A Justification for the Quantificational Hume Principle

Abstract

In recent work Bruno Whittle has presented a new challenge to the Cantorian idea that there are different infinite cardinalities. Most challenges of this kind have tended to focus on the status of the axioms of standard set theory; Whittle’s is different in that he focuses on the connection between standard set theory and intuitive concepts related to cardinality. Specifically, Whittle argues we are not in a position to know a principle I call the Quantificational Hume Principle (QHP), which connects the application of intuitive, quantificational cardinality concepts (including ‘at least as many’) to claims involving the existence of functions. This paper responds to Whittle’s skeptical arguments by providing an argument justifying the QHP.