Mathematical Proofs of the Absurdity of the Infinite Regress: Examination on the Basis of Set Theory



Some arguments against infinite regress in Islamic philosophy such as applied proof or argument of ones and thousands are based on the mathematical foundations and preliminaries. Extraction and analysis of these preliminaries exposes mathematical nature of these arguments and shows that besides philosophical approach to these arguments should also look at them from perspective of mathematics. Adopting this perspective becomes clear that the position of these arguments is similar to some paradoxes that have been raised about concept of “large infinity” in mathematics. Using the Cantor’s set theory, mentioned paradoxes were resolved and way of accepting mathematical infinity was paved. Considering mathematical nature of the arguments against infinite regress, using the set theory shows that mathematical foundations and preliminaries of mentioned arguments can be vulnerable and consequently, they are unable to prove the impossibility of infinite regress