, Volume 192, Issue 5, pp 1413–1444 | Cite as

Aristotle’s assertoric syllogistic and modern relevance logic

  • Philipp SteinkrügerEmail author


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 Syllogism Relevance logic History of logic Logic Relevance 



The first version of this paper was written during a DAAD funded stay at King’s College London and has been read at the Philosophisches Kolloquium in Cologne. I am grateful for the helpful remarks I received from the participants of this colloquium, especially Nicholas White and Marius Thomann. Since then, various versions of the paper have been read by Peter Adamson, Matthew Duncombe, Luca Gili, Jan Heylen, Peter Larsen, Jan Opsomer and Marius Thomann. Any remaining mistakes are my own. I would also like to thank two anonymous referees for their helpful comments on the paper in general and in particular on the issue discussed in Sect. 4.


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Authors and Affiliations

  1. 1.KU LeuvenKölnGermany

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