# [FOM] iterative conception/cumulative hierarchy

Thomas Forster T.Forster at dpmms.cam.ac.uk
Mon Feb 27 07:08:40 EST 2012

Sorry to interrupt again, but this is simply not true.   There are
ways of blocking paradoxes other than by making $\in$ wellfounded,
and some of these methods retain a recursive construction of V.
If you don't want to read my article, perhaps you'd rather learn
it from Church, whose set theory with a universal set of 1974
allows a recursive view of V.

>
> Now in order to block the paradoxes, we need to agree that sets cannot
> be dependent on themselves, nor can there be cycles of dependence, or,
> I suppose, descending chains of dependence.  But without some sort of
> temporal or spatial metaphor (in terms of the elements of a set "appearing
> before it" or "lying lower in the hierarchy") the justification for this
> condition seems to me not so clear --- we are simply presented with a
> blunt assertion that there is some notion of "metaphysical dependence"
> and it is well-founded.
>

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