Abstract:In order to provide a consistent explanation for Aristotelian modal syllogistic, this paper reveals the reductions between the Aristotelian modal syllogism ◊I�A◊I-3 and the other valid modal syllogisms. Specifically, on the basis of formalizing Aristotelian modal syllogisms, this paper proves the validity of ◊I�A◊I-3 by means of the truth value definition of (modal) categorical propositions. Then in line with the symmetry of Aristotelian quantifiers some and no, the definition of inner and outer negations of A… Show more
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