FOM: Comment on Mattes
DAVIEG at ALPHA.UNISA.AC.ZA
Tue Nov 11 01:40:10 EST 1997
I would like to comment on Josef Mattes' e-mail but before I do I'll
introduce myself. My name is George Davie and I am a PhD student in
Kolmogorov-Chaitin complexity, thanks for having me on the list!
Josef Mattes wrote:
"This does not seem to answer my question. It goes without saying that I
have no intention of denying
the importance of Goedel's results. But it seems to me that they are
considered important because they are statements about mathematics
computers, which in turn are considered important. In contrast,
for example is important because it is about nature (if you want to
appreciate it you just have to look at a clear night sky).
Several contributions made the point that it connects to algorithms: How
should the importance of Goedel's work have been explained to the
nonexpert before the advent of computers? By explaining
formalization of mathematics? Or was it not foundational then?"
I would think that one could explain the importance of Goedel's work
without referring to mathematics or computation by emphasizing that the
work shows the inevitable failure of systems (satisfying some minimal
conditions) which are set up to decide truth or falsehood of arbitrary
expressions in a language. I think that this would probably be the most
striking aspect to a non-mathematican.
"Truth" certainly seems to be a more fundamental concept to the "man in
the street" than "formal systems" or "computations" and is perhaps even
more fundamental than "nature".
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