Infinity: A Cognitive Challenge

Abstract

Dealing with infinity, an inherently abstract concept which defies concrete representation, involves distinct cognitive difficulties. I first review the research on the development of children's understanding of the endlessness of numbers and of the infinite gap between a large finite set and an infinite set. Second, I consider the contradictions with which mathematicians and philosophers have to cope when attempting to manipulate infinity concepts in a coherent way. These difficulties are highlighted by analyzing one perplexing paradox. Finally, I discuss the intellect's puzzling ability to transcend the limits of our finitely based intuitions, as manifested in science and higher mathematics, and the need to thoroughly explore the emergence of that kind of human capability.