, Volume 13, Issue 2, pp 107-126

The Axioms of Set Theory

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

In this paper I argue for the view that the axioms of ZF are analytic truths of a particular concept of set. By this I mean that these axioms are true by virtue only of the meaning attached to this concept, and, moreover, can be derived from it. Although I assume that the object of ZF is a concept of set, I refrain from asserting either its independent existence, or its dependence on subjectivity. All I presuppose is that this concept is given to us with a certain sense as the objective focus of a ”phenomenologically reduced“ intentional experience.

The concept of set that ZF describes, I claim, is that of a multiplicity of coexisting elements that can, as a consequence, be a member of another multiplicity. A set is conceived as a quantitatively determined collection of objects that is, by necessity, ontologically dependent on its elements, which, on the other hand, must exist independently of it. A close scrutiny of the essential characters of this conception seems to be sufficient to ground the set-theoretic hierarchy and the axioms of ZF.

This revised version was published online in August 2006 with corrections to the Cover Date.