Discrete supposition occurs whenever a discrete term, such as ‘Socrates‘, is the subject of a given proposition. I propose to examine this apparently simple notion. I shall draw attention to the incongruity, within a general theory of the semantic variation of terms in a propositional context, of the notion of discrete supposition, in which a term usually has a single semantic correlate. The incongruity comes to the fore in those treatises that attempt to describe discrete supposition as a sort of (...) personal supposition, although the same term cannot be in simple supposition in another propositional context, because it has no significate distinct from its suppositum. This shows a fundamental link between common signification, simple supposition and predicability, three notions that rely on the existence of a significate distinct and independent from the suppositum of the term. The connection is to be seen especially in William of Sherwood’s Introductiones, the only author of a terminist Summa who recognizes the existence of simple supposition for discrete terms. (shrink)