Re: Patriarchy: Re: What Matriarchy?
Eric Brunner (brunner@mandrake.think.com)
17 Aug 1996 03:30:25 GMT
Stephen Barnard (steve@megafauna.com) wrote:
: Eric Brunner wrote:
: >
: > Personally, I'm waiting on the advocates of High Scientism to explain the
: > work of a mathematician... Kurt Godel...
: >
: > I can wait, of course, I'm not a strict constructionist (mathematically
: > speaking that is).
: >
: I'm not an advocate of High Scientism, whatever that is, but I'll take a
: crack at it.
: Godel's famous Incompleteness Theorem proves that any formal deductive
: system of sufficient power (at least the power of Peano arithmetic,
: which isn't that powerful) will be incomplete. That is, it will be
: possible to state theorems in that system that cannot be proven true or
: false. This is very closely related to Turing's Halting Problem, but I
: won't go into that.
Pity. I'm sure that if anyone noticed that a fundamental theorem in
theoretical computer science was very closely related to a fundamental
theorem in foundations that there would be at least one paper in the
literature.
A single cite please, refereed, in SIAM, or AMS, or the equivalents.
: Godel's theorem is extremely interesting in that it calls into serious
: question the foundations of mathematics...
A modest appraisal, as it leaves every non-constructionist working without
a rope over a very awkward abyss -- which we manage to live with like the
uncomfortable cats on suspended floors of glass. We avoid vertigo by virtue
of keeping our peepers screwed shut.
: Godel's theorem has very little to do with physical science, however,
: because physical science is based on inductive reasoning.
Now that is an interesting statement. Here I thought that mathematics is
a representational system, a vocabulary, a construct of mind. Oh well, I
suppose that inductive reason must work for all of the (anumerate) exams
of (data) evidence, the interior logic of hypothetical frameworks, their
methods of test, not to mention all of the points at Schools Debates...
People look
: at evidence, make hypotheses, test the consequences of these hypotheses
: against new evidence, discard or refine the hypotheses, debate one
: another in often heated terms about their hypotheses (often calling one
: another nasty names), attempt to confirm others' hypotheses (when they
: often really want to refute them), and so on.
: This bears no resemblance to formal logical deduction, which is not a
: method for getting at the truth. Formal deduction is merely a way of
: transforming old truths (axioms) into different truths (theorems). Or,
: working backward, it's a way of transforming suspected truths
: (conjectures) into actual truths (theorems), thereby proving them.
: Sometimes science makes use of formal logical deduction to explore the
: consequences of it's conjectures, but these consequences always remain
: conjectures because they are not based on anything like real axioms.
Sigh. One reason why I don't enjoy reading the works of non-mathematicians
who have something less than the diety-struck to offer, or at least have
the decency to approach the discipline as yet-another-discipline (know of
any air-ticket agents who can actually fly multi-engine jet, or pretend
that they've got enough of the subject to add their narrative to the usual
ticket counter patter without fatally boring the customer?).
: What some people seem to be missing here is that there is no absolute
: certainty in science. Uncertainty is meat and drink to scientists.
: They have to deal with it all the time.
God. I should be paying for this. There are degrees of uncertainty.
: A much more interesting question, IMHO, is why nature seems to follow
: mathematics. That is, why are physical theories expressed in
: mathematical form so effective? There doesn't seem to be any a priori
: reason why this should be so, and a lot of scientists and philosophers
: are very puzzled by it. This should warm the cockles of the hearts of
: those who have an anti-science agenda, but, as far as I know, they
: haven't picked up on it yet.
Please, don't let me stop you Dr. Bernard. Continue until you find the
very last free parking spot.
May I make a suggestion? Try something fundamentally easier (I've a very
low opinion of the mathematical capabilities of all but a set of measure
zero of all of the academic and industrial research computer scientists
I've had the pleasure to work with (non-mathematically, numerical analysis
doesn't count, it being only just mathematics)) over the course of my life
after grade school, like catagory theory, or stick with the superficial
glitter of self-similar curves.
: Steve Barnard
--
Kitakitamatsinohpowaw,
Eric Brunner
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