[FOM] Is CH vague?

Vaughan Pratt 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.

Vaughan Pratt

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