Aristotle, Logic, and QUARC

Abstract

The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original text than other such reconstructions brought forward up to now. To accomplish this, we will not use classical logic, but a novel system developed by Ben-Yami [2014. ‘The quantified argument calculus’, The Review of Symbolic Logic, 7, 120–46] called ‘QUARC’. This system is apt for a more adequate reconstruction since it does not need first-order variables (‘x’, ‘y’, …) on which the usual quantifiers act—a feature also not to be found in Aristotle. Further, in the classical reconstruction, there is also need for binary connectives (‘∧’, ‘→’) that don't have a counterpart in Aristotle. QUARC, again, does not need them either to represent the Aristotelian sentence types. However, the full QUARC is also not called for so that I develop a subsystem thereof (‘QUARC’) which closely resembles Aristotle's way of developing his logic. I show that we can prove all of Aristotle's claims within this systems and, lastly, how it relates to classical logic.