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</pre>
 
</pre>
   −
==OLOD. Quine On The Limits Of Decision==
+
==NEKS. New Elements &bull; 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 &bull; Kaina Stoicheia &bull; 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 &bull; Kaina Stoicheia &bull; 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.)
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 +
 +
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 +
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 +
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 +
* http://stderr.org/pipermail/inquiry/2005-October/thread.html#3075
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 +
 +
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 +
 +
* http://stderr.org/pipermail/inquiry/2005-September/thread.html#3066
 +
* http://stderr.org/pipermail/inquiry/2005-October/thread.html#3070
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# http://stderr.org/pipermail/inquiry/2005-October/003074.html
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# http://stderr.org/pipermail/inquiry/2005-October/003087.html
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# http://stderr.org/pipermail/inquiry/2005-October/003091.html
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# http://stderr.org/pipermail/inquiry/2005-October/003117.html
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# http://stderr.org/pipermail/inquiry/2005-November/003263.html
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# http://stderr.org/pipermail/inquiry/2005-November/003269.html
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# http://stderr.org/pipermail/inquiry/2005-December/003276.html
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# http://stderr.org/pipermail/inquiry/2006-February/003366.html
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# http://stderr.org/pipermail/inquiry/2006-February/003367.html
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===NEKS. New Elements &bull; Kaina Stoicheia &bull; Discussion History===
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'''Inquiry List (Dec 2005)'''
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* http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272
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# http://stderr.org/pipermail/inquiry/2005-December/003272.html
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# http://stderr.org/pipermail/inquiry/2005-December/003282.html
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# http://stderr.org/pipermail/inquiry/2005-December/003296.html
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# http://stderr.org/pipermail/inquiry/2005-December/003297.html
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# http://stderr.org/pipermail/inquiry/2005-December/003298.html
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# http://stderr.org/pipermail/inquiry/2005-December/003299.html
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# http://stderr.org/pipermail/inquiry/2005-December/003300.html
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# http://stderr.org/pipermail/inquiry/2005-December/003301.html
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# http://stderr.org/pipermail/inquiry/2005-December/003302.html
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# http://stderr.org/pipermail/inquiry/2005-December/003303.html
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# http://stderr.org/pipermail/inquiry/2005-December/003304.html
    
===OLOD. Quine On The Limits Of Decision &bull; Document History===
 
===OLOD. Quine On The Limits Of Decision &bull; Document History===
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edits