12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Wednesday April 09, 2025
Jump to navigationJump to searchUser:Jon Awbrey/Philosophical Notes (view source)
Revision as of 14:00, 12 July 2017
, 14:00, 12 July 2017update
Line 4:
Line 4:
+
− +
−
− + + + +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
: [[User:Jon Awbrey/Philosophical Notes#HAPA. Hypostatic And Prescisive Abstraction|HAPA. Hypostatic And Prescisive Abstraction]]
: [[User:Jon Awbrey/Philosophical Notes#HAPA. Hypostatic And Prescisive Abstraction|HAPA. Hypostatic And Prescisive Abstraction]]
: [[User:Jon Awbrey/Philosophical Notes#JITL. Just In Time Logic|JITL. Just In Time Logic]]
: [[User:Jon Awbrey/Philosophical Notes#JITL. Just In Time Logic|JITL. Just In Time Logic]]
+: [[User:Jon Awbrey/Philosophical Notes#NEKS. New Elements • Kaina Stoicheia|NEKS. New Elements • Kaina Stoicheia]]
: [[User:Jon Awbrey/Philosophical Notes#OLOD. Quine On The Limits Of Decision|OLOD. Quine On The Limits Of Decision]]
: [[User:Jon Awbrey/Philosophical Notes#OLOD. Quine On The Limits Of Decision|OLOD. Quine On The Limits Of Decision]]
: [[User:Jon Awbrey/Philosophical Notes#POLA. Philosophy Of Logical Atomism|POLA. Philosophy Of Logical Atomism]]
: [[User:Jon Awbrey/Philosophical Notes#POLA. Philosophy Of Logical Atomism|POLA. Philosophy Of Logical Atomism]]
Line 3,673:
Line 3,674:
</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.)
Line 8,800:
Line 11,788:
==Document Histories==
==Document Histories==
−===Critical Reflection On Method • Document History===
+===CROM. Critical Reflection On Method • Document History===
'''Inquiry List (Oct 2003)'''
'''Inquiry List (Oct 2003)'''
Line 8,817:
Line 11,805:
# http://web.archive.org/web/20070313224500/http://suo.ieee.org/email/msg11279.html
# http://web.archive.org/web/20070313224500/http://suo.ieee.org/email/msg11279.html
−===Critical Reflection On Method • Discussion History===
+===CROM. Critical Reflection On Method • Discussion History===
'''Inquiry List (Oct 2003)'''
'''Inquiry List (Oct 2003)'''
Line 9,111:
Line 12,099:
# http://web.archive.org/web/20070306134231/http://suo.ieee.org/ontology/msg04979.html
# http://web.archive.org/web/20070306134231/http://suo.ieee.org/ontology/msg04979.html
# http://web.archive.org/web/20070306134241/http://suo.ieee.org/ontology/msg04980.html
# http://web.archive.org/web/20070306134241/http://suo.ieee.org/ontology/msg04980.html
+
+===NEKS. New Elements • Kaina Stoicheia • Document History===
+
+'''Inquiry List (Sep–Dec 2005)'''
+
+* http://stderr.org/pipermail/inquiry/2005-September/thread.html#3063
+* http://stderr.org/pipermail/inquiry/2005-October/thread.html#3075
+* http://stderr.org/pipermail/inquiry/2005-November/thread.html#3183
+* http://stderr.org/pipermail/inquiry/2005-December/thread.html#3274
+
+# http://stderr.org/pipermail/inquiry/2005-September/003063.html
+# http://stderr.org/pipermail/inquiry/2005-September/003065.html
+# http://stderr.org/pipermail/inquiry/2005-October/003075.html
+# http://stderr.org/pipermail/inquiry/2005-October/003090.html
+# http://stderr.org/pipermail/inquiry/2005-November/003183.html
+# http://stderr.org/pipermail/inquiry/2005-November/003186.html
+# http://stderr.org/pipermail/inquiry/2005-November/003187.html
+# http://stderr.org/pipermail/inquiry/2005-November/003189.html
