[Inquiry] Re: Futures Of Logical Graphs -- Discussion

[Jon Awbrey]

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FOLG.  Discussion Note 27

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Peirce List,

We have a couple of statements from Peirce that appear to be in conflict:

Statement 1.

| Every word is a symbol.  Every sentence is a symbol.
| Every book is a symbol.  Every representamen depending
| upon conventions is a symbol.  Just as a photograph is an
| index having an icon incorporated into it, that is, excited
| in the mind by its force, so a symbol may have an icon or an
| index incorporated into it, that is, the active law that it is
| may require its interpretation to involve the calling up of
| an image, or a composite photograph of many images of past
| experiences, as ordinary common nouns and verbs do;  or
| it may require its interpretation to refer to the actual
| surrounding circumstances of the occasion of its embodiment,
| like such words as 'that', 'this', 'I', 'you', 'which', 'here',
| 'now', 'yonder', etc.  Or it may be pure symbol, neither 'iconic'
| nor 'indicative', like the words 'and', 'or', 'of', etc.
|
| C.S. Peirce, 'Collected Papers', CP 4.447
|
|"Logical Tracts, No. 2" (c. 1903), in 'Collected Papers', CP 4.418-509.
| http://www.existentialgraphs.com/peirceoneg/existentialgraphs4.418-529.htm

Statement 2.

| My principal object in drawing attention to this symbol of similarity
| is to show that the significations of symbols have various grades of
| directness up to the limit of being themselves their own significations.
| An icon is significant with absolute directness of a character which it
| embodies;  and every symbol refers more or less indirectly to an icon.
|
| An index is directly denotative of a real object with which it is in reaction.
| Every symbol refers more or less indirectly to a real object through an index.
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 258
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, vol. 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.

To place the two statements in the starkest possible contrast,
we might paraphrase and summarize them in the following manner:

   S_1.  There are symbols that do not involve either icons or indices in any fashion.

   S_2.  Every symbol refers more or less indirectly to an icons and through an index.

This is not exactly a logical contradiction.  The "involve" of S_1
would have to be equated to the "refer to or through" of S_2, and
the generalizing or qualifying phrase "more or less indirectly"
would have to be omitted from S_2.  Furthermore, there is much
in the context of each statement that might blunt its force.
Still, it's enough to give one pause.  Real contradictions
are a source of uncertainty about the cogency of a theory,
and uncertainty is the spur of inquiry, so there is some
reason to inquire further here.

Among the questions that might emerge from the woodwork
after many moons of taking pauses, I've noted these two:

   What is a theory, anyway?

   In particular, what should constitute a theory of signs?

Do all of the things that a person says about X constitute a Theory of X?
Actually, the most general logical definitions of "theory" that I know of
specify that any collection of sentences from a language do in some slight
respect count as a theory, but it's a very slight respect indeed, and most
intellects will almost immediately insist on looking for something stronger
in the way of what an "interesting" theory, a theory worth having might be.

We'll look into that next time ...

Jon Awbrey

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