In search of $$aleph _{0}$$ ℵ 0

how infinity can be created

Markus Pantsar

pp. 2489-2511

in: History and philosophy of infinity, Synthese 192 (8), 2015.

Abstract

In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.