The NY Times article he explodes is here.
I have often wondered, sometimes with brain-whirling astonishment, how modern philosophers can persuade themselves, and persuade millions, of some proposition that any schoolboy with one semester of Logic 101 can see, if taken seriously, contradicts itself.
I conclude tentatively that the problem is the application of metaphors from empiricism to non-empirical ideas. An empiricist takes as his unquestioned axiom that no statement ABOUT A SENSE IMPRESSION can not be accepted as true until and unless a sense impression confirms it, or, to be more precise, fails to falsify it. This axiom is a metaphysical or epistemological one, not an empirical one. It is a conclusion of a theory of knowledge. It implies that all empirical statements must be held up to a skeptical test, doubted, and confirmed if they pass the test.
Imagine a fool with a pepper shaker, who discovers a little pepper makes his meat tastier. If a little pepper makes his meat taste better (so he reasons) a lot of pepper will make everything taste better: the fool proceeds to upend the whole pepper grinder into the ice cream, the mint tea, the toothpaste, the butter, the beer and the fluid he uses for cleaning his contact lenses. Likewise is our skeptic who takes a principle of skepticism from the empirical sciences, and applies it heedlessly to areas where skepticism about first principles will simply negate any conclusions whatsoever, including the conclusion that skepticism should be applied to first principles.
It is not a philosophy. It is madness. Let us coin the term "axiomophobia' to refer to this peculiar and self-defeating form of applying empirical reasoning to non-empirical disciplines.