one false, and there is nothing in the nature of | the symbol to show us which is the true one and which is the | false one. If there were, you could ascertain the truth | about the world by examining propositions without looking | around you. | | Russell, POLA, pp. 46-47. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 13
| 1. Facts and Propositions (concl.) | | There are two different relations, as you see, that a proposition | may have to a fact: the one the relation that you may call being | true to the fact, and the other being false to the fact. Both are | equally essentially logical relations which may subsist between the | two, whereas in the case of a name, there is only one relation that | it can have to what it names. A name can just name a particular, | or, if it does not, it is not a name at all, it is a noise. It | cannot be a name without having just that one particular relation | of naming a certain thing, whereas a proposition does not cease | to be a proposition if it is false. It has two ways, of being | true and being false, which together correspond to the property | of being a name. Just as a word may be a name or be not a name | but just a meaningless noise, so a phrase which is apparently a | proposition may be either true or false, or may be meaningless, | but the true and false belong together as against the meaningless. | That shows, of course, that the formal logical characterictics of | propositions are quite different from those of names, and that the | relations they have to facts are quite different, and therefore | propositions are not names for facts. You must not run away with | the idea that you can name facts in any other way; you cannot. | You cannot name them at all. You cannot properly name a fact. | The only thing you can do is to assert it, or deny it, or | desire it, or will it, or wish it, or question it, but all | those are things involving the whole proposition. You can | never put the sort of thing that makes a proposition to be | true or false in the position of a logical subject. You can | only have it there as something to be asserted or denied or | something of that sort, but not something to be named. | | Russell, POLA, p. 47. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 14
| 4. Propositions and Facts with More than One Verb: Beliefs, Etc. | | You will remember that after speaking about atomic propositions | I pointed out two more complicated forms of propositions which | arise immediately on proceeding further than that: the 'first', | which I call molecular propositions, which I dealt with last time, | involving such words as "or", "and", "if", and the 'second' involving | two or more verbs such as believing, wishing, willing, and so forth. | | In the case of molecular propositions it was not clear that we had to deal with | any new form of fact, but only with a new form of proposition, i.e. if you have | a disjunctive proposition such as "p or q" it does not seem very plausible to | say that there is in the world a disjunctive fact corresponding to "p or q" | but merely that there is a fact corresponding to p and a fact corresponding | to q, and the disjunctive proposition derives its truth or falsehood from | those two separate facts. Therefore in that case one was dealing only | with a new form of proposition and not with new form of fact. Today | we have to deal with a new form of fact. | | Russell, POLA, pp. 79-80. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 15
| 4. Propositions and Facts with More than One Verb: Beliefs, Etc. (cont.) | | I think that one might describe philosophical logic, the philosophical portion | of logic which is the portion that I am concerned with in these lectures since | Christmas (1917), as an inventory, or if you like a more humble word, a "zoo" | containing all the different forms that facts may have. I should prefer to | say "forms of facts" rather than "forms of propositions". | | To apply that to the case of molecular propositions which I dealt with | last time, if one were pursuing this analysis of the forms of facts, | it would be 'belief in' a molecular proposition that one would deal | with rather than the molecular proposition itself. In accordance | with the sort of realistic bias that should put into all study | of metaphysics, I should always wish to be engaged in the | investigation of some actual fact or set of facts, and it | seems to me that that is so in logic just as much as it | is in zoology. In logic you are concerned with the | forms of facts, with getting hold of the different | sorts of facts, different 'logical' sorts of facts, | that there are in the world. | | Russell, POLA, p. 80. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 16
| 4. Propositions and Facts with More than One Verb: Beliefs, Etc. (cont.) | | Now I want to point out today that the facts that occur when one | believes or wishes or wills have a different logical form from | the atomic facts containing a single verb which I dealt with | in my second lecture. (There are, of course, a good many | forms that facts that may have, a strictly infinite number, | and I do not wish you to suppose that I pretend to deal | with all of them.) | | Suppose you take any actual occurrence of a belief. I want you to | understand that I am not talking about beliefs in the sort of way | in which judgment is spoken of in theory of knowledge, in which | you would say there is 'the' judgment that two and two are four. | I am talking of the actual occurrence of a belief in a particular | person's mind at a particular moment, and discussing what sort of | fact that is. | | If I say "What day of the week is this?" and you say "Tuesday", | there occurs in your mind at that moment the belief that this is | Tuesday. The thing I want to deal with today is the question: | | What is the form of the fact which occurs when a person has a belief? | | Russell, POLA, pp. 80-81. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 17
| 4. Propositions and Facts with More than One Verb: Beliefs, Etc. (cont.) | | Of course you see that the sort of obvious first notion that one would | naturally arrive at would be that a belief is a relation to the proposition. | "I believe the proposition p." "I believe that today is Tuesday." "I believe | that two and two are four." Something like that. It seems on the face of it | as if you had there a relation of the believing subject to a proposition. | | That view won't do for various reasons which I shall go into. But you | have, therefore, got to have a theory of belief which is not exactly that. | Take any sort of proposition, say "I believe Socrates is mortal". Suppose | that that belief does actually occur. The statement that it occurs is a | statement of fact. You have there two verbs. You may have more than two | verbs, you may have any number greater than one. I may believe that Jones | is of the opinion that Socrates is mortal. There you have more than two | verbs. You may have any number, but you cannot have less than two. | | You will perceive that it is not only the proposition that has the two verbs, | but also the fact, which is expressed by the proposition, has two constituents | corresponding to verbs. I shall call those constituents verbs for the sake | of shortness, as it is very difficult to find any word to describe all those | objects which one denotes by verbs. Of course, that is strictly using the | word "verb" in two different senses, but I do not think it can lead to any | confusion if you understand that it is being so used. | | This fact (the belief) is one fact. It is not like what you had in molecular | propositions where you had (say) "p or q". It is just one single fact that | you have a belief. That is obvious from the fact that you can believe a | falsehood. It is obvious from the fact of false belief that you cannot | cut off one part; you cannot have: | | I believe / Socrates is mortal. | | There are certain questions that arise about such facts, | and the first that arises is, Are they undeniable facts | or can you reduce them in some way to relations of other | facts? Is it really necessary to suppose that there | are irreducible facts, of which that sort of thing | is a verbal expression? | | On that question until fairly lately I should certainly not have | supposed that any doubt could arise. It had not really seemed to | me until fairly lately that that was a debatable point. I still | believe that there are facts of that form, but I see that it is | a substantial question that needs to be discussed. | | Russell, POLA, pp. 81-82. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 18
| 4.1. Are Beliefs, Etc., Irreducible Facts? | | "Etc." covers understanding a proposition; it covers desiring, willing, | any other attitude of that sort that you may think of that involves | a proposition. It seems natural to say one believes a proposition | and unnatural to say one desires a proposition, but as a matter | of fact that is only a prejudice. What you believe and what | you desire are of exactly the same nature. You may desire | to get some sugar tomorrow and of course you may possibly | believe that you will. I am not sure that the logical | form is the same in the case of will. I am inclined | to think that the case of will is more analogous to | that of perception, in going direct to facts, and | excluding the possibility of falsehood. In any | case desire and belief are of exactly the same | form logically. | | Russell, POLA, p. 82. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 19
| 4.1. Are Beliefs, Etc., Irreducible Facts? (cont.) | | Pragmatists and some of the American realists, the school whom one calls | neutral monists, deny altogether that there is such a phenomenon as belief | in the sense I am dealing with. They do not deny it in words, they do not | use the same sort of language that I am using, and that makes it difficult | to compare their views with the views I am speaking about. One has really | to translate what they say into language more or less analogous to ours | before one can make out where the points of contact or difference are. | | If you take the works of James in his 'Essays in Radical Empiricism' | or Dewey in his 'Essays in Experimental Logic' you will find that they | are denying altogether that there is such a phenomenon as belief in the | sense I am talking of. They use the word "believe" but they mean something | different. You come to the view called "behaviourism", according to which | you mean, if you say a person believes a thing, that he behaves in a certain | fashion; and that hangs together with James's pragmatism. James and Dewey | would say: when I believe a proposition, that 'means' that I act in a certain | fashion, that my behaviour has certain characteristics, and my belief is a true | one if the behaviour leads to the desired result and is a false one if it does | not. That, if it is true, makes their pragmatism a perfectly rational account | of truth and falsehood, if you do accept their view that belief as an isolated | phenomenon does not occur. | | That is therefore the first thing one has to consider. | It would take me too far from logic to consider that | subject as it deserves to be considered, because it | is a subject belonging to psychology, and it is only | relevant to logic in this one way that it raises a | doubt whether there are any facts having the logical | form that I am speaking of. | | In the question of this logical form that involves two or more verbs you | have a curious interlacing of logic with empirical studies, and of course | that may occur elsewhere, in this way, that an empirical study gives you | an example of a thing having a certain logical form, and you cannot really | be sure that there are things having a given logical form except by finding | an example, and the finding of an example is itself empirical. Therefore in | that way empirical facts are relevant to logic at certain points. I think | theoretically one might know that there were those forms without knowing | any instance of them, but practically, situated as we are, that does not | seem to occur. Practically, unless you can find an example of the form | you won't know that there is that form. If I cannot find an example | containing two or more verbs, you will not have reason to believe | in the theory that such a form occurs. | | Russell, POLA, pp. 82-83. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 20
| 4.1. Are Beliefs, Etc., Irreducible Facts? (cont.) | | When you read the words of people like James and Dewey on the subject of belief, | one thing that strikes you at once is that the sort of thing they are thinking of | as the object of belief is quite different from the sort of thing I am thinking of. | They think of it always as a thing. They think you believe in God or Homer: you | believe in an object. That is the picture they have in their minds. It is common | enough, in common parlance, to talk that way, and they would say, the first crude | approximation that they would suggest would be that you believe truly when there | is such an object and that you believe falsely when there is not. I do not mean | they would say that exactly, but that would be the crude view from which they | would start. They do not seem to have grasped the fact that the objective side | in belief is better expressed by a proposition than by a single word, and that, | I think, has a great deal to do with their whole outlook on the matter of what | belief consists of. The object of belief in their view is generally, not | relations between things, or things having qualities, or what not, but | just single things which may or may not exist. That view seems to me | radically and absolutely mistaken. | | In the 'first' place there are a great many judgments you cannot possibly fit into | that scheme, and in the 'second' place it cannot possibly give any explanation to | false beliefs, because when you believe that a thing exists and it does not exist, | the thing is not there, it is nothing, and it cannot be the right analysis of a | false belief to regard it as a relation to what is really nothing. | | This an objection to supposing that belief consists simply in relation | to the object. It is obvious that if you say "I believe in Homer" and | there was no such person as Homer, your belief cannot be a relation to | Homer, since there is no "Homer". | | Every fact that occurs in the world must be composed entirely of constituents | that there are, and not of constituents that there are not. Therefore when | you say "I believe in Homer" it cannot be the right analysis of the thing | to put it like that. What the right analysis is I shall come on to in | the theory of descriptions. | | Russell, POLA, pp. 83-84. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 21
| 4.1. Are Beliefs, Etc., Irreducible Facts? (cont.) | | I come back now to the theory of behaviourism which I spoke of a moment ago. | Suppose, e.g. that you are said to believe that there is a train at 10.25. | This means, we are told, that you start for the station at a certain time. | When you reach the station you see it is 10.24 and you run. That behaviour | constitutes your belief that there is a train at that time. If you catch | your train by running, your belief was true. If the train went at 10.23, | you miss it, and your belief was false. That is the sort of thing that | they would say constitutes belief. There is not a single state of mind | which consists in contemplating this eternal verity, that the train | starts at 10.25. | | They would apply that even to the most abstract things. | I do not myself feel that that view of things is tenable. | It is a difficult one to refute because it goes very deep | and one has the feeling that perhaps, if one thought it | out long enough and became sufficiently aware of all | its implications, one might find after all that it | was a feasible view; but yet I do not 'feel' it | feasible. | | It hangs together, of course, with the theory of neutral monism, with | the theory that the material constituting the mental is the same as the | material constituting the physical, just like the Post Office directory | which gives you people arranged geographically and alphabetically. This | whole theory hangs together with that. I do not mean necessarily that | all the people that profess the one profess the other, but that the | two do essentially belong together. | | If you are going to take that view, you have to explain away belief | and desire, because things of that sort do seem to be mental phenomena. | They do seem rather far removed from the sort of thing that happens in | the physical world. Therefore people will set to work to explain away | such things as belief, and reduce them to bodily behaviour; and your | belief in a certain proposition will consist in the behaviour of your | body. In the crudest terms that is what that view amounts to. It | does enable you to get on very well without mind. | | Truth and falsehood in that case consist in the relation of your | bodily behaviour to a certain fact, the sort of distant fact which | is the purpose of your behaviour, as it were, and when your behaviour | is satisfactory in regard to that fact your belief is true, and when | your behaviour is unsatisfactory in regard to that fact your belief | is false. | | The logical essence, in that view, will be a relation between two facts | having the same sort of form as a causal relation, i.e. on the one hand | there will be your bodily behaviour which is one fact, and on the other | hand the fact that the train starts at such and such a time, which is | another fact, and out of a relation of those two the whole phenomenon | is constituted. | | The thing you will get will be logically of the same form as you have | in cause, where you have "This fact causes that fact". It is quite | a different logical form from the facts containing two verbs that | I am talking of today. | | Russell, POLA, pp. 84-86. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 22
| 4.1. Are Beliefs, Etc., Irreducible Facts? (concl.) | | I have naturally a bias in favour of the theory of neutral monism | because it exemplifies Occam's razor. I always wish to get on in | philosophy with the smallest possible apparatus, partly because | it diminishes the risk of error, because it is not necessary to | deny the entities you do not assert, and therefore you run less | risk of error the fewer entities you assume. The other reason -- | perhaps a somewhat frivolous one -- is that every diminution | in the number of entities increases the amount of work for | mathematical logic to do in building up things that look | like the entities you used to assume. Therefore the | whole theory of neutral monism is pleasing to me, | but I do find so far very great difficulty in | believing it. | | You will find a discussion of the whole question in some | articles I wrote in 'The Monist'*, especially in July 1914, | and in the two previous numbers also. I should really want | to rewrite them rather because I think some of the arguments | I used against neutral monism are not valid. I place most | reliance on the argument about "emphatic particulars", "this", | "I", all that class of words, that pick out certain particulars | from the universe by their relation to oneself, and I think by | the fact that they, or particulars related to them, are present | to you at the moment of speaking. "This", of course, is what | I call an "emphatic particular". It is simply a proper name | for the present object of attention, a proper name, meaning | nothing. It is ambiguous, because, of course, the object | of attention is always changing from moment to moment | and from person to person. | | I think it is extremely difficult, if you get rid of consciousness | altogether, to explain what you mean by such a word as "this", what | it is that makes the absence of impartiality. You would say that in | a purely physical world there would be a complete impartiality. All | parts of time and all regions of space would seem equally emphatic. | But what really happens is that we pick out certain facts, past and | future and all that sort of thing; they all radiate out from "this", | and I have not myself seen how one can deal with the notion of "this" | on the basis of neutral monism. I do not lay that down dogmatically, | only I do not see how it can be done. I shall assume for the rest of | this lecture that there are such facts as beliefs and wishes and so | forth. It would take me really the whole of my course to go into the | question fully. Thus we come back to more purely logical questions | from this excursion into psychology, for which I apologize. | |*Reprinted as: "On the Nature of Acquaintance", pp. 127-174 | in Bertrand Russell, 'Logic and Knowledge: Essays 1901-1950', | edited by Robert Charles Marsh, Routledge, London, UK, 1992. | | Russell, POLA, pp. 86-87. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 23
| 4.2. What is the Status of 'p' in "I believe 'p'"? | | You cannot say that you believe 'facts', because your beliefs are | sometimes wrong. You can say that you 'perceive' facts, because | perceiving is not liable to error. Wherever it is facts alone | that are involved, error is impossible. Therefore you cannot | say you believe facts. You have to say that you believe | propositions. The awkwardness of that is that obviously | propositions are nothing. Therefore that cannot be the | true account of the matter. | | When I say "Obviously propositions are nothing" it is not perhaps | quite obvious. Time was when I thought there were propositions, | but it does not seem to me very plausible to say that in addition | to facts there are also these curious shadowy things going about | such as "That today is Wednesday" when in fact it is Tuesday. | I cannot believe they go about the real world. It is more | than one can manage to believe, and I do think no person | with a vivid sense of reality can imagine it. | | One of the difficulties of the study of logic is that it is an | exceedingly abstract study dealing with the most abstract things | imaginable, and yet you cannot pursue it properly unless you have | a vivid instinct as to what is real. You must have that instinct | rather well developed in logic. I think otherwise you will get | into fantastic things. | | I think Meinong is rather deficient in just that instinct for reality. | Meinong maintains that there is such an object as the round square only | it does not exist, and it does not even subsist, but nevertheless there | is such an object, and when you say "The round square is a fiction", | he takes it that there is an object "the round square" and there is | a predicate "fiction". No one with a sense of reality would so | analyse that proposition. He would see that the proposition | wants analysing in such a way that you won't have to regard | the round square as a constituent of that proposition. | | To suppose that in the actual world of nature there is a whole set of false | propositions going about is to my mind monstrous. I cannot bring myself | to suppose it. I cannot believe that they are there in the sense in | which facts are there. There seems to me something about the fact | that "Today is Tuesday" on a different level of reality from the | supposition "That today is Wednesday". When I speak of the | proposition "That today is Wednesday" I do not mean the | occurrence in future of a state of mind in which you | think it is Wednesday, but I am talking about the | theory that there is something quite logical, | something not involving mind in any way; and | such a thing as that I do not think you can | take a false proposition to be. I think a | false proposition must, wherever it occurs, | be subject to analysis, be taken to pieces, | pulled to bits, and shown to be simply | separate pieces of one fact in which | the false proposition has been | analysed away. I say that | simply on the ground of | what I should call an | instinct of reality. | | Russell, POLA, pp. 87-88. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 24
| 4.2. What is the Status of 'p' in "I believe 'p'"? (concl.) | | I ought to say a word or two about "reality". It is a vague word, | and most of its uses are improper. When I talk about reality as | I am now doing, I can explain best what I mean by saying that | I mean everything you would have to mention in a complete | description of the world; that will convey to you what | I mean. | | Now I do 'not' think that false propositions would have to be | mentioned in a complete description of the world. False beliefs | would, of course, false suppositions would, and desires for what | does not come to pass, but not false propositions all alone, and | therefore when you, as one says, believe a false proposition, that | cannot be an accurate account of what occurs. | | It is not accurate to say "I believe the proposition 'p'" and | regard the occurrence as a twofold relation between me and 'p'. | The logical form is just the same whether you believe a false or | a true proposition. Therefore in all cases you are not to regard | belief as a two-term relation between yourself and a proposition, | and you have to analyse up the proposition and treat your belief | differently. | | Therefore the belief does not really contain a proposition as a constituent | but only contains the constituents of the proposition as constituents. You | cannot say when you believe, "What is it that you believe?" There is no | answer to that question, i.e. there is not a single thing that you are | believing. "I believe that today is Tuesday." You must not suppose | that "That today is Tuesday" is a single object which I am believing. | That would be an error. That is not the right way to analyse the | occurrence, although that analysis is linguistically convenient, | and one may keep it provided one knows that it is not the truth. | | Russell, POLA, pp. 88-89. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 25
|
4.3. How shall we describe the logical form of a belief? I want to try to get an account of the way that a belief is made up. That is not an easy question at all. You cannot make what I should call a map-in-space of a belief. You can make a map of an atomic fact but not of a belief, for the simple reason that space-relations always are of the atomic sort or complications of the atomic sort. I will try to illustrate what I mean. The point is in connexion with there being two verbs in the judgment and with the fact that both verbs have got to occur as verbs, because if a thing is a verb it cannot occur otherwise than as a verb. Suppose I take ‘A believes that B loves C’. ‘Othello believes that Desdemona loves Cassio’. There you have a false belief. You have this odd state of affairs that the verb ‘loves’ occurs in that proposition and seems to occur as relating Desdemona to Cassio whereas in fact it does not do so, but yet it does occur as a verb, it does occur in the sort of way that a verb should do. I mean that when A believes that B loves C, you have to have a verb in the place where ‘loves’ occurs. You cannot put a substantive in its place. Therefore it is clear that the subordinate verb (i.e. the verb other than believing) is functioning as a verb, and seems to be relating two terms, but as a matter of fact does not when a judgment happens to be false. That is what constitutes the puzzle about the nature of belief. You will notice that whenever one gets to really close quarters with the theory of error one has the puzzle of how to deal with error without assuming the existence of the non-existent. I mean that every theory of error sooner or later wrecks itself by assuming the existence of the non-existent. As when I say ‘Desdemona loves Cassio’, it seems as if you have a non-existent love between Desdemona and Cassio, but that is just as wrong as a non-existent unicorn. So you have to explain the whole theory of judgment in some other way. I come now to this question of a map. Suppose you try such a map as this:
This question of making a map is not so strange as you might suppose because it is part of the whole theory of symbolism. It is important to realize where and how a symbolism of that sort would be wrong: Where and how it is wrong is that in the symbol you have this relationship relating these two things and in the fact it doesn't really relate them. You cannot get in space any occurrence which is logically of the same form as belief. When I say ‘logically of the same form’ I mean that one can be obtained from the other by replacing the constituents of the one by the new terms. If I say ‘Desdemona loves Cassio’ that is of the same form as ‘A is to the right of B’. Those are of the same form, and I say that nothing that occurs in space is of the same form as belief. I have got on here to a new sort of thing, a new beast for our zoo, not another member of our former species but a new species. The discovery of this fact is due to Mr. Wittgenstein. Russell, POLA, pp. 89–91. |
Bertrand Russell, “The Philosophy of Logical Atomism”, pp. 35–155 in The Philosophy of Logical Atomism, edited with an introduction by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 26
| 4.3. How shall we describe the logical form of a belief? (cont.) | | There is a great deal that is odd about belief from a | logical point of view. One of the things that are odd | is that you can believe propositions of all sorts of forms. | I can believe that "This is white" and "Two and two are four". | They are quite different forms, yet one can believe both. The | actual occurrence can hardly be of exactly the same logical form | in those two cases because of the great difference in the forms | of the propositions believed. Therefore it would seem that | belief cannot strictly be logically one in all different | cases but must be distinguished according to the nature | of the proposition that you believe. | | If you have "I believe p" and I believe q" those two facts, if p and q are | not of the same logical form, are not of the same logical form in the sense | I was speaking of a moment ago, that is in the sense that from "I believe p" | you can derive "I believe q" by replacing the constituents of one by the | constituents of the other. | | That means that belief itself cannot be treated as being a proper sort of | single term. Belief will really have to have different logical forms | according to the nature of what is believed. So that the apparent | sameness of believing in different cases is more or less illusory. | | Russell, POLA, p. 91. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 27
| 4.3. How shall we describe the logical form of a belief? (concl.) | | There are really two main things that one wants to notice in this matter that | I am treating of just now. The 'first' is the impossibility of treating the | proposition believed as an independent entity, entering as a unit into the | occurrence of the belief, and the 'other' is the impossibility of putting | the subordinate verb on a level with its terms as an object term in the | belief. That is a point in which I think that the theory of judgment | which I set forth once in print some years ago was a little unduly | simple, because I did then treat the object verb as if one could | put it as just an object like the terms, as if one could put | "loves" on a level with Desdemona and Cassio as a term for | the relation "believe". That is why I have been laying | such an emphasis on this lecture today on the fact | that there are two verbs at least. | | I hope you will forgive the fact that so much of what I say today is tentative | and consists of pointing out difficulties. The subject is not very easy and | it has not been much dealt with or discussed. Practically nobody has until | quite lately begun to consider the problem of the nature of belief with | anything like a proper logical apparatus and therefore one has very | little to help one in any discussion and so one has to be content | on many points at present with pointing out difficulties rather | than laying down quite clear solutions. | | Russell, POLA, pp. 91-92. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 28
| 4.4. The Question of Nomenclature | | What sort of name shall we give to verbs like "believe" | and "wish" and so forth? I should be inclined to call | them "propositional verbs". This is merely a suggested | name for convenience, because they are verbs which have | the 'form' of relating an object to a proposition. As | I have been explaining, that is not what they really do, | but it is convenient to call them propositional verbs. | | Of course you might call them "attitudes", but I should not like that | because it is a psychological term, and although all the instances in | our experience are psychological, there is no reason to suppose that | all the verbs I am talking of are psychological. There is never any | reason to suppose that sort of thing. | | One should always remember Spinoza's infinite attributes of Deity. | It is quite likely that there are in the world the analogues of his | infinite attributes. We have no acquaintance with them, but there is | no reason to suppose that the mental and the physical exhaust the whole | universe, so one can never say that all the instances of any logical sort | of thing are of such and such a nature which is not a logical nature: you | do not know enough about the world for that. Therefore I should not suggest | that all the verbs that have the form exemplified by believing and willing are | psychological. I can only say all I know are. | | Russell, POLA, p. 92. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918.
