FOM: determinate truth values, coherent pragmatism
kanovei at wmwap1.math.uni-wuppertal.de
Thu Sep 7 12:52:12 EDT 2000
>Date: Tue, 5 Sep 2000 12:02:04
>From: Harvey Friedman <friedman at math.ohio-state.edu>
>On the other hand, we already know how to meet the following challenge by
>the statistical method of repeated trials:
>CHALLENGE 3. Find a way to confirm or reject a Pi-0-1 sentence of the form
>"for most bit strings of length at most 1000, such and such feasibly
>testable property holds" other than finding a proof or refutation of that
>statement from accepted axioms.
Can you make it more clear what do you mean by
"other than finding a proof ... from accepted axioms" ?
Well, in some cases you can execute a computation that
results in 0 or 1 and you interpret this as TRUE or FALSE
(a given sentence is).
Then (in fact, before) you have to demonstrate that this is
just a true answer, which cannot be anything other than a
mathematically rigorous "proof from accepted axioms", whatever
simple set of axioms is sufficient for such a demonstration.
Would you claim that SOME "accepted axioms", like e.g. m+n=n+m
for natural numbers, are really not axioms but rather physically
evident postulates which do not count as axioms in "CHALLENGE 3" ?
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