Walking Through Cantor's Paradise and Escher's Garden: Epistemological Reflections on the Mathematical Infinite (I)

Abstract

Infinity is not an easy concept. A number of difficulties that people cope with when dealing with problems related to infinity include its abstract nature: understanding of infinity as a never-ending process, understanding infinity as a set of an infinite number of elements, and understanding some well-known paradoxes. Infinity can be understood in a number of ways, some of which are incompatible, and can involve value judgments or assumptions that are neither explicit nor desired. In its definition, we distinguish several aspects, teleological, artistic (Escher 2000 Escher, M. C. Estampas y dibujos. Colonia: Ed. Taschen, 2000. (In Spanish).), some essential, some potential, and others actual. Cantor's work on set theory is linked to infinity and has implications for belief in God.