Quantifier Reasoning and Multiple Generality in Aristotle and Ancient Logic

TL;DR

This paper reevaluates Aristotelian logic, arguing it was more capable of handling complex, multi-layered reasoning than traditionally believed, thus challenging assumptions about its limitations in formalizing mathematics and science.

Contribution

It demonstrates that ancient logical theories, including Aristotle's, can formalize complex reasoning involving multiple generalities, contrary to common beliefs.

Findings

Aristotelian logic can formalize multi-layered reasoning.

Ancient logical theories are sufficient for complex scientific discourse.

Challenges the view that ancient logic was inadequate for mathematics.

Abstract

Aristotelian logic and its related traditions in antiquity are often held to have been equivalent to monadic predicate logic and as such inadequate to formalize mathematics as well as scientific and philosophical discourse in general. In this paper we argue that on the contrary the logical theories of Aristotle and ancient authors such as Galen and Boethius were in fact quite sufficient to account for the logically complex expressions and reasoning involving multiple generality fundamental to the aforementioned disciplines.