Abstract

It is common knowledge that many problems in contemporary physics, particularly in microphysics and cosmology, present various infinities of which it is difficult to dispose, and that their role in mathematics is so considerable that it is often defined as the discipline of the infinite. Therefore it would be difficult to deny that infinity exists. But it is just as well known that, over the entire history of science, recognition of infinity has resulted in various difficulties, contradictions, aporias, antinomies, paradoxes — in a word, "much that is impossible," as Aristotle puts it. As phrased by one of the outs tanding mathematicians of the last century, David Hilbert, infinity offers a real challenge to our thinking