ONT Re: Logic As Semiotic -- Still Quasi After All These Years
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
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.
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. 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 ...
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.
In math as in art, the name of that is poor technique.
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.
The name of that is poor 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: 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.
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.
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.
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.
I don't understand. Unless maybe you think that when
Peirce says "objects" he does not really mean objects.
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.
Well, that sounds ominous. Care to mention any?
JA: Taking Wittgenstein as a cure for Russell
is like morphine as a remedy for laudanum.
JC: Many of my best teachers were Wittgensteinians.
Some of my best teachers were Benedictines.
JC: His Philosophy of Mathematics shows profound misunderstandings, most of them would agree.
Nonetheless, I find the lessons of the 'Investigations' lead me to pretty much the same
place as does studying Peirce, at least after immersion in Russell, which I started at
the tender age of 14. Since Wittgenstein is explicit that his work is intended as
therapy, I think it is fair to say that appropriate therapy depends on the disease.
There are cases when a large dose of Russell is the medicine that will produce
the best results.
Russell was a childhood hero for me, too, and
Wittgenstein the popular icon of my undergrad
years, but that was yesterday ... and I have
so many nitty gritty bits of work to do that
all their "gaminess" will just not win over.
But I have had my shots, and will try to
stay out of your clinic.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