POLA. Note 29
| 4.4. The Question of Nomenclature (concl.) | | I notice that in my syllabus I said I was going to deal with truth and | falsehood today, but there is not much to say about them specifically | as they are coming in all the time. The thing one first thinks of as | true or false is a proposition, and a proposition is nothing. But a | belief is true or false in the same way as a proposition is, so that | you do have facts in the world that are true or false. | | I said a while back that there was no distinction of true and false among | facts, but as regards that special class of facts that we call "beliefs", | there is, in that sense that a belief which occurs may be true or false, | though it is equally a fact in either case. | | One 'might' call wishes false in the same sense when one wishes | something that does not happen. The truth or falsehood depends | upon the proposition that enters in. | | I am inclined to think that perception, as opposed to belief, does go | straight to the fact and not through the proposition. When you perceive | the fact you do not, of course, have error coming in, because the moment it | is a fact that is your object error is excluded. I think that verification | in the last resort would always reduce itself to the perception of facts. | Therefore the logical form of perception will be different from the logical | form of believing, just because of that circumstance that it is a 'fact' that | comes in. That raises also a number of logical difficulties which I do not | propose to go into, but I think you can see for yourself that perceiving | would also involve two verbs just as believing does. I am inclined to | think that volition differs from desire logically, in a way strictly | analogous to that in which perception differs from belief. But it | would take us too far from logic to discuss this view. | | Russell, POLA, p. 93. | | Bertrand Russell, "The Philosophy of Logical Atomism", pp. 35-155 | in 'The Philosophy of Logical Atomism', edited with an introduction | by David Pears, Open Court, La Salle, IL, 1985. First published 1918. o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
RTOK. Russell's Theory Of Knowledge
RTOK. Note 1
To anchor this thread I will copy out a focal passage from Russell's 1913 manuscript on the “Theory of Knowledge”, that was not published in full until 1984. If there is time, I will then go back and trace more of the development that sets out the background of this excerpt.
RTOK. Note 2
|
We come now to the last problem which has to be treated in this chapter, namely: What is the logical structure of the fact which consists in a given subject understanding a given proposition? The structure of an understanding varies according to the proposition understood. At present, we are only concerned with the understanding of atomic propositions; the understanding of molecular propositions will be dealt with in Part 3. Let us again take the proposition "A and B are similar". It is plain, to begin with, that the 'complex' "A and B being similar", even if it exists, does not enter in, for if it did, we could not understand false propositions, because in their case there is no such complex. It is plain, also, from what has been said, that we cannot understand the proposition unless we are acquainted with A and B and similarity and the form "something and something have some relation". Apart from these four objects, there does not appear, so far as we can see, to be any object with which we need be acquainted in order to understand the proposition. It seems to follow that these four objects, and these only, must be united with the subject in one complex when the subject understands the proposition. It cannot be any complex composed of them that enters in, since they need not form any complex, and if they do, we need not be acquainted with it. But they themselves must all enter in, since if they did not, it would be at least theoretically possible to understand the proposition without being acquainted with them. In this argument, I appeal to the principle that, when we understand, those objects with which we must be acquainted when we understand, and those only, are object-constituents (i.e. constituents other than understanding itself and the subject) of the understanding-complex. (Russell, TOK, pp. 116–117). |
Bertrand Russell, Theory of Knowledge : The 1913 Manuscript, edited by Elizabeth Ramsden Eames in collaboration with Kenneth Blackwell, Routledge, London, UK, 1992. First published, George Allen and Unwin, 1984.
RTOK. Note 3
|
It follows that, when a subject S understands "A and B are similar", "understanding" is the relating relation, and the terms are S and A and B and similarity and R(x, y), where R(x, y) stands for the form "something and something have some relation". Thus a first symbol for the complex will be: This symbol, however, by no means exhausts the analysis of the form of the understanding-complex. There are many kinds of five-term complexes, and we have to decide what the kind is. It is obvious, in the first place, that S is related to the four other terms in a way different from that in which any of the four other terms are related to each other. (It is to be observed that we can derive from our five-term complex a complex having any smaller number of terms by replacing any one or more of the terms by "something". If S is replaced by "something", the resulting complex is of a different form from that which results from replacing any other term by "something". This explains what is meant by saying that S enters in a different way from the other constituents.) It is obvious, in the second place, that R(x, y) enters in a different way from the other three objects, and that "similarity" has a different relation to R(x, y) from that which A and B have, while A and B have the same relation to R(x, y). Also, because we are dealing with a proposition asserting a symmetrical relation between A and B, A and B have each the same relation to "similarity", whereas, if we had been dealing with an asymmetrical relation, they would have had different relations to it. Thus we are led to the following map of our five-term complex:
A o
\ <
^\ *
\ *
% \ *
\ *
% \ R(x, y) *
o------o------> o---------<---------o Similarity
% / ^ * ^
/ | * /
/% | * /
/ |* /
/ % * | /
/ < | /
B o % | /
^ | /
\ % | /
\ | /
\ % | /
\ | /
\ % | /
\ | /
\ % | /
\ | /
\ % | /
\ | /
\%| /
\| /
o
S
In this figure, one relation goes from S to the four objects; one relation goes from R(x, y) to similarity, and another to A and B, while one relation goes from similarity to A and B. This figure, I hope, will help to make clearer the map of our five-term complex. But to explain in detail the exact abstract meaning of the various items in the figure would demand a lengthy formal logical discussion. Meanwhile the above attempt must suffice, for the present, as an analysis of what is meant by "understanding a proposition". (Russell, TOK, pp. 117–118). |
Bertrand Russell, Theory of Knowledge : The 1913 Manuscript, edited by Elizabeth Ramsden Eames in collaboration with Kenneth Blackwell, Routledge, London, UK, 1992. First published, George Allen and Unwin, 1984.
RTOP. Russell's Treatise On Propositions
RTOP. Note 1
September creeps forward on little cheetah's feet, and I cannot say when I will be able to return to these issues in any detail, so for the time being I'll just record what I regard as one significant passage from Russell's paper “On Propositions”.
RTOP. Note 2
| On Propositions: What They Are and How They Mean (1919) | | Let us illustrate the content of a belief | by an example. Suppose I am believing, | but not in words, that "it will rain". | What is happening? | | (1) Images, say, of the visual appearance of rain, | the feeling of wetness, the patter of drops, | interrelated, roughly, as the sensations | would be if it were raining, i.e., there | is a complex 'fact composed of images', | having a structure analogous to that | of the objective fact which would | make the belief true. | | (2) There is 'expectation', i.e., | that form of belief which | refers to the future; | we shall examine | this shortly. | | (3) There is a relation between (1) and (2), | making us say that (1) is "what is expected". | This relation also demands investigation. | | The most important thing about a proposition is that, whether | it consists of images or of words, it is, whenever it occurs, an | actual fact, having a certain analogy -- to be further investigated -- | with the fact which makes it true or false. A word-proposition, apart | from niceties, "means" the corresponding image-proposition, and an | image-proposition has an objective reference dependent upon the | meanings of its constituent images. | | Russell, OP, p. 309. | | Bertrand Russell, |"On Propositions: What They Are And How They Mean" (1919), | pp. 285-320 in 'Logic and Knowledge: Essays, 1901-1950', | edited by Robert Charles Marsh, Routledge, London, UK, 1956.
SABI. Synthetic/Analytic ≟ Boundary/Interior
Let's go back to Quine's topological metaphor: the "web of belief", "fabric of knowledge", or "epistemological field theory" picture, and see if we can extract something that might be useful in our present task, settling on a robust architecture for generic knowledge bases. | 6. Empiricism without the Dogmas | | The totality of our so-called knowledge or beliefs, from the most | casual matters of geography and history to the profoundest laws of | atomic physics or even of pure mathematics and logic, is a man-made | fabric which impinges on experience only along the edges. Or, to | change the figure, total science is like a field of force whose | boundary conditions are experience. A conflict with experience at | the periphery occasions readjustments in the interior of the field. | Truth values have to be redistributed over some of our statements. | Re-evaluation of some statements entails re-evaluation of others, | because of their logical interconnections -- the logical laws | being in turn simply certain further statements of the system, | certain further elements of the field. Having re-evaluated one | statement we must re-evaluate some others, which may be statements | logically connected with the first or may be the statements of logical | connections themselves. But the total field is so underdetermined by | its boundary conditions, experience, that there is much latitude of | choice as to what statements to re-evaluate in the light of any | single contrary experience. No particular experiences are | linked with any particular statements in the interior of | the field, except indirectly through considerations | of equilibrium affecting the field as a whole. | | Quine, "Two Dogmas", pp. 42-43. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980. | | http://suo.ieee.org/ontology/msg04935.html There are some things that I am not trying to do. One of them is reducing natural language to math, and another is reducing math to natural language. So I tend to regard the usual sorts of examples, Bachelors and Hesperus and Phosphorus and so on, as being useful for stock illustrations only so long as nobody imagines that all we do with our natural languages can really be ruled that way. The semantics of natural language is more like the semantics of music, and it would take many octaves of 8-track tapes just to keep track of all the meaning that is being layered into it. So let me resort to a mathematical example, where Frege really lived, and where all of this formal semantics stuff really has Frege's ghost of a chance of actually making sense someday, if hardly come what may. There is a "clear" distinction between equations like 2 = 0 and x = x, that are called "noncontingent equations", because they have constant truth values for all values of whatever variables they may have, and equations like x^2 + 1 = 0, that are called "contingent equations", because they are have different truth values for different values of their variables. But wait a minute, you or somebody says, the equation x^2 + 1 = 0 is false for all values of its variables, and of course I remind you that it does have solutions in the complex domain C. So models of numbers really are as fleeting as models of cars. And this explains the annoying habit that mathematicians have of constantly indexing formulas with the names of the mathematical domains over which they are intended to be interpreted as having their values. And then someone else reminds us that 2 = 0 is true mod 2. Those are the types of examples that I would like to keep in mind when we examime the relativity of the analytic/synthetic distinction, or, to put a finer point on this slippery slope, the contingency of the noncontingent/contingent distinction.
SYNF. Syntactic Fallacy
A syntactic fallacy is an error of mistaking the properties of signs for the properties of objects (that they may or may not have). For example, from the fact that signs exist, are actual, possible, necessary, or related in various syntactic ways, nothing follows about the existence, actuality, possibility, necessity, or objective relationships of their objects, since it is conceivable that a sign does not denote anything at all. Notice that a syntactic fallacy is an error even when signs are icons, that is, when they propose a denotation of their objects by virtue of sharing certain properties with them. So watch out for that ...
TDOE. Quine's Two Dogmas Of Empiricism
TDOE. Note 1
| Two Dogmas of Empiricism | | Modern empiricism has been conditioned in large part by two dogmas. | One is a belief in some fundamental cleavage between truths which | are 'analytic', or grounded in meanings independently of matters | of fact, and truths which are 'synthetic', or grounded in fact. | The other dogma is 'reductionism': the belief that each | meaningful statement is equivalent to some logical | construct upon terms which refer to immediate | experience. Both dogmas, I shall argue, are | ill-founded. One effect of abandoning them | is, as we shall see, a blurring of the | supposed boundary between speculative | metaphysics and natural science. | Another effect is a shift | toward pragmatism. | | Quine, "Two Dogmas", p. 20. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 2
| 1. Background for Analyticity | | Kant's cleavage between analytic and synthetic truths | was foreshadowed in Hume's distinction between relations | of ideas and matters of fact, and in Leibniz's distinction | between truths of reason and truths of fact. Leibniz spoke | of the truths of reason as true in all possible worlds. | Picturesqueness aside, this is to say that the truths | of reason are those which could not possibly be false. | In the same vein we hear analytic statements defined as | statements whose denials are self-contradictory. But this | definition has small explanatory value; for the notion of | self-contradictoriness, in the quite broad sense needed for | this definition of analyticity, stands in exactly the same | need of clarification as does the notion of analyticity | itself. The two notions are the two sides of a single | dubious coin. | | Kant conceived of an analytic statement as one that attributes to its | subject no more than is already conceptually contained in the subject. | This formulation has two shortcomings: it limits itself to statements of | subject-predicate form, and it appeals to a notion of containment which is | left at a metaphorical level. But Kant's intent, evident more from the use | he makes of the notion of analyticity than from his definition of it, can be | restated thus: a statement is analytic when it is true by virtue of meanings | and independently of fact. Pursuing this line, let us examine the concept of | 'meaning' which is presupposed. | | Quine, "Two Dogmas", pp. 20-21. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 3
| 1. Background for Analyticity (cont.) | | Meaning, let us remember, is not to be identified with naming. | Frege's example of "Evening Star" and "Morning Star", and Russell's | of "Scott" and "the author of 'Waverley'", illustrate that terms can | name the same thing but differ in meaning. The distinction between | meaning and naming is no less important at the level of abstract | terms. The terms "9" and "the number of the planets" name one | and the same abstract entity but presumably must be regarded as | unlike in meaning; for astronomical observation was needed, and | not mere reflection on meanings, to determine the sameness of the | entity in question. | | The above examples consists of singular terms, concrete and | abstract. With general terms, or predicates, the situation | is somewhat different but parallel. Whereas a singular term | purports to name an entity, abstract or concrete, a general | term does not; but a general term is 'true of' an entity, | or of each of many, or of none. The class of all entities | of which a general term is true is called the 'extension' | of the term. Now paralleling the contrast between the | meaning of a singular term and the entity named, we | must distinguish equally between the meaning of a | general term and its extension. The general terms | "creature with a heart" and "creature with kidneys", | for example, are perhaps alike in extension but unlike | in meaning. | | Quine, "Two Dogmas", p. 21. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 4
| 1. Background for Analyticity (cont.) | | Confusion of meaning with extension, in the case of general terms, | is less common than confusion of meaning with naming in the case | of singular terms. It is indeed a commonplace in philosophy to | oppose intension (or meaning) to extension, or, in a variant | vocabulary, connotation to denotation. | | The Aristotelian notion of essence was the forerunner, no doubt, | of the modern notion of intension or meaning. For Aristotle it | was essential in men to be rational, accidental to be two-legged. | But there is an important difference between this attitude and the | doctrine of meaning. From the latter point of view it may indeed | be conceded (if only for the sake of argument) that rationality is | involved in the meaning of the word "man" while two-leggedness is | not; but two-leggedness may at the same time be viewed as involved | in the meaning of "biped" while rationality is not. Thus from the | point of view of the doctrine of meaning it makes no sense to say | of the actual individual, who is at once a man and a biped, that | his rationality is essential and his two-leggedness accidental | or vice versa. Things had essences, for Aristotle, but only | linguistic forms have meanings. Meaning is what essence | becomes when it is divorced from the object of reference | and wedded to the word. | | Quine, "Two Dogmas", pp. 21-22. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 5
| 1. Background for Analyticity (cont.) | | For the theory of meaning a conspicuous question is the nature | of its objects: what sort of things are meanings? A felt need | for meant entities may derive from an earlier failure to appreciate | that meaning and reference are distinct. Once the theory of meaning | is sharply separated from the theory of reference, it is a short step | to recognizing as the primary business of the theory of meaning simply | the synonymy of linguistic forms and the analyticity of statements; | meanings themselves, as obscure intermediary entities, may well be | abandoned. | | The problem of analyticity then confronts us anew. Statements which are | analytic by general philosophical acclaim are not, indeed, far to seek. | They fall into two classes. Those of the first class, which may be | called 'logically true', are typified by: | | (1) No unmarried man is married. | | The relevant feature of this example is that it not merely | is true as it stands, but remains true under any and all | reinterpretations of "man" and "married". If we suppose | a prior inventory of 'logical' particles, comprising "no", | "un-", "not", "if", "then", "and", etc., then in general | a logical truth is a statement which is true and remains | true under all reinterpretations of its components than | than the logical particles. | | But there is also a second class of analytic statements, | typified by: | | (2) No bachelor is married. | | The characteristic of such a statement is that it can be | turned into a logical truth by putting synonyms for synonyms; | thus (2) can be turned into (1) by putting "unmarried man" for | its synonym "bachelor". We still lack a proper characterization | of this second class of analytic statements, and therewith of | analyticity generally, inasmuch as we have had in the above | description to lean on a notion of "synonymy" which is no | less in need of clarification than analyticity itself. | | Quine, "Two Dogmas", pp. 22-23. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 6
| 1. Background for Analyticity (concl.) | | In recent years Carnap has tended to explain analyticity by appeal to | what he calls state-descriptions. A state-description is any exhaustive | assignment of truth values to the atomic, or noncompound, statements of | the language. All other statements of the language are, Carnap assumes, | built up of their component clauses by means of familiar logical devices, | in such a way that the truth value of any complex statement is fixed for | each state-description by specifiable logical laws. A statement is then | explained as analytic when it comes out true under every state-description. | This account is an adaptation of Leibniz's "true in all possible worlds". | But note that this version of analyticity serves its purpose only if the | atomic statements of the language are, unlike "John is a bachelor" and | "John is married", mutually independent. Otherwise there would be a | state-description which assigned truth to "John is a bachelor" and to | "John is married", and consequently "No bachelors are married" would | turn out synthetic rather than analytic under the proposed criterion. | Thus the criterion of analyticity in terms of state-descriptions | serves only for languages devoid of extralogical synonym-pairs, | such as "bachelor" and "unmarried man" -- synonym-pairs of the | type which give rise to the "second class" of analytic statements. | The criterion in terms of state-descriptions is a reconstruction | at best of logical truth, not of analyticity. | | I do not mean to suggest that Carnap is under any illusions on this | point. His simplified model language with its state-descriptions | is aimed primarily not at the general problem of analyticity but | at another purpose, the clarification of probability and induction. | Our problem, however, is analyticity; and here the major difficulty | lies not in the first class of analytic statements, the logical truths, | but rather in the second class, which depends on the notion of synonymy. | | Quine, "Two Dogmas", pp. 23-24. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 7
| 2. Definition | | There are those who find it soothing to say that the analytic statements | of the second class reduce to those of the first class, the logical truths, | by 'definition'; "bachelor", for example, is 'defined' as "unmarried man". | But how do we find that "bachelor" is defined as "unmarried man"? Who | defined it thus, and when? Are we to appeal to the nearest dictionary, | and accept the lexicographer's formulation as law? Clearly this would | be to put the cart before the horse. The lexicographer is an empirical | scientist, whose business is the recording of antecedent facts; and if | he glosses "bachelor" as "unmarried man" it is because of his belief that | there is a relation of synonymy between those forms, implicit in general or | preferred usage prior to his own work. The notion of synonymy presupposed | here has still to be clarified, presumably in terms relating to linguistic | behavior. Certainly the "definition" which is the lexicographer's report | of an observed synonymy cannot be taken as the ground of the synonymy. | | Quine, "Two Dogmas", p. 24. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 8
| 2. Definition (cont.) | | Definition is not, indeed, an activity exclusively of philologists. | Philosophers and scientists frequently have occasion to "define" | a recondite term by paraphrasing it into terms of a more familiar | vocabulary. But ordinarily such a definition, like the philologist's, | is pure lexicography, affirming a relation of synonymy antecedent to | the exposition in hand. | | Just what it means to affirm synonymy, just what the interconnections | may be which are necessary and sufficient in order that two linguistic | forms be properly describable as synonymous, is far from clear; but, | whatever these interconnections may be, ordinarily they are grounded | in usage. Definitions reporting selected instances of synonymy come | then as reports upon usage. | | There is also, however, a variant type of definitional activity which does | not limit itself to the reporting of pre-existing synonymies. I have in | mind what Carnap calls 'explication' -- an activity to which philosophers | are given, and scientists also in their more philosophical moments. In | explication the purpose is not merely to paraphrase the definiendum into | an outright synonym, but actually to improve upon the definiendum by | refining or supplementing its meaning. But even explication, though | not merely reporting a pre-existing synonymy between definiendum and | definiens, does rest nevertheless on 'other' pre-existing synonymies. | The matter might be viewed as follows. Any word worth explicating | has some contexts which, as wholes, are clear and precise enough | to be useful; and the purpose of explication is to preserve the | usage of these favored contexts while sharpening the usage of | other contexts. In order that a given definition be suitable | for purposes of explication, therefore, what is required is not | that the definiendum in its antecedent usage be synonymous with | the definiens, but just that each of these favored contexts of | the definiendum, taken as a whole in its antecedent usage, be | synonymous with the corrsponding context of the definiens. | | Two alternative definientia may be equally appropriate for the purposes | of a given task of explication and yet not be synonymous with each other; | for they may serve interchangeably within the favored contexts but diverge | elsewhere. By cleaving to one of these definientia rather than the other, | a definition of explicative kind generates, by fiat, a relation of synonymy | between definiendum and definiens which did not hold before. But such a | definition still owes its explicative function, as seen, to pre-existing | synonymies. | | Quine, "Two Dogmas", pp. 24-25. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 9
| 2. Definition (cont.) | | There does, however, remain still an extreme sort of definition | which does not hark back to prior synonymies at all: namely, | the explicitly conventional introduction of novel notations | for purposes of sheer abbreviation. Here the definiendum | becomes synonymous with the definiens simply because it | has been created expressly for the purpose of being | synonymous with the definiens. Here we have a | really transparent case of synonymy created | by definition; would that all species of | synonymy were as intelligible. For the | rest, definition rests on synonymy | rather than explaining it. | | Quine, "Two Dogmas", pp. 25-26. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 10
| 2. Definition (concl.) | | The word "definition" has come to have a dangerously reassuring sound, | owing no doubt to its frequent occurrence in logical and mathematical | writings. We shall do well to digress now into a brief appraisal of | the role of definition in formal work. | | In logical and mathematical systems either of two mutually antagonistic | types of economy may be striven for, and each has its peculiar practical | utility. On the one hand we may seek economy of practical expression -- | ease and brevity in the statement of multifarious relations. This sort | of economy calls usually for distinctive concise notations for a wealth | of concepts. Second, however, and oppositely, we may seek economy in | grammar and vocabulary; we may try to find a minimum of basic concepts | such that, once a distinctive notation has been appropriated to each of | them, it becomes possible to express any desired further concept by mere | combination and iteration of our basic notations. This second sort of | economy is impractical in one way, since a poverty in basic idioms tends | to a necessary lengthening of discourse. But it is practical in another | way: it greatly simplifies theoretical discourse 'about' the language, | through minimizing the terms and the forms of construction wherein the | language consists. | | Both sorts of economy, though prima facie incompatible, are valuable in | their separate ways. The custom has consequently arisen of combining | both sorts of economy by forging in effect two langauges, the one | a part of the other. The inclsuive language, though redundant | in grammar and vocabulary, is economical in message lengths, | while the part, called primitive notation, is economical in | grammar and vocabulary. Whole and part are correlated by | rules of translation whereby each idiom not in primitive | notation is equated to some complex built up of primitive | notation. These rules of translation are the so-called | 'definitions' which appear in formalized systems. They | are best viewed not as adjuncts to one language but as | correlations between two languages, the one a part of | the other. | | But these correlations are not arbitrary. They are supposed | to show how the primitive notations can accomplish all purposes, | save brevity and convenience, of the redundant language. Hence | the definiendum and its definiens may be expected, in each case, | to be related in one or another of the three ways lately noted. | The definiens may be a faithful paraphrase of the definiendum | into the narrower notation, preseving a direct synonymy* as | of antecedent usage; or the definiens may, in the spirit | of explication, improve upon the antecedent usage of the | definiendum; or finally, the definiendum may be a newly | created notation, newly endowed with meaning here and now. | | In formal and informal work alike, thus, we find | that definition -- except in the extreme case of the | explicitly conventional introduction of new notations -- | hinges on prior relations of synonymy. Recognizing then | that the notion of definition does not hold the key to | synonymy and analyticity, let us look further into | synonymy and say no more of definition. | |*According to an important variant sense of "definition", the relation | preserved may be the weaker relation of mere agreement in reference; | see below, p. 132. But definition in this sense is better ignored in | the present connection, being irrelevant to the question of synonymy. | | Quine, "Two Dogmas", pp. 26-27. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 11
| 3. Interchangeability | | A natural suggestion, deserving close examination, is that the synonymy | of two linguistic forms consists simply in their interchangeability in | all contexts without change of truth value -- interchangeability, in | Leibniz's phrase 'salva veritate'. Note that synonyms so conceived | need not even be free from vagueness, as long as the vaguenesses | match. | | But it is not quite true that the synonyms "bachelor" and "unmarried man" | are everywhere interchangeable 'salva veritate'. Truths which become false | under substitution of "unmarried man" for "bachelor" are easily constructed | with the help of "bachelor of arts" or "bachelor's buttons"; also with the | help of quotation, thus: | | "Bachelor" has less than ten letters. | | Such counterinstances can, however, be set aside by treating | the phrases "bachelor of arts" and "bachelor's buttons" and the | quotation '"bachelor"' each as a single indivisible word and then | stipulating that the interchangeability 'salva veritate' which | is to be the touchstone of synonymy is not supposed to apply | to fragmentary occurrences inside of a word. This account of | synonymy, supposing it acceptable on other counts, has indeed | the drawback of appealing to a prior conception of "word" which | can be counted on to present difficulties of formulation in its | turn. Nevertheless some progress might be claimed in having | reduced the problem of synonymy to a problem of wordhood. | Let us pursue this line a bit, taking "word" for granted. | | Quine, "Two Dogmas", pp. 27-28. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 12
| 3. Interchangeability (cont.) | | The question remains whether interchangeability | 'salva veritate' (apart from occurrences within words) | is a strong enough condition for synonymy, or whether, | on the contrary, some heteronymous expressions might be thus | interchangeable. Now let us be clear that we are not concerned | here with synonymy in the sense of complete identity in psychological | associations or poetic quality; indeed no two expressions are synonymous | in such a sense. We are concerned only with what may be called 'cognitive' | synonymy. Just what this is cannot be said without successfully finishing the | present study; but we know something about it from the need which arose for | it in connection with analyticity in Section 1. The sort of synonymy needed | there was merely such that any analytic statement could be turned into a | logical truth by putting synonyms for synonyms. Turning the tables and | assuming analyticity, indeed, we could explain cognitive synonymy of | terms as follows (keeping to the familiar example): to say that | "bachelor" and "unmarried man" are cognitively synonymous is | to say no more or less than that the statement: | | (3) All and only bachelors are unmarried men | | is analytic.* | |*This is cognitive synonymy in a primary, broad sense. Carnap ([3], | pp. 56ff) and Lewis ([2], pp. 83ff) have suggested how, once this | notion is at hand, a narrower sense of cognitive synonymy which | is preferable for some purposes can in turn be derived. But | this special ramification of concept-building lies aside | from the present purposes and must not be confused with | the broad sort of cognitive synonymy here concerned. | | Quine, "Two Dogmas", pp. 28-29. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 13
| 3. Interchangeability (cont.) | | What we need is an account of cognitive synonymy | not presupposing analyticity -- if we are to explain | analyticity conversely with help of cognitive synonymy | as undertaken in Section 1. And indeed such an independent | account of cognitive synonymy is at present up for consideration, | namely, interchangeability 'salva veritate' everywhere except within | words. The question before us, to resume the thread at last, is whether | such interchangeability is a sufficient condition for cognitive synonymy. | We can quickly assure ourselves that it is, by examples of the following | sort. The statement: | | (4) Necessarily all and only bachelors are bachelors | | is evidently true, even supposing "necessarily" so narrowly construed as | to be truly applicable only to analytic statements. Then, if "bachelor" | and "unmarried man" are interchangeable 'salva veritate', the result: | | (5) Necessarily all and only bachelors are unmarried men | | of putting "unmarried man" for an occurrence of "bachelor" in (4) must, | like (4), be true. But to say that (5) is true is to say that (3) is | analytic, and hence that "bachelor" and "unmarried man" are cognitively | synonymous. | | Let us see what there is about the above argument that gives it its air | of hocus-pocus. The condition of interchangeability 'salva veritate' | varies in its force with variations in the richness of the language | at hand. The above argument supposes we are working with a language | rich enough to contain the adverb "necessarily", this adverb being so | construed as to yield truth when and only when applied to an analytic | statement. But can we condone a language which contains such an adverb? | Does the adverb really make sense? To suppose that it does is to suppose | that we have already made satisfactory sense of "analytic". Then what are | we so hard at work on right now? | | Our argument is not flatly circular, but something like it. | It has the form, figuratively speaking, of a closed curve | in space. | | Quine, "Two Dogmas", pp. 29-30. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 14
| 3. Interchangeability (cont.)
