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.
Signification was a conventional relationship between utterances and objects mediated by the particularities of a language.
Signification is the imposition of a meaning on an utterance, but supposition is taking a meaningful term as standing in for something.
The idea is that simple supposition happens when the term is standing in for a human concept rather than for the object itself.
Albert of Saxony gives 15 rules for determining which type of personal supposition a term is using.
Further the medieval logicians did not seem to dispute about the details of the syntactic rules for determining type of personal supposition.
However, the predicate of a universal affirmative claim won't really fit any of these models.
Some commentators, like Michael Loux,[4] have suggested that the theory of ascent and descent to particulars is intended to provide truth conditions for the quantifiers.
T. K. Scott has suggested that the theory of supposition proper was designed to answer the question What kind of thing are you talking about?
but the theory of personal supposition was aimed at answering the question How many of them are you talking about?
Paul Spade has suggested that by the 14th century the theory of modes of personal supposition wasn't aimed at anything at all anymore.
Peter of Spain says "Ampliation is the extension of a common term from a lesser supposition to a greater one.