Supposition theory

The Medieval logicians give elaborate sets of syntactical rules for determining when a term supposits discretely, determinately, confusedly, or confusedly and distributively. So for example the subject of a negative claim, or indefinite one supposits determinately, but the subject of a singular claim supposits discretely, while the subject of an affirmative claim supposits confusedly and determinately. 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. These rules seem to be important because they were linked to theories of descent to particulars and ascent from particulars.

I want to buy this cup or I want to buy that cup, or I want to buy that other cup - and so on for all cups.This cup isn't a table, AND that cup isn't a table, AND that other cup isn't a table, AND ...All coffee cups are this cup, and all coffee cups are that cup, and ...