Two remarkable contributions of Aristotle to the intellectual legacy of the West

Abstract

Although it does not need any justification to explore the rich legacy of Greek philosophy, an account of its lasting insights does need lifting out the significant elements of continuity, while disregarding those stances that reflect elements of discontinuity. With a sense of critical solidarity this investigation mainly focuses on two brilliant insights present in the philosophical works of Aristotle. The first one concerns the legal-ethical principle of equity. Since the universal scope of a law cannot possibly foresee all the unique circumstances that may occur in the future, it does happen that in a particular instance applying the law will lead to an injustice, in which case the applicable law has to be set aside on behalf of equity. However, the law itself cannot be eliminated since it is a condition for a stable legal order. The second one focuses on the remarkable fact that modern set theory still conforms to the two criteria which Aristotle stipulated for continuity. Aristotle held the view that something continuous must be infinitely divisible and that each point of division must be taken twice, namely as starting-point and as end-point. What appears to be perplexing is that whereas Aristotle rejects the actual infinite, modern set theory accepts it! This apparent contradiction becomes understandable (and is eliminated) once it is realised that the two alternative approaches merely represent different aspectual perspectives: when these two conditions are observed from the angle of approach of the aspect of space, only the successive infinite is needed (surfacing in the infinite divisibility of what is continuous – Aristotle’s approach), and when they are accounted for from the perspective of the numerical aspect, the actual infinite (the idea of an infinite totality) is required (Cantor-Dedekind)