|
| Interchangeability 'salva veritate' is meaningless until relativized to
| a language whose extent is specified in relevant respects. Suppose now
| we consider a language containing just the following materials. There
| is an indefinitely large stock of one-place predicates, (for example,
| "F" where "Fx" means that x is a man) and many-place predicates (for
| example, "G" where "Gxy" means that x loves y), mostly having to
| do with extralogical subject matter. The rest of the language
| is logical. The atomic sentences consist each of a predicate
| followed by one or more variables "x", "y", etc.; and the
| complex sentences are built up of the atomic ones by truth
| functions ("not", "and", "or", etc.) and quantification.
| In effect such a language enjoys the benefits also of
| descriptions and indeed singular terms generally,
| these being contextually definable in known ways.
| Even abstract singular terms naming classes,
| classes of classes, etc., are contextually
| definable in case the assumed stock of
| predicates includes the two-place
| predicate of class membership.
| Such a language can be adequate
| to classical mathematics and
| indeed to scientific discourse
| generally, except in so far as
| the latter involves debatable
| devices such as contrary-to-fact
| conditionals or modal adverbs like
| "necessarily". Now a language of this
| type is extensional, in this sense: any
| two predicates which agree extensionally
| (that is, are true of the same objects)
| are interchangeable 'salva veritate'.
|
| Quine, "Two Dogmas", p. 30.
|
| W.V. Quine,
|"Two Dogmas of Empiricism", 'Philosophical Review', January 1951.
| Reprinted as pages 20-46 in 'From a Logical Point of View',
| 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 15
| 3. Interchangeability (cont.) | | In an extensional language, therefore, interchangeability | 'salva veritate' is no assurance of cognitive synonymy of | the desired type. That "bachelor" and "unmarried man" are | interchangeable 'salva veritate' in an extensional language | assures us of no more than that (3) is true. There is no | assurance here that the extensional agreement of "bachelor" | and "unmarried man" rests on meaning rather than merely on | accidental matters of fact, as does the extensional agreement | of "creature with a heart" and "creature with kidneys". | | For most purposes extensional agreement is the nearest approximation | to synonymy we need care about. But the fact remains that extensional | agreement falls far short of cognitive synonymy of the type required for | explaining analyticity in the manner of Section 1. The type of cognitive | synonymy required there is such as to equate the synonymy of "bachelor" | and "unmarried man" with the analyticity of (3), not merely with the | truth of (3). | | So we must recognize that interchangeability 'salva veritate', | if construed in relation to an extensional language, is not | a sufficient condition of cognitive synonymy in the sense | needed for deriving analyticity in the manner of Section 1. | If a language contains an intensional adverb "necessarily" in | the sense lately noted, or other particles to the same effect, | then interchangeability 'salva veritate' in such a language | does afford a sufficient condition of cognitive synonymy; | but such a language is intelligible only in so far as the | notion of analyticity is already understood in advance. | | Quine, "Two Dogmas", p. 31. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 16
| 3. Interchangeability (concl.) | | The effort to explain cognitive synonymy first, for the sake | of deriving analyticity from it afterward as in Section 1, is | perhaps the wrong approach. Instead we might try explaining | analyticity somehow without appeal to cognitive synonymy. | Afterward we could doubtless derive cognitive synonymy from | analyticity satisfactorily enough if desired. We have seen | that cognitive synonymy of "bachelor" and "unmarried man" can | be explained as analyticity of (3). The same explanation works | for any pair of one-place predicates, of course, and it can | be extended in obvious fashion to many-place predicates. | Other syntactical categories can also be accommodated in | fairly parallel fashion. Singular terms may be said to be | cognitively synonymous when the statement of identity formed | by putting "=" between them is analytic. Statements may be said | simply to be cognitively synonymous when their biconditional (the | result of joining them by "if and only if") is analytic. If we | care to lump all categories into a single formulation, at the | expense of assuming again the notion of "word" which was | appealed to early in this section, we can describe any two | linguistic forms as cognitively synonymous when the two forms | are interchangeable (apart from occurrences within "words") | 'salva' (no longer 'veritate' but) 'analyticitate'. Certain | technical questions arise, indeed, over cases of ambiguity | or homonymy; let us not pause for them, however, for we | are already digressing. Let us rather turn our backs | on the problem of synonymy and address ourselves | anew to that of analyticity. | | Quine, "Two Dogmas", pp. 31-32. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 17
| 4. Semantical Rules | | Analyticity at first seemed most naturally definable by appeal | to a realm of meanings. On refinement, the appeal to meanings | gave way to an appeal to synonymy or definition. But definition | turned out to be a will-o'-the-wisp, and synonymy turned out to be | best understood only by dint of a prior appeal to analyticity itself. | So we are back at the problem of analyticity. | | I do not know whether the statement "Everything green is extended" | is analytic. Now does my indecision over this example really betray | an incomplete understanding, an incomplete grasp of the "meanings", | of "green" and "extended"? I think not. The trouble is not with | "green" or "extended", but with "analytic". | | It is often hinted that the difficulty in separating analytic | statements from synthetic ones in ordinary language is due to | the vagueness of ordinary language and that the distinction is | clear when we have a precise artificial language with explicit | "semantical rules". This, however, as I shall now attempt to | show, is a confusion. | | Quine, "Two Dogmas", p. 32. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 18
| 4. Semantical Rules (cont.) | | The notion of analyticity about which we are worrying is a purported | relation between statements and languages: a statement S is said to | be 'analytic for' a language L, and the problem is to make sense of | this relation generally, that is, for variable "S" and "L". The | gravity of this problem is not perceptibly less for artificial | languages than for natural ones. The problem of making sense | of the idiom "S is analytic for L", with variable "S" and "L", | retains its stubbornness even if we limit the range of the | variable "L" to artificial languages. Let me now try to | make this point evident. | | For artificial languages and semantical rules we look naturally | to the writings of Carnap. His semantical rules take various forms, | and to make my point I shall have to distinguish certain of the forms. | Let us suppose, to begin with, an artificial language L_0 whose semantical | rules have the form explicitly of a specification, by recursion or otherwise, | of all the analytic statements of L_0. The rules tell us that such and such | statements, and only those, are the analytic statements of L_0. Now here | the difficulty is simply that the rules contain the word "analytic", | which we do not understand! We understand what expressions the | rules attribute analyticity to, but we do not understand what | the rules attribute to those expressions. In short, before | we can understand a rule which begins "A statement S is | analytic for language L_0 if and only if ...", we must | understand the general relative term "analytic for"; | we must understand "S is analytic for L" where "S" | and "L" are variables. | | Alternatively we may, indeed, view the so-called rule as a conventional | definition of a new simple symbol "analytic-for-L_0", which might better | be written untendentiously as "K" so as not to seem to throw light on the | interesting word "analytic". Obviously any number of classes K, M, N, etc. | of statements of L_0 can be specified for various purposes or for no purpose; | what does it mean to say that K, as against M, N, etc., is the class of the | "analytic" statements of L_0? | | By saying what statements are analytic for L_0 we explain | "analytic-for-L_0" but not "analytic", not "analytic for". | We do not begin to explain the idiom "S is analytic for L" | with variable "S" and "L", even if we are content to limit | the range of "L" to the realm of artificial languages. | | Quine, "Two Dogmas", pp. 33-34. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 19
| 4. Semantical Rules (cont.) | | Actually we do know enough about the intended significance of | "analytic" to know that analytic statements are supposed to | be true. Let us then turn to a second form of semantical | rule, which says not that such and such statements are | analytic but simply that such and such statements are | included among the truths. Such a rule is not subject | to the criticism of containing the un-understood word | "analytic"; and we may grant for the sake of argument | that there is no difficulty over the broader term "true". | A semantical rule of this second type, a rule of truth, | is not supposed to specify all the truths of the language; | it merely stipulates, recursively or otherwise, a certain | multitude of statements which, along with others unspecified, | are to count as true. Such a rule may be conceded to be quite | clear. Derivatively, afterward, analyticity can be demarcated | thus: a statement is analytic if it is (not merely true but) | true according to the semantical rule. | | Still there is really no progress. Instead of appealing to an unexplained | word "analytic", we are now appealing to an unexplained phrase "semantical | rule". Not every true statement which says that the statements of some | class are true can count as a semantical rule -- otherwise 'all' truths | would be "analytic" in the sense of being true according to semantical | rules. Semantical rules are distinguishable, apparently, only by the | fact of appearing on a page under the heading "Semantical Rules"; | and this heading is itself then meaningless. | | We can say indeed that a statement is 'analytic-for-L_0' if and | only if it is true according to such and such specifically appended | "semantical rules", but then we find ourselves back at essentially the | same case which was originally discussed: "S is analytic-for-L_0" if and | only if ...". Once we seek to explain "S is analytic for L" generally for | variable "L" (even allowing limitation of "L" to artificial languages), | the explanation "true according to the semantical rules of L" is | unavailing; for the relative term "semantical rule of" is as | much in need of clarification, at least, as "analytic for". | | Quine, "Two Dogmas", p. 34. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 20
| 4. Semantical Rules (cont.) | | It may be instructive to compare the notion of semantical rule with that | of postulate. Relative to a given set of postulates, it is easy to say | what a postulate is: it is a member of the set. Relative to a given | set of semantical rules, it is equally easy to say what a semantical | rule is. But given simply a notation, mathematical or otherwise, | and indeed as thoroughly understood a notation as you please in | point of the translations or truth conditions of its statements, | who can say which of its true statements rank as postulates? | Obviously the question is meaningless -- as meaningless as | asking which points in Ohio are starting points. Any finite | (or effectively specifiable infinite) selection of statements | (preferably true ones, perhaps) is as much 'a' set of postulates | as any other. The word "postulate" is significant only relative | to an act of inquiry; we apply the word to a set of statements just | in so far as we happen, for the year or the moment, to be thinking of | those statements in relation to the statements which can be reached from | them by some set of transformations to which we have seen fit to direct our | attention. Now the notion of semantical rule is as sensible and meaningful as | that of postulate, if conceived in a similarly relative spirit -- relative, this | time, to one or another particular enterprise of schooling unconversant persons | in sufficient conditions for truth of statements of some natural or artificial | language L. But from this point of view no one signalization of a subclass | of the truths of L is intrinsically more a semantical rule than another; | and, if "analytic" means "true by semantical rules", no one truth of L | is analytic to the exclusion of another.* | |*The foregoing paragraph was not part of the present essay as | originally published. It was prompted by Martin [R.M. Martin, | "On 'Analytic'", 'Philosophical Studies', vol. 3 (1952), 42-47], | as was the end of Essay 7. | | Quine, "Two Dogmas", p. 35. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 21
| 4. Semantical Rules (concl.) | | It might conceivably be protested that an artificial language L | (unlike a natural one) is a language in the ordinary sense 'plus' | a set of explicit semantical rules -- the whole constituting, let | us say, an ordered pair; and that the semantical rules of L then | are specifiable simply as the second component of the pair L. But, | by the same token and more simply, we might construe an artificial | language L outright as an ordered pair whose second component is the | class of its analytic statements; and then the analytic statements of L | become specifiable simply as the statements in the second component of L. | Or better still, we might just stop tugging at our bootstraps altogether. | | Not all the explanations of analyticity known to Carnap | and his readers have been covered explicitly in the above | considerations, but the extension to other forms is not hard | to see. Just one additional factor should be mentioned which | sometimes enters: sometimes the semantical rules are in effect | rules of translation into ordinary language, in which case the | analytic statements of the artificial language are in effect | recognized as such from the analyticity of their specified | translations in ordinary language. Here certainly there | can be no thought of an illumination of the problem of | analyticity from the side of the artificial language. | | From the point of view of the problem of analyticity the notion of an | artificial language with semantical rules is a 'feu follet par excellence'. | Semantical rules determining the analytic statements of an artificial language | are of interest only in so far as we already understand the notion of analyticity; | they are of no help in gaining this understanding. | | Appeal to hypothetical languages of an artificially simple | kind could conceivably be useful in clarifying analyticity, | if the mental or behavioral or cultural factors relevant to | analyticity -- whatever they may be -- were somehow sketched | into the simplified model. But a model which takes analyticity | merely as an irreducible character is unlikely to throw light on | the problem of explicating analyticity. | | It is obvious that truth in general depends on both language and extralinguistic | fact. The statement "Brutus killed Caesar" would be false if the world had | been different in certain ways, but it would also be false if the word | "killed" happened rather to have the sense of "begat". Thus one is | tempted to suppose in general that the truth of a statement is | somehow analyzable into a linguistic component and a factual | component. Given this supposition, it next seems reasonable | that in some statements the factual component should be null; | and these are the analytic statements. But, for all its | a priori reasonableness, a boundary between analytic | and synthetic statements simply has not been drawn. | That there is such a distinction to be drawn at | all is an unempirical dogma of empiricists, | a metaphysical article of faith. | | Quine, "Two Dogmas", pp. 35-37. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 22
| 5. The Verification Theory and Reductionism | | In the course of these somber reflections we have taken a dim view first | of the notion of meaning, then of the notion of cognitive synonymy, and | finally of the notion of analyticity. But what, it may be asked, of | the verification theory of meaning? This phrase has established | itself so firmly as a catchword of empiricism that we should be | very unscientific indeed not to look beneath it for a possible | key to the problem of meaning and the associated problems. | | The verification theory of meaning, which has been conspicuous in the | literature from Peirce onward, is that the meaning of a statement is | the method of empirically confirming or infirming it. An analytic | statement is that limiting case which is confirmed no matter what. | | As urged in Section 1, we can as well pass over the question of | meanings as entities and move straight to sameness of meaning, | or synonymy. Then what the verification theory says is that | statements are synonymous if and only if they are alike in | point of method of empirical confirmation or infirmation. | | This is an account of cognitive synonymy not of linguistic forms generally, | but of statements.* However, from the concept of synonymy of statements | we could derive the concept of synonymy for other linguistic forms, by | considerations somewhat similar to those at the end of Section 3. | Assuming the notion of "word", indeed, we could explain any | two forms as synonymous when the putting of one form for | an occurrence of the other in any statement (apart from | occurrences within "words") yields a synonymous statement. | Finally, given the concept of synonymy thus for linguistic | forms generally, we could define analyticity in terms of | synonymy and logical truth as in Section 1. For that | matter, we could define analyticity more simply in | terms of just synonymy of statements together with | logical truth; it is not necessary to appeal to | synonymy of linguistic forms other than statements. | For a statement may be described as analytic simply | when it is synonymous with a logically true statement. | |*The doctrine can indeed be formulated with terms rather than statements as the | units. Thus Lewis describes the meaning of a term as "'a criterion in mind', | by reference to which one is able to apply or refuse to apply the expression | in question in the case of presented, or imagined, things or situations" | [C.I. Lewis, 'An Analysis of Knowledge and Valuation', Open Court, LaSalle, | IL, 1946, p. 133]. -- For an instructive account of the vicissitudes of | the verification theory of meaning, centered however on the question | of meaning'fulness' rather than synonymy and analyticity, see Hempel. | | Quine, "Two Dogmas", pp. 37-38. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 23
| 5. The Verification Theory and Reductionism (cont.) | | So, if the verification theory can be accepted as an adequate account | of statement synonymy, the notion of analyticity is saved after all. | However, let us reflect. Statement synonymy is said to be likeness | of method of empirical confirmation or infirmation. Just what are | these methods which are to be compared for likeness? What, in | other words, is the nature of the relation between a statement | and the experiences which contribute to or detract from its | confirmation? | | The most naive view of the relation is that it is one of direct report. | This is 'radical reductionism'. Every meaningful statement is held to be | translatable into a statement (true or false) about immediate experience. | Radical reductionism, in one form or another, well antedates the verification | theory of meaning explicitly so called. Thus Locke and Hume held that every | idea must either originate directly in sense experience or else be compounded | of ideas thus originating; and taking a hint from Tooke we might rephrase | this doctrine in semantical jargon by saying that a term, to be significant | at all, must be either a name of a sense datum or a compound of such names or | an abbreviation of such a compound. So stated, the doctrine remains ambiguous | as between sense data as sensory events and sense data as sensory qualities; | and it remains vague as to the admissible ways of compounding. Moreover, the | doctrine is unnecessarily and intolerably restrictive in the term-by-term | critique which it imposes. More reasonably, and without yet exceeding | the limits of what I have called radical reductionism, we may take full | statements as our significant units -- thus demanding that our statements | as wholes be translatable into sense-datum language, but not that they be | translatable term by term. | | This emendation would unquestionably have been welcome to Locke and Hume | and Tooke, but historically it had to await an important reorientation in | semantics -- the reorientation whereby the primary vehicle of meaning came | to be seen no longer in the term but in the statement. This reorientation, | seen in Bentham and Frege, underlies Russell's concept of incomplete symbols | defined in use; also it is implicit in the verification theory of meaning, | since the objects of verification are statements. | | Quine, "Two Dogmas", pp. 38-39. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 24
| 5. The Verification Theory and Reductionism (cont.) | | Radical reductionism, conceived now with statements as units, | set itself the task of specifying a sense-datum language and | showing how to translate the rest of significant discourse, | statement by statement, into it. Carnap embarked on this | project in the 'Aufbau'. | | The language which Carnap adopted as his starting point was not | a sense-datum language in the narrowest conceivable sense, for | it included also the notations of logic, up through higher set | theory. In effect it included the whole language of pure | mathematics. The ontology implicit in it (that is, the | range of values of its variables) embraced not only | sensory events but classes, classes of classes, and | so on. Empiricists there are who would boggle at | such prodigality. Carnap's starting point is | very parsimonious, however, in its extralogical | or sensory part. In a series of constructions in | which he exploits the resources of modern logic with | much ingenuity, Carnap succeeds in defining a wide array | of important additional sensory concepts which, but for his | constructions, one would not have dreamed were definable on | so slender a basis. He was the first empiricist who, not | content with asserting the reducibility of science to | terms of immediate experience, took serious steps | toward carrying out the reduction. | | Quine, "Two Dogmas", p. 39. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 25
| 5. The Verification Theory and Reductionism (cont.) | | If Carnap's starting point is satisfactory, | still his constructions were, as he himself | stressed, only a fragment of the full program. | The construction of even the simplest statements | about the physical world was left in a sketchy state. | Carnap's suggestions on this subject were, despite their | sketchiness, very suggestive. He explained spatio-temporal | point-instants as quadruples of real numbers and envisaged | assignment of sense qualities to point-instants according | to certain canons. Roughly summarized, the plan was that | qualities should be assigned to point-instants in such a | way as to achieve the laziest world compatible with our | experience. The principle of least action was to be | our guide in constructing a world from experience. | | Carnap did not seem to recognize, however, that his treatment | of physical objects fell short of reduction not merely through | sketchiness, but in principle. Statements of the form "Quality | q is at point-instant x;y;z;t" were, according to his canons, | to be apportioned truth vakues in such a way as to maximize | and minimize certain over-all features, and with growth of | experience the truth values were to be progressively revised | in the same spirit. I think that this is a good schematization | (deliberately oversimplified, to be sure) of what science really | does; but it provides no indication, not even the sketchiest, of | how a statement of the form "Quality q is at x;y;z;t" could ever | be translated into Carnap's initial language of sense data and | logic. The connective "is at" remains an added undefined | connective; the canons counsel us in its use but not | in its elimination. | | Carnap seems to have appreciated this point afterward; | for in his later writings he abandoned all notion of | the translatability of statements about the physical | world into statements about immediate experience. | Reductionism in its radical form has long since | ceased to figure in Carnap's philosophy. | | Quine, "Two Dogmas", pp. 39-40. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 26
| 5. The Verification Theory and Reductionism (cont.) | | But the dogma of reductionism has, in a subtler and more tenuous form, | continued to influence the thought of empiricists. The notion lingers | that to each statement, or each synthetic statement, there is associated | a unique range of possible sensory events such that the occurrence of any | of them would add to the likelihood of truth of the statement, and that | there is associated also another unique range of possible sensory events | whose occurrence would detract from that likelihood. This notion is of | course implicit in the verification theory of meaning. | | The dogma of reductionism survives in the supposition that each statement, | taken in isolation from its fellows, can admit of confirmation or infirmation | at all. My countersuggestion, issuing essentially from Carnap's doctrine of | the physical world in the 'Aufbau', is that our statements about the external | world face the tribunal of sense experience not individually but only as a | corporate body.* | |*This doctrine was well argued by Duhem [Pierre Duhem, 'La Theorie Physique: | Son Object et Sa Structure', Paris, 1906, pp. 303-328]. Or see Lowinger | Armand Lowinger, 'The Methodology of Pierre Duhem', Columbia University | Press, New York, NY, 1941, pp. 132-140]. | | Quine, "Two Dogmas", pp. 40-41. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 27
| 5. The Verification Theory and Reductionism (concl.) | | The dogma of reductionism, even in its attenuated form, is intimately | connected with the other dogma -- that there is a cleavage between | the analytic and the synthetic. We have found ourselves led, | indeed, from the latter problem to the former through the | verification theory of meaning. More directly, the one | dogma clearly supports the other in this way: as long | as it is taken to be significant in general to speak | of the confirmation and infirmation of a statement, | it seems significant to speak also of a limiting | kind of statement which is vacuously confirmed, | 'ipso facto', come what may; and such | a statement is analytic. | | The two dogmas are, indeed, at root identical. We lately reflected | that in general the truth of statements does obviously depend both | upon language and upon extralinguistic fact; and we noted that | this obvious circumstance carries in its train, not logically | but all too naturally, a feeling that the truth of a statement | is somehow analyzable into a linguistic component and a factual | component. The factual component must, if we are empiricists, | boil down to a range of confirmatory experiences. In the | extreme case where the linguistic component is all that | matters, a true statement is analytic. But I hope we are | now impressed with how stubbornly the distinction between | analytic and synthetic has resisted any straightforward | drawing. I am impressed also, apart from prefabricated | examples of black and white balls in an urn, with how | baffling the problem has always been of arriving at | any explicit theory of the empirical confirmation of | a synthetic statement. My present suggestion is that | it is nonsense, and the root of much nonsense, to speak | of a linguistic component and a factual component in the | truth of any individual statement. Taken collectively, | science has its double dependence upon language and | experience; but this duality is not significantly | traceable into the statements of science taken | one by one. | | The idea of defining a symbol in use was, as remarked, an advance | over the impossible term-by-term empiricism of Locke and Hume. | The statement, rather than the term, came with Bentham to be | recognized as the unit accountable to an empiricist critique. | But what I am now urging is that even in taking the statement | as unit we have drawn our grid too finely. The unit of empirical | significance is the whole of science. | | Quine, "Two Dogmas", pp. 41-42. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 28
| 6. Empiricism without the Dogmas | | The totality of our so-called knowledge or beliefs, from the most | casual matters of geography and history to the profoundest laws of | atomic physics or even of pure mathematics and logic, is a man-made | fabric which impinges on experience only along the edges. Or, to | change the figure, total science is like a field of force whose | boundary conditions are experience. A conflict with experience at | the periphery occasions readjustments in the interior of the field. | Truth values have to be redistributed over some of our statements. | Re-evaluation of some statements entails re-evaluation of others, | because of their logical interconnections -- the logical laws | being in turn simply certain further statements of the system, | certain further elements of the field. Having re-evaluated one | statement we must re-evaluate some others, which may be statements | logically connected with the first or may be the statements of logical | connections themselves. But the total field is so underdetermined by | its boundary conditions, experience, that there is much latitude of | choice as to what statements to re-evaluate in the light of any | single contrary experience. No particular experiences are | linked with any particular statements in the interior of | the field, except indirectly through considerations | of equilibrium affecting the field as a whole. | | Quine, "Two Dogmas", pp. 42-43. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 29
