In many essays over a large number of years, Leibniz attacked the Cartesian doctrine that extension constitutes the essence of a substance. In some of these essays, he, nonetheless, advocated a doctrine of corporeal substance, although, perhaps, his enthusiasm for it flagged as the years went on. In the letters he wrote to Arnauld, between 1686 and 1690, both the critical attack and Leibniz's own account of bodily substance are prominent. At this stage, he was presenting this theory of substance to a truly formidable critic, perhaps for the first time. He did not insist that it is true, but he did set himself up to explain what the theory is: given that no substance could be merely extended, what would be required for a substance to be corporeal? Substantial forms, in a word. Arnauld immediately raised a couple of central questions. As the correspondence proceeded, he learned more about Leibniz's proposal, but he kept coming back to these two central points. The strategy of this chapter is to exploit the fact that Leibniz's responses occur in the context of this ongoing dialogue. Each letter of Leibniz can – I would say, must – be understood in light of the ground covered in previous letters. The mutual understanding built up between the two is directly relevant to an appreciation of the force of Arnauld's final queries and the demands they make on his correspondent. Any extended exchange between philosophers uniquely creates this sort of interpretive resource.