- 25 Jul 2007 12:09
#1277367
@galactus:
As I've already said, theories cannot be verified, only falsified. Therefore I can't show you why a thing is possible.
Check out Gödel's theories:
http://en.wikipedia.org/wiki/G%C3%B6del ... s_theorems
As I've already said, theories cannot be verified, only falsified. Therefore I can't show you why a thing is possible.
Check out Gödel's theories:
http://en.wikipedia.org/wiki/G%C3%B6del ... s_theorems
In mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest.
The theorems are also of considerable importance to the philosophy of mathematics. They are widely regarded as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem. Authors such as J. R. Lucas have argued that the theorems have implications in wider areas of philosophy and even cognitive science, but these claims are less generally accepted.
Falling down is no shame, but staying on the ground