[Arisbe] Re: Inquiry Into Inquiry

[Jon Awbrey]

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Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):

JA: I guess I just do not understand the use of the word "formal"
    as you appear to be using it in several of the above statements.
    I grasp "formal" as meaning something like "concerned with form"
    or "pertaining to form".  To my way of thinking, this contains
    no implication of "being limited exclusively to form", since
    form and matter are just two diverse aspects of being.

HP: I am using "formal" in the mathematician's sense where it just means those
    axiomatic symbolic sets and their manipulations that are performed by rules
    that do not require assigning extrinsic meaning to the symbols or rules for
    their manipulation (like adding a column of numbers).  Such intrinsically
    meaningless systems (fun for mathematicians) often exhibit structures that
    later, when given observational interpretations, turn out to be excellent
    models of the physical world (e.g., matrices, differentiable manifolds,
    group theory, etc.).  Wigner famously called this the "unreasonable
    effectiveness" of mathematics for modelling physical systems.

I was afraid of that, but did not want to be charged with pushing you to it.
In spite of your next disclaimer, you have just given the usual description
and the stereotypical rationalization of the point of view that is commonly
called "formalism".  As a reformed formalist, I know all too well how this
story goes, but it no longer has  much to do with the way that I now use
the words "form" and "matter", having traced their meanings as far back
as Aristotle to pick up the uncut stuff.  And though it's been a while
since I encountered Wigner's motto in context, I am pretty sure that
I always felt he was hinting at a form of pythagorean realism here,
though I may well have guessed his meaning wrong both then and now.

As it happens, I recently wrote a narrative about my conversion
in response to a series of questions from another correspondent:

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Subj:  Re: I am astonished by mathematicians' reluctance/refusal to consider seriously Gödel's Platonism
Date:  Fri, 08 Jun 2001 18:50:59 -0400
From:  Jon Awbrey <jawbrey@oakland.edu>
  To:  Reader X

Reader X wrote (RX):
Jon Awbrey wrote (JA):

RX: I am astonished by mathematicians' reluctance/refusal
    to consider seriously Godel's Platonism ...

JA: From my experience, I think the truth is more that they
    simply take it for granted, but have heard that it is
    unfashionable, and so they keep quiet about it ...

JA: Just from the characters that I have known in mathematics when I was passing through
    their neighborhood, I would guess that it is purely a matter of economy of effort.
    Someone pegs you in the hall and asks you about your "philosophy of math" -- you
    are itching to get back to your office where you can write down the latest idea
    about some problem that has passionately engaged your every free moment for all
    the last year or decade or three, so you tell 'em the short answer that you are
    guessing they'll be the happiest to hear -- "Oh, it's just a meaningless formal
    game played with glass beads according to rules that we make up as we go along",
    chuckle sagely, and race off up the stairs to your secret lair.  It's not like
    you were going to change any minds, anyway, and years of futile wrangling in
    your undergrad years have taught you that this is the most practical strategy.
    It is only on the very rare occasion, every now and then, when someone like
    Gödel gets provoked enough by the village idiocies of someone like Russell
    that they will interrupt their main affairs to try and stem the tides of
    fashion.  But the popular lunacy goes on anyway, acting as if it has
    absorbed the result into whatever system of preveilng belief they
    had before you bothered to raise the curtain.  And so it goes.

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HP: I am not referring to the philosophical and psychological disputes over ontology
    or the sources of mathematical creativity (formalists, intuitionists, logicists,
    platonists, etc.).  Most un-programmed calculation is formal.  (One can argue
    about memory-stored-program computers).

In the context of mathematics and the theory of computation, I mostly understand
the word "formal" in the adjectiveal senses of formal grammars, formal languages,
and formal systems.  In this case I hear it to mean something roughly synonymous
with "explicit".  For example, the grammar rules, the sentences, or the axioms
and inference rules are explicitly enumerated in a finitary fashion, but this
aspect of form can be featured in relief without any prejudice that requires
its formalities to be meaningless, perfunctory, or, if you will, pro forma.

HP: The Hertz's modelling relation is instructive because:

HP: (1) it clearly separates the formal logical syntax of our models (laws)
        from the empirical observational semantics (initial conditions),
        which is essential for physics, and

HP: (2) it emphasizes the limits of scientific knowledge:
        "We do not know, nor have we any means of knowing,
        whether our conception of things are in conformity
        with [external reality] in any other than this one
        fundamental respect."

