The Existence of Infinity

Abstract

Modern mathematics has built ingenious and exact theories of infinity, but these theories did not make much contribution to the philosophical analysis of infinity, because mathematicians pay little attention to the traditional concept of infinity, and ignored the fact that the infinite is essentially unknowable.
In this paper, I examine the Cantorian concept of set and try to show that infinite sets must contain some indefinite elements, which are not actual objects, but mere possibilities. Although Cantor defined a set as “any collection into a whole of definite and separate objects, ” it is impossible for us to identify every element of such a set, if the set is infinite. I also try to show, however, that under certain conditions, possibilities can be treated as actual existence and infinite possibilities exist in our world.