[Arisbe] Re: Inquiry Into Inquiry

[Jon Awbrey]

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

JA: 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".

HP: Fear not!  Push on!  But what rule of logic, polemics,
    or ethics allows you to disclaim my disclaimer?

No rule of logic.  I am making an empirical observation.
I am merely setting out a rough description of a sample
of behavior, as I observe its effects from my point of
view, and making a hypothesis, informed by my previous
experience, about a form of conduct that may plausibly
be guessed to underlie it.  It's an extremely fallible
process.

HP: As I warned, I'm not talking stereotypic rationalizations.
    I'm simply defining my usage by stating a simple, empirically
    testable condition for a formal process.  Just follow the rules.
    Adding a column of numbers can be accomplished whether or not
    the numbers refer to apples, bytes, or nothing but number.
    It's called calculating.

Oh, you mean an algorithm?
Id est, an effective procedure?
To wit, an effective description
of a particular pattern of behavior?
You regard this as empirically testable?
I worry about that.  Some things I know of
say yes, okay.  Other things say no, no way.
I will have to think about this for a while.

But I still perceive a residue of the attitude called "formalist" in this seemingly,
all too seemingly innocent definition of "formal".  It shows up in the tendency to
use qualifiers like "just", "merely", "nothing but" in the invitation to follow.

JA: 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.

HP: How you and Aristotle choose to use words is fine, but for this discussion
    I chose to use "formal" to indicate just following rules.  In my usage,
    either you follow the rules, or you don't.

Okay, this is something that I have at least thought about.
Because I have had this same discussion many times before,
and that is just in this lifetime.  In fact, we were just
talking about this same problem the other day, perhaps in
slightly different words.  It's the very same boggle that
I ran into way back then, when I was just a poor innocent
mathematics and physics student, who would have scoffed --
who recursively scoffed -- at the very idea of reading up
on what such Ancients as Plato and Aristotle wrote.  But,
willy nilly, pursuing a course of inquiry more nilly than
willy, at least, at first, in those dim initial conditions
that I half-deplored, half-explored at the time, following
my own gnosis where it led, and executing, or so I thought,
a plan not a whit more sophisticated than a simple backtrack
algorithm, I found myself running backwards evermore and again
recursively to the timeworn topoi where the knot was first tied.

> If you don't, you get the wrong answer.  Of course I use the word
> more broadly in other contexts, but if you want to understand me
> in this context you have to listen to how I use it.

When I say I do not understand your usage, I really mean it.
Oh, it's not like I never heard this way of talking before,
or even that I did not speak this way for years and years.
No, I mean that I do not understand this form of talking
in the way that I no longer understand expressions that
I am beginning to suspect are irreducibly ambiguous
or even irredeemably inconsistent.  It's still just
a suspicion at this point, but it grows stronger.

Example of a false 2-chotomy:  Particle Versus Wave.
For pragmatic thinkers, conceptual distinctions are
only tools, and some just do not do the job anymore.

These (com)putative concepts of "following a rule" (FAR) or "following a set of rules" (FASOR),
that you seem to regard as being so clear, so consistent, so unambiguous, just do not strike me
as being that way at all.  And this is exactly why I found myself forced back to the Ancients to
locate the urliest manifestation of the anomaly, and why I tried to introduce a 3-fold staple to
mend the rent of these faulty 2-chotomies, between FAR and ~FAR, or else betwixt FASOR and ~FASOR.
So my best guess about how to clear this up is to acknowledge a 3-fold spectrum of models, to wit:

1.  "Models of Potential" (MOP's)
2.  "Models of Execution" (MOE's)
3.  "Models of Criticism" (MOC's)

For instance, I am probably following all sorts of rules right now that I know not of.
For me to follow up on even a little bit of all of this following would require me to
take up a "form of reflective critique" (FORC) on my own polydidactic followings that
I can but anticipate the due bifurcations of my unitary, all too unitary self thereof.

And then there is a theorem of Rice ...

JA: 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.

