Comp. by: Amoudha Stage: Proof Chapter No.: 4 Title Name: AlgraandIerodiakonou Date:31/12/14 Time:19:07:10 Page Number: 130 chapter 4 Body: M 9.359–440 Gábor Betegh Introduction In view of the prevalent corporealism of the Hellenistic schools, one may expect Sextus’ examination of body to be of special importance in the whole of Against the Physicists. Sextus’ introductory remarks only reinforce this expectation. Yet Sextus almost immediately appears to leave behind the corporealist natural philosophers and other protagonists of the previous chapters of Against the Physicists to turn to an examination of the math- ematicians’ conception of body. By far the largest part of the chapter is then devoted to arguments against the conceivability of fundamental geometrical notions, making long sections of our chapter basically identical to the main bulk of Against the Geometers. The chapter in many respects is at odds with Sextus’ more usual sceptical strategy. Because of its almost exclusive focus on the mathemat- icians’ conceptions, it is not a systematic consideration of alternative positions of different schools, although, as we shall see, Sextus is well aware of the variety of options, and the motivation behind why one may prefer one conception over another. In particular, he spends very little time and energy on that conception of body which can be ascribed to the most important members of the corporealist camp, namely the Stoics and the Epicureans. He does not discuss in an explicit manner whether, and if so I am paricularly grateful to Keimpe Algra and Dorathea Frede for written comments, to Charles Brittain, Jim Hankinson, Malcolm Schofield, David Sedley and Emidio Spinelli for their helpful remarks during the discussion at the Symposium, and to the participants of the graduate seminar on M 9–10 that I co-taught with Charles Brittain at Cornell. I received further helpful comments from Mike Griffin, Christian Pfeiffer and Pieter Sjoerd Hasper. For the completion of the paper, I received help from the ERC_HU BETEGH09 research grant. The research leading to these results has received funding from, the European Commission’s Seventh Framework Programme FP7/2007-2013 under grant agreement no. FP7-238128. I would like to dedicate this chapter to the memory of Michael Frede, with whom I had the priviledge to have long and outstandingly instructive discussions, including about this work. 130