6533b870fe1ef96bd12cfdad
RESEARCH PRODUCT
Logical Sentential Calculi Inspired by the Chrysippean Sentential Calculus
Robert Sochackisubject
Interpretation (logic)Deductive reasoningComputer science010102 general mathematics06 humanities and the arts0603 philosophy ethics and religionPropositional calculus01 natural sciencesLinguisticsFragment (logic)Negation060302 philosophy0101 mathematicsRule of inferenceSentencedescription
The aim of the present paper is to consider an approach, different from that presented by J. Łukasiewicz, concerning the interpretation of the so-called stoic undemonstrables, which were given by Chrysippus. Stoic undemonstrables have been interpreted in two different ways: using the notion of “negation of a sentence” (Łukasiewicz) and using the notion of “a sentence inconsistent with a given one” (Mates). According to the Stoics, two sentences are inconsistent if one of them is negation of the other. The Mates’ interpretation generates five different inference rules. Based on one of these rules we can consider (with other undemonstrables) four different stoic propositional calculi. Taking into account the interpretation of Łukasiewicz, we obtain Stoic logic as a fragment of classical sentential logic, but with the interpretation of Mates, Stoic logic is the whole of classical sentential logic.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-01-01 |