Le 03-nov.-05, à 12:12, Quentin Anciaux a écrit :

Hi Bruno,

Le Jeudi 3 Novembre 2005 11:14, vous avez écrit :
Le 02-nov.-05, à 21:23, Quentin Anciaux a écrit :
I could'nt imagine what would it be for a human to knows the why and
able to prove it...

Then you should like comp (and its generalisation) because it explain
the why, and it justifies completely wxhy we cannot and will never been
able to prove it.

In fact I "like" comp... your theory is what come closer to what I think about the world (even if what I think is of none importance in front of realities)

Actually science never proves anything on "reality". It proves
propositions only relatively to a theory/worl-view which is postulated,
and in the waiting of being falsified.


Yes sure, you always have to have axiom, thing accepted as true without being able to prove them in the framework generated by choosing them. By this, a theory cannot explain its base (fondement).

Yes, although in the comp framework (or more generally in the self-reference framework) there is a little subtlety, mainly due to the incompleteness phenomenon.

It is true that we cannot prove the axioms of a theory ... from nothing. Once the axioms are chosen, then we can prove the axioms! (Indeed by a one line proof mentioning the axiom and just saying that it is an axiom). But for a sufficiently rich theory (like a TOE!) it could be that we will believe in actually unprovable (in the TOE) statement of the theory. The simplest example being the consistency of the theory, which can be falsified (the day we prove a falsity in the TOE), or only verified (the days we don't get a contradiction in the theory). Those statements (like the consistency) are non provable but, not like the axioms are (in some other natural sense) provable, but for the incompleteness theorem reason.

More on this in any textbook of logic going up to the second incompleteness theorem by Godel.



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