What does teaching introductory philosophy consist in? What makes a particular introduction to philosophy pedagogically a good one? I argue that the main purpose of teaching introductory philosophy is not to instill skills needed to do philosophy or pass down philosophical knowledge; rather, teaching philosophy aims to illuminate what philosophy is and generate motivation, curiosity and wonder. I develop this view through a comparison between teaching philosophy and Greek tragedy, as Aristotle understood it. A lecture succeeds when leaners experience catharsis, a relief of fear that arises when foundational views are brought into conflict. Based on this conception of teaching philosophy, I propose a substantial pedagogical model for lecture design and a diagnostic for flaws and imperfections.