This article focuses on a denotational semantics for Aristotle’s syllogistic for modal propositions, one which associates terms not with a single set of designata, but with triples of such sets. Referring to the intuitions contained in traditionally conducted analyses of truth relationships between modal statements, a criticism of selected laws of Aristotelian modal syllogistic is presented, indicating the inconsistencies in the intuitions used by the Stagirite while constructing his modal system.
This work analyses four formulations of syllogistic with negative terms. The first one is a well-known formulation of the system given by Anders Wedberg. The second formulation is a simplification of the axiomatics of Wedberg’s system given by Bogusław Iwanuś. The author of the third formulation is Albert Menne. In the article, a simplification of the axiomatics of Menne’s system is proposed. It is here regarded as the fourth formulation of syllogistic with negative terms. Logical connections between these constructions are examined.
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