| 6. Empiricism without the Dogmas (cont.) | | If this view is right, it is misleading to speak of the empirical content of | an individual statement -- especially if it is a statement at all remote from | the experiential periphery of the field. Furthermore it becomes folly to seek | a boundary between synthetic statements, which hold contingently on experience, | and analytic statements, which hold come what may. Any statement can be held | true come what may, if we make drastic enough adjustments elsewhere in the | system. Even a statement very close to the periphery can be held true in | the face of recalcitrant experience by pleading hallucination or by amending | certain statements of the kind called logical laws. Conversely, by the same | token, no statement is immune to revision. Revision even of the logical law | of the excluded middle has been proposed as a means of simplifying quantum | mechanics; and what difference is there in principle between such a shift | and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or | Darwin Aristotle? | | For vividness I have been speaking in terms of varying distances | from a sensory periphery. Let me try now to clarify this notion | without metaphor. Certain statements, though 'about' physical | objects and not sense experience, seem peculiarly germane to | sense experience -- and in a selective way: some statements to | some experiences, others to others. Such statements, especially | germane to particular experiences, I picture as near the periphery. | But in this relation of "germaneness" I envisage nothing more than a | loose association reflecting the relative likelihood, in practice, of | our choosing one statement rather than another for revision in the event | of recalcitrant experience. For example, we can imagine recalcitrant | experiences to which we would surely be inclined to accommodate our | system by re-evaluating just the statement that there are brick | houses on Elm Street, together with related statements on the | same topic. We can imagine other recalcitrant experiences | to which we would be inclined to accommodate our system by | re-evaluating just the statement that there are no centaurs, | along with kindred statemnts. A recalcitrant experience can, | I have urged, be accommodated by any of various alternative | re-evaluations in various alternative quarters of the total | system; but, in the cases which we are now imagining, our | natural tendency to disturb the total system as little as | possible would lead us to focus our revisions upon these | specific statements concerning brick houses or centaurs. | These statements are felt, therefore, to have a sharper | empirical reference than highly theoretical statements | of physics or logic or ontology. The latter statements | may be thought of as relatively centrally located within | the total network, meaning merely that little preferential | connection with any particular sense data obtrudes itself. | | Quine, "Two Dogmas", pp. 43-44. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 30
| 6. Empiricism without the Dogmas (cont.) | | As an empiricist I continue to think of the conceptual scheme of science as | a tool, ultimately, for predicting future experience in the light of past | experience. Physical objects are conceptually imported into the situation | as convenient intermediaries -- not by definition in terms of experience, | but simply as irreducible posits comparable, epistemologically, to the | gods of Homer. For my part I do, qua lay physicist, believe in physical | objects and not in Homer's gods; and I consider it a scientific error | to believe otherwise. But in point of epistemological footing the | physical objects and the gods differ only in degree and not in kind. | Both sorts of entities enter our conception only as cultural posits. | The myth of physical objects is epistemologically superior to most | in that it has proved more efficacious than other myths as a device | for working a manageable structure into the flux of experience. | | Positing does not stop with macroscopic physical objects. | Objects at the atomic level are posited to make the laws of | macroscopic objects, and ultimately the laws of experience, | simpler and more manageable; and we need not expect or demand | full definition of atomic and subatomic entities in terms of | macroscopic ones, any more than definition of macroscopic things | in terms of sense data. Science is a continuation of common sense, | and it continues the common-sense expedient of swelling ontology to | simplify theory. | | Physical objects, small and large, are not the only posits. | Forces are another example; and indeed we are told nowadays that | the boundary between energy and matter is obsolete. Moreover, the | abstract entities which are the substance of mathematics -- ultimately | classes and classes of classes and so on up -- are another posit in the | same spirit. Epistemologically these are myths on the same footing with | physical objects and gods, neither better nor worse except for differences | in the degree to which they expedite our dealings with sense experiences. | | The over-all algebra of rational and irrational numbers is | underdetermined by the algebra of rational numbers, but is | smoother and more convenient; and it includes the algebra | of rational numbers as a jagged or gerrymandered part. | Total science, mathematical and natural and human, | is similarly but more extremely underdetermined | by experience. The edge of the system must be | kept squared with experience; the rest, with | all its elaborate myths or fictions, has as | its objective the simplicty of laws. | | Quine, "Two Dogmas", pp. 44-45. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
TDOE. Note 31
| 6. Empiricism without the Dogmas (concl.) | | Ontological questions, under this view, are on a par with questions | of natural science. Consider the question whether to countenance | classes as entities. This, as I have argued elsewhere, is the | question whether to quantify with respect to variables which | take classes as values. Now Carnap [*] has maintained that | this is a question not of matters of fact but of choosing | a convenient language form, a convenient conceptual scheme | or framework for science. With this I agree, but only on the | proviso that the same be conceded regarding scientific hypotheses | generally. Carnap ([*], p. 32n) has recognized that he is able to | preserve a double standard for ontological questions and scientific | hypotheses only by assuming an absolute distinction between the | analytic and the synthetic; and I need not say again that | this is a distinction which I reject. | | The issue over there being classes seems more a question of convenient | conceptual scheme; the issue over there being centaurs, or brick houses | on Elm street, seems more a question of fact. But I have been urging that | this difference is only one of degree, and that it turns upon our vaguely | pragmatic inclination to adjust one strand of the fabric of science rather | than another in accommodating some particular recalcitrant experience. | Conservatism figures in such choices, and so does the quest for | simplicity. | | Carnap, Lewis, and others take a pragmatic stand on the question of choosing | between language forms, scientific frameworks; but their pragmatism leaves | off at the imagined boundary between the analytic and the synthetic. In | repudiating such a boundary I espouse a more thorough pragmatism. Each | man is given a scientific heritage plus a continuing barrage of sensory | stimulation; and the considerations which guide him in warping his | scientific heritage to fit his continuing sensory promptings are, | where rational, pragmatic. | |*Rudolf Carnap, "Empiricism, Semantics, and Ontology", |'Revue Internationale de Philosphie', vol. 4 (1950), pp. 20-40. | Reprinted in Leonard Linsky (ed.), 'Semantics and the Philosophy | of Language', University of Illinois Press, Urbana, IL, 1952. | | Quine, "Two Dogmas", pp. 45-46. | | W.V. Quine, |"Two Dogmas of Empiricism", 'Philosophical Review', January 1951. | Reprinted as pages 20-46 in 'From a Logical Point of View', | 2nd edition, Harvard University Press, Cambridge, MA, 1980.
VOLS. Verities Of Likely Stories
VOLS. Note 1
| These are the forms of time, | which imitates eternity and | revolves according to a law | of number. | | Plato, "Timaeus", 38 A, | Benjamin Jowett (trans.)
VOLS. Note 2
| Now first of all we must, in my judgement, make the following distinction. | What is that which is Existent always and has no Becoming? And what is | that which is Becoming always and never is Existent? Now the one of | these is apprehensible by thought with the aid of reasoning, since | it is ever uniformly existent; whereas the other is an object of | opinion with the aid of unreasoning sensation, since it becomes and | perishes and is never really existent. Again, everything which becomes | must of necessity become owing to some Cause; for without a cause it is | impossible for anything to attain becoming. But when the artificer of any | object, in forming its shape and quality, keeps his gaze fixed on that which | is uniform, using a model of this kind, that object, executed in this way, | must of necessity be beautiful; but whenever he gazes at that which | has come into existence and uses a created model, the object thus | executed is not beautiful. Now the whole Heaven, or Cosmos, or | if there is any other name which it specially prefers, by that | let us call it -- so, be its name what it may, we must first | investigate concerning it that primary question which has to be | investigated at the outset in every case -- namely, whether it has | existed always, having no beginning of generation, or whether it has | come into existence, having begun from some beginning. It has come into | existence; for it is visible and tangible and possessed of a body; and all | such things are sensible, and things sensible, being apprehensible by opinion | with the aid of sensation, come into existence, as we saw, and are generated. | And that which has come into existence must necessarily, as we say, have | come into existence by reason of some Cause. Now to discover the | Maker and Father of this Universe were a task indeed; and | having discovered Him, to declare Him unto all men were | a thing impossible. However, let us return and inquire | further concerning the Cosmos -- after which of the Models | ['paradeigmaton'] did its Architect construct it? Was it after | that which is self-identical and uniform, or after that which has | come into existence? Now if so be that this Cosmos is beautiful and | its Constructor good, it is plain that he fixed his gaze on the Eternal; | but if otherwise (which is an impious supposition), his gaze was on that | which has come into existence. But it is clear to everyone that his gaze | was on the Eternal; for the Cosmos is the fairest of all that has come | into existence, and He is the best of all the Causes. So having | in this wise come into existence, it has been constructed | after the pattern of that which is apprehensible by | reason and thought and is self-identical. | | Plato, "Timaeus", 27D-29A. | | Plato, "Timaeus", R.G. Bury (trans.), |'Plato, Volume 9', G.P. Goold (ed.), | William Heinemann, London, UK, 1929.
VOLS. Note 3
| Again, if these premisses be granted, it is wholly necessary that this Cosmos | should be a Copy ['eikona'] of something. Now in regard to every matter it is | most important to begin at the natural beginning. Accordingly, in dealing with | a copy and its model, we must affirm that the accounts given will themselves be | akin to the diverse objects which they serve to explain; those which deal with | what is abiding and firm and discernible by the aid of thought will be abiding | and unshakable; and in so far as it is possible and fitting for statements to | be irrefutable and invincible, they must in no wise fall short thereof; whereas | the accounts of that which is copied after the likeness of that Model, and is | itself a likeness, will be analogous thereto and possess likelihood; for as | Being is to Becoming, so is Truth to Belief. Wherefore, Socrates, if in our | treatment of a great host of matters regarding the Gods and the generation of | the Universe we prove unable to give accounts that are always in all respects | self-consistent and perfectly exact, be not thou surprised; rather we should | be content if we can furnish accounts that are inferior to none in likelihood, | remembering that both I who speak and you who judge are but human creatures, | so that it becomes us to accept the likely account of these matters and | forbear to search beyond it. | | Plato, "Timaeus", 29B-29D. | | Plato, "Timaeus", R.G. Bury (trans.), |'Plato, Volume 9', G.P. Goold (ed.), | William Heinemann, London, UK, 1929.
VOLS. Note 4
| Many likelihoods informed me of this before, | which hung so tott'ring in the balance that | I could neither believe nor misdoubt. | | 'All's Well That Ends Well', 1.3.119-121
VOLS. Note 5
| We have Reduction [abduction, Greek 'apagoge'] (1) when it is obvious | that the first term applies to the middle, but that the middle applies | to the last term is not obvious, yet nevertheless is more probable or | not less probable than the conclusion; or (2) if there are not many | intermediate terms between the last and the middle; for in all such | cases the effect is to bring us nearer to knowledge. | | (1) E.g., let A stand for "that which can be taught", B for "knowledge", | and C for "morality". Then that knowledge can be taught is evident; | but whether virtue is knowledge is not clear. Then if BC is not less | probable or is more probable than AC, we have reduction; for we are | nearer to knowledge for having introduced an additional term, whereas | before we had no knowledge that AC is true. | | (2) Or again we have reduction if there are not many intermediate terms | between B and C; for in this case too we are brought nearer to knowledge. | E.g., suppose that D is "to square", E "rectilinear figure" and F "circle". | Assuming that between E and F there is only one intermediate term -- that the | circle becomes equal to a rectilinear figure by means of lunules -- we should | approximate to knowledge. When, however, BC is not more probable than AC, or | there are several intermediate terms, I do not use the expression "reduction"; | nor when the proposition BC is immediate; for such a statement implies knowledge. | | Aristotle, "Prior Analytics", 2.25. | | Aristotle, "Prior Analytics", | Hugh Tredennick (trans.), in: |'Aristotle, Volume 1', G.P. Goold (ed.), | William Heinemann, London, UK, 1938, 1983.
VOLS. Note 6
| A probability [Greek 'eikos'] is not the same as a sign ['semeion']. | The former is a generally accepted premiss; for that which people | know to happen or not to happen, or to be or not to be, usually | in a particular way, is a probability: e.g., that the envious | are malevolent or that those who are loved are affectionate. | A sign, however, means a demonstrative premiss which | is necessary or generally accepted. That which | coexists with something else, or before or | after whose happening something else has | happened, is a sign of that something's | having happened or being. | | An enthymeme is a syllogism from probabilities or signs; | and a sign can be taken in three ways -- in just as many ways | as there are of taking the middle term in the several figures ... | | We must either classify signs in this way, and regard their middle term as | an index ['tekmerion'] (for the name "index" is given to that which causes | us to know, and the middle term is especially of this nature), or describe | the arguments drawn from the extremes as "signs", and that which is drawn | from the middle as an "index". For the conclusion which is reached through | the first figure is most generally accepted and most true. | | Aristotle, "Prior Analytics", 2.27. | | Aristotle, "Prior Analytics", | Hugh Tredennick (trans.), in: |'Aristotle, Volume 1', G.P. Goold (ed.), | William Heinemann, London, UK, 1938, 1983.
VOLS. Note 7
| Rhetoric is a counterpart [Greek 'antistrophos'] of Dialectic; | for both have to do with matters that are in a manner within the | cognizance of all men and not confined to any special science. | Hence all men in a manner have a share of both; for all, up to | a certain point, endeavour to criticize or uphold an argument, | to defend themselves or to accuse. Now, the majority of people | do this either at random or with a familiarity arising from habit. | But since both these ways are possible, it is clear that matters | can be reduced to a system, for it is possible to examine the | reason why some attain their end by familiarity and others by | chance; and such an examination all would at once admit to be | the function of an art ['techne']. (1-2) | | Now, previous compilers of "Arts" of Rhetoric have provided us with | only a small portion of this art, for proofs are the only things in | it that come within the province of art; everything else is merely | an accessory. And yet they say nothing about enthymemes which are | the body of proof, but chiefly devote their attention to matters | outside the subject; for the arousing of prejudice, compassion, | anger, and similar emotions has no connexion with the matter in | hand, but is directed only to the dicast. (3-4) | | Aristotle, "Art of Rhetoric", 1.1.1-4. | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 8
| It is obvious, therefore, that a system arranged according to the rules of art | is only concerned with proofs; that proof ['pistis'] is a sort of demonstration | ['apodeixis'], since we are most strongly convinced when we suppose anything to | have been demonstrated; that rhetorical demonstration is an enthymeme, which, | generally speaking, is the strongest of rhetorical proofs; and lastly, that | the enthymeme is a kind of syllogism. Now, as it is the function of Dialectic | as a whole, or one of its parts, to consider every kind of syllogism in a similar | manner, it is clear that he who is most capable of examining the matter and forms | of a syllogism will be in the highest degree a master of rhetorical argument, if | to this he adds a knowledge of the subjects with which enthymemes deal and the | differences between them and logical syllogisms. For, in fact, the true and that | which resembles it come under the purview of the same faculty, and at the same time | men have a sufficient natural capacity for the truth and indeed in most cases attain | to it; wherefore one who divines well ['stochastikos echein'] in regard to the truth | will also be able to divine well in regard to probabilities ['endoxa']. | | Aristotle, "Art of Rhetoric", 1.1.11. | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 9
| It is thus evident that Rhetoric does not deal with any one definite class | of subjects, but, like Dialectic, [is of general application -- Trans.]; | also, that it is useful; and further, that its function is not so much | to persuade, as to find out in each case the existing means of persuasion. | The same holds good in respect to all the other arts. For instance, it | is not the function of medicine to restore a patient to health, but only | to promote this end as far as possible; for even those whose recovery is | impossible may be properly treated. It is further evident that it belongs | to Rhetoric to discover the real and apparent means of persuasion, just | as it belongs to Dialectic to discover the real and apparent syllogism. | For what makes the sophist is not the faculty but the moral purpose. | But there is a difference: in Rhetoric, one who acts in accordance with | sound argument, and one who acts in accordance with moral purpose, are | both called rhetoricians; but in Dialectic it is the moral purpose that | makes the sophist, the dialectician being one whose arguments rest, not | on moral purpose but on the faculty. | | Aristotle, "Art of Rhetoric", 1.1.14. | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 10
| Rhetoric then may be defined as the faculty of discovering the possible means | of persuasion in reference to any subject whatever. This is the function of | no other of the arts, each of which is able to instruct and persuade in its | own special subject; thus, medicine deals with health and sickness, geometry | with the properties of magnitudes, arithmetic with number, and similarly with | all the other arts and sciences. But Rhetoric, so to say, appears to be able | to discover the means of persuasion in reference to any given subject. That is | why we say that as an art its rules are not applied to any particular definite | class of things. | | As for proofs, some are inartificial, others artificial. By the former | I understand all those which have not been furnished by ourselves but were | already in existence, such as witnesses, tortures, contracts, and the like; | by the latter, all that can be constructed by system and by our own efforts. | Thus we have only to make use of the former, whereas we must invent the latter. | | Now the proofs furnished by the speech are of three kinds. | The first depends upon the moral character of the speaker, | the second upon putting the hearer into a certain frame | of mind, the third upon the speech itself, in so far as | it proves or seems to prove. | | Aristotle, "Art of Rhetoric", 1.2.1-3. | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 11
| But for purposes of demonstration, real or apparent, just as Dialectic possesses | two modes of argument, induction and the syllogism, real or apparent, the same is | the case in Rhetoric; for the example is induction, and the enthymeme a syllogism, | and the apparent enthymeme an apparent syllogism. Accordingly I call an enthymeme | a rhetorical syllogism, and an example rhetorical induction. Now all orators produce | belief by employing as proofs either examples or enthymemes and nothing else; so that | if, generally speaking, it is necessary to prove any fact whatever either by syllogism | or by induction -- and that this is so is clear from the 'Analytics' -- each of the | two former must be identical with each of the two latter. The difference between | example and enthymeme is evident from the 'Topics', where, in discussing syllogism | and induction, it has previously been said that the proof from a number of particular | cases that such is the rule, is called in Dialectic induction, in Rhetoric example; | but when, certain things being posited, something different results by reason of | them, alongside of them, from their being true, either universally or in most | cases, such a conclusion in Dialectic is called a syllogism, in Rhetoric an | enthymeme. | | Aristotle, "Art of Rhetoric", 1.2.8-9. | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 12
| The function ['ergon'] of Rhetoric, then, is to deal with things about | which we deliberate, but for which we have no systematic rules; and in | the presence of such hearers as are unable to take a general view of many | stages, or to follow a lengthy chain of argument. But we only deliberate | about things which seem to admit of issuing in two ways; as for those things | which cannot in the past, present, or future be otherwise, no one deliberates | about them, if he supposes that they are such; for nothing would be gained | by it. Now, it is possible to draw conclusions and inferences partly from | what has been previously demonstrated syllogistically, partly from what | has not, which however needs demonstration, because it is not probable. | The first of these methods is necessarily difficult to follow owing to | its length, for the judge is supposed to be a simple person; the second | will obtain little credence, because it does not depend upon what is either | admitted of probable. The necessary result then is that the enthymeme and | the example are concerned with things which may, generally speaking, be other | than they are, the example being a kind of induction and the enthymeme a kind | of syllogism, and deduced from few premisses, often from fewer than the regular | syllogism; for if any one of these is well known, there is no need to mention it, | for the hearer can add it himself. For instance, to prove that Dorieus was the | victor in a contest at which the prize was a crown, it is enough to say that | he won a victory at the Olympic games; there is no need to add that the | prize at the Olympic games is a crown, for everybody knows it. | | Aristotle, "Art of Rhetoric", 1.2.12-13. | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 13
| But since few of the propositions of the rhetorical syllogism | are necessary ['anagkaion'], for most of the things which we | judge and examine can be other than they are, human actions, | which are the subject of our deliberation and examination, | being all of such a character and, generally speaking, none of | them necessary; since, further, facts which only generally happen | or are merely possible can only be demonstrated by other facts of | the same kind, and necessary facts by necessary propositions (and | that this is so is clear from the 'Analytics'), it is evident that | the materials from which enthymemes are derived will be sometimes | necessary, but for the most part only generally true; and these | materials being probabilities and signs, it follows that these | two elements must correspond to these two kinds of propositions, | each to each. For that which is probable is that which generally | happens, not however unreservedly, as some define it, but that | which is concerned with things that may be other than they are, | being so related to that in regard to which it is probable as | the universal to the particular. As to signs, some are related | as the particular to the universal, others as the universal to | the particular. Necessary signs are called 'tekmeria'; those | which are not necessary have no distinguishing name. I call | those necessary signs from which a logical syllogism can be | constructed, wherefore such a sign is called 'tekmerion'; | for when people think that their arguments are irrefutable, | they think that they are bringing forward a 'tekmerion', | something as it were proved and concluded; for in | the old language 'tekmar' and 'peras' have the | same meaning (limit, conclusion). | | Aristotle, "Art of Rhetoric", 1.2.14-17. | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 14
| Among signs, some are related as the particular to the universal; | for instance, if one were to say that all wise men are just, because | Socrates was both wise and just. Now this is a sign, but even though | the particular statement is true, it can be refuted, because it cannot | be reduced to syllogistic form. But if one were to say that it is a sign | that a man is ill, because he has a fever, or that a woman has had a child | because she has milk, this is a necessary sign. This alone among signs is | a 'tekmerion'; for only in this case, if the fact is true, is the argument | irrefutable. Other signs are related as the universal to the particular, | for instance, if one were to say that it is a sign that this man has a fever, | because he breathes hard; but even if the fact be true, this argument also | can be refuted, for it is possible for a man to breathe hard without having | a fever. We have now explained the meaning of probable, sign, and necessary | sign, and the difference between them; in the 'Analytics' we have defined | them more clearly and stated why some of them can be converted into logical | syllogisms, while others cannot. | | Aristotle, "Art of Rhetoric", 1.2.18 | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 15
| We have now stated the materials of proofs which are thought to be demonstrative. | But a very great difference between enthymemes has escaped the notice of nearly | every one, although it also exists in the dialectical method of syllogisms. | For some of them belong to Rhetoric, some syllogisms only to Dialectic, | and others to other arts and faculties, some already existing and | others not yet established. Hence its is that this escapes | the notice of the speakers, and the more they specialize | in a subject, the more they transgress the limits of | Rhetoric and Dialectic. But this will be clearer | if stated at greater length. | | I mean by dialectical and rhetorical syllogisms those which are concerned with what | we call "topics", which may be applied alike to Law, Physics, Politics, and many | other sciences that differ in kind, such as the topic of the more or less, which | will furnish syllogisms and enthymemes equally well for Law, Physics, or any | other science whatever, although these subjects differ in kind. Specific | topics on the other hand are derived from propositions which are peculiar | to each species or genus of things; there are, for example, propositions | about Physics which can furnish neither enthymemes nor syllogisms about | Ethics, and there are propositions concerned with Ethics which will be | useless for furnishing conclusions about Physics; and the same holds | good in all cases. The first kind of topics will not make a man | practically wise about any particular class of things, because | they do not deal with any particular subject matter; but as | to the specific topics, the happier a man is in his choice | of propositions, the more he will unconsciously produce | a science quite different from Dialectic and Rhetoric. | For if once he hits upon first principles, it will | no longer be Dialectic or Rhetoric, but that | science whose principles he has arrived at. | Most enthymemes are constructed from | these special topics, which are | called particular and special, | fewer from those that are | common or universal. | | Aristotle, "Art of Rhetoric", 1.2.20-22 | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 16
| We have said that example ['paradeigma', analogy] is a kind of induction and with | what kind of material it deals by way of induction. It is neither the relation | of part to whole, nor of whole to part, nor of one whole to another whole, but | of part to part, of like to like, when both come under the same genus, but one | of them is better known than the other. For example, to prove that Dionysius | is aiming at a tyranny, because he asks for a bodyguard, one might say that | Pisistratus before him and Theagenes of Megara did the same, and when they | obtained what they asked for made themselves tyrants. All the other | tyrants known may serve as an example of Dionysius, whose reason, | however, for asking for a bodyguard we do not yet know. All these | examples are contained under the same universal proposition, that | one who is aiming at a tyranny asks for a bodyguard. | | Aristotle, "Art of Rhetoric", 1.2.19 | | Aristotle, "The 'Art' of Rhetoric", | John Henry Freese (trans.), in: |'Aristotle, Volume 22', G.P. Goold (ed.), | William Heinemann, London, UK, 1926, 1982.