+# http://stderr.org/pipermail/inquiry/2005-November/003190.html
+# http://stderr.org/pipermail/inquiry/2005-November/003207.html
+# http://stderr.org/pipermail/inquiry/2005-November/003208.html
+# http://stderr.org/pipermail/inquiry/2005-November/003222.html
+# http://stderr.org/pipermail/inquiry/2005-November/003253.html
+# http://stderr.org/pipermail/inquiry/2005-November/003261.html
+# http://stderr.org/pipermail/inquiry/2005-November/003264.html
+# http://stderr.org/pipermail/inquiry/2005-November/003265.html
+# http://stderr.org/pipermail/inquiry/2005-December/003274.html
+# http://stderr.org/pipermail/inquiry/2005-December/003277.html
+# http://stderr.org/pipermail/inquiry/2005-December/003278.html
+# http://stderr.org/pipermail/inquiry/2005-December/003279.html
+# http://stderr.org/pipermail/inquiry/2005-December/003283.html
+# http://stderr.org/pipermail/inquiry/2005-December/003359.html
+# http://stderr.org/pipermail/inquiry/2005-December/003360.html
+
+===NEKS. New Elements • Kaina Stoicheia • Commentary History===
+
+'''Inquiry List (Sep 2005 – Feb 2006)'''
+
+* http://stderr.org/pipermail/inquiry/2005-September/thread.html#3066
+* http://stderr.org/pipermail/inquiry/2005-October/thread.html#3070
+* http://stderr.org/pipermail/inquiry/2005-November/thread.html#3263
+* http://stderr.org/pipermail/inquiry/2005-December/thread.html#3276
+* http://stderr.org/pipermail/inquiry/2006-February/thread.html#3366
+
+# http://stderr.org/pipermail/inquiry/2005-September/003066.html
+# http://stderr.org/pipermail/inquiry/2005-September/003067.html
+# http://stderr.org/pipermail/inquiry/2005-October/003070.html
+# http://stderr.org/pipermail/inquiry/2005-October/003071.html
+# http://stderr.org/pipermail/inquiry/2005-October/003073.html
+# http://stderr.org/pipermail/inquiry/2005-October/003074.html
+# http://stderr.org/pipermail/inquiry/2005-October/003087.html
+# http://stderr.org/pipermail/inquiry/2005-October/003091.html
+# http://stderr.org/pipermail/inquiry/2005-October/003117.html
+# http://stderr.org/pipermail/inquiry/2005-November/003263.html
+# http://stderr.org/pipermail/inquiry/2005-November/003269.html
+# http://stderr.org/pipermail/inquiry/2005-December/003276.html
+# http://stderr.org/pipermail/inquiry/2006-February/003366.html
+# http://stderr.org/pipermail/inquiry/2006-February/003367.html
+
+===NEKS. New Elements • Kaina Stoicheia • Discussion History===
+
+'''Inquiry List (Dec 2005)'''
+
+* http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
+
+# http://stderr.org/pipermail/inquiry/2005-December/003272.html
+# http://stderr.org/pipermail/inquiry/2005-December/003282.html
+# http://stderr.org/pipermail/inquiry/2005-December/003296.html
+# http://stderr.org/pipermail/inquiry/2005-December/003297.html
+# http://stderr.org/pipermail/inquiry/2005-December/003298.html
+# http://stderr.org/pipermail/inquiry/2005-December/003299.html
+# http://stderr.org/pipermail/inquiry/2005-December/003300.html
+# http://stderr.org/pipermail/inquiry/2005-December/003301.html
+# http://stderr.org/pipermail/inquiry/2005-December/003302.html
+# http://stderr.org/pipermail/inquiry/2005-December/003303.html
+# http://stderr.org/pipermail/inquiry/2005-December/003304.html
===OLOD. Quine On The Limits Of Decision • Document History===
===OLOD. Quine On The Limits Of Decision • Document History===
