The Expressive Power of Medieval Logic

Abstract

Abstract This paper is about the development of logic in the Aristotelian tradition, from Aristotle to the mid-fourteenth century. I will compare four systems of logic with regard to their expressive power. 1. Aristotle’s own logic, based mostly on chapters 1-2 and 4-7 of his Prior Analytics 2. An expanded version of Aristotle’s logic that one finds, e.g., in Sherwood’s Introduction to Logic and Peter of Spain’s Tractatus 3-5. Versions of the logic of later supposition theorists such as William Ockham, John Buridan, and Paul of Venice. Version 4 is the logic without relatives (anaphoric pronouns); version 5 adds relatives. I am ignoring modals, conditionals that are not ut nunc, infinitizing negation, exclusives and exceptives, all exponibles, all insolubles, and terms with simple or material supposition, ampliation and restriction, and many other things.