Is the Axiom of Choice Hume's Principle in Disguise?

This short note explores whether the Axiom of Choice can be understood as structurally analogous to Hume’s Principle within a Neo-Fregean setting. The central suggestion is that both principles rely on a rule-governed pairing relation that permits the formation of a new logical entity: cardinal number in the case of Hume’s Principle, and a choice concept in the case of the Axiom of Choice.

 

An earlier version of this short note was shared privately with researchers active in the relevant philosophical debate; this revised and clarified version is deposited publicly to provide a stable, citable record for scholarly discussion. Although the resulting logical entities are distinct, the note argues that the underlying logical movement may be read as continuous.