The Groundability of Four Figures of Aristotelian’s Syllogism

The purpose of this research is to provide a new concept in Aristotelian categorical syllogism which is called groundability. A valid mood is called groundable if one would derive all the 24 valid moods in the Aristotelian’s syllogism by assuming only the valid mood and applying a chain of the following rules: simple conversion, reduction-ad-absurdum, sub-alternation, obversion and quantification negation. In this paper, we will prove that only the fifteen valid moods have the groundability property. Because Aristotle proves all the valid moods of other figures based on the four moods in the first figure, he considers these moods of the first figure as moods having the groundability property. We show that the groundability is not restricted to the first valid moods of the first figure--they are fifteen moods as stated. Thus, it can be shown that Aristotle's purpose from the self-evidence of the first figure is not the groundability of the four moods in the first figure. This important logical result in Aristotle's system is gained through the introducing the concept of the groundability of the moods in syllogism. We show that unlike the common view in the Aristotelian tradition, it is not the case that the groundability of the first figure must be the basis for explaining of being self-evidence of the four moods of the first figure. Regardless of what lies behind the evidence of the first figure valid moods, this paper will eliminate one of the options which is somehow a common wrong interpretation for answering the problem