Abstract

Aristotle axiomatically divides the 28 syllogisms of necessity of Anal, prior. I 9-11 into two classes: those with a necessary conclusion and those with a non-necessary conclusion. The fact that Aristotle axiomatically comprehends only 24 syllogisms of necessity, however, raises two questions: 1. What method does he use to decide about the remaining four syllogisms? 2. Is this method consistent with the initial one? This essay pursues the answers to these questions first by means of semantic analysis, showing that Aristotle ultimately considers assertoric propositions to be possible and therewith non-necessary propositions. Aristotle employs this approach, developed within the axiomatic, to the four syllogisms in question, thereby integrating them into the axiomatic. Finally, this essay answers the question of consistency by way of a formalization of the syllogisms of necessity.