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

[Jon Awbrey]

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QUIPS.  Discussion Note 47

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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

Auke, Bernard, List,

Comments interspersed below ...

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).

If the underpinnings of the architectonic were really nailed down then
this would be a straightforward combinatorial problem, and I know that
several different workers have approached it this way, but the problem
is that they come up with different answers.  I have seen this sort of
thing before, however, where something that seems like a mere question
of counting leads people who count to diferrent counts, and it usually
happens because different counters have different ideas of what things
count as different and what things count as the same.  Another way to
say it is that different folks have different equivalence relations
in mind, often associated with different symmetry groups, but they
haven't yet rendered their presupposed symmetries explicit enough.
These are some of the typical symptoms of an ill-posed problem.

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).

The character of the discussion, as I continue to hear, still
strikes me as being mostly a priori, and without much content.
I see no examples of non-trivial sign relations being brought
to the table.  A non-trivial sign relation has more than just
a single triple in it.  Think of mathematical structures like
geometries and groups.  As examples of groups think about the
addition tables for addition mod k.  Addition tables are sets
of triples of the form {<x, y, z> : x = y + z}.  Would we try
to classify groups by staring at some of our favorite triples,
say <4, 2, 2> or <12, 7, 5>, until the cows come home, or try
to figure out the different sorts of triples that might exist?
No, such strategies are far too isolated and decontextualized.

Jon Awbrey

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