Gödel, p 18-19
Gödel
had the insight that a statement of number theory could be
about a statement of number theory (possibly even itself), if
only numbers could somehow stand for statements.
[...]
The grand conclusion? That the system of Principia
Mathematica is "incomplete" —there are true statements of number
theory which its methods of proof are too weak to demonstrate.
[...]
Gödel proof pertained to any axiomatic system which purported
to achieve the aims which Whitehead and Russell had set to themselves.
[...]
Modern readers may not be as nonplussed by this as readers of 1931
were, since in the interim our culture has absorbed Gödel's Theorem,
along with the conceptual revolutions of relativity and quantum
mechanics, and their philosophically disorienting messages have
reached the public [...] There is a general mood of
expectation, these days, of "limitative" results —but back in 1931,
this came as a bolt from the blue.
GEB ToC
Marc Girod
Last modified: Thu Oct 12 16:51:34 EETDST 2000