[FOM] Re: Mathematical Experiments

Don Fallis fallis at email.arizona.edu
Mon Jun 23 10:57:13 EDT 2003


Bill Taylor?s essay seems to me to be a good presentation of
mathematicians? standard view about mathematical evidence.  However,
I am not sure that this essay gives us good reason to believe that this
view is correct.  Consider, for example, what Taylor says about
probabilistic verification:

>>And the confirmatory type are not as in science (as explained above),
>>but merely the collecting of satisying evidence.    Thay have no real
>>mathematical significance. Such things as searches for counter-
>>examples to the twin prime conjecture and Goldbach's conjecture are of
>>this type, as are the "almost-proofs" of large-primeness by using the
>>converse of Fermat's little theorem's.  This latter type is as close
>>to a confirmatory science experiment as one might get in math, but
>>they are still not a *validation* - that still requires a proof.

However, it is not clear that deductive proofs do provide any more
?validation? than some of these ?almost-proofs of
large-primeness.?  For example, some probablitistic primality tests
arguably provide as much certainty and a prioricity as deductive proofs
of primality.  I have argued previously that there is no epistemically
important difference between deductive proof and (at least some forms
of) probabilistic verification.  See, for example,

take care,

Don Fallis
School of Information Resources
University of Arizona

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