VOLS. Note 17
The Likely Story: Its likely Moral. Those of you who stayed with the tour have been strolling with me through the Socratic and the Peripatetic wings of a gallery devoted to the Classical background of Peirce's theory of signs and inquiry, and the exhibits that I have collected there have been gathering dust in that Museum of Incidental Musements for a score of Summers or more. If I were to state the theme of the show it'd come out a bit like this: | There is a continuity between approximate (likely, probable) | and apodeictic (demonstrative, exact) patterns of reasoning, | with the latter being the limiting ideal of the former type. Having spent the lion's share of my waking and my dreaming life trying to put things together that others are busy taking apart, I found that it often helps to return to the sources of streams, where opposing banks of perspectives are a bit less riven apart. For example, modus tollens is a pattern of inference in deductive reasoning that takes the following form: A => B ~B -------- ~A Probably the most common pattern of inference in empirical reasoning takes a form like this: H_0 = the null hypothesis. Typically, H_0 says that a couple of factors X and Y are independent, in effect, that they have no lawlike relationship. D_0 = the null distribution of outcomes. In part, D_0 says that particular types of possible outcomes have probabilities of happening that are very near to zero. Let us assume that D_0 => G_0, with G_0 being the proposition that an event E_0 has a close to zero chance of happening. We are given the theoretical propositions: (1) H_0 => D_0 and (2) D_0 => G_0, and so we may assume that (3) H_0 => G_0. Let's say that we do the relevant experiment, and, lo and behold, we observe the event E_0, that is supposed to be unlikely if H_0 holds. Now it's not a logical contradiction, but we take E_0 as evidence against G_0 anyway, and by modus tollens as evidence contrary to H_0. We may view this typical pattern of "significance testing" as a statistical generalization of the modus tollens rule. o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o VOLS. Note 17 -- Dup or Correction? o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o The Likely Story: Its likely Moral. Those of you who stayed with the tour have been strolling with me through the Socratic and the Peripatetic wings of a gallery devoted to the Classical background of Peirce's theory of signs and inquiry, and the exhibits that I have collected there have been gathering dust in that Museum of Incidental Musements for a score of Summers or more. If I were to state the theme of the show it'd come out a bit like this: | There is a continuity between approximate (likely, probable) | and apodeictic (demonstrative, exact) patterns of reasoning, | with the latter being the limiting ideal of the former type. Having spent the lion's share of my waking and my dreaming life trying to put things together that others are busy taking apart, I found that it often helps to return to the sources of streams, where opposing banks of perspectives are a bit less riven apart. For example, modus tollens is a pattern of inference in deductive reasoning that takes the following form: A => B ~B -------- ~A Probably the most common pattern of inference in empirical reasoning takes a form like this: H_0 = the null hypothesis. Typically, H_0 says that a couple of factors X and Y are independent, in effect, that they have no lawlike relationship. D_0 = the null distribution of outcomes. In part, D_0 says that particular types of possible outcomes have probabilities of happening that are very near to zero. Let us assume that D_0 => G_0, with G_0 being the proposition that an event E_0 has a close to zero chance of happening. We are given the theoretical propositions: (1) H_0 => D_0 and (2) D_0 => G_0, and so we may assume that (3) H_0 => G_0. Let's say that we do the relevant experiment, and, lo and behold, we observe the event E_0, that is supposed to be unlikely if H_0 holds. Now it's not a logical contradiction, but we take E_0 as evidence against G_0 anyway, and by modus tollens as evidence contrary to H_0. We may view this typical pattern of "significance testing" as a statistical generalization of the modus tollens rule.
VOLS. Note 18
| The dull green time-stained panes | of the windows look upon each other | with the cowardly glances of cheats. | | Maxim Gorky, 'Creatures That Once Were Men' Peirce is a reflective practitioner of pragmatic thinking, which is to say that he puts the interpreter back into the scene of observation, from whence he has, from time to time, been elevated beyond implication, or exiled beyond redemption.
VOLS. Verities Of Likely Stories • Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Seth,
> P1. "we think each one of our beliefs to be true,
> and, indeed, it is mere tautology to say so" (CP 5.375).
>
> And here are the pair of sentences which you impute to Peirce qua fallibilist,
> which you regard as being paradoxical in import. S1 is your restatement of P1,
> and S2 is what you believe to be the fallibilist view.
>
> S1. (For every x)(I believe x -> x is true).
This has been said before, by Peter Skagestad and
probably others, but S1 is not a paraphrase of P1.
A better try would be, for all propositions P and persons Q,
If P is a belief of Q, then Q thinks that P is true.
And that is a tautology, in the sense of repeating oneself.
This is aside from the fact that Peirce's semantics
for "Q believes P" is not what you assume for it,
nor is his usage of quantifiers what you assume.
The first time I heard this one, it was posed as being about
"referential opacity" or "non-substitutability of identicals"
in intentional contexts, which is a typical symptom of using
2-adic relations where 3-adic relations are called for, and
even Russell and Quine briefly consider this, though both
of them shy away on the usual out-Occaming Occam grounds.
If you were going to take a lesson from Quine,
I think you might well begin with his holism,
and quit parapharsing texts out of context.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
JA = Jon Awbrey
SS = Seth Sharpless
SS: Well at last you address the issue directly, saying what
Peter Skagestad already said, to which I have previously
given my response for what it was worth.
SS: As for your comment,
| If you were going to take a lesson from Quine,
| I think you might well begin with his holism,
| and quit parapharsing texts out of context,
SS: the context of the P1 quote in the 1877 paper on "Fixation of Belief" is very familiar
to most contributors to this list, my S1 paraphrase was explicit and could be (and was)
judged for its fidelity to the original, and I have scrupulously given sources for other
passages to which I have referred, quoting the less familiar passages verbatim.
SS: Yes, holism, theories of belief revision, theories of the structure of propositions
and the logic of relations, intensional and situational logic, Gricean conversational
maxims, theories of inquiry and the history of science, these and much else could be
brought to bear on this little problem, which is one of the things that make it
interesting.
SS: I have taken note of your admonitions on how I ought to behave.
May I suggest that a little collegiality on your part would
not be out of place.
Seth,
I will try to tell you where I am really coming from,
in this and all of the other matters of interest to
this Forum, as it appears that my epigraphic use of
quotations from Russell, Dewey, and Julius Caesar
may have confused you about the name of the camp
from which I presently look out.
I studied analytic, existential, oriental, phenomenological,
and pragmatic philosophy, among several others, pretty much
in parallel, for many years as an undergraduate (1967-1976) --
yes, that long, for it was an "interesting time", after all --
then I pursued graduate studies in mathematics, then later
psychology, in the meantime working mostly as a consulting
statistician and computer jockey for a mix of academic and
professional school research units.
The more experience that I gained in applying formal sciences --
mathematical, computational, statistical, and logical methods --
to the problems that I continued to see coming up in research,
the more that my philosophical reflections on my work led me
choose among those that "worked" and those that did not.
I can do no better than to report my observations from this experience.
The mix of ideas that I learned from analytic philosophy just never
quite addresses the realities of phenomena and practices that are
involved in real-live inquiry, while the body of ideas contained
in the work of Peirce and Dewey, and sometimes James and Mead,
continues to be a source of genuine insight into the actual
problems of succeeding at science.
From this perspective, the important thing is whether a philosophical outlook
address the experiential phenomena that are present in the field, and whether
it gives us some insight into why the methods that work there manage to do so,
for the sake of improving how they manage to do so in the future.
An approximate formulation that addresses the realities of phenomena,
practices, and problems in inquiry is vastly preferable to an exact
formulation of some other subject, that has no relation to the job.
I directly addressed the material issues that raised from the very first.
That is, after all, a rather old joke. But you have simply ignored all
of the alternate directions that I indicated, all of them arising from
the substance and the intent of Peirce's work.
The little puzzle that you have been worrying us over is typical of
the sort of abject silliness that so-called analytic philosophy has
wasted the last hundred years of intellectual history with, and I,
for one, believe that it is time to move on.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Seth,
> P1. "we think each one of our beliefs to be true,
> and, indeed, it is mere tautology to say so" (CP 5.375).
>
> And here are the pair of sentences which you impute to Peirce qua fallibilist,
> which you regard as being paradoxical in import. S1 is your restatement of P1,
> and S2 is what you believe to be the fallibilist view.
>
> S1. (For every x)(I believe x -> x is true).
JA: This has been said before, by Peter Skagestad and
probably others, but S1 is not a paraphrase of P1.
JA: A better try would be, for all propositions P and persons Q,
JA: If P is a belief of Q, then Q thinks that P is true.
JA: And that is a tautology, in the sense of repeating oneself.
JA: This is aside from the fact that Peirce's semantics
for "Q believes P" is not what you assume for it,
nor is his usage of quantifiers what you assume.
JA: The first time I heard this one, it was posed as being about
"referential opacity" or "non-substitutability of identicals"
in intentional contexts, which is a typical symptom of using
2-adic relations where 3-adic relations are called for, and
even Russell and Quine briefly consider this, though both
of them shy away on the usual out-Occaming Occam grounds.
JA: If you were going to take a lesson from Quine,
I think you might well begin with his holism,
and quit parapharsing texts out of context.
What Peirce says here is simply the common sense truism
that what a person believes is what that person believes
to be true, and therefore the appendix "to be true" is
veriformly redundant. This has no special bearing on
fallibility except that when a person changes a belief
then that person ipso facto changes a belief as to what
is true.
When one changes a belief
from something of the form A
to something of the form ~A,
then 1 of 3 things can occur:
1. A is true, in which case one is now wrong to believe ~A.
2. A is not true, in which case one was wrong to believe A.
3. The distinction between A and ~A is ill-formed, in which
case one was wrong in believing that it was well-formed.
In either case, one has has actualized one's fallibility.
As I explained in my first remarks on this issue, the proper context for understanding
Peirce's statements about belief -- for anyone who really wishes to do that -- since
belief is a state that he calls the end of inquiry, is Peirce's theory of inquiry,
which process he analyzes in terms of the three principal types of inference that
he recognizes, placing that study within the study of logic, which he treats
as more or less equivalent to semiotics, or the theory of sign relations.
Since Peirce holds that all of our thoughts and beliefs and so on are
signs, and since sign relations are 3-adic relations, the ultimate
context for understanding what Peirce says about belief and error
and so on -- for anyone who really wishes to do that -- is the
context of 3-adic sign relations and the semiotic processes
that take place in these frames. Quine's holism, as best
I can remember from my studies of 30 years ago, says that
we cannot translate single statements, but only whole
theories, and I find that an admirable sentiment,
independently of how consistent Quine may have
been in his application of it. Your attempt
at a paraphrase, which I can only suspect
began with the punchline and tried to
attach Peirce as the fall guy, fails
already on syntactic grounds, since
it does not preserve even the form
of what Peirce said, and although
you provide no explicit semantics
for the concept of belief you are
attempting to attach to Peirce's
statement, whereas Peirce's gave
us many further statements of
what he meant, fails on the
minimal semantic grounds
that no false statement
can be the paraphrase
of a true sentence.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
JA = Jon Awbrey
JR = Joe Ransdell
SS = Seth Sharpless
SS: I shall try to address your objection to my argument with the kind
of civility that I wish you could show for me. You were apparently
not satisfied with my reply to Peter Skagestad and Mark Silcox when
they made the same objection you are now making, so I will try to
make my argument clearer.
I only have a moment, and so I will save this note for a more careful review later.
I can see that you are in earnest, but my general impression is that you are moving
at a high rate of speed down a no outlet alley, and perhaps a bit too focussed on the
syntactic peculiarities of one particular fragment, when Peirce himself has provided us
with ample paraphrases and amplifications of his intended sense on this very same point.
I wish I could convince you that the quantifiers and their interlacings
are irrelevant to the actual sense of what Peirce is saying here, as he
is merely observing a pragmatic equivalence between two situations that
may be expressed in relational predicates of yet to be determined arity.
Failing that, we will have to examine what Peirce in 1877 might have
meant by what you are assuming is the implicit quantifier signalled
by "each". This is an issue that I have studied long and hard, but
have avoided raising it so far, mostly out of a prospective despair
at my present capacity to render it clear. Maybe it is time.
But really, it is not necesssary to get what Peirce is
saying here, which is a fairly simple, common sense
point, idiomatically expressed, and, most likely,
irreducibly so. It would be a far better thing
we do if we adopt the hermeneutic principle of
looking for the author's own paraphrases and
approximations, even if not exact from
a purely syntactic point of view.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
SS, quoting JA, citing JR, paraphrasing SS, interpreting CSP:
| And here are the pair of sentences which you impute to Peirce qua
| fallibilist, which you regard as being paradoxical in import.
|
| P1. "we think each one of our beliefs to be true, and,
| indeed, it is mere tautology to say so" (CP 5.375)
|
| S1 is your restatement of P1 ...
|
| S1. (For every x)(I believe x -> x is true).
SS, quoting JA:
| This has been said before, by Peter Skagestad and
| probably others, but S1 is not a paraphrase of P1.
|
| A better try would be, for all propositions P and persons Q,
|
| If P is a belief of Q, then Q thinks that P is true.
|
| And that is a tautology, in the sense of repeating oneself.
SS: No, Jon, you have not got it quite right. S1 was not my restatement of P1;
I gave S1 as a paraphrase of what a believer must believe, given that P1 is true.
That is not quite the same (though in later passages, I did sometimes carelessly
refer to S1 as a "paraphrase of P1").
SS: In response to the objection of Peter Skagestad and Mark Silcox,
which is the same as that which you are now making, I conceded that:
SS: (1) (For every x)I believe(I believe x -> x is true)
SS: is not the same as:
SS: (2) I believe(For every x)(I believe x-> x is true).
SS: But on the assumption that the believer is intelligent,
and that he sees the conditional in (1) as a necessary
("tautologous") truth, he should be able to make an
inference like the following:
SS: "Any arbitrarily chosen belief of mine must be believed by me to be true"
SS: Therefore,
SS: "All my beliefs are believed by me to be true"
SS: which is a valid universal generalization of the same kind as:
SS: Any arbitrarily chosen natural number must be a product of primes;
therefore, all natural numbers are products of primes.
SS: Any arbitrarily chosen cat must be a mammal;
therefore, all cats are mammals.
SS: It is true that this is an inference that calls for some logical skill on the part of
the believer, so that someone could believe P1 without believing S1, but we are talking
about Peirce, and whether HIS belief in fallibilism is consistent with HIS belief in P1.
I think there can be no doubt about his belief in P1. As to what it is exactly that he
believes, when he believes in fallibilism, that is a more difficult question. I am now
having doubts that "Some of my beliefs are false," or
SS: (S2) (For some x)(I believe x & x is not true)
SS: fairly expresses Peirce's Fallibilism. I discussed that possibility in my
summary letter, under the heading "First Solution." More needs to be said
about it, but I'll keep it for another communication, possibly in response
to Joseph's forthcoming letter.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
JA = Jon Awbrey
JR = Joe Ransdell
SS = Seth Sharpless
SS: I shall try to address your objection to my argument with the kind
of civility that I wish you could show for me. You were apparently
not satisfied with my reply to Peter Skagestad and Mark Silcox when
they made the same objection you are now making, so I will try to
make my argument clearer.
I would try to address the issue of civility,
but my defense would have to take the form,
"But Ma, he hit me first!", and I long ago
learned the recursive futility of setting
foot on such a path.
JA: I only have a moment, and so I will save this note for
a more careful review later. I can see that you are in
earnest, but my general impression is that you are moving
at a high rate of speed down a no outlet alley, and perhaps
a bit too focussed on the syntactic peculiarities of one
particular fragment, when Peirce himself has provided
us with ample paraphrases and amplifications of his
intended sense on this very same point.
I have already mentioned another locus where Peirce adverts to this issue,
but this time with all of the requisite qualifiers and all of the nuanced
indicators of relative significance intact, and that is in this passage:
| Two things here are all-important to assure oneself of
| and to remember. The first is that a person is not
| absolutely an individual. His thoughts are what
| he is "saying to himself", that is, is saying
| to that other self that is just coming into
| life in the flow of time. When one reasons,
| it is that critical self that one is trying
| to persuade; and all thought whatsoever is a
| sign, and is mostly of the nature of language.
| The second thing to remember is that the man's
| circle of society (however widely or narrowly
| this phrase may be understood), is a sort of
| loosely compacted person, in some respects of
| higher rank than the person of an individual
| organism. It is these two things alone that
| render it possible for you -- but only in
| the abstract, and in a Pickwickian sense --
| to distinguish between absolute truth
| and what you do not doubt.
|
| CSP, CP 5.421.
|
| Charles Sanders Peirce, "What Pragmatism Is",
|'The Monist', Volume 15, 1905, pages 161-181,
| Also in the 'Collected Papers', CP 5.411-437.
If we wanted a bone to pick,
this one promises more beef.
Another approach that might be more productive,
if no less controversial, would be through the
examination of the distinction between what we
frequently call "belief" and "knowledge", and
why the distinction collapses or degenerates
for the fictively isolated individual agent.
JA, amending JA:
I wish I could convince you that the quantifiers and their interlacings
are irrelevant to the actual sense of what Peirce is saying here, as he
is merely observing a pragmatic equivalence between two situations that
may be expressed in relational predicates of yet to be determined arity.
Failing that, we will have to examine what Peirce in 1877 might have
meant by what you are assuming is the implicit quantifier signalled
by "each". This is an issue that I have studied long and hard, but
have avoided raising so far, mostly out of a prospective despair
at my present capacity to render it clear. Maybe it is time.
But really, it is not necesssary to do this just in order to
get what Peirce is saying here, which is a fairly simple,
common sense point, idiomatically expressed, and, most
likely, irreducibly so. It would be a far better
thing we do if we adopt the hermeneutic principle
of looking for the author's own paraphrases and
approximations, even if not exactly identical
from a purely syntactic point of view.
A minimal caution about this point would require us to recognize
two distinct dimensions of variation in the usage of quantifiers:
1. The difference in usage between Peirce 1877 and the
post-Fregean scene of our contemporary discussions.
2. The difference in usage between most mathematicians, then and now,
and people who identify themselves as "logicists" or "linguists".
We probably cannot help ourselves from translating Peirce 1877
into our own frame of reference, but we should be aware of the
potential for distortion that arises from the anachronisms and
the dialectic disluxations that will as a consequence result.
SS, quoting JA, citing JR, paraphrasing SS, interpreting CSP:
| And here are the pair of sentences which you impute to Peirce qua
| fallibilist, which you regard as being paradoxical in import.
|
| P1. "we think each one of our beliefs to be true, and,
| indeed, it is mere tautology to say so" (CP 5.375)
|
| S1 is your restatement of P1 ...
|
| S1. (For every x)(I believe x -> x is true).
SS, quoting JA:
| This has been said before, by Peter Skagestad and
| probably others, but S1 is not a paraphrase of P1.
|
| A better try would be, for all propositions P and persons Q,
|
| If P is a belief of Q, then Q thinks that P is true.
|
| And that is a tautology, in the sense of repeating oneself.
SS: No, Jon, you have not got it quite right. S1 was not my restatement of P1;
I gave S1 as a paraphrase of what a believer must believe, given that P1 is true.
That is not quite the same (though in later passages, I did sometimes carelessly
refer to S1 as a "paraphrase of P1").
I have no probleme with the idea that interpretation is inescapably abductive:
http://www.chss.montclair.edu/inquiry/fall95/awbrey.html
The question is whether the interpretant preserves a semblance of the meaning.
SS: In response to the objection of Peter Skagestad and Mark Silcox,
which is the same as that which you are now making, I conceded that:
SS: (1) (For every x)I believe(I believe x -> x is true)
Peirce did not say this.
SS: is not the same as:
SS: (2) I believe(For every x)(I believe x-> x is true).
Peirce did not say this.
SS: But on the assumption that the believer is intelligent,
and that he sees the conditional in (1) as a necessary
("tautologous") truth, he should be able to make an
inference like the following:
The conditional in (1) is not necessary.
I don't know anybody who would say this.
SS: "Any arbitrarily chosen belief of mine must be believed by me to be true"
This is a non-sequitur. Oh wait.
Any arbitrarily chosen belief of mine must be believed-by-me-to-be-true.
Okay. But that's what he said in the first place.
And this statement does not confict with believing
that some belief of mine may turn-out-to-be-false.
A statement can be believed-by-me-to-be-true and turn-out-to-be-false.
Peirce's statement again:
| But we think each one of our beliefs to be true,
| and, indeed, it is mere tautology to say so.
|
| CSP, 'Collected Papers', CP 5.375
This has the form of:
| But we can cover any distance we can run at a pace faster than a walk.
Straightened out a bit:
| Any distance we can run is a distance we can cover faster than a walk.
The tautology is one that occurs at the level of the two predicates:
"runnable" and "coverable at a pace faster than a walk". It would
be better to avoid worrying about the quantifiers in this reading.
SS: Therefore,
SS: "All my beliefs are believed by me to be true"
SS: which is a valid universal generalization of the same kind as:
SS: Any arbitrarily chosen natural number must be a product of primes;
therefore, all natural numbers are products of primes.
SS: Any arbitrarily chosen cat must be a mammal;
therefore, all cats are mammals.
SS: It is true that this is an inference that calls for some logical skill on the
part of the believer, so that someone could believe P1 without believing S1,
but we are talking about Peirce, and whether HIS belief in fallibilism is
consistent with HIS belief in P1. I think there can be no doubt about
his belief in P1. As to what it is exactly that he believes, when he
believes in fallibilism, that is a more difficult question. I am now
having doubts that "Some of my beliefs are false," or
SS: (S2) (For some x)(I believe x & x is not true)
SS: fairly expresses Peirce's Fallibilism. I discussed that possibility in my
summary letter, under the heading "First Solution". More needs to be said
about it, but I'll keep it for another communication, possibly in response
to Joseph's forthcoming letter.
I believe that the generic problem here is a "poverty of syntax".
Syntax, expecially isolated syntax fragments of natural language
idioms, may constrain but it cannot utterly determine the models.
You have to gather independent evidence as to what the intended
models may be. In Peirce's case, his use of the word "belief",
as in "state of belief" as in "The irritation of doubt causes a
struggle to attain a state of belief", simply points to a whole
different order of models (universes + predicates) than the ones
that you are presently taking for granted as the only possible
models, most likely importing them from the discussions with
which you have become familiar on the contemporary scene.
One of the most significant aspects of Peirce's whole
approach is that he is talking about a process, one
in which signs, in particular, beliefs and concepts,
can enter and exit the pool of accepted, acted on,
adopted, trusted, utilized resources. Your use
of quantifiers is assuming a static situation,
as if the population of beliefs were fixed,
no pun, for once, intended. This is why
you appear to be repeating Parmenidean
paradoxes in the mental realm, as if
to show that changing one's mind is
impossible. It is not necessary
to invent modal or tensed logic
to deal with this, as change
can be modeled in the ways
that mathematics has been
doing it for a long time.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Note 13
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
I believe that one should always steer into a skid, but I doubt it.
