FOM: Reply to Machover on conclusiveness jshipman at
Tue Dec 16 10:52:24 EST 1997

OK, I went too far at the end there -- obviously there is a certain level of
complexity below which it doesn't make sense to talk about certainty being less
than absolute.  For example, in the case of Euclid's proof of the infinity of
primes, I really am certain this is a valid proof.  But consider a truly tiny
probablilty like 10^-300.  Are you really sure with a subjective probability
greater than 0.99999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999999999 that
you are not actually a crank who thinks he has a proof but is really just
invincibly ignorant?  Maybe it is necessary for human psychology to be able to
say "yes", and maybe it is not useful to insist that certainty is less than
absolute in this case; but if you want to distinguish this level of certainty
as somehow being greater than the certainty that a number is prime after it
passes 500 random trials of Rabin's test (p>(1-(10^-300))), good luck!--JShipman

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