Abstract

In [1] Chapter IV Lukasiewicz presents a system of syllogistic which is an extension of Aristotle’s ordinary syllogistic 1 . In spite of this difference Lukasiewicz speaks about it, as do we, as the Aristotelian system. One of the well-known interpretation of syllogistic is Leibnitz’s interpretation described in [1] . Syllogistic formulas are interpreted there in an arithmetical manner. A second, very natural interpretation, has been given by S lupecki , who interprets syllogistic formulas set theoretically. Although every formula which is not a syllogistic thesis can be rejected by using a finite number of objects , there is not any fixed finite number of objects that would falsify every formula not being a syllogistic thesis 2 . Our first interpretation has the advantage of interpreting Aristotle’s syllogistic in a finite- valued propositional calculus. We also give an interpretation of Aristotle’s syllogistic and a fragment of set theory in the modal calculus S5