[FOM] Re: Mathematical Experiments
Don Fallis
fallis at email.arizona.edu
Mon Jun 23 10:57:13 EDT 2003
Hi,
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,
http://links.jstor.org/sici?sici=0022-362X%28199704%2994%3A4%3C165%3ATESOPP%3E2.0.CO%3B2-B
take care,
don
Don Fallis
School of Information Resources
University of Arizona
http://www.sir.arizona.edu/faculty/fallis.html
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