I look at incompatibilist arguments aimed at showing that the conjunction of the thesis that a subject has privileged, a priori access to the contents of her own thoughts, on the one hand, and of semantic externalism, on the other, lead to a putatively absurd conclusion, namely, a priori knowledge of the external world. I focus on arguments involving a variety of externalism resulting from the singularity or object-dependence of certain terms such as the demonstrative ‘that’. McKinsey argues that incompatibilist (...) arguments employing such externalist theses are at their strongest, and conclusively show that privileged access must be rejected. While I agree on the truth of the relevant externalist theses, I show that all plausible versions of the incompatibilist reductio argument as applied to such theses are fundamentally flawed, for these versions of the argument must make assumptions that lead to putatively absurd knowledge of the external world independently of the thesis of privileged access. (shrink)