Full Idea
Some have argued that eliminativism about propositional attitudes is self-refuting. If no one believes anything, then how could we believe the eliminativist thesis?
Gist of Idea
It seems contradictory to be asked to believe that we can be eliminativist about beliefs
Source
John Heil (Philosophy of Mind [1998], Ch.5)
Book Reference
Heil,John: 'Philosophy of Mind' [Routledge 1998], p.170
A Reaction
Sounds slick, but it doesn't strike me as a big problem. Presumably you don't 'believe' eliminativism. You treat some of your brain processes as if they fell into the fictional category of 'belief'.