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: [[User:Jon Awbrey/Philosophical Notes#OLOD. Quine On The Limits Of Decision|OLOD. Quine On The Limits Of Decision]]
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</pre>
</pre>
==OLOD. Quine On The Limits Of Decision==
==NEKS. New Elements • Kaina Stoicheia==
===OLOD. Note 1===
===NEKS. Note 1===
<pre>
<pre>
| On the Limits of Decision
|
| I now proceed to explain the difference between a theoretical
| Because these congresses occur at intervals of five years, they make
| and a practical proposition, together with the two important
| for retrospection. I find myself thinking back over a century of logic.
| parallel distinctions between 'definite' and 'vague', and
| A hundred years ago George Boole's algebra of classes was at hand. Like
| 'individual' and 'general', noting, at the same time,
| so many inventions, it had been needlessly clumsy when it first appeared;
| some other distinctions connected with these.
| 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
| A 'sign' is connected with the "Truth", i.e. the entire Universe
| relations. Then, around a century ago, C.S. Peirce published three papers
| of being, or, as some say, the Absolute, in three distinct ways.
| 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
| In the first place, a sign is not a real thing.
| conception of truth-function logic in terms of truth tables, which is so clear
| It is of such a nature as to exist in 'replicas'.
| and obvious as to seem inevitable today, was not yet explicit in the writings
| Look down a printed page, and every 'the' you see
| of that time. As for the logic of quantification, it remained unknown until
| is the same word, every 'e' the same letter. A real
| 1879, when Frege published his 'Begriffsschrift'; and it was around three
| thing does not so exist in replica. The being of a
| years later still that Peirce began to become aware of this idea, through
| sign is merely 'being represented'. Now 'really being'
| independent efforts. And even down to litle more than a half century ago
| and 'being represented' are very different. Giving to
| we were weak on decision procedures. It was only in 1915 that Löwenheim
| the word 'sign' the full scope that reasonably belongs
| published a decision procedure for the Boolean algebra of classes, or,
| to it for logical purposes, a whole book is a sign; and
| what is equivalent, monadic quantification theory. It was a clumsy
| a translation of it is a replica of the same sign. A whole
| procedure, and obscure in the presentation -- the way, again, with
| literature is a sign. The sentence "Roxana was the queen of
| new inventions. And it was less than a third of a century ago that
| Alexander" is a sign of Roxana and of Alexander, and though
| we were at last forced, by results of Gödel, Turing, and Church, to
| there is a grammatical emphasis on the former, logically the
| despair of a decision procedure for the rest of quantification theory.
| name "Alexander" is as much 'a subject' as is the name "Roxana";
|
| and the real persons Roxana and Alexander are 'real objects' of
| Quine, "Limits of Decision", pp. 156-157.
| the sign.
|
|
| W.V. Quine, "On the Limits of Decision", pp. 156-163 in
| Every sign that is sufficiently complete refers refers to sundry
|'Theories and Things, Harvard University Press, Cambridge,
| real objects. All these objects, even if we are talking of Hamlet's
| MA, 1981. A shorter version of this paper appeared in the
| madness, are parts of one and the same Universe of being, the "Truth".
|'Akten des XIV. internationalen Kongresses für Philosophie',
| But so far as the "Truth" is merely the 'object' of a sign, it is merely
| vol. 3, 1969.
| the Aristotelian 'Matter' of it that is so.
</pre>
|
| In addition however to 'denoting' objects every
===OLOD. Note 2===
| sign sufficiently complete 'signifies characters',
| or qualities.
<pre>
|
| On the Limits of Decision (cont.)
| We have a direct knowledge of real objects in every
|
| experiential reaction, whether of 'Perception' or of
| It is hard now to imagine not seeing truth-function logic
| 'Exertion' (the one theoretical, the other practical).
| as a trivial matter of truth tables, and it is becoming hard
| These are directly 'hic et nunc'. But we extend the
| even to imagine the decidability of monadic quantification theory
| category, and speak of numberless real objects with
| as other than obvious. For monadic quantification theory in a modern
| which we are not in direct reaction.
| perspective is essentially just an elaboration of truth-function logic.
|
| I want now to spend a few minutes developing this connection.
| We have also direct knowledge of qualities in feeling,
|
| peripheral and visceral. But we extend this category
| What makes truth-function logic decidable by truth tables
| to numberless characters of which we have no immediate
| is that the truth value of a truth function can be computed
| consciousness.
| from the truth values of the arguments. But is a formula of
|
| quantification theory not a truth-function of quantifications?
| All these characters are elements of the "Truth".
| Its truth vaue can be computed from whatever truth values may be
| Every sign signifies the "Truth". But it is only
| assigned to its component quantifications. Why does this not make
| the Aristotelian 'Form' of the universe that it
| quantification theory decidable by truth tables? Why not test a
| signifies.
| formula of quantification theory for validity by assigning all
|
| combinations of truth values to its component quantifications
| The logician is not concerned with any metaphysical
| and seeing whether the whole comes out true every time?
| theory; still less, if possible, is the mathematician.
|
| But it is highly convenient to express ourselves in terms
| Quine, "Limits of Decision", p. 157.
| of a metaphysical theory; and we no more bind ourselves to
|
| an acceptance of it than we do when we use substantives such
| W.V. Quine, "On the Limits of Decision", pp. 156-163 in
| as "humanity", "variety", etc. and speak of them as if they
|'Theories and Things, Harvard University Press, Cambridge,
| were substances, in the metaphysical sense.
| MA, 1981. A shorter version of this paper appeared in the
|
|'Akten des XIV. internationalen Kongresses für Philosophie',
| But, in the third place, every sign is intended to determine a
| vol. 3, 1969.
| sign of the same object with the same signification or 'meaning'.
