John, List
You say "When trying to relate different terminologies by Peirce and
others, always ask how or whether they could be mapped to FOL."
I agree wholeheartedly that Peirce's lifelong main interest was in logic,
and that we should evaluate his semiotic doctrines assuming that he is
talking logic.
But what does "map his terminologies to FOL" mean, really? Peirce
discovered quantification theory. This theory proved that a proposition is
not composed of general signs alone (symbols), but needs to use indices.
Thus a proposition as "Something loves anything" requires two indices
("something" and "anything") and a symbol ("---loves----"). A symbol is a
sign whose object is general, an index a sign whose object is individual.
This is a "grammatical" (= semiotic) analysis of the proposition, and is
informed by the discovery of quantification (in a sense, the discovery of
FOL). But what could it mean to "map his grammatical (= semiotic)
terminologies to FOL" if not this? It cannot mean that we should describe
his grammatical (=semiotic) terms by means of FOL. For in that case, we
would need FOL to describe his grammatical notions, which in their turn are
the instrument for a grammatical description of FOL. We would be launched
in a vicious circle.
So, it is one thing to say that we should evaluate Peirce's semiotic ideas
on the background of logic: this I agree wholeheartedly and I wrote a book
based precisely on this idea. Another thing would be to describe those
ideas by means of that which those ideas were intended to describe.
best
Francesco
On Fri, Sep 7, 2018 at 4:39 PM, John F Sowa <s...@bestweb.net> wrote:
> Francesco, Edwina, and Jon AS,
>
> FB
>
>> "Subject and Object are the same thing except for trifling distinctions"
>> (EP 2:494)
>>
>
> Yes! And they're the same as the "arguments" of relations by
> logicians today. This quotation and the others cited by Francesco
> confirm the point I was trying to make: From age 12 to 74, Peirce
> was a logician. Every version of logic that he used or invented
> had a precise mapping to his algebra of 1885, to his later EGs,
> and to the most widely used logics today.
>
> Peirce was also a professional lexicographer. Note his letter
> to the editor of the Century Dictionary, Benjamin E. Smith, who
> had also been one of his students at Johns Hopkins:
>
> The task of classifying all the words of language, or what's the
>> same thing, all the ideas that seek expression, is the most
>> stupendous of logical tasks. Anybody but the most accomplished
>> logician must break down in it utterly; and even for the strongest
>> man, it is the severest possible tax on the logical equipment and
>> faculty.
>>
>
> Implication: Over the years, Peirce had described his logics and
> the versions designed by other logicians in various ways. He also
> explored other versions in his Gamma graphs, 3-valued logic, modal
> logics, and metalanguage. But his first-order logic was equivalent
> to the core (Alpha + Beta) of existential graphs, and to "classical
> first-order logic" today. For the history, see "Peirce the logician"
> by Hilary Putnam: http://jfsowa.com/peirce/putnam.htm
>
> When trying to relate different terminologies by Peirce and others,
> always ask how or whether they could be mapped to FOL. If they
> can't, then ask what extensions or variations would be needed.
>
> ET
>
>> I'm trying to emphasize... that Peircean semiotics is not
>> expressed simply in language and/or logic, but in its pragmatic
>> application to material life.
>>
>> My concern is that much of the focus of our examination of Peirce
>> is often on terminology, on which term he used for..___. Since
>> Peirce often changed these terms, then, to me, they are not the
>> vital ground of Peircean semiosis and even sidesteps the fundamental
>> nature of Peircean semiotics - which is its pragmaticism.
>>
>
> I completely agree. But Peirce's logic was constant while his
> terminology was changing. Peirce put far more emphasis on mapping
> logic to and from perception and action than anyone else. But his
> terminology was idiosyncratic. His logic is the foundation for
> relating his terminology to any versions in use today.
>
> That foundation is key to bringing Peirce into the 21st century.
> Logicians, philosophers, and computer scientists today will never
> study Peirce unless we can show exactly how his writings relate
> to what they're doing now and what they still need to do.
>
> JAS
>
>> my own purpose in focusing so much on Peirce's concepts and
>> terminology in logic as semeiotic is not for its own sake, but
>> primarily for the purpose of making our ideas clear.
>>
>
> Yes. That was Peirce's motivation throughout his career. And logic
> was always his primary tool, as he said explicitly in 1877.
