Thomas Reid, William Hamilton, and Augustus De Morgan

Abstract

Abstract Thomas Reid’s importance lies primarily in the clear way he asserts that the syllogism is an inadequate tool for carrying out mathematical demonstrations. Reid argues that even a simple inference such as the one asserting the transitivity of equality cannot be recast in syllogistic form. William Hamilton, in his edition of Reid’s works, attempts to recast the statement concerning the transitivity of equality into a syllogistic inference. In the dispute for or against the syllogism, a very special place is held by Augustus De Morgan, who, while on the one hand considering the traditional syllogism insufficient as a tool for proving mathematical theorems, on the other hand proposes to interpret the copula as a generic relation, thus giving rise to valid relational inferences and paving the way for a logic of relations, which will be developed and refined later by Peirce and Schröder.