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|Title:||Stoic Propositional Logic: A New Reconstruction|
|Keywords:||Stoicism;logic;history of logic;Stoic logic;Chrysippus;reconstruction;propositional logic;soundness;completeness;Philosophy;Philosophy|
|Abstract:||<p>I reconstruct Stoic propositional logic, from the ancient testimonies, in a way somewhat different than the 10 reconstructions published before 2002, building especially on the work of Michael Frede (1974) and Suzanne Bobzien (1996, 1999). In the course of reconstructing the system, I draw attention to several of its features that are rarely remarked about, such as its punctuation-free notation, the status of the premisses of an argument as something intermediate between a set and a sequence of propositions, the incorrectness of the almost universal translation of the Greek label for the primitives of the system as indemonstrable arguments, the probable existence of an extended set of primitives which accommodates conjunctions with more than two conjuncts and disjunctions with more than two disjuncts, the basis for the system’s exclusion of redundant premisses, and the reason why the hypothetical syllogisms of Theophrastus are not derivable in the system. I argue that, though sound according to its originator’s (Chrysippus’s) conception of validity, the system as reconstructed is not complete according to that conception. It is an open problem what one needs to add to the system in order to make it Chrysippean-complete, or even whether it is possible to do so without making it Chrysippean-unsound.</p>|
|Description:||<p>This article was presented at a conference (entitled 'Mistakes of Reason') in honour of John Woods held at the University of Lethbridge, April 19–21, 2002. Some corrections and additions were made in November 2012, in response to annotations by Erik Krabbe, for which I am grateful to him. Part of this paper formed the basis of my chapter entitled ‘The peculiarities of Stoic logic’ in Andrew D. Irvine and Kent A. Peacock, eds., Mistakes of Reason: Essays in Honour of John Woods (Toronto: University of Toronto Press, 2006), 224-242.</p>|
|Appears in Collections:||Philosophy Publications|
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