Boghossian argued that externalism is incompatible with a transparency thesis according to which we can know a priori whether any two of our occurrent thoughts have the same or distinct content, and that this transparency thesis is integral to our commonsense conception of rationality, which requires the apriority of our logical abilities. Stalnaker offered a detailed compatibilist response to Boghossian. Boghossian criticized this response, and Stalnaker replied. But the outcome of that important discussion remained unclear, partly because it was unclear (...) how to understand the amended transparency thesis at which Stalnaker was gesturing. My aim in this paper is to settle the matter. I wish to clarify the terms of the debate, also by highlighting the relevant commitments of Stalnaker’s two-dimensionalist account, and to show that his compatibilist response, which appeals to diagonal propositions, is unsuccessful. (shrink)