De la determinación del infinito a la inaccesibilidad en los cardinales transfinitos

Abstract

In this paper I deal with two problems in mathematical philosophy: the (very old) question about the nature of infinity, and the possible answer to this question after Cantor’s theory of transfinite numbers. Cantor was the first to consider that his transfinite numbers theory allows to speak, within mathematics, of an actual infinite and allows to leave behind the Aristotelian statement that infinity exists only as potential infinity. In the first part of this paper I discuss Cantorian theory of transfinite numbers and his particular point of view about this matter. But the development of the theory of transfinite numbers, specially the theory of transfinite cardinal numbers, has reached with the inaccessible cardinal numbers a new dilemma which makes us think that Aristotelian characterization of the infinity as potential is again a possible answer. The second part gives a general view of this development and of the theory of the inaccessible cardinal numbers in order to make clear my point of view concerning Aristotelian potential infinity.