The Axioms of Set Theory

Axiomathes 13 (2):107-126 (2002)

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

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References found in this work

Logical Investigations.Edmund Husserl - 1970 - London, England: Routledge.
Logical Investigations.Edmund Husserl & J. N. Findlay - 1972 - Journal of Philosophy 69 (13):384-398.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.

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