Institute of Philosophy Slovak Academy of Sciences, v. v. i.
The Origins of Propositional Logic: Theophrastus on Hypothetical Syllogisms
(public talk)
On April 13, 2026 | 10:30 am
Institute of Philosophy SAS, v. v. i.
Room 94 (4th floor)
Klemensova 19
811 09 Bratislava 1
Slovak Republic
Speaker:
Marko Malink (New York University)
Marko Malink is Professor of Philosophy & Classics. He received an M. A. from the University of Leipzig (2004), where he studied Logic and Ancient Greek. He earned a Dr. Phil. in Philosophy from Humboldt University of Berlin (2008). His primary area of research is ancient philosophy, especially ancient logic and metaphysics. Malink also has interests in the history of logic, philosophy of language, and linguistics. His book Aristotle’s Modal Syllogistic was published by Harvard University Press in 2013. Some of his articles were selected for inclusion in The Philosopher’s Annual, which aims to collect the ten best articles published in philosophy each year (2013, 2016, 2018). Prior to joining the Faculty at NYU in 2014, Malink has held positions at Humboldt University of Berlin and the University of Chicago.
Abstract: Theophrastus, Aristotle’s pupil and eventual successor as head of the Peripatos, developed a paraconsistent theory of hypothetical syllogisms in which he sought to reduce various modes of propositional reasoning to categorical syllogisms. Jonathan Barnes has argued that Theophrastus’ attempted reduction of propositional to categorical logic is incoherent and ‘doomed to failure’. Others have gone still further, denying that Theophrastus’ hypothetical syllogistic constitutes any sort of contribution to the study of propositional logic at all. The present paper offers, in place of such negative assessments, an alternative view of what we shall argue are, in fact, significant and noteworthy achievements on Theophrastus’ part in the field of propositional logic. We reconstruct Theophrastus’ calculus and show that it gives rise to a coherent and natural system of propositional logic, namely, first-degree intensional linear logic. This system captures exactly the early Peripatetic theories of wholly and mixed hypothetical syllogisms. Theophrastus’ calculus also underwrites Aristotle’s rule of reductio ad impossibile and his commitment to the connexive law that no proposition entails its own negation.
This talk is supported by VEGA 2/0055/26, The Principle of Explosion as a Foundational Philosophical Principle