That expresses the swerve of my learned dispositions, in cars with
rear-wheel drives on icy roads, and its corrective waylaying by my
first trip in a rental car, with front-wheel drive, on an icy road,
about as well as any collection of mere linguistic mechanisms will.
The circumstunts that mere words will not convey what I learned by
way of this adventition and all of my other near-death experiences
in this life is merely the insufficiency of words and their author.
Phenomena come first, theories come later,
on the evolutionary scale of time, anyway.
The circumstance that theories are always
falling short of phenomena in some degree,
does not stay the phenomenon in its orbit.
Animate creatures capable of inquiry, people like us, acted on dispositions
that we call "belief" and experienced experiences that we call "doubt" long
before they had the concepts, much less the words, "belief" and "doubt", or
universal quantifiers "all" and "each", with or without existential import,
with or without hypostatic general import, with or without game-theoretic
import, with or without predesignated domains of quantification, with or
without you name what comes next. Concepts, mental symbols to pragmatic
thinkers, are instrumental goods that we import through the customs of
biology and culture. They come and go. I love the game of etymology
and enjoy an apt bit of ordinary language analysis as much as anyone
has a right to, but the theory that you can wring all your theories
of phenomena, no matter how complex, out of commonsense word usage
is a notion whose time has come and gone. It just ain't science.
| Belief and doubt may be conceived to be distinguished only in degree.
|
| CSP, CE 3, pages 21.
|
| C.S. Peirce, MS 182, 1872, "Chapter 1 (Enlarged Abstract)", pages 20-21 in:
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 3, 1872-1878',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1986.
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
VOOP. Varieties Of Ontology Project
Problem Statement.
A. What are the different types of ontology projects
that are covered by our current scope and purpose?
B. What are the criteria that are appropriate
to each of the different ontology projects?
Given, then, that different types of ontology projects
will have different criteria for the acceptability and
the adequacy of proposals at each stage of development,
let us see if we can formulate the respective criteria
for a number of ontology projects that fall within the
charge, scope and purpose of a standard upper ontology.
A variety of ontology projects come to mind.
I will give them these working designations:
1. ROSO
What are the minimal criteria of acceptability of
a "research oriented scientific ontology" (ROSO)?
2. ULTO
What are the minimal criteria of acceptability for
an "upper level technical ontology" (ULTO)?
3. URFO
What are the minimal criteria of acceptability for
an "un-reflective folk ontology" (URFO)?
We've all concurred, or at least relented, that there's
room enough under the Standard Umbrella Ontology for the
type of "un-reflective folk ontology" (URFO) that concerns
itself mostly with "shoes, ships, sealing wax", and so on,
but the question remains, on less rainy days, whether the
principles and the parameters that suit the garden variety
URFO are adaptable to the rigors of the ROSO and the ULTO.
After we have settled on the minimal criteria of acceptability,
we might then venture into establishing the ideal criteria of
adequacy for the respective types of ontologies.
Defining, or at least characterizing these types
of ontology projects would of course be a major
part of the task of developing the respective
criteria for acceptability and adequacy.
Notes from previous exchanges:
JA = Jon Awbrey
JH = Jay Halcomb
PG = Pierre Grenon
PG: Never the less, it seems to me that this group would be
better off if proposed material was judged on criteria
similar to those by which the final product shall be
evaluated, rather than dependent upon pleasant
email exchanges.
JH: I agree with this view, which was the essential point
of my last e-mail -- getting more specific about such
criteria for working documents.
JA: Many people, present writer included, have observed that the criteria
appropriate to different kinds of ontology applications and projects,
all of them nonetheless falling under the rather large tent of our
scope and purpose document, may be radically different.
JA: In particular, I have pointed to the differences in working methodology
and goals of research oriented ontologies and, for the lack of a better
name, so-called commonsense ontologies.
JH: Precisely so. I think that we've many of us said these similar
things at one time or another, and we always return to them when
a proposal is made (recall the discussion about the CycL language
when that proposal was made). That is why I think that developing
clearer acceptance criteria, upfront, for specifying these various
targets is important, when it comes to working documents for the
group. Specifically, developing specification criteria for
terminologies, languages, and logic(s). I would hope the
IFF folks should have some specific thoughts about this.
JA: Until a better term comes along, I'm using the word "project"
somewhat in the way that people speak of cultural projects or
existential projects -- broad, compelling, if slightly vague
intimations of something that needs to be done.
JA: Here is a narrative about one sort of ontology project,
the aims, criteria, and working assumptions of which
I am acquainted with, and feel like I understand:
JA: I once got sold on the project of building software bridges between
qualitative and quantitative research. For example, in many areas
of clinical practice, medical anthropology, and public health one
has "practitioner-scientist models" where people accumulate lots
of free-floating informal hunches and qualitative impressions in
their on-the-job settings, that they then need to follow up with
hard data gathering, quantitatively measurable constructs, and
the usual battery of statistical methods. A lot of practical
savvy never gets widely distributed, and a lot of benighted
mythology never gets tested, all for the lack of good ways
to refine this "personal knowledge" into scientific truth.
JA: It still seems to me that properly designed lexical and logical resources
ought to provide us with some of the plancks we need to build this bridge.
JA: At first strike, it sounds like this ought to involve an integration of
research oriented and common sense ontologies. But there has seemed to
arise one insurmountable obstacle after another in trying to do this.
JA: Just by way of focusing on a concrete illustration, take the word "event".
Formalizing the concept of "event" for a research oriented ontology does
not require any discusssion on our part. Those discussions were carried
out somewhere between the days of powdered-wig-wearing-high-rollers and
the days of manurial comparisons. To get the standard axioms, one goes
to a standard reference book and copies them into one's knowledge base:
| PAS. Probability And Statistics -- Ontology List
|
| 01. http://suo.ieee.org/ontology/msg04885.html
| 02. http://suo.ieee.org/ontology/msg04886.html
| 03. http://suo.ieee.org/ontology/msg04887.html
| 04. http://suo.ieee.org/ontology/msg04888.html
|
| et sic deinceps ...
JA: The only question is whether one's favorite ontology prover is up to
the snuff of proving whatever theorems need to be proved thereon.
JA: There can be no compromise with these criteria.
The research market simply will not bear it.
So if there is to be an integration with
nontechnical language and methodology,
it must be an augmentation of these
basics and not their overwriting.
JA: I have gotten used to the idea that there is another sort of ontology project,
but since I do not get the cogency of it, it seems like its definition and its
criteria of validity would have to come from the critical self-examination of
those whose project it is. All I know at present is that the obvious course
that I suggested above for formalizing the concept "event" is probably the
course of last resort from the standpoint of this alternative project.
JA: That is what I mean by radical differences in working criteria for acceptance.
JA: Similar disjunctions of approach and acceptability could be observed
for several other dimensions of diversity among ontological projects,
for example, the "already been chewed" vs. the "knowledge soup" brands,
that is, those who expect full-fledged axiom systems from the outset
vs. those who would gel their knowledge chunks out of a semiotic sol.
VORE. Varieties Of Recalcitrant Experience
VORE. Note 1
| Once upon a time and a very good time it was there was | a moocow coming down along the road and this moocow that | was down along the road met a nicens little boy named | baby tuckoo .... | | His father told him that story: his father looked at him | through a glass: he had a hairy face. | | He was baby tuckoo. The moocow came down the road where | Betty Byrne lived: she sold lemon platt. | | O, the wild rose blossoms | On the little green place. | | He sang that song. That was his song. | | O, the green wothe botheth. | | Joyce, 'Portrait', p. 1. | | James Joyce, 'A Portrait of the Artist as a Young Man', | Bantam, New York, NY, 1992. Originally published 1916.
VORE. Note 2
| It was the hour for sums. Father Arnall wrote a hard sum on the | board and then said: | | -- Now then, who will win? Go ahead, York! Go ahead, Lancaster! | | Stephen tried his best but the sum was too hard and he felt confused. | The little silk badge with the white rose on it that was pinned on the | breast of his jacket began to flutter. He was no good at sums but he | tried his best so that York might not lose. Father Arnall's face looked | very black but he was not in a wax: he was laughing. Then Jack Lawton | cracked his fingers and Father Arnall looked at his copybook and said: | | -- Right. Bravo Lancaster! The red rose wins. Come on now, York! | Forge ahead! | | Jack Lawton looked over from his side. The little silk badge with | the red rose on it looked very rich because he had a blue sailor top | on. Stephen felt his own face red too, thinking of all the bets about | who would get first place in Elements, Jack Lawton or he. Some weeks | Jack Lawton got the card for first and some weeks he got the card for | first. His white silk badge fluttered and fluttered as he worked at | the next sum and heard Father Arnall's voice. Then all his eagerness | passed away and he felt his face quite cool. He thought his face must | be white because it felt so cool. He could not get out the answer for | the sum but it did not matter. White roses and red roses: those were | beautiful colours to think of. And the cards for first place and third | place were beautiful colours too: pink and cream and lavender. Lavender | and cream and pink roses were beautiful to think of. Perhaps a wild rose | might be like those colours and he remembered the song about the wild rose | blossoms on the little green place. But you could not have a green rose. | But perhaps somewhere in the world you could. | | Joyce, 'Portrait', pp. 6-7. | | James Joyce, 'A Portrait of the Artist as a Young Man', | Bantam, New York, NY, 1992. Originally published 1916.
VORE. Note 3
| The equation on the page of his scribbler began to spread out a widening tail, | eyed and starred like a peacock's; and, when the eyes and stars of its indices | had been eliminated, began slowly to fold itself together again. The indices | appearing and disappearing were eyes opening and closing; the eyes opening | and closing were stars being born and being quenched. The vast cycle | of starry life bore his weary mind outward to its verge and inward | to its centre, a distant music accompanying him outward and inward. | What music? The music came nearer and he recalled the words, the | words of Shelley's fragment upon the moon wandering companionless, | pale for weariness. The stars began to crumble and a cloud of | fine star-dust fell through space. | | The dull light fell more faintly upon the page whereon another equation | began to unfold itself slowly and to spread abroad its widening tail. | It was his own soul going forth to experience, unfolding itself | sin by sin, spreading abroad the balefire of its burning stars | and folding back upon itself, fading slowly, quenching its | own lights and fires. They were quenched: and the | cold darkness filled chaos. | | Joyce, 'Portrait', p. 97. | | James Joyce, 'A Portrait of the Artist as a Young Man', | Bantam, New York, NY, 1992. Originally published 1916.
VORE. Note 4
| The formula which he wrote obediently on the sheet of paper, the coiling and | uncoiling calculations of the professor, the spectrelike symbols of force and | velocity fascinated and jaded Stephen's mind. He had heard some say that the | old professor was an atheist freemason. Oh, the grey dull day! It seemed a | limbo of painless patient consciousness through which souls of mathematicians | might wander, projecting long slender fabrics from plane to plane of ever rarer | and paler twilight, radiating swift eddies to the last verges of a universe ever | vaster, farther and more impalpable. | | -- So we must distinguish between elliptical and ellipsoidal. | Perhaps some of you gentlemen may be familiar with the works | of Mr W.S. Gilbert. In one of his songs he speaks of the | billiard sharp who is condemned to play: | | On a cloth untrue | With a twisted cue | And elliptical billiard balls. | | -- He means a ball having the form of the ellipsoid | of the principal axes of which I spoke a moment ago. -- | | Joyce, 'Portrait', pp. 185-186. | | James Joyce, 'A Portrait of the Artist as a Young Man', | Bantam, New York, NY, 1992. Originally published 1916.
VORE. Note 5
| I was, at that time, in Germany, whither the wars, | which have not yet finished there, had called me, | and as I was returning from the coronation of the | Emperor to join the army, the onset of winter held | me up in quarters in which, finding no company to | distract me, and having, fortunately, no cares or | passions to disturb me, I spent the whole day shut | up in a room heated by an enclosed stove, where I | had complete leisure to meditate on my own thoughts. | | Descartes, DOM, p. 35. | | Rene Descartes, "Discourse on the Method | of Properly Conducting One's Reason and | of Seeking the Truth in the Sciences", | pp. 25-91 in 'Discourse on Method and | the Meditations', translated with an | introduction by F.E. Sutcliffe, | Penguin, London, UK, 1968.
VORE. Note 6
| A very young child may always be observed to watch its own | body with great attention. There is every reason why this | should be so, for from the child's point of view this body | is the most important thing in the universe. Only what it | touches has any actual and present feeling; only what it | faces has any actual color; only what is on its tongue | has any actual taste. | | C.S. Peirce, "Questions", CP 5.229. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 7
| No one questions that, when a sound is heard by a child, he thinks, | not of himself as hearing, but of the bell or other object as sounding. | How when he wills to move a table? Does he then think of himself as | desiring, or only of the table as fit to be moved? That he has the | latter thought, is beyond question; that he has the former, must, | until the existence of an intuitive self-consciousness is proved, | remain an arbitrary and baseless supposition. There is no good | reason for thinking that he is less ignorant of his own peculiar | condition than the angry adult who denies that he is in a passion. | | C.S. Peirce, "Questions", CP 5.230. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 8
| The child, however, must soon discover by observation | that things which are thus fit to be changed are apt | actually to undergo this change, after a contact with | that peculiarly important body called Willy or Johnny. | This consideration makes this body still more important | and central, since it establishes a connection between | the fitness of a thing to be changed and a tendency in | this body to touch it before it is changed. | | C.S. Peirce, "Questions", CP 5.231. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 9
| The child learns to understand the language; that is to say, a connection | between certain sounds and certain facts becomes established in his mind. | He has previously noticed the connection between these sounds and the | motions of the lips of bodies somewhat similar to the central one, | and has tried the experiment of putting his hand on those lips | and has found the sound in that case to be smothered. He thus | connects that language with bodies somewhat similar to the | central one. By efforts, so unenergetic that they should | be called rather instinctive, perhaps, than tentative, he | learns to produce those sounds. So he begins to converse. | | C.S. Peirce, "Questions", CP 5.232. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 10
| It must be about this time that he begins to find that what | these people about him say is the very best evidence of fact. | So much so, that testimony is even a stronger mark of fact than | 'the facts themselves', or rather than what must now be thought | of as the 'appearances' themselves. (I may remark, by the way, | that this remains so through life; testimony will convince a | man that he himself is mad.) | | A child hears it said that the stove is hot. But it is not, he says; | and, indeed, that central body is not touching it, and only what that | touches is hot or cold. But he touches it, and finds the testimony | confirmed in a striking way. Thus, he becomes aware of ignorance, | and it is necessary to suppose a 'self' in which this ignorance can | inhere. So testimony gives the first dawning of self-consciousness. | | C.S. Peirce, "Questions", CP 5.233. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 11
| But, further, although usually appearances are either | only confirmed or merely supplemented by testimony, yet | there is a certain remarkable class of appearances which | are continually contradicted by testimony. These are those | predicates which 'we' know to be emotional, but which 'he' | distinguishes by their connection with the movements of that | central person, himself (that the table wants moving, etc.) | These judgments are generally denied by others. Moreover, he | has reason to think that others, also, have such judgments which | are quite denied by all the rest. Thus, he adds to the conception | of appearance as the actualization of fact, the conception of it as | something 'private' and valid only for one body. In short, 'error' | appears, and it can be explained only by supposing a 'self' which | is fallible. | | Ignorance and error are all that | distinguish our private selves | from the absolute 'ego' of | pure apperception. | | C.S. Peirce, "Questions", CP 5.234-235. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 12
| Now, the theory which, for the sake of perspicuity, has thus | been stated in a specific form, may be summed up as follows: | | At the age at which we know children to be self-conscious, we know that | they have been made aware of ignorance and error; and we know them to | possess at that age powers of understanding sufficient to enable them | to infer from ignorance and error their own existence. | | Thus we find that known faculties, acting under conditions known | to exist, would rise to self-consciousness. The only essential | defect in this account of the matter is, that while we know that | children exercise 'as much' understanding as is here supposed, | we do not know that they exercise it in precisely this way. | Still the supposition that they do so is infinitely more | supported by facts, than the supposition of a wholly | peculiar faculty of the mind. | | C.S. Peirce, "Questions", CP 5.236. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 13
| The only argument worth noticing | for the existence of an intuitive | self-consciousness is this: | | We are more certain of our own existence than of any other fact; | a premiss cannot determine a conclusion to be more certain than | it is itself; hence, our own existence cannot have been inferred | from any other fact. | | The first premiss must be admitted, but the second premiss is founded | on an exploded theory of logic. A conclusion cannot be more certain | than that some one of the facts which support it is true, but it may | easily be more certain than any one of those facts. | | Let us suppose, for example, that a dozen witnesses testify to an occurrence. | Then my belief in that occurrence rests on the belief that each of those men | is generally to be believed upon oath. Yet the fact testified to is made | more certain than that any one of those men is generally to be believed. | | In the same way, to the developed mind of man, his own existence is supported | by 'every other fact', and is, therefore, incomparably more certain than any | one of these facts. But it cannot be said to be more certain than that there | is another fact, since there is no doubt perceptible in either case. | | It is to be concluded, then, that there is no necessity of supposing an intuitive | self-consciousness, since self-consciousness may easily be the result of inference. | | C.S. Peirce, "Questions", CP 5.237. | | C.S. Peirce, "Questions Concerning Certain Faculties Claimed for Man", | paragraphs CP 5.213-263 in 'Collected Papers', Harvard University Press, | Cambridge, MA, 1960. First published, 'Journal of Speculative Philosophy', | vol. 2, pp. 103-114, 1868.
VORE. Note 14
| His soul had arisen from the grave of boyhood, spurning her graveclothes. | Yes! Yes! Yes! He would create proudly out of the freedom and power of | his soul, as the great artificer whose name he bore, a living thing, | new and soaring and beautiful, impalpable, imperishable. | | Joyce, 'Portrait', pp. 163-164. | | James Joyce, 'A Portrait of the Artist as a Young Man', | Bantam, New York, NY, 1992. Originally published 1916.
VORE. Note 15
| On another occasion I heard one of the grown-ups saying to | another "When is that young Lyon coming?" I pricked up my | ears and said "Is there a lion coming?" "Yes," they said, | "he's coming on Sunday. He'll be quite tame and you shall | see him in the drawing-room." I counted the days till Sunday | and the hours through Sunday morning. At last I was told the | young lion was in the drawing-room and I could come and see him. | I came. And he was an ordinary young man named Lyon. I was | utterly overwhelmed by the disenchantment and still remember | with anguish the depths of my despair. | | Russell, 'Autobiography', p. 18. | | Bertrand Russell, 'Autobiography', with an introduction by | Michael Foot, Routledge, London, UK, 1998. First published | in 3 volumes by George Allen & Unwin, 1967-1969.
VORE. Varieties Of Recalcitrant Experience • Application
VORE. Application Note 1
Most of the year I spend my time wondering when logicians will begin to take the phenomena and the problems of Truth In Science seriously -- but for a brief time in summer my fancy turns to wondering when they will get around to taking Truth In Literature seriously. Now, there is a market for this -- I especially remember an editorial or letter in the 'Chronicle of Higher Education' a few years back, the gist of which was a literature teacher's half plaintive half wistful wishing for software that would help researchers and students with the truly insightful analysis of literary texts, tools that would be sensitive to something more than simple-minded syntactic similarities and help us to deal with the full complexity of meanings that folks pack into narratives, novels, poems, and other expressions of human experience. To sharpen the point a bit, we might well ask ourselves: Just how far do the customary categories of first order logic take us in approaching this realm of applications? For instance, take the term "Stephen Dedulus", in any of its variant spellings, as it is used by James Joyce in his various works. Just for starters, is this term a constant or a variable? Is this term individual or general? Are these even the primary questions to ask about such a term, or do we perhaps miss the whole point of the text -- not that I would try to be more holistic than Quine -- in approaching it from this direction?
VORE. Application Note 2
Sometimes a typo is just a typo -- among the variant spellings
of "Stephen Dedalus" that James Joyce actually uses, I mostly
had in mind "Stephen Daedelus" and "Stephanos Dedalos", but
not what I spelled out before, which was my own mistyping.
Consider the following bits of "metadata":
1. In her introduction to the Signet edition of Joyce's 'Dubliners',
Edna O'Brien tells us this:
| He chose a pseudonym, that of his future fictional character,
| Stephen Daedelus, because he was ashamed of writing, as he said,
| for the "Pigs Paper".
2. The blurb on the back of my Bantam paperback copy of 'Portrait'
tells me this:
| James Joyce's highly autobiographical novel was first published
| in the United States in 1916 to immediate acclaim. Ezra Pound
| accurately predicted that Joyce's book would "remain a permanent
| part of English literature", while H.G. Wells dubbed it "by far
| the most important living and convincing picture that exists of
| an Irish Catholic upbringing". A remarkably rich study of a
| developing mind, 'A Portrait of the Artist as a Young Man'
| made an indelible mark on literature and confirmed Joyce's
| reputation as one of the world's great and lasting writers.
What do I mean by taking the phenomena and the problems of Truth In Literature
seriously? Perhaps I can explain some of what it means to me in the following
way. From the beginning of my reading experience, I am sure at least from the
days of 'See Spot Run' and 'Funny Funny Puff', it has been a standard exercise
to read a text and then to give some report of its meaning. I couldn't put my
finger on when exactly the transition occurred, but I know that it soon became
insufficient to comment on nothing more than literal aspects of the stories in
question. I'm sure that all my readers have had a similar upbringing. So you
know the brands of evasions up with which none of your teachers would have put.
In contrast with that, one of the favorite patterns of reasoning among
certain schools of logic in the last century, along with many of their
AI disciples, has gone a bit like this:
Method X is adequate to all important problems.
Problem Y is resistant to solution by Method X.
---------------------------------------------------
Therefore, Problem Y is not an important problem.
Perhaps it is just envy that I could not have gone to such a school,
but I find myself constitutionally incapable of taking these orders
of answers seriously.
VORE. Application Note 3
Many currents have brought us to the current juncture. I will not endeavor to untangle their viscosities and vortices, but lean to respond as responsibly as I can to the full complex of their flows or their frictions. If we dare, in our ship of logic, to coast past the siren shores of literature without more than the ordinary quota of wax in our ears, then let us lash ourselves to the mast with this guideline: Logic should not make us stupid.
VORE. Application Note 4
What I really want to understand is the What, the How, and the Why of stories, what stories are, their "quiddity", how stories work and why people tell them. If I understood the Why then I might have a clue to the what -- that would be a functional explanation, in the way that the word "function" used to be used in anthropology and sociology, that is, before the "(neo-)functionalist turn" turned its sense around into the opposite of what it used to mean -- but that, as they say, is another story. If I understood the How, then maybe it would tell me something about the what and the why of the story -- in the way that Aristotle told us that studying the action can reveal to us the character and the motivation. A very pragmant suggestion, that. This study began, ostensibly enough, as what seemed like a theme out of Quine's "Two Dogmas of Empiricism, but perusers of Peirce will already have experienced their all too private recognition that "recalcitrant experience" is just another name for the "brute reaction" with which the world greets our daydreams of theory, and that he characterized far less picaresquely under the category of "Secondness". In order to understand Quine's story it becomes necessary to examine not only the sources that he rightly acknowledged but the springs of his action that he failed to acknowledge or misrepresented, plus the the backcloth of ideas that he protagonized about or reacted against. Some data on several of these scores can be had by looking at Russell's work, and I have in mind tracing the trajectory of a particular development there, the plot of which I am charting out on the Ontology List, in progress here: POLA. Philosophy Of Logical Atomism -- Ontology List 01-19 Other information on this score must come from a study of Peirce's work. Personally, I always find that it helps to return to the source, in two senses, at least, the precursory authors and their earliest expressions. Two investigations along these lines have been initiated here: JITL. Just In Time Logic -- Ontology List 01-04 VOLS. Verities Of Likely Stories -- Ontology List 01-03 The "Just In Time Logic" thread, to express it in contemporary terms -- that's one way to make it sound smarter, I guess -- will contemplate Peirce's early ideas about the "temporal dynamics of belief revision", taking a view of the inquiry process as the time-evolution of thought. The "Verities Of Likely Stories" theme will return to the sources of our contemporary ideas about analogies, homologies, icons, metaphors, models, morphisms, ..., to mention just a few kin of a Proteus-resembling family. This is not the bottom line, but it will have to suffice for a middling one, since I and you and we and ontology are as always in medias res.
