ONT Re: Logic As Semiotic -- Still Quasi After All These Years
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John Collier wrote (JC):
Jon Awbrey wrote (JA):
JA: I am puzzled by the persistence of this image of form.
All of the mathematical circles that I used to run in
have long ago forgotten about the peculiar notions of
that tiny parochial school of self-styled "formalists"
and have returned to the form of platonic realism that
was always their native code, no matter what a few of
them say to student reporters. This was the attitude
of Peirce, the attitude of Gödel, and calling the bug
that Gödel found in Russell's gear a techne-logical
advance is like calling denatured alcohol a medical
miracle. For the mathematics that I know, "form",
"pattern", "structure", as revealed by invariants
and morphisms, is what it's all about. Period.
JC: I think we have to agree to disagree here. I can judge your
sentence 'For the mathematics that I know, "form", "pattern",
"structure", as revealed by invariants and morphisms, is what
it's all about' true, but not agree with your critique.
JA: Critique? What critique? I am merely informing you about my personal experience:
the deep personal disillusionment that I experienced when I discovered that I had
been conned by a "group identity myth, moderately entrenched" (GIMME) that nobody
in the discipline of actual practice really believes.
JC: The one in your first sentence, which you repeat here.
It doesn't seem to apply to me or my experience.
Ah, well, then everything reduces to the well-known
characteristics of existential and experiential truths,
that they can be so diverse and sundry in the mean times,
so I'll just the leave the story as an unfinished sympathy.
JA: And this should not have been such a big surprise. It is not humanely possible
for healthy human beings to devote their lives to an activity that they themselves
consider meaningless. I work with formal systems that I conform to custom in calling
"uninterpreted", but the reason why these systems of forms are privileged, indeed, so
highly prized, is that they have so many splendored and sundry interpretations, not
because they have none. I do not know how to convey this -- it is a fact of life
discovered, not a thing to be proved from any axioms -- I could write a story or
a novel maybe, but Hesse already wrote it, with far more skill than I could muster,
and still so few get it. I could try to relate my personal philosophy of mythematics,
but I have done that before and have seen people think I am joking, and even before
Howard explained to me the nature of a joke I could have told you that it does
no good to explain why the joke is no joke. So I must leave it at that ...
JC: If this is your notion of uninterpreted, I can see why you might have had trouble.
I see uninterpreted as abstracting from specific interpretation, but not lacking
an interpretation in the abstract. I see the alternative you propose as nonsense.
Of course it's nonsense -- that's what I have been been saying the whole time.
But I am not the one who has been proposing it. If you have never heard a hint
before of the phrases "meaningless formal calculus" and "just follow the rules",
then I am sorry that I ever troubled you. I just finished another reading of
Plato's 'Republic' over vacation and arrived at some fresh insights into what
he was saying, especially reguarding all that business about exiling the poets.
Plato is not proposing a model for a society, he is laying out the blueprints
for a nursery, and what he is telling the poets is "You gotta stop saying that
stuff -- you are confusing the children!" And maybe that is what is going on
here, adults telling each other diverting stories that adolescent students
take far too seriously.
JC: One would get bored at having to deal with nonsense for very long.
My understanding of this distinction comes from reading Russell on
proper names and on incomplete symbols, as well as Kaplan and Perry
on demonstratives and identification.
JA: Beauty is Form, and Form Beauty,
And that's all you need to know.
There's more to follow for sure,
Quasi modo gratuitous corollary.
In life as in mathematics, only
Beauty can render it worthwhile.
JA: Still, by posing things in all-or-none terms,
saying "X cannot be formalized" when we need
to say "X cannot be exhaustively formalized",
we characteristically miss the whole point
of the exercise, partially to formalize X,
and deny ourselves the practical benefits
of doing just that. I see a certain type
of psychodynamic here that needs to be
interpreted in a therapeutic remedium.
JC: Granted, but there is a tendency to resort to technique
when it is available to the ignorance of everything else.
JA: In math as in art, the name of that is poor technique.
JC: I don't think so. It is poor practice, but can yield excellent technical work.
De gustibus, and so on, ...
