FOM: Re: chess challenge to experts
Harvey Friedman
friedman at math.ohio-state.edu
Sun Nov 12 09:23:31 EST 2000
Rely to Kanovei 1:36PM 11/12/00.
It appears that you claiming
"every true mathematical statement is provable"
since you write in the middle of your e-mail, and I quote exactly:
"Every math. statmnt which is (ontologically) true is (mathematically
provable)."
But in the beginning of your e-mail, you seem to shy away from making this
claim.
Do you wish to claim this or not?
If you are not claiming this, then what are you claiming?
If you are claiming that no specific example can be explicitly presented
together with an explicit refutation, then this is trivially correct (in
the sense that you intend), but has no content. In this case, you are
merely claiming a contentless triviality.
Thus as far as I can tell, you are either claiming this statement, or
instead claiming a contentless triviality. If you are claiming this
statement, then the burden is on you to give a proof, or at least a
justification for why (you believe) it is true. If you are claiming a
contentless triviality, then I ask:
why are you bothering to claim a contentless triviality?
Once you affirm that you are claiming
"every true mathematical statement is provable"
there are a number of issues as to what this means. Under some
interpretations, it is clearly false. But to proceed carefully with this,
you should make it clear that you are or are not making this claim (as you
wrote in the middle of your e-mail).
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