Quantifier Reasoning and Multiple Generality in Aristotle and Ancient Logic

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.