Quantification

Abstract

Medieval authors approached the semantic phenomenon now known as quantification essentially by means of the concept of supposition, more specifically the different modes of personal supposition. The modes of personal supposition were meant to codify the quantificational behavior of what we now refer to as quantifier expressions, and what the medievals referred to as syncategorematic terms. Perhaps the best way to understand the medieval approach to these quantifier expressions by means of the notion of supposition is as a two-step procedure that explicates their meaning and semantic behavior. First, the syntactical structure of the proposition, that is, the presence and order of its syncategorematic terms, determines the kind of personal supposition that each categorematic term has. Then, the semantic definitions of each mode of personal supposition determine the effect of quantifying syncategoremata over the quantity of objects involved in the assertion of a proposition. This entry discusses both groups of rules, and the contrasting thirteenth and fourteenth century approaches. The former is based on the verification of propositions and focuses on the semantics of quantifier expressions taken individually; the latter focuses on the inferential relations of ascent and descent between propositions with quantifying syncategorematic terms and singular propositions of the form “This a is b,” and on the study of the global quantificational effect of syncategorematic terms in wider propositional contexts.