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

[Jon Awbrey]

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

QUIPS.  Discussion Note 51

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

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

Re: QUIPS-DIS 46.  http://stderr.org/pipermail/inquiry/2005-May/002739.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

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

JA: 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:

BM: May be there is some form like this besides the problem.
    However the problem is not a simple combinatorial one.

I'm simply saying that the source of vacillation on Peirce's part and
consequential controversy on our parts seems to be mainly the absence
of clear enough definitions of the intended dimensions and structures
that Peirce had in mind.  I feel that if those could be made explicit
then progress would be rather quick and straightforward from there on.

BM: When I refered to an operation upon an operation I would have
    better done to precise this:  The first operation consists in
    elaborating (by combination) the characters of each one of the
    divisions, starting with the following trichotomies:

    a.  the phaneron in itself (SOI)
    b.  Modes of presence of the phaneron
    c.  raison d'être of the phaneron

BM: Under the 3 constraints on the sign relation ordering,
    the correlates ordering and the phaneron composition
    ordering we get 10 divisions.  Formally the operation
    is identical to the one that lead to the 10 classes
    of 1903.

BM: The second operation consist in passing from the 10 divisions to
    66 classes.  What I know from the limited sources at my disposal
    is that Peirce was convinced of the necessity of 66 classes.  But
    I don't know why.  Formally we can be sure that if the 10 divisions
    are ordered in the usual peircian way we will get 66 classes.  But
    what we ignore (with the published sources) what is the order of the
    10 divisions.  It is this order that makes the real dispute between
    peircean scholars on the subject I think (except R. Marty who ends
    with 6 divisions).  I think too that (a) there is no proof that
    a unique ordering is possible, (b) this ordering needs to be
    determined by induction (so the apparent indecisions of
    Peirce).

BM: It doesn't seem to be a simple combinatorial problem.

It is just my sense that if and when it is well-posed, it would be.
More likely it'll happen that there are manifold different ways of
posing it, perhaps according to incommensurable aesthetic delights,
each one leading to a different arrangement as its chosen solution.

Jon Awbrey

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