A Completed System for Robin Smith’s Incomplete Ecthetic Syllogistic

Abstract

In this paper we first show that Robin Smith’s ecthetic system $\mathit{SE}$ for Aristotle’s assertoric syllogistic is not complete, despite what is claimed by Smith. $\mathit{SE}$ is then not adequate to establish that ecthesis allows one to dispense with indirect or per impossibile deductions in Aristotle’s assertoric logic. As an alternative to $\mathit{SE}$, we then present a stronger system $\mathit{EC}$ which is adequate for this purpose. $\mathit{EC}$ is a nonexplosive ecthetic system which is shown to be sound and complete with respect to all valid syllogistic arguments with a consistent set of premises.