[FOM] Con(ZFC) is trivial

[Nik Weaver]

Mart Dowd wrote:

> Axioms which have been stringently justified imply that the class of
> strongly inaccessible cardinals is stationary.  Thus, Con(ZFC) is a
> triviality even in this much more limited setting.

Please clarify "stringently justified"?

Back in February 2012 we had a debate on this list over the force of
the iterative conception as a justification for ZFC.  It seemed to me
that we ended up concluding that the language about "forming sets in
stages" was really supposed to be understood as a metaphor for some
abstract notion of metaphysical "dependence" or "presupposition", but
then it turned out that the direct axiomatization of this notion of
presupposition (due to van Aken) was far too weak to justify ZFC.

Do you base your comment about stringent justification on some version
of the iterative conception, or on something else?

Nik Weaver
Math Dept.
Washington University
St. Louis, MO 63130
nweaver at math.wustl.edu