In the private language argument (PLA), Wittgenstein raises a paradox, namely that a sensation is not a something, but not a nothing either. McDowell argues that Wittgenstein unnecessarily eliminates inner sensations. By contrast, McDowell insists that sensations are perfectly good somethings, namely concept-involving objects. Hao Tang praises McDowell’s idea that Wittgenstein’s target is the myth of the inner given, namely the private object, but he criticises McDowell’s interpretation of Wittgenstein as eliminating inner sensations. On his interpretation, Wittgenstein does not eliminate (...) the sensation as a concept-involving object. In this article, I advance two main arguments: (1) Wittgenstein objects to inner sensations being concept-involving objects because he rejects the model of “object-designation”; and (2) despite (1), Wittgenstein does not eliminate sensations nor does he deny that we can conceive of them; rather, he thinks that people conceptualise sensations in ways other than as concept-involving objects. (shrink)