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

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

QUIPS.  Discussion Note 25

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

JW = Jim Willgoose

Re: QUIPS-DIS 17.  http://stderr.org/pipermail/inquiry/2005-May/002682.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

JW: I find this all very interesting (and strangely so).
    In fact, I sometimes find myself unable to get away
    from it.  I heard that the philosopher Nelson Goodman
    once said that he would like to get away from philosophy
    and logic but could not.

Jim,

Seems like I remember a similar statement from John Dewey,
something about the impossibility of doing anything else?

JW: In any case, I butchered the number/numeral distinction
    in a recent post.  Have you seen Joe Ransdell's entry
    (Encyclopedia of Semiotics, at Arisbe) on signs and
    especially the 1st trichtomy?  There is an interesting
    discussion of the type/token distinction, which though
    frequently credited to Peirce, may or may not bear any
    resemblance to the way he understands it, in so far as
    "mentioning" and "use" is the way the debtors understand
    it.  (this has a little to do with contextual definition
    or "definition in use.")

Yes, this has been a bedeviled issue on some other lists that I won't mention.

JW: I often thought that one could mention a symbol in order
    to define how it is used.  This gives the type.  How the
    symbol works in a sentence is its token-use.  But it seems
    to me that Peirce does not mention the symbol "the" (CP 2)
    in order to contextually or intensively define it, but only
    to ostensively point out the number of tokens on a page.
    That is effectively an extensional definition.  More to
    the point, the type of symbol does not suggest a rule or
    law governing replicas.  Thus, a type is not a legisign.
    But if it did incorporate or "involve" a legisign such
    as a set of instructions for generating a "language-L",
    then one would have implicitly or contextually defined
    something like a pure symbol.

The spectrum of topics through "contextual definition", "definition in use",
"paraphrastic definition", and "pragmatic definition" is a motley crew, but
a suitable sort of family resemblance might bring them under the heading of
"regular representations" or "term models".  This is related to that whole
biz about combinators and the "propositions as types" (PAT) analogy that
I referred you to through the following links:

PAT.    Propositions As Types
PAT.    http://forum.wolframscience.com/showthread.php?threadid=490
PAT A.  http://stderr.org/pipermail/inquiry/2004-June/thread.html#1643
PAT A.  http://stderr.org/pipermail/inquiry/2004-July/thread.html#1677
PAT B.  http://stderr.org/pipermail/inquiry/2004-June/thread.html#1647
PAT B.  http://stderr.org/pipermail/inquiry/2004-July/thread.html#1684

But I'm trying to stay focussed on the end-in-view,
so I'll leave this stuff until it actually forces
itself on my attention.

A suitably generic way of handling these type/token issues,
with regard to signs in a text or anything else, is by way
of equivalence relations and equivalence classes, designed
to fit the occasional purpose and capable of being refined
or coarsened as need be.  Do you want the count of <the>'s
to be case-sensitive or case-insensitive? -- Fine, you can
define type/token-hood any way you like.  I think that you
get the idea.

At any rate, that was not my interpretation
of what Peirce was talking about in CP 4.447,
since it would hardly account for what he wrote.

Jon Awbrey

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