</pre>
| 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",
===OLOD. Note 3===
| 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.
</pre>
===NEKS. Note 2===
<pre>
| 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.
</pre>
===NEKS. Note 3===
<pre>
| 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.
</pre>
===NEKS. Note 4===
<pre>
| 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.
</pre>
===NEKS. Note 5===
<pre>
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.
</pre>
===NEKS. Note 6===
<pre>
| 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.
</pre>
===NEKS. Note 7===
<pre>
| 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.
</pre>
===NEKS. Note 8===
<pre>
| 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.
</pre>
===NEKS. Note 9===
<pre>
| 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.
</pre>
===NEKS. Note 10===
<pre>
| 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.
</pre>
===NEKS. Note 11===
<pre>
| 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.
</pre>
===NEKS. Note 12===
<pre>
| 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.
</pre>
===NEKS. Note 13===
<pre>
| 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.
</pre>
===NEKS. Note 14===
<pre>
| 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
</pre>
===NEKS. Note 15===
<pre>
| 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.
</pre>
===NEKS. Note 16===
<pre>
| 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.
</pre>
===NEKS. Note 17===
<pre>
| 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.
</pre>
===NEKS. Note 18===
<pre>
| 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.
</pre>
===NEKS. Note 19===
<pre>
| 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.
</pre>
===NEKS. Note 20===
<pre>
| 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.
</pre>
===NEKS. Note 21===
<pre>
| 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.
</pre>
===NEKS. Note 22===
<pre>
| 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.
</pre>
===NEKS. Note 23===
<pre>
| 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.
</pre>
===NEKS. Note 24===
<pre>
...
| 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.
</pre>
==NEKS. New Elements • Kaina Stoicheia • Commentary==
===NEKS. Commentary Note 1===
<pre>
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.
</pre>
===NEKS. Commentary Note 2===
<pre>
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.
</pre>
===NEKS. Commentary Note 3===
<pre>
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.
</pre>
===NEKS. Commentary Note 4===
<pre>
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.
</pre>
===NEKS. Commentary Note 5===
<pre>
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.
</pre>
===NEKS. Commentary Note 6===
<pre>
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.
</pre>
===NEKS. Commentary Note 7===
<pre>
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.
</pre>
===NEKS. Commentary Note 8===
<pre>
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.
</pre>
===NEKS. Commentary Note 9===
<pre>
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 ...
</pre>
===NEKS. Commentary Note 10===
<pre>
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.
</pre>
===NEKS. Commentary Note 11===
<pre>
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.
</pre>
===NEKS. Commentary Note 12===
<pre>
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
</pre>
===NEKS. Commentary Note 13===
<pre>
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
</pre>
===NEKS. Commentary Note 14===
<pre>
| Incidental Muse ~~~ Loreena McKennitt, ''Elemental'' ~~~
| http://www.quinlanroad.com/explorethemusic/elemental.asp
</pre>
</pre>
==NEKS. Commentary Work Area==
===NEKS. Commentary Work Area 1===
<pre>
Some folks have yet to discover the basic
fact of life that conception is an action.
</pre>
===NEKS. Commentary Work Area 2===
<pre>
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.
</pre>
==NEKS. New Elements • Kaina Stoicheia • Discussion==
===NEKS. Discussion Note 1===
<pre>
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".
</pre>
===NEKS. Discussion Note 2===
<pre>
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.
</pre>
===NEKS. Discussion Note 3===
<pre>
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.
</pre>
===NEKS. Discussion Note 4===
<pre>
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.
</pre>
===NEKS. Discussion Note 5===
<pre>
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.
</pre>
===NEKS. Discussion Note 6===
<pre>
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.
</pre>
===NEKS. Discussion Note 7===
<pre>
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.
</pre>
===NEKS. Discussion Note 8===
<pre>
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 ...
</pre>
===NEKS. Discussion Note 9===
<pre>
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.
</pre>
===NEKS. Discussion Note 10===
<pre>
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.
</pre>
===NEKS. Discussion Note 11===
<pre>
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.
</pre>
==OLOD. Quine On The Limits Of Decision==
===OLOD. Note 1===
<pre>
| 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.
</pre>
===OLOD. Note 2===
<pre>
| 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.
</pre>
===OLOD. Note 3===
<pre>
<pre>
| On the Limits of Decision (cont.)
| On the Limits of Decision (cont.)
==Document Histories==
==Document Histories==
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===OLOD. Quine On The Limits Of Decision • Document History===
===OLOD. Quine On The Limits Of Decision • Document History===
