[Inquiry] Re: Logic Of The Sciences -- Discussion

[Jon Awbrey]

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LOTS.  Discussion Note 8

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Bernard,

I will make another try at addressing this portion of your last remarks:

BM: The difference relies I think, not in the objects but in the method of
    study.  Unfortunately the leading experimental science, namely physics,
    made for more than a century all what it could to mask the distinction.
    In the same vein, I wonder if the "set" concept as it is now understood
    doesn't fulfill just the epistemological role of common place between
    mathematicians and experimental scientists:  each community has his own
    specific conception of it but everybody agrees to meet under its auspices.
    Are you trying otherwise when you equate the sign relation with a set of
    triples?

Let me go back to the two dimensions of emphasis that I highlighted earlier:

JA: I can't see any sort of absolute distinction between logic and mathematics,
    but relative to the arena of the present topic I seem to have some sense
    of a difference between the logic of relative terms and the mathematics
    of relations.  Logic and mathematics cannot be disentangled, making up
    the warp and woof of a coherent science, but the fabric may be biased
    in different directions, depending on how we stress it from moment
    to moment.  The logical emphasis bears slightly heavier on the
    terms, propositions, and arguments in the sign-interpretant
    plane, while the mathematical emphasis has a tendency to
    dismiss matters of "mere notation" in understandable
    preference to the objective focus.

There are many different philosophical orientations and projects for
doing logic, mathematics, and experimental science.  We can classify
a number of the different emphases in sign relational terms as being
OS-planar or SI-planar.  Every now and then, all too often I believe,
enthusiasts of a given project will think they can reduce the entire
study to one plane of thinking, and then we have an ism gone bananas.
Isms have a normal function as heuristic spotlights for focussing on
a particular face of what may otherwise be an overwhelmingly complex
situation, and in this role they work work in tandem, paired up with
their opposing ism like intellectual muscles, but never in isolation.

We have just come out of a time -- well, some people are still doing
all they can to ignore the news -- when many people believed that it
should be possible to eliminate consideration of the OS dimension by
by reducing it to contemplation of constructs in the SI plane itself.
Of course, there have been as many times when the opposite trend was
all the rage, but I am guessing that fewer people here lean that way.

The contrast that I'm attempting to indicate between the
logic of relative terms and the mathematics of relations
is somewhat like the constrast between SI-ism and OS-ism,
respectively.  In LOR we begin with "relative terms" and
do not necessarily think of formal objects corresponding
to these signs, things that we'd call "relatives" per se.
In MOR we regard relations as "mathematical objects" and
treat the many different ways of signifying them as just
so many secondary representations of the primary objects.

As far as the extensional "set" concept goes, we could
replace it with "manifold of sense impressions" if you
wish.  The point is that the experiential world greets
us with an evergreen diversity of a-priori imperfectly
predic(a)table instances of phenomena that we're bound
to contrive ever new concepts for the sake of unifying.

In any case, whether we invoke the concept of a class,
collection, manifold, multitude, population, set, or
whatever, there has to be some way of dealing with
the relation between things that are interpreted
as elementary instances and the concepts that
unify them under one head.  And in the end,
it does not matter whether we start with
rational comprehensions or empirical
extensions -- either without the
other is ultimately useless.

Jon Awbrey

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