In this paper, we zoom in on some important features of Chrysippus’ logic by framing them in a natural deduction system for relevant logic. Our view is alternative to other recent reconstructions of Chrysippus’ view based on the sequent calculus. We show how, adding suitable elimination rules (akin to the five indemonstrables) that are missing in the Chrysippean system, one automatically obtains classical logic as a kind of deductive upper bound.

Chrysippus' logic in a natural deducting setting

Mario Piazza;Marcello D'Agostino
2022

Abstract

In this paper, we zoom in on some important features of Chrysippus’ logic by framing them in a natural deduction system for relevant logic. Our view is alternative to other recent reconstructions of Chrysippus’ view based on the sequent calculus. We show how, adding suitable elimination rules (akin to the five indemonstrables) that are missing in the Chrysippean system, one automatically obtains classical logic as a kind of deductive upper bound.
Settore M-FIL/02 - Logica e Filosofia della Scienza
Thinking and Calculating : Essays in Logic, Its History and Its Philosophical Applications in Honour of Massimo Mugnai
Springer International Publishing
Stoic logic; Natural Deduction; Relevant logic; Classical logic
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/113108
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