Volume 4, 2011
Selected Essays from Northern Europe
On Absolute Infinity in Cantor
Georg Cantor, the originator of set theory, distinguishes between two kinds of actual infinity: he separates the transfinite from the absolutely infinite. Whereas the transfinite is the proper object of set theory, the absolutely infinite remains inaccessible to mathematical inquiry. In Cantor’s writings, the absolutely infinite seems to have both a positive and a negative aspect. It is shown in this paper how Cantor’s remarks on his forerunners in the history of philosophy—and especially on Nicholas of Cusa—help us to understand the inseparability of these two aspects.