Abstract

The history of the search for a minimal set of inference rules for syllogistic reasoning starts with Aristotle, with one of the metatheorems proved in Prior Analytics stating that all syllogistic deductions are ultimately reducible to two universal moods in the first figure: Barbara and Celarent. In the present work, we will consider what is the greatest reduction one can achieve when proving all the moods indirectly. The question we shall answer is whether, when proved indirectly, syllogisms behave the same way and, consequently, whether the Aristotelian reduction to Barbara and Celarent holds for indirect proofs as well. To achieve this, we shall consider four different scenarios of applying single-premise inference rules to syllogism. The results for each scenario will then be analyzed and displayed as tables. Considering the tables, we shall claim that in certain cases, the Aristotelian reduction does not hold and further propose our division of all the syllogistic moods, which will be different from the usual figure arrangement. Finally, we will analyze the results quantitatively and show that they can provide insight into the nature of the division to regular and the so-called subalternated moods.