Six infinite regresses

pp. 9-16

in: Michael Huemer, Approaching infinity, Basingstoke, Palgrave Macmillan, 2016

Abstract

It is commonly thought that there are some kinds of infinite series that one should avoid in one's philosophical theories — infinite series such that, if a theory requires one of them, then the theory should therefore be rejected. These are referred to as "vicious infinite regresses". On the other hand, it is also commonly thought that not all infinite series need be avoided; sometimes a theory entails the existence of an infinite series, but the theory should not therefore be rejected. These are referred to as "virtuous' or (less misleadingly) "benign infinite regresses".