[FOM] iterative conception/cumulative hierarchy

[Hendrik Boom]

On Thu, Feb 23, 2012 at 08:13:32AM -0600, Nik Weaver wrote:
> 
> Without invoking the "metaphor" of formation in stages, what is the
> explanation of why we should understand the universe of sets to be
> layered in a cumulative hierarchy?

What's really needed is for the sets all to be well-founded in the 
membership relation.  Except you probably can't say that within the set 
theory, because well-founded is one of these intuitively clear slippery 
concepts that goes awry when things become too general.

Ordinally-indexed stages is a formal way to approximate this concept.

-- hendrik