Aristotle’s assertoric syllogistic and modern relevance logic

Abstract

This paper sets out to evaluate the claim that Aristotle's Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap's Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises of a proof are actually used to derive the conclusion. Turning to Aristotle's Prior Analytics, I argue that there is evidence that Aristotle's Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle's analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle's logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle's logic is a relevance logic.

Aristotle’s Syllogistic as a Deductive System

“…The classical interpretation of operators is, however, by no means obvious. The definition of syllogism itself, as derived from Prior Analytics: "[a] syllogism is an argument in which, certain things being posited, something other then what was laid down results by necessity because these things are so", [21] (24b, 20) suggests two features of syllogisms that the classical calculus ignores-non-tautologicality "something other then what was laid down" and relevance: "because these things are so" (see e.g., [3] for a discussion of the issue of relevance).…”

“…[...] Independently of these rather recent developments, there has been a renewed interest in matters of formalization of Aristotelian logic by a small group of logicians, philosophers and philologists." Since then, many new works have been published either directly on the writings of Aristotle [3][4][5] or on extensions or technical aspects of his syllogistic [6][7][8][9][10][11][12][13][14][15][16][17][18][19], to mention only a few. After Aristotle, syllogistic was for many centuries the dominant form of logic attracting interest of many generations of scholars.…”