[FOM] Is CH vague?
pratt at cs.stanford.edu
Fri Feb 1 02:12:32 EST 2008
Arnon Avron wrote:
> Again it is obvious that something is very wrong with my way
> of thinking. I always thought that the confidence in the
> validity of a mathematical proof can never be greater than
> that of the assumptions on which that proof is based. But it seems
> that now the logic goes in the opposite direction. Now it is
> taken as *given* and beyond doubt that some proof is correct,
> and from this one infers the truth of its
> underlying assumptions! I feel depressed for being unable
> to accept this new approach to mathematical rigor and logic.
So if you were a Greek publisher and Euclid came to you with his
Elements, you'd reject it because his axioms were too creative for you?
There is indeed a strong correlation between axioms and theorems, the
only question is the direction of the arrow of causality. Logicians
like to orient it from axioms to theorems. Mathematicians know better.
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