Ingo Schwarze wrote:
Reid Nichol wrote on Mon, Jan 07, 2008 at 12:02:19AM -0800:
Duncan Patton a Campbell <[EMAIL PROTECTED]> wrote:
"Eliah Kagan" <[EMAIL PROTECTED]> wrote:
(There are also multiple useful,
mutually-inconsistent formal systems in both fields.)
Provably so?
I'd love an example of Math being inconsistent.
Quite frankly, I'd be surprised if this is true.
Eliah has beautifully demonstrated this for both Mathematics
and Physics. What is flabbergasting me about such questions
is that these are extremely old facts - essentially, known for
more than 70 years - and many people still believe that formal
science can be both complete and consistent.
http://en.wikipedia.org/wiki/Nicolas_Bourbaki
- nicely narrating how the attempt to transform mathematics
into a single unified and consistent theory miserable failed
http://wiki/G%C3%B6del%27s_incompleteness_theorem
- explaining why
http://en.wikipedia.org/wiki/Kurt_G%C3%B6del (1906-1978)
- "One of the most significant logicians of all time, GC6el's work
has had immense impact upon scientific and philosophical thinking
in the 20th century, a time when many, such as Bertrand Russell,
A. N. Whitehead and David Hilbert, were attempting to use logic
and set theory to understand the foundations of mathematics."
Still, many people appearantly never heard of the problems he
described, even though we are now well into the 3rd millenium...
Reply-To: poster set, we are *terribly* off-topic.
I would be little bit more careful about dragging the incompletness
theorem into the discussion without properly understanding
the statement of the theorem, its meaning, and corollaries.
The connections that you are trying to make between the incompletness
theorem and Burbaki project are very shallow at best and I certainly
have not heard them before.
Kind Regards,
Predrag
Department of Mathematics
University of Arizona
P. S. I am no expert on mathematical logic but definitely know little
bit better than your average bystander.
