The ambiguities associated with Bernard Bolzano's 'definition' of the infinite set

Abstract

The aim of the paper is to remove the ambiguities contained in the 20th Section Bernard Bolzano's 'Paradoxien des Unendlichen'. Conclusion is that Bolzano originally wanted only to present in the 20th Section one of the (many) paradoxes of infinite sets: an infinite set may be equivalent with its subset. The proof in the 20th Section applies only to this property. Later added Bolzano to the text of the 20th Section a generalizing remark. Only this remark suggests that Bolzano anticipated the reflexive (Dedekindian) definition of the infinity set.