JA: I do not know what you mean by "strictly separate" in this context.
    I understand the relations among objects, signs, and ideas to make
    sense only within the context of one or another 3-adic sign relation.

HP: Hertz's epistemic condition is also irreducibly triadic with the same
    terms (object, image/sign, observer/interpreter), but he goes on to
    explain the necessary conditions for a good model, a homomorphism.

But an arrow or morphism is a 2-adic artifact.  Sure, its categorical context
exhibits a couple of salient 3-adic structures, the composition operation and
the anchoring of natural transformations, but the map itself is a very special
sort of 2-adic relation.  In PTOS (the pragmatic theory of signs), it would be
classified as an "iconic notation".  An icon is a sign that denotes its object
by virtue of a property that it shares with it.  For a "structure-preserving"
mapping, this property is clearly just the structure that is being preserved.

But iconic notations and indexical notations imply very special types
of sign relations, being almost "degenerate" in view of the fact that
they are "nearly 2-adic".  "Symbolic notations", in the PTOS sense of
sense of the term "symbolic", constitute sign relations that are more
generic and more genuine, in a sense, than iconic and indexical kinds.

HP: When we want to use a formal symbol system to model a physical system ...

There it is!  I spy the crux of our misunderstanding ...

The formal symbol system may be iconic of the object system,
but it does not have to be, nor does its virtue of denoting
have to be exhausted by whatever iconic powers it does have.

The rationalization that you have so far given of how a symbol system can achieve
its "unreasonable effectiveness" in relating us to real pragmata fails to capture
the effective ingredient of the generic phenomenon by which symbols acquire their
natures and effect the conveyance of their meanings.  When it comes to accounting
for the conditions of possibility that explain how symbols motivate interpretants
with regard to an object, there is a deficit, a shortfall here that the exchequer
of the 2-dim map just cannot cover.

HP: When we want to use a formal symbol system to model a physical system we have to
    assign observable qualities to some of the otherwise meaningless symbols and then
    provide initial conditions for them by measurement.  If you do not make a strict
    distinction between the formal rule-system that represent universal, inexorable
    laws and the initial conditions which may be different for every observer, the
    model no longer makes sense.  To survive, inquiring physicists (bacteria and
    all living systems) want to know what they cannot influence and what they
    can change.

HP: So, to restate my main question:

HP: Are Peircean rules of inquiry formal?

When I am able to use my sense of "formal", and my sense of "logic",
then I am able to say that logic is the formal and normative branch
of semiotics, where semiotics is the general study of sign relations.

And yet my sense of "formal" does not seem to be your sense of "formal".
For now I can only anticipate that we may agree on the gloss "explicit".
But now you have, quite aptly I think, broadened your sense of "logic"
from a sense that appeared limited to deduction to include the whole
of "inquiry", of which we might say with Dewey-eyed enthusiasm that
logic is the theory thereof.  And this brings us to the hard part
of one definition of pragmatic thinking, to wit, the tenet that
makes it out au fond to be the "logic of abduction".

HP: They appear to be formal and therefore
    to apply universally for all inquiry
    conditions, like "laws of inquiry".

There may be such laws.
There may be such rules.
They may turn out formal.
But I don't know that yet.

HP: How, then, do the unique conditions of a specific observer or system under study
    enter the formal inquiry?  How is this different from normal physicist's inquiry?

I think that this sounds very similar to a question that I ask in my dissertation:

| 1.2.2  A Fugitive Canon
|
| The principal difficulties associated with this task appear to spring from two roots.
|
| First, there is the issue of "computational mediation".  In using the sorts of sequences
| that computers go through to mediate discussion of the sorts of sequences that people
| go through, it becomes necessary to re-examine all of the facilitating assumptions
| that are commonly taken for granted in relating one human experience to another,
| that is, in describing and building structural relationships among the
| experiences of human agents.
|
| Second, there is the problem of "representing the general in the particular".
| How is it possible for the most particular imaginable things, namely, the
| transient experiential states of agents, to represent the most general
| imaginable things, namely, the agents' own conceptions of the abstract
| categories of experience?
|
| Finally, not altogether as an afterthought, there is a question
| that binds these issues together.  How does it make sense to
| apply one's individual conceptions of the abstract categories
| of experience, not only to the experiences of oneself and
| others, but in points of form to compare them with the
| structures present in mathematical models?
|
| http://www.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm

Jon Awbrey

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