HP: You guessed wrong.  Wigner is as open-minded and puzzled as
    Peirce whom, as a prolusion to his paper, he quotes thus:
    "... and it is probable that there is some secret here
    which remains to be discovered."  Wigner also means
    what he says in conclusion:  "... fundamentally,
    we do not know why our theories work so well."

Okay, I guess I will leave it until I get a chance to read this stuff again,
but I do not see how being an open-minded, puzzled, wondering spirit weighs
against acquiring a sense of pragmatic, platonic, and pythagorean realities.

HP: Incidentally, just to see more how you think about mathematics,
    what is your guess on the ultimate source of complex Hilbert spaces?

Oh, it's always a toothache or something.
I worry about the impact of modern dentistry
on the health in future of modern mathematics.

And, by way of definition:
1.  General Relativity =>
2.  Pythagorean Realism =>
3.  Equation: Form = Matter.
Just blame it on my toothache.

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.

JA: But an arrow or morphism is a 2-adic artifact ... etc., etc.
 
HP: I don't know the definition of a "2-adic artifactual arrow" ...

The series of terms, "homomorphism", "morphism", "arrow",
following a gradient from more concrete to more abstract,
are used by category theorists to refer to basically the
same entity, but when they want to emphasize the nuances
of concrete existence versus abstract axiomatic sketches.
The monicker "arrow" falls out of the picture f : X -> Y.
A function is, of course, just a brand of 2-adic relation.

HP: I don't know the definition of a "2-adic artifactual arrow",
    but neither Hertz nor I drew any arrows.  I drew some edges,
    as I've caught you and Peirce doing often enough, to indicate
    some kind of relation.  Hertz's statement is only 40 words.
    It is an elegantly phrased, general statement in the introduction
    of a long book. I am sure, like Peirce, he would not have wished
    to restrict the skill and ingenuity of the observer in choosing
    the types of phenomena, the types of symbols or signs, and the
    n-adicity of relations that might help integrate experience
    into a model.  You have no justification for imposing the
    elaborate, idiosyncratic Percean distinctions on Hertz's
    mere 40 words.

The only question of interest to me here is whether a given statement
about the subject in question -- in so many words, or more, or less --
is adequate to the subject in question, that is, whether the words
are assembled in such a way that they describe the subject, being
general enough to capture the theme of its protean variations.

The Erlangen Programme was a very pretty picture of all possible geometry,
but it turned out to be just a little bit too pretty to be truly complete.

I have good reasons to say that any notion of how signs relate to objects
that is limited to commutative diagrams and linear (homomorphic) mappings
is just not general enough to cover all of the conceivable and all of the
observable cases of sign relations that are useful in adapting to reality.

JA: 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: An impressive 85 big words of indisputable discourse --
    unless, of course, you claim to have the answers.

I am pretty much just footnoting CSP.

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?

JA: 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.

HP: You are able to say whatever you say,
    but if you use my definition of formal,
    may I put you down for a, "No"?

You may put me down any way that pleases you.
I have told you that I do not think in these
terms that you seem to think that no one can
possibly think and do without.  I do without.

HP: Final question:  Can you say how Percean inquiry fundamentally differs from
    processes of physical or mathematical inquiry as introspectively described by,
    say, Faraday, Maxwell, Hertz, Boltzmann, Hadamard, Poincare, Heisenberg,
    Einstein, Turing, Wigner, and von Neumann?

I have learned that introspection is very often a form of self-deception.
It is just about as useful and as fallible as every other human faculty.

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

HP: No, I don't think your dissertation task list would answer my question.
    I have some idea of how the above scientists went about their inquiries,
    because they wrote about it.  I do not yet know enough about how you or
    Peirce would go about scientific inquiry to know how you would do it,
    or think about it, differently.  That is my question.

My chosen task is to figure out the conditions affording the possibility of inquiry,
where "inquiry" is just a convenient name for a process, both dynamic and symbolic,
by which an agent transits from a state of doubt, ignorance, obscurity, uncertainty, ...,
about a phenomenon or a problem to a state of belief, knowledge, clarity, certainty, ...,
about the same issue.  Why would I begin an inquiry into inquiry if I already knew
the answer well enough to write out the code for a universal program of inquiry?

Jon Awbrey

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