Document Histories
CROM. Critical Reflection On Method • Document History
Inquiry List (Oct 2003)
Ontology List (Oct 2003)
SUO List (Oct 2003)
CROM. Critical Reflection On Method • Discussion History
Inquiry List (Oct 2003)
Ontology List (Oct 2003)
SUO List (Oct 2003)
DIEP. De In Esse Predication • Document History
Inquiry List (Sep 2003)
- http://web.archive.org/web/20061014001359/http://stderr.org/pipermail/inquiry/2003-September/000780.html
- http://web.archive.org/web/20061014001009/http://stderr.org/pipermail/inquiry/2003-September/000781.html
- http://web.archive.org/web/20061014000944/http://stderr.org/pipermail/inquiry/2003-September/000782.html
- http://web.archive.org/web/20061014001114/http://stderr.org/pipermail/inquiry/2003-September/000783.html
- http://web.archive.org/web/20061014000941/http://stderr.org/pipermail/inquiry/2003-September/000784.html
- http://web.archive.org/web/20061014001104/http://stderr.org/pipermail/inquiry/2003-September/000785.html
- http://web.archive.org/web/20061014001241/http://stderr.org/pipermail/inquiry/2003-September/000787.html
- http://web.archive.org/web/20061014000909/http://stderr.org/pipermail/inquiry/2003-September/000788.html
- http://web.archive.org/web/20061014000902/http://stderr.org/pipermail/inquiry/2003-September/000789.html
- http://web.archive.org/web/20061014001131/http://stderr.org/pipermail/inquiry/2003-September/000792.html
- http://web.archive.org/web/20061014001200/http://stderr.org/pipermail/inquiry/2003-September/000793.html
- http://web.archive.org/web/20061014001215/http://stderr.org/pipermail/inquiry/2003-September/000794.html
- http://web.archive.org/web/20061014001218/http://stderr.org/pipermail/inquiry/2003-September/000795.html
- http://web.archive.org/web/20061014001332/http://stderr.org/pipermail/inquiry/2003-September/000800.html
- http://web.archive.org/web/20061014001154/http://stderr.org/pipermail/inquiry/2003-September/000801.html
- http://web.archive.org/web/20061014001226/http://stderr.org/pipermail/inquiry/2003-September/000802.html
- http://web.archive.org/web/20061014001402/http://stderr.org/pipermail/inquiry/2003-September/000804.html
- http://web.archive.org/web/20061014001001/http://stderr.org/pipermail/inquiry/2003-September/000805.html
- http://web.archive.org/web/20061014001347/http://stderr.org/pipermail/inquiry/2003-September/000834.html
Ontology List (Sep 2003)
- http://web.archive.org/web/20070313230956/http://suo.ieee.org/ontology/msg05026.html
- http://web.archive.org/web/20070316003847/http://suo.ieee.org/ontology/msg05027.html
- http://web.archive.org/web/20070317131614/http://suo.ieee.org/ontology/msg05028.html
- http://web.archive.org/web/20070320020154/http://suo.ieee.org/ontology/msg05029.html
- http://web.archive.org/web/20070323144756/http://suo.ieee.org/ontology/msg05030.html
- http://web.archive.org/web/20070328013010/http://suo.ieee.org/ontology/msg05031.html
- http://web.archive.org/web/20050826220928/http://suo.ieee.org/ontology/msg05033.html
- http://web.archive.org/web/20070316003856/http://suo.ieee.org/ontology/msg05034.html
- http://web.archive.org/web/20070313231006/http://suo.ieee.org/ontology/msg05035.html
- http://web.archive.org/web/20070313231017/http://suo.ieee.org/ontology/msg05038.html
- http://web.archive.org/web/20070313231027/http://suo.ieee.org/ontology/msg05039.html
- http://web.archive.org/web/20070313231037/http://suo.ieee.org/ontology/msg05040.html
- http://web.archive.org/web/20070313231048/http://suo.ieee.org/ontology/msg05041.html
- http://web.archive.org/web/20070313231058/http://suo.ieee.org/ontology/msg05048.html
- http://web.archive.org/web/20070310113354/http://suo.ieee.org/ontology/msg05049.html
- http://web.archive.org/web/20070313231108/http://suo.ieee.org/ontology/msg05050.html
- http://web.archive.org/web/20070310113519/http://suo.ieee.org/ontology/msg05052.html
- http://web.archive.org/web/20070222033549/http://suo.ieee.org/ontology/msg05053.html
- http://web.archive.org/web/20070219035929/http://suo.ieee.org/ontology/msg05082.html
DIEP. De In Esse Predication • Discussion History
Inquiry List (Sep 2003)
- http://web.archive.org/web/20061014001032/http://stderr.org/pipermail/inquiry/2003-September/000786.html
- http://web.archive.org/web/20061014001019/http://stderr.org/pipermail/inquiry/2003-September/000790.html
- http://web.archive.org/web/20061014000906/http://stderr.org/pipermail/inquiry/2003-September/000796.html
- http://web.archive.org/web/20061014001045/http://stderr.org/pipermail/inquiry/2003-September/000797.html
- http://web.archive.org/web/20061014000930/http://stderr.org/pipermail/inquiry/2003-September/000799.html
- http://web.archive.org/web/20061014001253/http://stderr.org/pipermail/inquiry/2003-September/000803.html
- http://web.archive.org/web/20061014001212/http://stderr.org/pipermail/inquiry/2003-September/000806.html
- http://web.archive.org/web/20061014000859/http://stderr.org/pipermail/inquiry/2003-September/000798.html
Ontology List (Sep 2003)
- http://web.archive.org/web/20070317221422/http://suo.ieee.org/ontology/msg05032.html
- http://web.archive.org/web/20070316003906/http://suo.ieee.org/ontology/msg05036.html
- http://web.archive.org/web/20121010204912/http://suo.ieee.org/ontology/msg05043.html
- http://web.archive.org/web/20070222033717/http://suo.ieee.org/ontology/msg05045.html
- http://web.archive.org/web/20070222033504/http://suo.ieee.org/ontology/msg05047.html
- http://web.archive.org/web/20070222033848/http://suo.ieee.org/ontology/msg05051.html
- http://web.archive.org/web/20070219072137/http://suo.ieee.org/ontology/msg05054.html
- http://web.archive.org/web/20070222033828/http://suo.ieee.org/ontology/msg05046.html
HAPA. Hypostatic And Prescisive Abstraction • Document History 1
Inquiry List (Sep–Oct 2003)
- http://web.archive.org/web/20120505135759/http://stderr.org/pipermail/inquiry/2003-September/thread.html#841
- http://web.archive.org/web/20150111162004/http://stderr.org/pipermail/inquiry/2003-October/thread.html#899
- http://web.archive.org/web/20061014001256/http://stderr.org/pipermail/inquiry/2003-September/000841.html
- http://web.archive.org/web/20061014001328/http://stderr.org/pipermail/inquiry/2003-September/000842.html
- http://web.archive.org/web/20061014000958/http://stderr.org/pipermail/inquiry/2003-September/000843.html
- http://web.archive.org/web/20061014001026/http://stderr.org/pipermail/inquiry/2003-September/000851.html
- http://web.archive.org/web/20061014001036/http://stderr.org/pipermail/inquiry/2003-September/000858.html
- http://web.archive.org/web/20061014000913/http://stderr.org/pipermail/inquiry/2003-September/000859.html
- http://web.archive.org/web/20061014001029/http://stderr.org/pipermail/inquiry/2003-September/000863.html
- http://web.archive.org/web/20061014001138/http://stderr.org/pipermail/inquiry/2003-September/000866.html
- http://web.archive.org/web/20061014010325/http://stderr.org/pipermail/inquiry/2003-October/000899.html
- http://web.archive.org/web/20061014010230/http://stderr.org/pipermail/inquiry/2003-October/000902.html
- http://web.archive.org/web/20061014010349/http://stderr.org/pipermail/inquiry/2003-October/000903.html
- http://web.archive.org/web/20061014010042/http://stderr.org/pipermail/inquiry/2003-October/000906.html
Ontology List (Sep–Oct 2003)
- http://web.archive.org/web/20070214054035/http://suo.ieee.org/ontology/msg05089.html
- http://web.archive.org/web/20070216005823/http://suo.ieee.org/ontology/msg05090.html
- http://web.archive.org/web/20070214054045/http://suo.ieee.org/ontology/msg05091.html
- http://web.archive.org/web/20070216005832/http://suo.ieee.org/ontology/msg05093.html
- http://web.archive.org/web/20070218070102/http://suo.ieee.org/ontology/msg05100.html
- http://web.archive.org/web/20050523211120/http://suo.ieee.org/ontology/msg05101.html
- http://web.archive.org/web/20070218041512/http://suo.ieee.org/ontology/msg05105.html
- http://web.archive.org/web/20070216102336/http://suo.ieee.org/ontology/msg05108.html
- http://web.archive.org/web/20070216102358/http://suo.ieee.org/ontology/msg05118.html
- http://web.archive.org/web/20070218041305/http://suo.ieee.org/ontology/msg05121.html
- http://web.archive.org/web/20060912171726/http://suo.ieee.org/ontology/msg05122.html
- http://web.archive.org/web/20070218041325/http://suo.ieee.org/ontology/msg05125.html
SUO List (Sep–Oct 2003)
- http://web.archive.org/web/20070219035737/http://suo.ieee.org/email/msg10964.html
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- http://web.archive.org/web/20070305075208/http://suo.ieee.org/email/msg10966.html
- http://web.archive.org/web/20070305075228/http://suo.ieee.org/email/msg10991.html
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- http://web.archive.org/web/20070305075258/http://suo.ieee.org/email/msg11028.html
- http://web.archive.org/web/20070305075309/http://suo.ieee.org/email/msg11079.html
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- http://web.archive.org/web/20070219035816/http://suo.ieee.org/email/msg11271.html
- http://web.archive.org/web/20070222005616/http://suo.ieee.org/email/msg11277.html
- http://web.archive.org/web/20070305075432/http://suo.ieee.org/email/msg11290.html
HAPA. Hypostatic And Prescisive Abstraction • Discussion History 1
Inquiry List (Sep–Oct 2003)
- http://web.archive.org/web/20120505135759/http://stderr.org/pipermail/inquiry/2003-September/thread.html#844
- http://web.archive.org/web/20150111162004/http://stderr.org/pipermail/inquiry/2003-October/thread.html#891
- http://web.archive.org/web/20150111162004/http://stderr.org/pipermail/inquiry/2003-October/thread.html#900
- http://web.archive.org/web/20061014001237/http://stderr.org/pipermail/inquiry/2003-September/000844.html
- http://web.archive.org/web/20061014010057/http://stderr.org/pipermail/inquiry/2003-October/000891.html
- http://web.archive.org/web/20061014010111/http://stderr.org/pipermail/inquiry/2003-October/000892.html
- http://web.archive.org/web/20061014010204/http://stderr.org/pipermail/inquiry/2003-October/000893.html
- http://web.archive.org/web/20061014010247/http://stderr.org/pipermail/inquiry/2003-October/000894.html
- http://web.archive.org/web/20061014010258/http://stderr.org/pipermail/inquiry/2003-October/000895.html
- http://web.archive.org/web/20061014010308/http://stderr.org/pipermail/inquiry/2003-October/000896.html
- http://web.archive.org/web/20061014010054/http://stderr.org/pipermail/inquiry/2003-October/000897.html
- http://web.archive.org/web/20061014010342/http://stderr.org/pipermail/inquiry/2003-October/000898.html
- http://web.archive.org/web/20061014010141/http://stderr.org/pipermail/inquiry/2003-October/000900.html
- http://web.archive.org/web/20061014010339/http://stderr.org/pipermail/inquiry/2003-October/000901.html
Ontology List (Sep–Oct 2003)
- http://web.archive.org/web/20070214054025/http://suo.ieee.org/ontology/msg05092.html
- http://web.archive.org/web/20070214053809/http://suo.ieee.org/ontology/msg05110.html
- http://web.archive.org/web/20070211023423/http://suo.ieee.org/ontology/msg05111.html
- http://web.archive.org/web/20070214053920/http://suo.ieee.org/ontology/msg05112.html
- http://web.archive.org/web/20070219040057/http://suo.ieee.org/ontology/msg05113.html
- http://web.archive.org/web/20060720162947/http://suo.ieee.org/ontology/msg05114.html
- http://web.archive.org/web/20060720163027/http://suo.ieee.org/ontology/msg05115.html
- http://web.archive.org/web/20060720163042/http://suo.ieee.org/ontology/msg05116.html
- http://web.archive.org/web/20070218041225/http://suo.ieee.org/ontology/msg05117.html
- http://web.archive.org/web/20070216102345/http://suo.ieee.org/ontology/msg05119.html
- http://web.archive.org/web/20070218041014/http://suo.ieee.org/ontology/msg05120.html
SUO List (Sep–Oct 2003)
- http://web.archive.org/web/20060517022017/http://suo.ieee.org/email/thrd45.html#10967
- http://web.archive.org/web/20070128135114/http://suo.ieee.org/email/thrd53.html#11227
- http://web.archive.org/web/20070305075218/http://suo.ieee.org/email/msg10967.html
- http://web.archive.org/web/20070305075320/http://suo.ieee.org/email/msg11227.html
- http://web.archive.org/web/20070305075331/http://suo.ieee.org/email/msg11228.html
- http://web.archive.org/web/20070305075342/http://suo.ieee.org/email/msg11229.html
- http://web.archive.org/web/20070222144959/http://suo.ieee.org/email/msg11231.html
- http://web.archive.org/web/20060721222834/http://suo.ieee.org/email/msg11232.html
- http://web.archive.org/web/20070305075351/http://suo.ieee.org/email/msg11234.html
- http://web.archive.org/web/20070305075401/http://suo.ieee.org/email/msg11236.html
- http://web.archive.org/web/20070305075411/http://suo.ieee.org/email/msg11237.html
- http://web.archive.org/web/20070219035806/http://suo.ieee.org/email/msg11240.html
- http://web.archive.org/web/20070305075421/http://suo.ieee.org/email/msg11267.html
HAPA. Hypostatic And Prescisive Abstraction • Document History 2
- Continuous Predicate
- Dormitive Virtue
- Dulcitive Virtue
- Math Abstraction
- Reading Runes
- Hypostatization
- Abstract Objects
- Subjectal Abstraction
- Definition of Predicate
- Second Intentions
- Logical Reflexion
- Epea Apteroenta
- Continuous Predicate
- Dormitive Virtue
- Dulcitive Virtue
- Math Abstraction
- Reading Runes
- Hypostatization
- Abstract Objects
- Subjectal Abstraction
- Definition of Predicate
- Second Intentions
- Logical Reflexion
- Epea Apteroenta
HAPA. Hypostatic And Prescisive Abstraction • Discussion History 2
- Metaphormazes
- Deciduation Problems
- Thematic Recapitulation
- Field Key, Kitchen Recipe
- Indirect Self Reference
- Genealogy & Paraphrasis
- Intention & Reflection
- Rhematic Saturation
- Relational Turn
- Tabula Erasa
- Directions
SUO List (Sep–Oct 2003) • (1) • (2)
- Metaphormazes
- Deciduation Problems
- Thematic Recapitulation
- Field Key, Kitchen Recipe
- Indirect Self Reference
- Genealogy & Paraphrasis
- Intention & Reflection
- Rhematic Saturation
- Relational Turn
- Tabula Erasa
- Directions
JITL. Just In Time Logic • Document History
Inquiry List (Aug 2003 – Apr 2005)
- http://web.archive.org/web/20120518012303/http://stderr.org/pipermail/inquiry/2003-August/thread.html#712
- http://web.archive.org/web/20120601160642/http://stderr.org/pipermail/inquiry/2005-April/thread.html#2542
- http://web.archive.org/web/20050330084824/http://stderr.org/pipermail/inquiry/2003-August/000712.html
- http://web.archive.org/web/20050330084832/http://stderr.org/pipermail/inquiry/2003-August/000714.html
- http://web.archive.org/web/20050330084845/http://stderr.org/pipermail/inquiry/2003-August/000717.html
- http://web.archive.org/web/20050330084852/http://stderr.org/pipermail/inquiry/2003-August/000719.html
- http://web.archive.org/web/20050330084904/http://stderr.org/pipermail/inquiry/2003-August/000722.html
- http://web.archive.org/web/20050330084816/http://stderr.org/pipermail/inquiry/2003-August/000723.html
- http://web.archive.org/web/20050330084908/http://stderr.org/pipermail/inquiry/2003-August/000724.html
- http://web.archive.org/web/20050330084912/http://stderr.org/pipermail/inquiry/2003-August/000725.html
- http://web.archive.org/web/20050330084916/http://stderr.org/pipermail/inquiry/2003-August/000726.html
- http://web.archive.org/web/20050330084921/http://stderr.org/pipermail/inquiry/2003-August/000727.html
- http://web.archive.org/web/20050330084925/http://stderr.org/pipermail/inquiry/2003-August/000728.html
- http://web.archive.org/web/20050330084929/http://stderr.org/pipermail/inquiry/2003-August/000729.html
- http://web.archive.org/web/20050330084933/http://stderr.org/pipermail/inquiry/2003-August/000730.html
- http://web.archive.org/web/20050331051247/http://stderr.org/pipermail/inquiry/2003-August/000731.html
- http://web.archive.org/web/20050331051252/http://stderr.org/pipermail/inquiry/2003-August/000732.html
- http://web.archive.org/web/20121113152840/http://stderr.org/pipermail/inquiry/2005-April/002542.html
- http://web.archive.org/web/20081120222140/http://stderr.org/pipermail/inquiry/2005-April/002543.html
- http://web.archive.org/web/20121113152903/http://stderr.org/pipermail/inquiry/2005-April/002544.html
Ontology List (Aug 2003)
- http://web.archive.org/web/20140405160400/http://suo.ieee.org/ontology/thrd11.html#04961
- http://web.archive.org/web/20140405160400/http://suo.ieee.org/ontology/thrd11.html#04965
- http://web.archive.org/web/20140405161017/http://suo.ieee.org/ontology/msg04961.html
- http://web.archive.org/web/20070306133915/http://suo.ieee.org/ontology/msg04962.html
- http://web.archive.org/web/20140405160005/http://suo.ieee.org/ontology/msg04965.html
- http://web.archive.org/web/20070306134016/http://suo.ieee.org/ontology/msg04967.html
- http://web.archive.org/web/20070306134046/http://suo.ieee.org/ontology/msg04970.html
- http://web.archive.org/web/20070306134056/http://suo.ieee.org/ontology/msg04971.html
- http://web.archive.org/web/20070306134107/http://suo.ieee.org/ontology/msg04972.html
- http://web.archive.org/web/20070306134117/http://suo.ieee.org/ontology/msg04973.html
- http://web.archive.org/web/20070306134128/http://suo.ieee.org/ontology/msg04974.html
- http://web.archive.org/web/20070306134138/http://suo.ieee.org/ontology/msg04975.html
- http://web.archive.org/web/20070306134155/http://suo.ieee.org/ontology/msg04976.html
- http://web.archive.org/web/20070306134206/http://suo.ieee.org/ontology/msg04977.html
- http://web.archive.org/web/20070306134220/http://suo.ieee.org/ontology/msg04978.html
- http://web.archive.org/web/20070306134231/http://suo.ieee.org/ontology/msg04979.html
- http://web.archive.org/web/20070306134241/http://suo.ieee.org/ontology/msg04980.html
NEKS. New Elements • Kaina Stoicheia • Document History
Inquiry List (Sep–Dec 2005)
- http://web.archive.org/web/20140927032017/http://stderr.org/pipermail/inquiry/2005-September/thread.html#3063
- http://web.archive.org/web/20150224133200/http://stderr.org/pipermail/inquiry/2005-October/thread.html#3075
- http://web.archive.org/web/20140930152003/http://stderr.org/pipermail/inquiry/2005-November/thread.html#3183
- http://web.archive.org/web/20120512004315/http://stderr.org/pipermail/inquiry/2005-December/thread.html#3274
- http://web.archive.org/web/20140927031226/http://stderr.org/pipermail/inquiry/2005-September/003063.html
- http://web.archive.org/web/20140927032400/http://stderr.org/pipermail/inquiry/2005-September/003065.html
- http://web.archive.org/web/20150221163001/http://stderr.org/pipermail/inquiry/2005-October/003075.html
- http://web.archive.org/web/20150221163001/http://stderr.org/pipermail/inquiry/2005-October/003090.html
- http://web.archive.org/web/20140927152409/http://stderr.org/pipermail/inquiry/2005-November/003183.html
- http://web.archive.org/web/20140930151632/http://stderr.org/pipermail/inquiry/2005-November/003186.html
- http://web.archive.org/web/20140927031019/http://stderr.org/pipermail/inquiry/2005-November/003187.html
- http://web.archive.org/web/20140930152056/http://stderr.org/pipermail/inquiry/2005-November/003189.html
- http://web.archive.org/web/20140927145521/http://stderr.org/pipermail/inquiry/2005-November/003190.html
- http://web.archive.org/web/20140927152552/http://stderr.org/pipermail/inquiry/2005-November/003207.html
- http://web.archive.org/web/20140930152201/http://stderr.org/pipermail/inquiry/2005-November/003208.html
- http://web.archive.org/web/20140930152230/http://stderr.org/pipermail/inquiry/2005-November/003222.html
- http://web.archive.org/web/20140930152251/http://stderr.org/pipermail/inquiry/2005-November/003253.html
- http://web.archive.org/web/20140930152400/http://stderr.org/pipermail/inquiry/2005-November/003261.html
- http://web.archive.org/web/20140930152424/http://stderr.org/pipermail/inquiry/2005-November/003264.html
- http://web.archive.org/web/20140930152454/http://stderr.org/pipermail/inquiry/2005-November/003265.html
- http://web.archive.org/web/20061013233820/http://stderr.org/pipermail/inquiry/2005-December/003274.html
- http://web.archive.org/web/20061013233713/http://stderr.org/pipermail/inquiry/2005-December/003277.html
- http://web.archive.org/web/20061013233746/http://stderr.org/pipermail/inquiry/2005-December/003278.html
- http://web.archive.org/web/20061013233637/http://stderr.org/pipermail/inquiry/2005-December/003279.html
- http://web.archive.org/web/20061013234032/http://stderr.org/pipermail/inquiry/2005-December/003283.html
- http://web.archive.org/web/20061013234059/http://stderr.org/pipermail/inquiry/2005-December/003359.html
- http://web.archive.org/web/20061013234103/http://stderr.org/pipermail/inquiry/2005-December/003360.html
NEKS. New Elements • Kaina Stoicheia • Commentary History
Inquiry List (Sep 2005 – Feb 2006)
- http://web.archive.org/web/20140927032017/http://stderr.org/pipermail/inquiry/2005-September/thread.html#3066
- http://web.archive.org/web/20150224132601/http://stderr.org/pipermail/inquiry/2005-October/thread.html#3070
- http://web.archive.org/web/20140930152003/http://stderr.org/pipermail/inquiry/2005-November/thread.html#3263
- http://web.archive.org/web/20120512004315/http://stderr.org/pipermail/inquiry/2005-December/thread.html#3276
- http://web.archive.org/web/20120428203612/http://stderr.org/pipermail/inquiry/2006-February/thread.html#3366
- http://web.archive.org/web/20140927032227/http://stderr.org/pipermail/inquiry/2005-September/003066.html
- http://web.archive.org/web/20140927032200/http://stderr.org/pipermail/inquiry/2005-September/003067.html
- http://web.archive.org/web/20150224132513/http://stderr.org/pipermail/inquiry/2005-October/003070.html
- http://web.archive.org/web/20140930212839/http://stderr.org/pipermail/inquiry/2005-October/003071.html
- http://web.archive.org/web/20120204201416/http://stderr.org/pipermail/inquiry/2005-October/003073.html
- http://web.archive.org/web/20120206122908/http://stderr.org/pipermail/inquiry/2005-October/003074.html
- http://web.archive.org/web/20120204201721/http://stderr.org/pipermail/inquiry/2005-October/003087.html
- http://web.archive.org/web/20150224132436/http://stderr.org/pipermail/inquiry/2005-October/003091.html
- http://web.archive.org/web/20150224132419/http://stderr.org/pipermail/inquiry/2005-October/003117.html
- http://web.archive.org/web/20140930152611/http://stderr.org/pipermail/inquiry/2005-November/003263.html
- http://web.archive.org/web/20140930152637/http://stderr.org/pipermail/inquiry/2005-November/003269.html
- http://web.archive.org/web/20061013233936/http://stderr.org/pipermail/inquiry/2005-December/003276.html
- http://web.archive.org/web/20061013232908/http://stderr.org/pipermail/inquiry/2006-February/003366.html
- http://web.archive.org/web/20061013232911/http://stderr.org/pipermail/inquiry/2006-February/003367.html
