Stoic Syllogistic


Authors
Susanne Bobzien
Oxford University
Abstract
ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out.
Keywords syllogistic  Stoic logic  tableau method  cut rule  antilogism  theories of deduction  relevant logic  Stoic indemonstrables  Stoic themata
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Stoic Sequent Logic and Proof Theory.Susanne Bobzien - forthcoming - History and Philosophy of Logic:1-32.
The Peculiarities of Stoic Propositional Logic.David Hitchcock - 2005 - In John Woods, Kent A. Peacock & A. D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods. University of Toronto Press. pp. 224--242.

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Logic: The Stoics (Part Two).Susanne Bobzien - 1999 - In Keimpe Algra, Jonathan Barnes & et al (eds.), The Cambridge History of Hellenistic Philosophy. Cambridge University Press.
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