This paper argues that Aristotle’s Metaphysics Z.3 deploys a reductio against the claim that ‘substances underlie by being the subjects of predication’, in order to demonstrate the need for a new explanation of how substances underlie. Z.13 and H.1 corroborate this reading: both allude to an argument originally contained in Z.3, but now lost from our text, that form, matter and compound ‘underlie’ in different ways. This helps explain some of Z’s peculiarities—and it avoids committing Aristotle to self-contradiction about whether (...) matter is substance, a claim denied in the reductio but endorsed elsewhere. (shrink)