Proponents of cognitive penetration often argue for the thesis on the basis of combined intuitions about categorical perception and perceptual learning. The claim is that beliefs penetrate perceptions in the course of learning to perceive categories. I argue that this "diachronic" penetration thesis is false. In order to substantiate a robust notion of penetration, the beliefs that enable learning must describe the particular ability that subjects learn. However, they cannot do so, since in order to help with learning they must instruct learners to employ previously existing abilities. I argue that a better approach recognizes that we can have sophisticated causal precursors to perceptual learning, but that the learning process itself must operate outside of cognitive influence.