Re: Godel proved maths inconsistent not incompleteness theorem
- From: David C. Ullrich <dullrich@xxxxxxxxxxx>
- Date: Tue, 06 May 2008 05:02:59 -0500
On Mon, 5 May 2008 11:48:34 -0700 (PDT), Charlie-Boo
<shymathguy@xxxxxxxxx> wrote:
On Apr 30, 2:33 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Apr 30, 8:29 am, Chris Menzel <cmen...@xxxxxxxxxxxxxxxxxxxx> wrote:
On Wed, 30 Apr 2008 01:08:29 -0700 (PDT), Charlie-Boo
<shymath...@xxxxxxxxx> said:
...
Why is any particular part of Mathematics ordinary or not ordinary?
By its common presence in the literature of textbooks and journal
articles.
That's your formal definition of what ZF can prove? That's frickin'
ridiculous.
I'd have to agree it is not a good characterization.
And note that it was NOT a characterization of a "formal definition of
what ZF can prove".
The way it is
usually put is that ZF can prove (under proper definitions) all of
"classical" or, perhaps better, "traditional" mathematics, where this is
understood to include arithmetic, computability theory, real analysis,
complex analysis, abstract algebra, linear algebra, geometry, topology,
and so on.
And I have told Charlie-Boo that about a hundred times already. And
that is mathematics that is found commonly in textbooks and journal
articles. The meat and potatoes mathematics that is studied in
undergraduate and graduate programs - and as covered in textbooks and
journal articles - is probably about as extensionally precise as we
can make - or at least gives an adequate ostensive characterization -
of 'ordinary mathematics' without begging the question indeed by
defining 'ordinary mathematics' to be whatever is provable by ZFC.
Meanwhile I did NOT characterize it as a "formal definition of what ZF
can prove". Those are words Charlie-Boo put in my mouth.
It makes no sense to say that if it's common then ZF can prove it.
You are equating a mathematical statement with an historical one.
Er, no. _You_ are the one equating the two! Of course when
people say that ZFC suffices to prove most of ordinary mathematics
that's _not_ a mathrmatical fact, it's an empirical observation,
or if you wish a "historical statement". The fact that it's a
"historical statement" doesn't make it false.
Rather than "ZF can prove ordinary mathematics" the correct statement
is "ZF can't prove anything but a small fraction of mathematics"
Giggle. You just _love_ that ignorance of yours.
and
"ZF is so poorly suited for proving theorems that it is so complex
that nobody has done hardly any of it and so we don't know for sure if
it would even work."
C-B
MoeBlee
David C. Ullrich
.
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