Re: Patriarchy: Re: What Matriarchy?

William Edward Woody (woody@alumni.caltech.edu)
Tue, 20 Aug 1996 00:41:55 -0700

brunner@mandrake.think.com (Eric Brunner) wrote:
> Stephen Barnard (steve@megafauna.com) wrote:
> : 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.

Sorry, Eric, but here I have to step in and defend Stephen Banard.
In my Theory of Computation class, we used Godel's theorem to prove
the halting problem, and showed them equivalent. It was the only
interesting part of the class (a class which pretty much reduced
itself to writing state graphs for Turing machines by the end of the
first trimester).

[Or at least, my fuzzy little head *remembers* doing this. It's been
a few years...but Godel certainly did show up. It was right about the
same time I read the book "Godel, Echer, Bach," and hurt my poor brain.]

> : 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...

Now here is where I stop.

Somehow he's decided that 'induction' and 'deduction' aren't even
kissing cousins. And as science uses 'induction' instead of 'deduction'
to arrive at the original conclusions, Godel's theorem doesn't apply.

A crock, to be sure.

But an amusing crock. Though dancing naked around the fire invoking
the Gods to come down from heaven and bless the dancers is certainly
a lot more entertaining.

- Bill

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