ONT Re: Inquiry Into Inquiry
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Howard, I continue to be at a loss for how to interpret many
of the technical terms and phrases that you use in this text.
I do not know what else to do but keep pressing for clarity.
Many of my most familiar terms and phrases are being used in
ways the meaning of which to you I can neither grasp, guess,
nor for which invent any consistent sense. Most of these
problematic themes appear to arise in the neighborhood of
the rootword "forma" -- which to me is an old Latin word
for "beauty", and so not a conceit that I would gladly
let go. I have had some training in what are commonly
called the "formal sciences". But the way that you
treat the word "formal" and many of the predicates
in which you wrap the phrase "formal system" are
all against the grain of that training for me,
or else contain a hint of some novel subject
altogether. You have written out some lines
that you call "definitions" of these items,
but so far I do not see that they bound.
I am afraid that there is nothing for
it but just to keep inquiring into
their purports of meaningfulness.
Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):
HP: As I warned, I'm not talking stereotypic rationalizations.
I'm simply defining my usage [of "formal"] by stating a simple,
empirically testable condition for a formal process.
Just follow the rules.
I guess that the trouble starts right at the very beginning, but
I did not realize before that you meant this as formal definition.
Are you then saying that you're saying:
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| Definition. A "formal process" is "just follow the rules".
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HP: 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.
I see an act of abstraction, and then I see an activity of calculation.
JA: 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.
HP: Within the limits of error a formal system
is probably more empirically testable than
any other empirically testable system. But,
you are well-justified in worrying about that,
since all empirical tests are noisy and have
some error. Therefore, on this general ground
alone we never can verify with certainty that
a "formal system" is more than just very good
statistics.
Again, I see that you are using this phrase "formal system" in a way
that I cannot unify with the long-accustomed uses that I know for it --
id est, I can see that you are enclausing it in express predications
in which it would never occur to me to enclose it, and so this tends
to make me suspect that you are using it to describe a subject other
than those that I have formerly described, expressed, or known by it.
Just by way of seeking a point of common origin and reference, the first things
that pop into my mind when I see "formal system" are things that by other names
many call "axiom systems", "formal grammars", "formal languages", and their ilk.
Is that anything like what you intend to indicate here?
JA: 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.
HP: Your perception of my attitude is incorrect. You are mistaking my attempt
to clearly communicate (by defining my words) with what I actually believe
about formal systems. While you are thinking about this, I will summarize
what I think about the physics of symbols.
HP: http://www.c3.lanl.gov/~rocha/pattee/
I started reading this a while back.
And I was once a heavy consumer of
that Santa Fe strain of semiotics.
HP: The conceptual problem with formal systems is worse than simply the
fact that we cannot, with certainty, empirically verify their existence.
Now here is an example of what I mean, a "formal system"-related sentence
that gives me such a jolt when I read it that I do a double take and then
conclude for the moment that we must be using radically diverse languages.
Can you elaborate on what this sentence means?
HP: The deeper problem from the physicist's view is that every single step
of a formal [process?] is subject to empirical error. This is assuming
measurement and control are irreversible events, hence dissipative and
noisy. (I'm ignoring Landauer, Bennett, et al. who claim "in principle"
reversibility because nobody has done it.) In this view, a mathematical
proof is nothing more than a series of noisy empirical measurement
(recognizing symbol vehicles) controlled by noisy rules (rewriting,
storing, etc.). This holds for all reading and writing of symbols
(symbol vehicles being in part defined as arbitrary coded physical
structures).
Okay, this more like stuff that I have at least thought about a little.
HP: The fact that the accumulated statistical errors may be very small is an
important practical fact, but that would not satisfy Platonic formalism.
But now you are jolting me again. "Platonic formalism" clangs like
a contradiction in terms to my mind's ear -- of course, if you were
to capitalize the pun in the form "Platonic Formalism" then perhaps
that would have telegraphed the punchline in a way that you thought
was just too easy. If this be not a joke, then can you tell me
what it means?
HP: There is also the related Lakatos-type problem that we cannot completely
define sets, rules, and domains of applicability leaving no ambiguity.
The "formal" logic problems of infinite sets, consistency and completeness
are also real, but ignored by most physicists as "just formal." They have
more pragmatic problems.
And thereby hangs a tale. Let me try pull it through the form of a riddle:
Can you tell me what was the first widely-used "Virtual Reality" system in
the field of computer science?
JA: 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.
HP: So we appear to agree about the inadequacy of formal systems, ...
We might, just perhaps, but we would first have to arrive at
an accommodation as to what the phrase "formal system" names.
HP: So we appear to agree about the inadequacy of formal systems,
if perhaps for different reasons. And yet, we all continue
to use formal systems. Why is this? Well, it's because we
have nothing better. Noise is built in to the universe.
It is everywhere, and the ideal of formal systems is not
only to reduce noise to the minimum, it also frees us from
the bounds of everyday experience. How else but by formal
systems could the imagination unambiguously manipulate (and
communicate) imaginary numbers in infinite dimensional spaces?
(That was the reason for my Hilbert space question.) Galileo and
all physicists thereafter have followed Nicholas Cusanus's advice
with unreasonable success: "If the transcendental is accessible to
us only through the medium of images and symbols, let the symbols at
least be as distinct and unambiguous as mathematics will permit."
Well, now I am getting the sense that you are posing all symbol systems
to fall out under the banner of "formal systems". Is that a good guess?
If so, then I can almost see a connection with the pragmatic picture of
logic as "formal and normative semiotic", but there would be a twist or
two before the tie could be made tight, if at all.
HP: It is also wise to remember that evolution by natural selection requires noise
in the genetic symbol system. There is good evidence that creative thought, and
therefore inquiry, also require some noise. As Spinoza and Martha Stewart always
say, sub specie aeternitatis, a little noise is a good thing. The greatest danger
of formal language, as Stan would agree, is its premature or inappropriate application
to imaginative, vague, or creative thought.
Okay, I can warm to this a little, as it was always less the noise factor,
the big hullaballo over ambiguity and all that -- than the sampling ratio,
all the stuff that gets left out of our formal acounts, that brings me to
the point, almost, of decrying how "inadequate" formal systems always are,
though, on reflection, I'm apt to back off pressing this point when I wit
of how "adequacy" is adequately judged only relative to an intendable aim.
JA: 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.
HP: I agree, although I would like to hear your good reasons.
When you think on this, and you will ... [standard joke follows].
HP: My point about Hertz's 40 words was just that it was not a formal statement, and
therefore should not be limited by your characterization of it in formal terms.
This is why physicists often reject logic in the formative stages of inquiry.
Who doesn't?
Jon Awbrey
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