The logic of categorematic and syncategorematic infinity

Abstract

The medieval distinction between categorematic and syncategorematic words is usually given as the distinction between words which have signification or meaning in isolation from other words (such as nouns, pronouns, verbs) and those which have signification only when combined with other words (such as conjunctions, quantifiers, and articles). Some words, however, are classified as both categorematic and syncategorematic. One such word is Latin infinita ‘infinite’. Because infinita can be either categorematic or syncategorematic, it is possible to form sophisms (logical puzzles or paradoxes) using infinita whose solutions turn on the distinction between categorematic and syncategorematic uses of infinita. As a result, medieval logicians were interested in identifying correct logical rules governing the categorematic and syncategorematic uses of the term. In this paper, we look at 13th–15th-century logical discussions of infinita used syncategorematically and categorematically. We also relate the distinction to other medieval distinctions with which it has often been conflated in modern times, and show how and where these conflations go wrong.