Re: Godel's Incompleteness theorem

On Jul 1, 11:59 am, Tonico <Tonic...@xxxxxxxxx> wrote:

<snip>

You shouldn't get pissed off: the definition of complete axiomatic
system is really NOT what you said: an axiomatic system is complete if
for any (well-formed) statement P, either P or ~P can be proved within
the axioms.

Put in another form, it could be said that the system is complete if
any well-defined valid formula is a (provable) theorem within the
system.

If you say "any truthful statement can be derived", you are messing
things up: how can you know whether a statement is truthful if you
haven't yet proved it? It sounds like a tautology: if the statement
can be derived (I understand this as meaning proved), then it is
truthful, and of course the other way around: if it is truthful then
it is so because it can be "derived" (= proved) in the system.

Regards
Tonio

The original poster asked:

"Can somebody provide me some good explanation on Godel's
incompleteness theorem in a simple way."

I knew I'd get criticism for being inexact. Fine.

But when you or others start discussing P and ~P and talking axioms,
complexity of systems, etc., I think you're getting away from what the
original poster requested, which was a good yet simple explanation.

Of course, the original poster did not require 30 words or less, and
the original poster did not say "no math or logic symbols".

But how would you explain Godel's work, consistency, and completeness
without resorting to symbolic equations? I tried, since I did not
know the expertise of the original poster.

It must rankle mathematicians when a theorem or mathematical result is
paraphrased, and even without math or logic symbols, for it loses
exactness. Horror!
.