Probability, certainty and illusions

Abstract

Some philosopheis (e.g. Ayer, Reichenbach, Lewis) use a version of the argument from illusion to prove that empirical statements are never certain. But this argument, unwittingly, also calls into doubt the certainty of calculations in logic and mathematics. The argument seems to call into question the application of any rule on the grounds that one might at some future time find out that one had misapplied it. But the argument from illusion is only the illusion of an argument.