The Counterexample Problem in the Aristotle's Syllogism; Łukasiewicz's Analysis and Critique

To have an applied attitude to Aristotelian logic it is necessary to understand deeply and correctly his syllogism and hence its figures. In this paper، we will discuss syllogism carefully in more details; one of the most important topics in syllogism is the valid and invalid moods، but the problem is that thinkers have not paid so much attention to invalid and sterile moods as they have paid to valid moods. Here we give an equal importance to these two kinds of moods، and will indicate their practical role in the Aristotelian logic.