Finite mathematics and the justification of the axiom of choicet

Philosophia Mathematica 8 (1):9-25 (2000)
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Abstract

I discuss a difficulty concerning the justification of the Axiom of Choice in terms of such informal notions such as that of iterative set. A recent attempt to solve the difficulty is by S. Lavine, who claims in his Understanding the Infinite that the axioms of set theory receive intuitive justification from their being self-evidently true in Fin(ZFC), a finite counterpart of set theory. I argue that Lavine's explanatory attempt fails when it comes to AC: in this respect Fin(ZFC) is no better off than the iterative notion

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