[FOM] A Defence of Set Theory as Foundations

[Roger Bishop Jones]

Weaver has recently posted criticism of justifications
of the axioms of set theory, claiming that the iterative
conception is incoherent.

Despite my own doubts about the completability of the
universe of sets described in the iterative conception
I still regard the ideas as fundamentally sound and as
a good intuitive foundation for axiomatic set theory.

Weaver seems to think that the iterative conception
can be construed in only two ways, platonistically
or constructively. (or does he to think it
inconsistent because it can only be construed in
both ways?)

It seems to me that it can be construed "semantically",
as a description of a collection of sets which is to
be considered the domain of discourse of set theory
but without any claim or presumption that the sets
or the domain of sets "really" exist or that they
can be "constructed".  Both of these elements are
undesirable because they introduce considerations
which are irrelevant to the mathematics for which
a foundation is sought.

I would be interested to know from Weaver whether
he finds such an interpretation of the iterative
conception intelligible, and what criticism he
would offer against such an account of set theory.

Roger Jones