JC: This has led many contemporary philosophers of logic,
some of them friends of mine, to argue that truth and
validity are restricted to what we can constructively
define through one or another specific technique. I
believe that, much as formalization is useful, it must
systematically push out issues of truth and validity
for any logic as strong as 1st order.
JA: The name of that is poor formalization.
JC: No, unless all formalization is poor formalization.
See my paper on the dynamics of information and the
origins of semiosis for my reasons.
I think that we just attach different meanings to the word "formalization".
JC: Truth functional logic and modal logic, on the other hand, are complete.
As I have said before on this list, that is one of the reasons I favour
an information based logic. It gives us both sides of the coin within
the logic itself, as Greg Chaitin argues admirably, in my opinion,
but not in the opinion of many logicians who do not see intuitively
how distinctions are relevant to logic. I do think that they need
therapy, and Wittgenstein is as good as Peirce for this, I think.
JA: Logical systems can be "complete" in their own terms,
but sign systems are never complete when you wake up
and recall their due function in describing a world,
JC: I don't believe the first phrase makes sense in contrast
to the second (see my remarks on "uninterpreted" above).
The word "complete" is ambiguous here, if not a complete cipher.
I cannot say yet whether the ambiguity can be made systematic.
JC: Funny, I would take it that once we have done the latter,
it follows that the complete formal systems are complete.
I wouldn't say that they are complete in their own terms,
because I couldn't even venture to say what that meant.
JA: I informally use phrases like "complete relative to itself" to mean that
all expressions with universal model sets in some universe are provable.
Propositional calculus is like that, and this means that one can check
its theorems quasi modo model theory over a suitably chosen universe.
JC: More than that, Prop Calc applies to all possible universes,
so one does not have to check it in particular universes.
I have no practical and usable conception of "all possible universes" --
I have always had to take my universes one or two or three at a time.
I am talking about the measures of computational work that it takes
in real terms to check whether a given proposition is a tautology.
From my practical experience in writing theorem checking, proving,
and applied logic programs, I have learned that model-theoretic
methods are very often more efficient, useful, and all-round
much more informative for the types of problems that arise
in real applications. I am engaged in applied logic here,
not just decorating the study with tautologies, but using
propositions to describe situations of interest and then
computing derived facts about these situations. Now, it
does makes a lot of practical sense to factor out a core
of pure logic at the heart of this applied enterprise,
but unless it helps to keep the engine running it is
not all that interesting for the sake of a' that.
JA: But the abstract calculus can be used to describe the features and
regions of many such universes, and it is not really complete in
the applied or descriptive sense until a concrete object domain
has been specified.
JC: Again, see my remarks on "uninterpreted" above.
JA: a fact that Peirce's sign relations keep constantly
before our minds, not to mention under our gnosis.
JC: Again, I think we will have to agree to disagree here.
JA: I don't understand. Unless maybe you think that when
Peirce says "objects" he does not really mean objects.
JC: Precisely. He was a raving idealist, a metaphysics
I cannot understand in the sense of being able to
give foundations for interpretation.
Sez you.
JA: The whole point of my current slow skippy reading
of Peirce's 1865 Lectures is to examine the way
that he develops a theory of information out of
logic as a theory of inquiry by exploiting the
very forms of continuity between the two areas.
JC: In think you have already run into more serious problems than you realize.
JA: Well, that sounds ominous. Care to mention any?
JC: After I said this, I decided that I wish I hadn't, just
because I don't think it is useful to mention any right now.
Try to forget I said it. It was more a marker to myself than
anything, and I should have kept it private. The problems
might dissolve as you move into Peirce's more mature thought.
(no doubt you can't miss the implicit "but I suspect not"
in there, but I don't want to distract you right now)
Phew, that's a relief ...
JA: Taking Wittgenstein as a cure for Russell
is like morphine as a remedy for laudanum.
JC: Many of my best teachers were Wittgensteinians.
JA: Some of my best teachers were Benedictines.
JC: One of my best teachers was Benedictine.
"When you get the message, hang up the phone"
JC: Peirce is still talking, in any case.
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