Le 25-oct.-06, à 13:57, 1Z a écrit :
> Brent Meeker wrote:
>
>> It's even more than seeing where axioms and rules of inference lead.
>> Given some axioms and rules of inference the only truths you can
>> reach are those of the form "It is true that axioms => theorems".
>
> For formalists, all mathematical truths are of this form.
And that is why the doctrine of formalism in mathematics (or just
number theory) is dead since Godel has proved his incompleteness
theorem.
We definitely know today that number theoretical truth escapes all
formal theories.
Physicists can still dream today about a formal and complete theory of
"everything-physical", but number scientist knows that the number realm
is not completely formally unifiable.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Oct 26 2006 - 06:07:09 PDT