A familiar sort of argument for skepticism about the external world appeals to the evidential similarity between what is presumed to be the normal case and the case where one is a brain in a vat (or BIV). An argument from Putnam (1981, ch. 1) has been taken by many to provide an a priori refutation of this sort of skeptical argument. The question I propose to address in this paper is whether Putnam's argument affords us an a priori refutation of skeptical arguments that appeal to the claim that one does not know that one is not a BIV. I will develop a negative answer to this question along two related fronts. Along the first front I defend against new criticisms the common position that the externalism on which Putnam's argument is based entails skepticism about the meanings of sentences in our language and the contents of our thoughts. I do not take this to be a refutation of externalism or externalist arguments; rather, I see this as a motivation to locate the difficulty with arguments for externalism. But if externalism is abandoned, of course, the anti-skeptical argument it has widely been taken to support must be abandoned along with it. I will argue, however, that this is not a significant loss, because along a second front I will argue that externalism cannot be given a priori justification; it is therefore ill-suited to ground an a priori refutation of BIV skepticism anyway.