>
> JAS
>
>> Peirce defined pragmatism as "no attempt to determine any truth
>> of things," but rather "merely a method of ascertaining the meanings
>> of hard words and of abstract concepts" (CP 5.464, EP 2:400; 1907).
>>
>
> Yes. And remember his comment to Benjamin Smith.
>
> JAS
>
>> no one on the List is advocating "Platonic idealism."
>> Why keep bringing it up?
>>
>
> I was citing Peirce's "three universes": possibility, actuality,
> and the necessitated. Mathematical entities are "real possibles"
> in Peirce's terms. For an analysis of Peirce's ideas about these
> issues, I recommend an article by Susan Haack:
> https://www.researchgate.net/publication/247935387_Peirce_an
> d_Logicism_Notes_Towards_an_Exposition_1993
>
> On page 9, she wrote
>
>> at CP 4.118 (1893) Peirce speaks of "the Platonic world of pure
>> forms with which mathematics is always dealing," and in the
>> prospectus for his 12-volume _Principles of Philosophy_ (c. 1893)
>> he entitles the third volume, _Plato's World: an Elucidation of
>> the Ideas of Modern Mathematics_. But at 4.161 (c. 1897) we read...
>>
>> If this is Platonism, it is Platonism of a very distinctively
>> Peircean stripe.
>>
>
> Edwina
>
>> I think one can get trapped in the isolation of words and should
>> instead, consider their function in the actual world.
>>
>
> Yes. But Peirce claimed that math and logic, formal and informal,
> are the foundation for all the sciences and all the ways of thinking
> and acting in the world. (See his 1903 classification.)
>
> William James could not fully understand Peirce because he did
> not know logic. WJ was never able to understand Peirce's
> logic and his distinction between pragmatism and pragmaticism.
>
> In the excerpts below, note that nearly every sentence uses logical
> terminology. (This excerpt happens to be something I was recently
> reading, but you can find many more examples in all his writings.)
>
> John
> ___________________________________________________________________
>
> 5.448. Perhaps a more scientific pair of definitions would be that
> anything is general in so far as the principle of excluded middle does
> not apply to it and is vague in so far as the principle of contradiction
> does not apply to it.†1 Thus, although it is true that "Any proposition
> you please, once you have determined its identity, is either true or
> false"; yet so long as it remains indeterminate and so without identity,
> it need neither be true that any proposition you please is true, nor
> that any proposition you please is false. So likewise, while it is
> false that "A proposition whose identity I have determined is both true
> and false," yet until it is determinate, it may be true that a
> proposition is true and that a proposition is false.†P1
>
> †P1 These remarks require supplementation. Determination, in general,
> is not defined at all; and the attempt at defining the determination of
> a subject with respect to a character only covers (or seems only to
> cover) explicit propositional determination. The incidental remark
> [447] to the effect that words whose meaning should be determinate would
> leave "no latitude of interpretation" is more satisfactory, since the
> context makes it plain that there must be no such latitude either for
> the interpreter or for the utterer. The explicitness of the words would
> leave the utterer no room for explanations of his meaning. This
> definition has the advantage of being applicable to a command, to a
> purpose, to a medieval substantial form; in short to anything capable of
> indeterminacy. (That everything indeterminate is of the nature of a
> sign can be proved inductively by imagining and analyzing instances of
> the surdest description. Thus, the indetermination of an event which
> should happen by pure chance without cause, /sua sponte/, as the Romans
> mythologically said, /spontanément /in French (as if what was done of
> one's own motion were sure to be irrational), does not belong to the
> event — say, an explosion — /per se/, or as explosion. Neither is it by
> virtue of any real relation: it is by virtue of a relation of reason.
> Now what is true by virtue of a relation of reason is representative,
> that is, is of the nature of a sign. A similar consideration applies to
> the indiscriminate shots and blows of a Kentucky free fight.) Even a
> future event can only be determinate in so far as it is a consequent.
> Now the concept of a consequent is a logical concept. It is derived
> from the concept of the conclusion of an argument. But an argument is a
> sign of the truth of its conclusion; its conclusion is the rational
> interpretation of the sign. This is in the spirit of the Kantian
> doctrine that metaphysical concepts are logical concepts applied
> somewhat differently from their logical application. The difference,
> however, is not really as great as Kant represents it to be, and as he
> was obliged to represent it to be, owing to his mistaking the logical
> and metaphysical correspondents in almost every case. Another advantage
> of this definition is that it saves us from the blunder of thinking that
> a sign is indeterminate simply because there is much to which it makes
> no reference; that, for example, to say, "C.S. Peirce wrote this
> article," is indeterminate because it does not say what the color of the
> ink used was, who made the ink, how old the father of the ink-maker
> [was] when his son was born, nor what the aspect of the planets was when
> that father was born. By making the definition turn upon the
> interpretation, all that is cut off. [Cf. 3.93.]
