When the world is not enough: medieval ways to deal with the lack of referents (Q2354879)

Our `logical constants' emerged in the medieval logic as `syncathegorematic terms', and among them maybe the most important was the universal quantifier (omnis). A peculiar aspect in its employment -- analyzed in this paper -- was that, to be satisfied, it required the existence of at least three instances of the quantified entity. This was an immediate consequence of the ancient fuzzy distinction between arithmetical and grammatical numbers (as in Plato's \textit{Sophist}, 238), and of deep features of ancient and medieval logic, as the existential presupposition and the confusion between intensional and extensional semantics.