Alexander and the Aristotelian formula of the principle of excluded middle in Metaphysics Γ 7

Lisa Dalla Valeria


Alexander of Aphrodisias’s comment to the arguments on the principle of excluded middle, held by Aristotle in Metaphysics Γ 7-8, seems to interpret that text in a specific perspective that, considering the subsequent researches carried out in different areas, is a predominantly logical and philosophical. This perspective emerges from the particular importance that the exegete reserves to the concepts of true and false with respect to the principle’s formula (For neither can there be anything intermediate in a contradiction, but of one thing we must either affirm or deny one thing, whatever it is 1011 b 23-24) and its first demonstration, but generally also to the axioms and the concept of contradiction. It can, moreover, be traced back to Alexander the attribution to the principle of a meaning closely related to those concepts.
The reason for the Alexander’s interpretative choice could be found in its own conception of first philosophy as a demonstrative science, which seems to find out a consistent criterion for truth in the principle, establishing so the existence of something true and how to find it. However, such a requirement would be purely Alexandrian, because in Aristotle, as it can be demonstrated by the texts, the true is nothing more that the speech which describes the reality in a consistent way. In fact, it expresses a relationship between terms, and this relationship may be said to subsist, in the case of the affirmative statement, or does not subsist, in the case of denial.

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