FOM: On Absolute Truth

Thu Feb 5 16:54:26 EST 1998

In an earlier dialogue with Machover I remarked that we can achieve "moral
certainty" about certain statements that were not feasibly provable classically
(e.g. primality of integers--since I am speaking to Vaughan here I should be
extra careful to note that I know he showed that feasible classical proofs of
primality exist, I am talking about the difficulty of finding them), and the
level of subjective certainty about such statements is as high as it is for
well-established mathematical theorems (because the probability of bad luck in
the random algorithm can be made so small, say less than 1/(10^300), that it is
dwarfed by the chance we've made a mistake, are dreaming, are cranks, etc.).
But subjective certainty is not the only criterion, so I can't agree that there
is no "absolute truth" in mathematics.  A classical proof is still the "gold
standard", and when we have a solid, reliable one it no longer makes sense to
insist, as it might in my chess example or in primality testing, that we are
not justified in simply calling the result *true* in an *unqualified* sense--the
remaining uncertainties (e.g. "we are dreaming") are outside the discourse!--JLS

Severity of a system's failure is proportional to the intensity of faith in it.

More information about the FOM mailing list