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Abstract

This paper has the following aims. We study the metalogic of the Organon and other works of Aristotle with special attention to the evidence provided by the later work of Galen. We attempt to formalize the metalogic implicit in the Analytics which is at the same time, so we argue, the logic implicit in the Topics, and our proposal is that this consists in an extension of second-order logic presented in a variant of natural deduction including non-monadic predicates. Furthermore we argue that Aristotle made conscious use of the key quantifier rules as well as propositional rules thus lending further support to the thesis argued for by Bobzien\cite{bob1} that ancient logic had sufficient means to deal effectively with multiple generality. The second part of the paper is dedicated to deploying the above extension of second-order logic to formalize the Topics and showing the logical, linguistic and philosophical interest of this work.