For reasons of space, I can only present the rough lines of the approach to quantification based on supposition. But medieval authors developed it further in several different directions, such as: the definition of valid inferences among different categorical propositions (see Karger 1993; Dutilh Novaes 2004); an analysis of multiple quantification (of subject and predicate) and of other quantifier expressions (see Ashworth 1978); discussions on what are now known as anaphoric pronouns (see Parsons 1994). Here I have discussed thirteenth and fourteenth century authors only, but fifteenth and sixteenth century authors refined the framework even further, dealing in particular with the difficulties that emerged from the earlier theories (see Ashworth 1974, 1978; Karger 1997; Dutilh Novaes 2008).
The modes of personal supposition have been a topic of heated debate in the literature, but a consensus as to their purpose and some of the technical details involved has not yet been reached. It is clear that they can be said to be a general theory of quantification, but one must bear in mind that the overall approach is fundamentally different from modern post-Fregean theories of quantification.
See also: > John Buridan > Peter of Spain > Supposition Theory > Syncategoremata > Terms, Properties of > William of Ockham > William of Sherwood
World History
