Stoic Syllogistic
DOI:
https://doi.org/10.12775/LLP.2026.014Keywords
Stoic syllogistic, syllogism, ; proof, completenessAbstract
TThis paper reconstructs the Stoic syllogistic as equivalent to classical propositional calculus. The method that has been used has three distinctive features: (i) the Stoics' proof routine is considered a source on a par with explicit declarations, (ii) all atomic formulae are consequently considered schemata, i.e.\ true or false relative to a value assignment, (iii) the view is held that only some of the permissible proof steps are classified as based upon syllogisms. The Stoic syllogistic turns out to be a complete axiomatic system of derivation rules and consists of three parts: (a) a decision procedure for formulae, which is a part of an axiomatic system rather than a formal semantics, (b) an axiomatic system of designated derivation rules, called indemonstrable syllogisms, (c) a method to effectively generate any valid derivation rule by means of the true formulae and indemonstrable syllogisms. A completeness result for the Stoic syllogistic is provided. Arguably, this result is highly congruent with the account known to have existed in the lost sources of antiquity.
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