Re: Godel's Incompleteness theorem

On Jul 1, 5:20 pm, Neilist <Neilis...@xxxxxxxxx> wrote:
On Jun 28, 12:57 pm, Aatu Koskensilta <aatu.koskensi...@xxxxxx> wrote:

Neilist <Neilis...@xxxxxxxxx> writes:
Complete means that any truthful statement can be derived from the
axioms of the system.

No, it doesn't.

What a lousy response!  "No, it doesn't".  Childish.  I'll just say
"yes it does".

Give the correct definition then, genius (sarcasm)!

********************************************************************

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
.