[Inquiry] Re: Kaina Stoicheia -- Discussion

[Jon Awbrey]

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KS.  Discussion Note 7

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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

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 that 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 a 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 the "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.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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