>
> At the same time, it is tolerably evident that the definition, as it
> stands, is not sufficiently explicit, and further, that at the present
> stage of our inquiry cannot be made altogether satisfactory. For what
> is the interpretation alluded to? To answer that convincingly would be
> either to establish or to refute the doctrine of pragmaticism. Still
> some explanations may be made. Every sign has a single object, though
> this single object may be a single set or a single continuum of objects.
> No general description can identify an object. But the common sense of
> the interpreter of the sign will assure him that the object must be one
> of a limited collection of objects. Suppose, for example, two
> Englishmen to meet in a continental railway carriage. The total number
> of subjects of which there is any appreciable probability that one will
> speak to the other perhaps does not exceed a million; and each will have
> perhaps half that million not far below the surface of consciousness, so
> that each unit of it is ready to suggest itself. If one mentions
> Charles the Second, the other need not consider what possible Charles
> the Second is meant. It is no doubt the English Charles Second.
> Charles the Second of England was quite a different man on different
> days; and it might be said that without further specification the
> subject is not identified. But the two Englishmen have no purpose of
> splitting hairs in their talk; and the latitude of interpretation which
> constitutes the indeterminacy of a sign must be understood as a latitude
> which might affect the achievement of a purpose. For two signs whose
> meanings are for all possible purposes equivalent are absolutely
> equivalent. This, to be sure, is rank pragmaticism; for a purpose is an
> affection of action.
>
> What has been said of subjects is as true of predicates. Suppose the
> chat of our pair of Englishmen had fallen upon the color of Charles II's
> hair. Now that colors are seen quite differently by different retinas
> is known. That the chromatic sense is much more varied than it is
> positively known to be is quite likely. It is very unlikely that either
> of the travelers is trained to observe colors or is a master of their
> nomenclature. But if one says that Charles II had dark auburn hair, the
> other will understand him quite precisely enough for all their possible
> purposes; and it will be a determinate predication.
>
> The October remarks [i.e. those in the above paper] made the proper
> distinction between the two kinds of indeterminacy, viz.:
> indefiniteness and generality, of which the former consists in the
> sign's not sufficiently expressing itself to allow of an indubitable
> determinate interpretation, while the [latter] turns over to the
> interpreter the right to complete the determination as he please. It
> seems a strange thing, when one comes to ponder over it, that a sign
> should leave its interpreter to supply a part of its meaning; but the
> explanation of the phenomenon lies in the fact that the entire universe
> — not merely the universe of existents, but all that wider universe,
> embracing the universe of existents as a part, the universe which we are
> all accustomed to refer to as "the truth" — that all this universe is
> perfused with signs, if it is not composed exclusively of signs. Let us
> note this in passing as having a bearing upon the question of
> pragmaticism. [Cf. 4.539.]
>
> The October remarks, with a view to brevity, omitted to mention that
> both indefiniteness and generality might primarily affect either the
> logical breadth or the logical depth of the sign to which it belongs.
> It now becomes pertinent to notice this. When we speak of the depth, or
> signification, of a sign we are resorting to hypostatic abstraction,
> that process whereby we regard a thought as a thing, make an
> interpretant sign the object of a sign. It has been a butt of ridicule
> since Molière's dying week, and the depth of a writer on philosophy can
> conveniently be sounded by his disposition to make fun of the basis of
> voluntary inhibition, which is the chief characteristic of mankind. For
> cautious thinkers will not be in haste to deride a kind of thinking that
> is evidently founded upon observation — namely, upon observation of a
> sign. At any rate, whenever we speak of a predicate we are representing
> a thought as a thing, as a substantia, since the concepts of substance
> and subject are one, its concomitants only being different in the two
> cases. It is needful to remark this in the present connexion, because,
> were it not for hypostatic abstraction, there could be no generality of
> a predicate, since a sign which should make its interpreter its deputy
> to determine its signification at his pleasure would not signify
> anything, unless nothing be its significate. — From "Basis of
> Pragmaticism," 1906, following somewhat after 554.
>
>
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