FOM: geometrical reasoning, logic and proof

[Kanovei]

<Date: Wed, 24 Feb 1999 13:35:07 -0500
<From: Michael Detlefsen <Detlefsen.1 at nd.edu>

Detlefsen, citing Poincare:

<"If all the propositions it enunciates can be
<deduced from one another by the rules of formal logic, why is not
<mathematics reduced to an immense tautology?

There is apparently no any example of a 
mathematical statement commonly accepted as a 
true theorem but not deducible logically from 
some (also commonly accepted) list of axioms, 
say ZFC.
Therefore, the output of mathematics has been 
just a long list of "tautologies". 
Even then, mathematics is rather an art 
of finding "tautologies" (more often called: 
theorems) by a human, 
than a tautology itself. 

Vladimir Kanovei