From: Scott R (jse885@spinn.net)
Date: Thu Nov 20 2003 - 05:17:41 GMT
Nathan,
> I studied Godel's theorem and what it says is that under any system there
> can be statements which are neither true nor false and are therefore
> undecideable.
Not quite. It says that a system as complicated as arithmetic is either
incomplete (there are true statements that are not provable within the
system) or inconsistent (it contains a statement that is both provably true
and provably false). Since we've been doing arithmetic for millenia without
running into an inconsistency, it is generally accepted that arithmetic is
incomplete. Undecidability (that there is no mechanical procedure to
determine the validity of an arbitrary statement of the system) is a
different problem, proved about six years later (by Alonzo Church and Alan
Turing).
> Kurt Godel's theorem applies to mathematics but it has been
> hijacked into other areas of human endeavour.
I agree that the theorem has little relevance outside of mathematics.
- Scott
MOQ.ORG - http://www.moq.org
Mail Archives:
Aug '98 - Oct '02 - http://alt.venus.co.uk/hypermail/moq_discuss/
Nov '02 Onward - http://www.venus.co.uk/hypermail/moq_discuss/summary.html
MD Queries - horse@darkstar.uk.net
To unsubscribe from moq_discuss follow the instructions at:
http://www.moq.org/md/subscribe.html
This archive was generated by hypermail 2.1.5 : Thu Nov 20 2003 - 05:34:43 GMT