In this paper we first show that Robin Smith’s ecthetic system for Aristotle’s assertoric syllogistic is not complete, despite what is claimed by Smith. 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 , we then present a stronger system which is adequate for this purpose. 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.
Pierre Joray. "A Completed System for Robin Smith’s Incomplete Ecthetic Syllogistic." Notre Dame J. Formal Logic 58 (3) 329 - 342, 2017. https://doi.org/10.1215/00294527-3882234