I consider two notable recent philosophical theories of concepts (Fodor and Peacocke) in relation to some challenges set by Wittgenstein in his notorious private language argument. The challenge is formulated in terms of contraints on the explanation of the relation between thought and language. I try to show how these theories of concepts relate to constraints that arise from this challenge. I also relate the challenge to a recent contribution in the debate about narrow and broad content. In so doing I try to illuminate how this philosophical debate bears on some issues in cognitive psychology. In particular, I suggest it bears on nativism about concepts, the relation between an adequate notion of public language and thought, and the idea that concepts are “in” mentalese, a Language of Thought. Accommodating these considerations requires increasing the consideration of linguistic evidence and the linguistic character of concepts in laboratory research if distinctively human thought is to be explained.