[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

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QUIPS.  Discussion Note 17

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JW = Jim Willgoose

Re: QUIPS-COM 2.  http://stderr.org/pipermail/inquiry/2005-May/002678.html
In: QUIPS-COM.    http://stderr.org/pipermail/inquiry/2005-May/thread.html#2648

JW: Peirce says:

CSP: | there is a great saving of trouble and gain of
     | accuracy in employing a logical "algebra", or
     | perfectly systematic written language or body
     | of symbols ..." (NEM 4, p. 106)
     |
     | Peirce, "Qualitative Logic",
     | NEM 4, p. 106 & CE 5, p. 361

More complete reference here:

| C.S. Peirce, "Qualitative Logic", MS 736, pp. 101-115 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, vol. 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. C.S. Peirce, "Qualitative Logic", MS 582 (Fall-Winter 1886), pp. 323-371 in:
|'Writings of Charles S. Peirce:  A Chronological Edition, Volume 5, 1884-1886',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1993.

Jim,

I seem to be getting mail from the Peirce List in random order ...

JW: Not all of those symbols can be defined explicitly (ostensive or intensive).
    Some of them must be "defined in use".  Do you think that Peirce could have
    had in mind pure symbols that are neither indicative nor iconic and must be,
    therefore, dealt with in other ways?

I quoted this passage in order to begin dispelling the notion that
Peirce only rarely considered syntactic entities like sentences
and langauges, formal or natural, in his treatment of logic.
The whole idea of algebraic logic, logical algebra, or
symbolic logic sprang from the analogies that could be
cooked up between the well-formed formulas of algebra
and the syntactic expressions of a logical system.

To see what actually happened, consider once again the all-important
distinction between numbers (the objects) and numerals (the signs).
How do we normally mark this distinction in real-life discourse,
that is, once we have grasped it?  Mostly we ignore the whole
fussy bit, saying "number" when we really mean "numeral",
and relying on the duly cognizant interpreter to guess
from the context of usage which moiety of the divided
meaning we actually mean.

It's pretty much the same with the all-important, if a bit
fussy distinction between propositions (the abstract objects)
and sentences, paragraphs, articles, discourses, essays, texts,
and whole literatures (the concrete signs).  Important as it is,
we ignore it in all but the most extreme forms of technical talk,
in most cases postponing any attention to the border between the
dominions until some problem forces negotiations to be re-opened.
In particular, the reason why we don't see the word "sentence"
all that much in Peirce is (1) he has so many other ways of
saying the same thing, and (2) he follows the common custom
of using the word "proposition" equivocally, leaving the
task of interpretation to the interpreter thereof.

Jon Awbrey

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