We can now recognize Aristotle's many accomplishments in logical theory, not the least of which is treating the deduction process itself as a subject matter and thus establishing the science of logic. Aristotle took logic to be that part of epistemolo gy used to establish knowledge of logical consequence. Prior Analytics is a metalogical treatise on his syllogistic system in which Aristotle modelled his deduction system to demonstrate certain logical relationships among its rules. Aristotle's n otion of substitution distinguishes logical (...) syntax from semantics and enabled him to distinguish validity from deducibility sufficiently to note the completeness of his logic. (shrink)

Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of metalogical (...) sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ‘sullogimos’ to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle’s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction. (shrink)