[FOM] iterative conception/cumulative hierarchy
nweaver at math.wustl.edu
Sat Feb 25 00:57:35 EST 2012
Michael Kremer wrote:
> Here's an old paper by Jim van Aken (RIP) which explains the axioms of
> ZFC in terms of the idea of one entity presupposing others for its
> existence (so doing away with the notion of "forming sets" from the
This paper looks interesting, but I don't see how you can say it explains
ZFC. The basic system he presents, MSU, is extremely weak --- it doesn't
prove the existence of pairs, or infinite sets, or power sets.
You only get to ZFC by adding a reflection scheme which the author openly
acknowledges lacks a compelling informal justification (bottom of p. 1001).
He points out that "It is known that Ref does not consistently generalize
to the case of third-order formulas" and "To date, no informal rationale
for reflection explains why the same rationale does not extend to the
So your gloss seems like rather an overstatement.
More information about the FOM