NEKS. New Elements • Kaina Stoicheia • Discussion History
Inquiry List (Dec 2005)
- http://web.archive.org/web/20061013234010/http://stderr.org/pipermail/inquiry/2005-December/003272.html
- http://web.archive.org/web/20061013234040/http://stderr.org/pipermail/inquiry/2005-December/003282.html
- http://web.archive.org/web/20061013233753/http://stderr.org/pipermail/inquiry/2005-December/003296.html
- http://web.archive.org/web/20061013234050/http://stderr.org/pipermail/inquiry/2005-December/003297.html
- http://web.archive.org/web/20061013233848/http://stderr.org/pipermail/inquiry/2005-December/003298.html
- http://web.archive.org/web/20061013233659/http://stderr.org/pipermail/inquiry/2005-December/003299.html
- http://web.archive.org/web/20061013233721/http://stderr.org/pipermail/inquiry/2005-December/003300.html
- http://web.archive.org/web/20061013234152/http://stderr.org/pipermail/inquiry/2005-December/003301.html
- http://web.archive.org/web/20061013233802/http://stderr.org/pipermail/inquiry/2005-December/003302.html
- http://web.archive.org/web/20061013234055/http://stderr.org/pipermail/inquiry/2005-December/003303.html
- http://web.archive.org/web/20061013233903/http://stderr.org/pipermail/inquiry/2005-December/003304.html
OLOD. Quine On The Limits Of Decision • Document History
Inquiry List (Sep 2003)
- http://web.archive.org/web/20061014001340/http://stderr.org/pipermail/inquiry/2003-September/000791.html
- http://web.archive.org/web/20061014000951/http://stderr.org/pipermail/inquiry/2003-September/000853.html
- http://web.archive.org/web/20061014001355/http://stderr.org/pipermail/inquiry/2003-September/000854.html
Ontology List (Sep 2003)
- http://web.archive.org/web/20070304201252/http://suo.ieee.org/ontology/thrd9.html#05037
- http://web.archive.org/web/20070219035906/http://suo.ieee.org/ontology/msg05037.html
- http://web.archive.org/web/20070219035951/http://suo.ieee.org/ontology/msg05095.html
- http://web.archive.org/web/20070219040008/http://suo.ieee.org/ontology/msg05096.html
POLA. Philosophy Of Logical Atomism • Document History
Inquiry List (Aug 2003)
- http://web.archive.org/web/20050325182153/http://stderr.org/pipermail/inquiry/2003-August/000674.html
- http://web.archive.org/web/20050325182157/http://stderr.org/pipermail/inquiry/2003-August/000675.html
- http://web.archive.org/web/20050325182137/http://stderr.org/pipermail/inquiry/2003-August/000679.html
- http://web.archive.org/web/20050325182233/http://stderr.org/pipermail/inquiry/2003-August/000685.html
- http://web.archive.org/web/20050325182238/http://stderr.org/pipermail/inquiry/2003-August/000686.html
- http://web.archive.org/web/20050325182245/http://stderr.org/pipermail/inquiry/2003-August/000688.html
- http://web.archive.org/web/20050325182249/http://stderr.org/pipermail/inquiry/2003-August/000689.html
- http://web.archive.org/web/20050325182253/http://stderr.org/pipermail/inquiry/2003-August/000690.html
- http://web.archive.org/web/20050326203820/http://stderr.org/pipermail/inquiry/2003-August/000691.html
- http://web.archive.org/web/20050326203828/http://stderr.org/pipermail/inquiry/2003-August/000693.html
- http://web.archive.org/web/20050326203833/http://stderr.org/pipermail/inquiry/2003-August/000694.html
- http://web.archive.org/web/20050326203836/http://stderr.org/pipermail/inquiry/2003-August/000695.html
- http://web.archive.org/web/20050326203844/http://stderr.org/pipermail/inquiry/2003-August/000697.html
- http://web.archive.org/web/20050326203848/http://stderr.org/pipermail/inquiry/2003-August/000698.html
- http://web.archive.org/web/20050326203852/http://stderr.org/pipermail/inquiry/2003-August/000699.html
- http://web.archive.org/web/20050326203856/http://stderr.org/pipermail/inquiry/2003-August/000700.html
- http://web.archive.org/web/20050326203900/http://stderr.org/pipermail/inquiry/2003-August/000701.html
- http://web.archive.org/web/20050326203928/http://stderr.org/pipermail/inquiry/2003-August/000709.html
- http://web.archive.org/web/20050326203932/http://stderr.org/pipermail/inquiry/2003-August/000710.html
- http://web.archive.org/web/20050331051339/http://stderr.org/pipermail/inquiry/2003-August/000745.html
- http://web.archive.org/web/20050331051343/http://stderr.org/pipermail/inquiry/2003-August/000746.html
- http://web.archive.org/web/20050331051347/http://stderr.org/pipermail/inquiry/2003-August/000747.html
- http://web.archive.org/web/20050331051351/http://stderr.org/pipermail/inquiry/2003-August/000748.html
- http://web.archive.org/web/20050331051355/http://stderr.org/pipermail/inquiry/2003-August/000749.html
- http://web.archive.org/web/20051215123628/http://stderr.org/pipermail/inquiry/2003-August/000750.html
- http://web.archive.org/web/20040906141737/http://stderr.org/pipermail/inquiry/2003-August/000751.html
- http://web.archive.org/web/20040906141709/http://stderr.org/pipermail/inquiry/2003-August/000752.html
- http://web.archive.org/web/20040906141717/http://stderr.org/pipermail/inquiry/2003-August/000756.html
- http://web.archive.org/web/20040906141837/http://stderr.org/pipermail/inquiry/2003-August/000757.html
Ontology List (Aug 2003)
- http://web.archive.org/web/20080502102247/http://suo.ieee.org/ontology/msg04939.html
- http://web.archive.org/web/20080502073506/http://suo.ieee.org/ontology/msg04940.html
- http://web.archive.org/web/20080621104338/http://suo.ieee.org/ontology/msg04944.html
- http://web.archive.org/web/20070306115257/http://suo.ieee.org/ontology/msg04945.html
- http://web.archive.org/web/20070306115309/http://suo.ieee.org/ontology/msg04946.html
- http://web.archive.org/web/20070306115323/http://suo.ieee.org/ontology/msg04947.html
- http://web.archive.org/web/20070306115333/http://suo.ieee.org/ontology/msg04948.html
- http://web.archive.org/web/20070306115343/http://suo.ieee.org/ontology/msg04949.html
- http://web.archive.org/web/20070306115353/http://suo.ieee.org/ontology/msg04950.html
- http://web.archive.org/web/20070306115404/http://suo.ieee.org/ontology/msg04951.html
- http://web.archive.org/web/20070306115413/http://suo.ieee.org/ontology/msg04952.html
- http://web.archive.org/web/20070305003408/http://suo.ieee.org/ontology/msg04953.html
- http://web.archive.org/web/20080409021341/http://suo.ieee.org/ontology/msg04954.html
- http://web.archive.org/web/20080622160902/http://suo.ieee.org/ontology/msg04955.html
- http://web.archive.org/web/20080409021347/http://suo.ieee.org/ontology/msg04956.html
- http://web.archive.org/web/20070305003451/http://suo.ieee.org/ontology/msg04957.html
- http://web.archive.org/web/20070305003503/http://suo.ieee.org/ontology/msg04958.html
- http://web.archive.org/web/20070305003513/http://suo.ieee.org/ontology/msg04959.html
- http://web.archive.org/web/20070305003523/http://suo.ieee.org/ontology/msg04960.html
- http://web.archive.org/web/20070305003535/http://suo.ieee.org/ontology/msg04995.html
- http://web.archive.org/web/20070305003545/http://suo.ieee.org/ontology/msg04996.html
- http://web.archive.org/web/20070305003557/http://suo.ieee.org/ontology/msg04997.html
- http://web.archive.org/web/20070305003605/http://suo.ieee.org/ontology/msg04998.html
- http://web.archive.org/web/20070305003616/http://suo.ieee.org/ontology/msg04999.html
- http://web.archive.org/web/20070305003626/http://suo.ieee.org/ontology/msg05000.html
- http://web.archive.org/web/20070305003636/http://suo.ieee.org/ontology/msg05001.html
- http://web.archive.org/web/20070305003700/http://suo.ieee.org/ontology/msg05002.html
- http://web.archive.org/web/20070305003710/http://suo.ieee.org/ontology/msg05006.html
- http://web.archive.org/web/20070305003719/http://suo.ieee.org/ontology/msg05007.html
POLA. Philosophy Of Logical Atomism • Discussion History
Ontology List (Aug 2003)
RTOK. Russell's Theory Of Knowledge • Document History
Inquiry List (Aug 2003)
- http://web.archive.org/web/20040906141725/http://stderr.org/pipermail/inquiry/2003-August/000758.html
- http://web.archive.org/web/20040906141628/http://stderr.org/pipermail/inquiry/2003-August/000759.html
- http://web.archive.org/web/20040906141729/http://stderr.org/pipermail/inquiry/2003-August/000760.html
Ontology List (Aug 2003)
- http://web.archive.org/web/20070306151622/http://suo.ieee.org/ontology/msg05008.html
- http://web.archive.org/web/20070324073231/http://suo.ieee.org/ontology/msg05009.html
- http://web.archive.org/web/20070324073241/http://suo.ieee.org/ontology/msg05010.html
RTOP. Russell's Treatise On Propositions • Document History
Inquiry List (Aug 2003)
- http://web.archive.org/web/20040906141603/http://stderr.org/pipermail/inquiry/2003-August/000761.html
- http://web.archive.org/web/20040906141807/http://stderr.org/pipermail/inquiry/2003-August/000762.html
Ontology List (Aug 2003)
- http://web.archive.org/web/20070328165409/http://suo.ieee.org/ontology/msg05011.html
- http://web.archive.org/web/20070316003836/http://suo.ieee.org/ontology/msg05012.html
SABI. Synthetic/Analytic ≟ Boundary/Interior • Document History
Inquiry List (Aug 2003)
Ontology List (Aug 2003)
SYNF. Syntactic Fallacy • Document History
TDOE. Two Dogmas Of Empiricism • Document History
Inquiry List (Jul 2003)
- Background for Analyticity
- http://web.archive.org/web/20061013233132/http://stderr.org/pipermail/inquiry/2003-July/000638.html
- http://web.archive.org/web/20061013233212/http://stderr.org/pipermail/inquiry/2003-July/000639.html
- http://web.archive.org/web/20061013233048/http://stderr.org/pipermail/inquiry/2003-July/000640.html
- http://web.archive.org/web/20061013233020/http://stderr.org/pipermail/inquiry/2003-July/000641.html
- http://web.archive.org/web/20061013232930/http://stderr.org/pipermail/inquiry/2003-July/000642.html
- Definition
- http://web.archive.org/web/20061013232959/http://stderr.org/pipermail/inquiry/2003-July/000643.html
- http://web.archive.org/web/20061013233215/http://stderr.org/pipermail/inquiry/2003-July/000644.html
- http://web.archive.org/web/20061013233054/http://stderr.org/pipermail/inquiry/2003-July/000645.html
- http://web.archive.org/web/20061013232914/http://stderr.org/pipermail/inquiry/2003-July/000646.html
- Interchangeability
- http://web.archive.org/web/20061013232955/http://stderr.org/pipermail/inquiry/2003-July/000647.html
- http://web.archive.org/web/20061013233149/http://stderr.org/pipermail/inquiry/2003-July/000648.html
- http://web.archive.org/web/20061013233139/http://stderr.org/pipermail/inquiry/2003-July/000649.html
- http://web.archive.org/web/20061013233115/http://stderr.org/pipermail/inquiry/2003-July/000650.html
- http://web.archive.org/web/20061013233119/http://stderr.org/pipermail/inquiry/2003-July/000651.html
- http://web.archive.org/web/20061013233219/http://stderr.org/pipermail/inquiry/2003-July/000652.html
- Semantical Rules
- http://web.archive.org/web/20061013233129/http://stderr.org/pipermail/inquiry/2003-July/000653.html
- http://web.archive.org/web/20061013232943/http://stderr.org/pipermail/inquiry/2003-July/000654.html
- http://web.archive.org/web/20061013233201/http://stderr.org/pipermail/inquiry/2003-July/000655.html
- http://web.archive.org/web/20061013232947/http://stderr.org/pipermail/inquiry/2003-July/000656.html
- http://web.archive.org/web/20061013233013/http://stderr.org/pipermail/inquiry/2003-July/000657.html
- The Verification Theory and Reductionism
- http://web.archive.org/web/20061013233009/http://stderr.org/pipermail/inquiry/2003-July/000658.html
- http://web.archive.org/web/20061013232933/http://stderr.org/pipermail/inquiry/2003-July/000659.html
- http://web.archive.org/web/20061013233005/http://stderr.org/pipermail/inquiry/2003-July/000660.html
- http://web.archive.org/web/20061013233233/http://stderr.org/pipermail/inquiry/2003-July/000661.html
- http://web.archive.org/web/20061013233034/http://stderr.org/pipermail/inquiry/2003-July/000662.html
- http://web.archive.org/web/20061013233122/http://stderr.org/pipermail/inquiry/2003-July/000663.html
- Empiricism without the Dogmas
- http://web.archive.org/web/20061013232923/http://stderr.org/pipermail/inquiry/2003-July/000664.html
- http://web.archive.org/web/20061013233146/http://stderr.org/pipermail/inquiry/2003-July/000665.html
- http://web.archive.org/web/20061013233136/http://stderr.org/pipermail/inquiry/2003-July/000666.html
- http://web.archive.org/web/20061013233104/http://stderr.org/pipermail/inquiry/2003-July/000667.html
The above material is excerpted from:
- W.V. Quine, “Two Dogmas of Empiricism”, Philosophical Review, January 1951.
Reprinted, W.V. Quine, From a Logical Point of View, 2nd edition, pp. 20–46,
Harvard University Press, Cambridge, MA, 1980.
Ontology List (Jul 2003)
- Background for Analyticity
- http://web.archive.org/web/20070304210042/http://suo.ieee.org/ontology/msg04909.html
- http://web.archive.org/web/20070304210052/http://suo.ieee.org/ontology/msg04910.html
- http://web.archive.org/web/20070304210102/http://suo.ieee.org/ontology/msg04911.html
- http://web.archive.org/web/20070304210112/http://suo.ieee.org/ontology/msg04912.html
- http://web.archive.org/web/20070304210122/http://suo.ieee.org/ontology/msg04913.html
- Definition
- http://web.archive.org/web/20070304210132/http://suo.ieee.org/ontology/msg04914.html
- http://web.archive.org/web/20070304210143/http://suo.ieee.org/ontology/msg04915.html
- http://web.archive.org/web/20070304210153/http://suo.ieee.org/ontology/msg04916.html
- http://web.archive.org/web/20070304210203/http://suo.ieee.org/ontology/msg04917.html
- Interchangeability
- http://web.archive.org/web/20070304210214/http://suo.ieee.org/ontology/msg04918.html
- http://web.archive.org/web/20070304210223/http://suo.ieee.org/ontology/msg04919.html
- http://web.archive.org/web/20070304210234/http://suo.ieee.org/ontology/msg04920.html
- http://web.archive.org/web/20070304181104/http://suo.ieee.org/ontology/msg04921.html
- http://web.archive.org/web/20070304210244/http://suo.ieee.org/ontology/msg04922.html
- http://web.archive.org/web/20070304210310/http://suo.ieee.org/ontology/msg04923.html
- Semantical Rules
- http://web.archive.org/web/20070304210321/http://suo.ieee.org/ontology/msg04924.html
- http://web.archive.org/web/20070304210332/http://suo.ieee.org/ontology/msg04925.html
- http://web.archive.org/web/20070304210350/http://suo.ieee.org/ontology/msg04926.html
- http://web.archive.org/web/20070304210401/http://suo.ieee.org/ontology/msg04927.html
- http://web.archive.org/web/20070304210411/http://suo.ieee.org/ontology/msg04928.html
- The Verification Theory and Reductionism
- http://web.archive.org/web/20070304210423/http://suo.ieee.org/ontology/msg04929.html
- http://web.archive.org/web/20070304210431/http://suo.ieee.org/ontology/msg04930.html
- http://web.archive.org/web/20070305022135/http://suo.ieee.org/ontology/msg04931.html
- http://web.archive.org/web/20070304210441/http://suo.ieee.org/ontology/msg04932.html
- http://web.archive.org/web/20070304210451/http://suo.ieee.org/ontology/msg04933.html
- http://web.archive.org/web/20080419061751/http://suo.ieee.org/ontology/msg04934.html
- Empiricism without the Dogmas
- http://web.archive.org/web/20080411152023/http://suo.ieee.org/ontology/msg04935.html
- http://web.archive.org/web/20080411152028/http://suo.ieee.org/ontology/msg04936.html
- http://web.archive.org/web/20080411152033/http://suo.ieee.org/ontology/msg04937.html
- http://web.archive.org/web/20080622160852/http://suo.ieee.org/ontology/msg04938.html
The above material is excerpted from:
- W.V. Quine, “Two Dogmas of Empiricism”, Philosophical Review, January 1951.
Reprinted, W.V. Quine, From a Logical Point of View, 2nd edition, pp. 20–46,
Harvard University Press, Cambridge, MA, 1980.
VOLS. Verities Of Likely Stories • Document History
Inquiry List (Aug 2003)
- http://web.archive.org/web/20050330084828/http://stderr.org/pipermail/inquiry/2003-August/000713.html
- http://web.archive.org/web/20050330084836/http://stderr.org/pipermail/inquiry/2003-August/000715.html
- http://web.archive.org/web/20050330084849/http://stderr.org/pipermail/inquiry/2003-August/000718.html
- http://web.archive.org/web/20050330084900/http://stderr.org/pipermail/inquiry/2003-August/000721.html
- http://web.archive.org/web/20050331051255/http://stderr.org/pipermail/inquiry/2003-August/000733.html
- http://web.archive.org/web/20050331051259/http://stderr.org/pipermail/inquiry/2003-August/000734.html
- http://web.archive.org/web/20050331051303/http://stderr.org/pipermail/inquiry/2003-August/000735.html
- http://web.archive.org/web/20050331051307/http://stderr.org/pipermail/inquiry/2003-August/000736.html
- http://web.archive.org/web/20050331051311/http://stderr.org/pipermail/inquiry/2003-August/000737.html
- http://web.archive.org/web/20050331051315/http://stderr.org/pipermail/inquiry/2003-August/000738.html
- http://web.archive.org/web/20050331051243/http://stderr.org/pipermail/inquiry/2003-August/000739.html
- http://web.archive.org/web/20050331051319/http://stderr.org/pipermail/inquiry/2003-August/000740.html
- http://web.archive.org/web/20050331051323/http://stderr.org/pipermail/inquiry/2003-August/000741.html
- http://web.archive.org/web/20050331051327/http://stderr.org/pipermail/inquiry/2003-August/000742.html
- http://web.archive.org/web/20050331051331/http://stderr.org/pipermail/inquiry/2003-August/000743.html
- http://web.archive.org/web/20050331051335/http://stderr.org/pipermail/inquiry/2003-August/000744.html
Ontology List (Aug 2003)
- http://web.archive.org/web/20140405160400/http://suo.ieee.org/ontology/thrd11.html#04963
- http://web.archive.org/web/20140405160400/http://suo.ieee.org/ontology/thrd11.html#04966
- http://web.archive.org/web/20140405161010/http://suo.ieee.org/ontology/msg04963.html
- http://web.archive.org/web/20070306133936/http://suo.ieee.org/ontology/msg04964.html
- http://web.archive.org/web/20070306134007/http://suo.ieee.org/ontology/msg04966.html
- http://web.archive.org/web/20070306134036/http://suo.ieee.org/ontology/msg04969.html
- http://web.archive.org/web/20070306132756/http://suo.ieee.org/ontology/msg04981.html
- http://web.archive.org/web/20070306134251/http://suo.ieee.org/ontology/msg04982.html
- http://web.archive.org/web/20070306134301/http://suo.ieee.org/ontology/msg04983.html
- http://web.archive.org/web/20070306134313/http://suo.ieee.org/ontology/msg04984.html
- http://web.archive.org/web/20070306134343/http://suo.ieee.org/ontology/msg04986.html
- http://web.archive.org/web/20070306134353/http://suo.ieee.org/ontology/msg04987.html
- http://web.archive.org/web/20070306134406/http://suo.ieee.org/ontology/msg04989.html
- http://web.archive.org/web/20070306134422/http://suo.ieee.org/ontology/msg04990.html
- http://web.archive.org/web/20070306134433/http://suo.ieee.org/ontology/msg04991.html
- http://web.archive.org/web/20070306134443/http://suo.ieee.org/ontology/msg04992.html
- http://web.archive.org/web/20070306134454/http://suo.ieee.org/ontology/msg04993.html
- http://web.archive.org/web/20070306115437/http://suo.ieee.org/ontology/msg04994.html
VOOP. Varieties Of Ontology Project • Document History
VORE. Varieties Of Recalcitrant Experience • Document History
Inquiry List (Aug 2003)
- http://web.archive.org/web/20050324203753/http://stderr.org/pipermail/inquiry/2003-August/000668.html
- http://web.archive.org/web/20050324203757/http://stderr.org/pipermail/inquiry/2003-August/000669.html
- http://web.archive.org/web/20050325182141/http://stderr.org/pipermail/inquiry/2003-August/000671.html
- http://web.archive.org/web/20050325182145/http://stderr.org/pipermail/inquiry/2003-August/000672.html
- http://web.archive.org/web/20050325182205/http://stderr.org/pipermail/inquiry/2003-August/000677.html
- http://web.archive.org/web/20050325182209/http://stderr.org/pipermail/inquiry/2003-August/000678.html
- http://web.archive.org/web/20050325182213/http://stderr.org/pipermail/inquiry/2003-August/000680.html
- http://web.archive.org/web/20050325182217/http://stderr.org/pipermail/inquiry/2003-August/000681.html
- http://web.archive.org/web/20050325182221/http://stderr.org/pipermail/inquiry/2003-August/000682.html
- http://web.archive.org/web/20050325182229/http://stderr.org/pipermail/inquiry/2003-August/000683.html
- http://web.archive.org/web/20050325182225/http://stderr.org/pipermail/inquiry/2003-August/000684.html
- http://web.archive.org/web/20050325182241/http://stderr.org/pipermail/inquiry/2003-August/000687.html
- http://web.archive.org/web/20050326203824/http://stderr.org/pipermail/inquiry/2003-August/000692.html
- http://web.archive.org/web/20050326203841/http://stderr.org/pipermail/inquiry/2003-August/000696.html
- http://web.archive.org/web/20050326203924/http://stderr.org/pipermail/inquiry/2003-August/000708.html
SUO List (Aug 2003)
- http://web.archive.org/web/20070306110551/http://suo.ieee.org/email/msg10497.html
- http://web.archive.org/web/20070310134749/http://suo.ieee.org/email/msg10498.html
- http://web.archive.org/web/20070310135842/http://suo.ieee.org/email/msg10501.html
- http://web.archive.org/web/20070310135852/http://suo.ieee.org/email/msg10503.html
- http://web.archive.org/web/20070309010913/http://suo.ieee.org/email/msg10513.html
- http://web.archive.org/web/20070309010923/http://suo.ieee.org/email/msg10515.html
- http://web.archive.org/web/20070310135943/http://suo.ieee.org/email/msg10520.html
- http://web.archive.org/web/20070310113310/http://suo.ieee.org/email/msg10521.html
- http://web.archive.org/web/20070310113529/http://suo.ieee.org/email/msg10522.html
- http://web.archive.org/web/20070309010933/http://suo.ieee.org/email/msg10524.html
- http://web.archive.org/web/20070309010944/http://suo.ieee.org/email/msg10526.html
- http://web.archive.org/web/20070309010953/http://suo.ieee.org/email/msg10533.html
- http://web.archive.org/web/20070310140027/http://suo.ieee.org/email/msg10539.html
- http://web.archive.org/web/20070309011003/http://suo.ieee.org/email/msg10540.html
- http://web.archive.org/web/20070309011016/http://suo.ieee.org/email/msg10545.html
VORE. Varieties Of Recalcitrant Experience • Application History
Inquiry List (Aug 2003)
- http://web.archive.org/web/20050324203802/http://stderr.org/pipermail/inquiry/2003-August/000670.html
- http://web.archive.org/web/20050325182149/http://stderr.org/pipermail/inquiry/2003-August/000673.html
- http://web.archive.org/web/20050325182201/http://stderr.org/pipermail/inquiry/2003-August/000676.html
- http://web.archive.org/web/20050330084856/http://stderr.org/pipermail/inquiry/2003-August/000720.html
SUO List (Aug 2003)
- http://web.archive.org/web/20070310134759/http://suo.ieee.org/email/msg10499.html
- http://web.archive.org/web/20070313223944/http://suo.ieee.org/email/msg10504.html
- http://web.archive.org/web/20070310135902/http://suo.ieee.org/email/msg10512.html
- http://web.archive.org/web/20070306164806/http://suo.ieee.org/email/msg10556.html
