Supposition theory was a branch of medieval logic that was probably aimed at giving accounts of issues similar to modern accounts of reference, plurality, tense, and modality, within an Aristotelian context. Philosophers such as John Buridan, William of Ockham, William of Sherwood, Walter Burley, Albert of Saxony, and Peter of Spain were its principal developers. By the 14th century it seems to have drifted into at least two fairly distinct theories, the theory of "supposition proper", which included an "ampliation" and is much like a theory of reference, and the theory of "modes of supposition" whose intended function is not clear. Supposition proper Supposition was a semantic relation between a term and what that term was being used to talk about. So, for example, in the suggestion Drink another cup, the term cup is suppositing for the wine contained in the cup. The logical suppositum of a term was the object the term referred to. (In grammar, suppositum was used in a different way). However, supposition was a different semantic relationship from signification. Signification was a conventional relationship between utterances and objects mediated by the particularities of a language. Poculum signifies in Latin what cup signifies in English. Signification is the imposition of a meaning on an utterance, but supposition is taking a meaningful term as standing in for something. According to Peter of Spain "Hence signification is prior to supposition. Neither do they belong to the same thing. For to signify belongs to an utterance, but to supposit belongs to a term already, as it were, put together out of an utterance and a signification." An easy way to see the difference is in our drink another cup example. Here cup as an utterance signifies a cup as an object, but cup as a term of the language English is being used to supposit for the wine contained in the cup. Medieval logicians divided supposition into many different kinds; the jargons for the different kinds, their relations and what they all mean get complex, and differ greatly from logician to logician. Paul Spade's webpage has a series of helpful diagrams here. The most important division is probably between material, simple, personal, and improper supposition. A term supposits materially when it is used to stand in for an utterance or inscription, rather than for what it signifies. When I say Cup is a monosyllabic word, I am using the word