2. De Morgan and Logic

Abstract

From 1847 onwards, Augustus De Morgan propounded an extension of classical syllogistic logic by the introduction of ‘contraries’. These are negative terms in the sense that, for example, x means non-x within a given ‘universe’. In this chapter, we will focus on De Morgan’s early research on logic between 1847 and 1850, and address De Morgan’s revisions of traditional syllogistic logic in his ‘system of contraries’ and his ‘numerically definite system’. We will discuss his approach to determining portions of ‘universes’, which is based on determining extensions by numbers of instances of terms. The main point will be that De Morgan conceived of logical quantities as scopes and of conjunctive or disjunctive enumeration as quantifications over given domains—which is one of the systematic reasons behind his being involved in a long-lasting debate over the ‘quantification of the predicate’. It will be argued that, despite its relative lack of influence on later developments, De Morgan’s work still represented a notable departure from traditional syllogistic methods and anticipated the modern understanding of quantification in logic.