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.
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Notes
- 1.
By “proof rule” in the context of this paper we mean a rule that takes proofs as premisses and conclusion, as opposed to an “inference rule” that takes propositions as premisses and conclusion.
- 2.
On this point see Bobzien (2019).
- 3.
What is essentially the same argument in a slightly different setting presented in Hitchcock (2006).
- 4.
According to most scholars, the Stoics did no allow inferences with less than two premisses; see Bobzien (2019).
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D’Agostino, M., Piazza, M. (2022). Chrysippus’ Logic in a Natural Deduction Setting. In: Ademollo, F., Amerini, F., De Risi, V. (eds) Thinking and Calculating. Logic, Epistemology, and the Unity of Science, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-030-97303-2_4
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