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

[Jon Awbrey]

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QUIPS.  Discussion Note 46

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AB = Auke van Breemen
BM = Bernard Morand
JA = Jon Awbrey

Re: QUIPS-DIS 37.  http://stderr.org/pipermail/inquiry/2005-May/002727.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

BM: Sorry for entering the discussion late.  I could not resist
    expressing my brute secondness on this subject (see below).

JA: Let me check out some aspects of your reading before proceeding.

AB: Well, to me it does not look like a correspondence, my reading of my
    text and my reading of your check of it.  My comment between the lines.

JA: The Lady Welby correspondence in Wiener's volume is some of my
    first reading in Peirce, but all in all I find no innovations
    but the purely expository there, and the passages that we are
    discussing in CP 8 are noted by the Editors as being revised
    in way that is "unintelligible", which led them to leave the
    text as it was originally given.  All of this would put us
    on extremely shaky ground if we try to say that this was
    Peirce's last, best thoughts on the matter.  In cases
    like this I have to be ruled by what interpretation
    makes the most consistent overall account, when
    taken in the context of a writer's known work.

AB: 1.  Sources.  I use the 1977 edition of the correspondence as
        my main source on this.  Would like to have more material.

JA: I have Philip Wiener's 'Charles S. Peirce: Selected Writings' and CP 8.
    In CP 8.349, at "'Copulants', which neither describe nor denote their
    Objects, but merely express the logical relations of these latter to
    something otherwise referred to", the Editors add the following note:
    "(Ed.) Peirce had revised the manuscript here, but since his revision
    is unintelligible, we give the text as it was originally."

AB: 2.  Shaky grounds.  As Joe already indicated it is highly tentative work
        of Peirce, his work on speculative grammar at the end of his life.
        No dispute about that amongst any of the Peirce interpreters that
        seriously tried to apply the speculative grammar, I presume.

BM: It would be interesting to make more precise what is really tentative
    in this late work.  Undoubtedly, it is the case for the inscription of
    words into places of the classification.  This is in fact a matter of
    precision, accuracy, etc.  In some cases no word being available, it
    has to be invented.  It is also true that the Welby classification
    is hypothetical and put to practical test by Peirce.

BM: But I think that the classification itself, its architectonic,
    is not at all tentative but that it obeys to a general plan or
    hypothesis.  This is what is generally not seen as possible by
    two opposed interpretations.  The first one, a representative
    of which seems to be Jon, don't see that there is something
    really new at work here because they seem to estimate that
    all is definitively contained in the formal-universal
    definition of the sign relation (see his answer to
    Auke below).

BM: Another misunderstanding perhaps is to require exactness everywhere.
    Here we are in the domain of approximations, errors, etc.  If a metaphor
    could serve, Peirce is estimating the value of the parameter of the law
    of gravitation.  The second interpretation, don't see that before this
    apparently botanical classification, there was a lot of logical work
    and that it remains there.  It would be necessary to make a special
    case for people like D. Savan, R. Marty and some others who have
    taken seriously the subject.  I can't give my idea of the general
    plan at work in the Welby classification but it was the main
    line of argument of my book (sorry for the self reference).

BM: Just two directions:

BM: Firstly I have shown there that there are exactly 10 divisions
    in the Welby classification for the same reason that there are
    10 classes in the 1903 classification.  The main difference is
    that we have a logical operation upon another logical operation
    and the question amounts to explain why there is such a second
    operation.

BM: Secondly I have argued (without being absolutely sure of the
    result) that the relationship between the two classifications
    is the well known iliative relation, 1903 being the antecedent
    and Welby the consequent, so that the first remains into the
    second (It would not be necessary to push me long further as
    to say that the 1903 classification was designed with the
    future Welby classification in view, but this would have
    to be tested with the sources at hand).

Auke, Bernard, List,

I will have to take this in pieces over the weekend,
so will restrain myself to a few remarks in preface.

I love a good combinatorial problem, my affection but slightly dimmed
by the fact that I'm not nearly so sharp at solving them as I used to
think I was, and this "elementary sign class" (ESC) question semes as
if it "ought to be in principle" a rousing good combinatorial problem,
say, on a par with the one about counting elementary k-adic relations
to which Peirce published a solution in 1880 (CP 3.229), that between
us may be called the "Peirce Triangle", since he apparently published
it some decades before the other people whom it's usually named after:

| N.J.A. Sloane, "Sequence Number A011971",
|'On-Line Encyclopedia of Integer Sequences'
| http://www.research.att.com/~njas/sequences/
| http://www.research.att.com/projects/OEIS?Anum=A011971

| Eric W. Weisstein, "Bell Triangle",
| From 'MathWorld -- A Wolfram Web Resource'
| http://mathworld.wolfram.com/BellTriangle.html

"In principle", but not yet apparently in practice,
as there is something with the air of an ill-posed
problem that lingers on about its manifold posings.

Or so it seems to me ...

Jon Awbrey

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