T.Forster at dpmms.cam.ac.uk
Fri Aug 17 21:07:37 EDT 2007
I have been trying to persuade Randall to publish his article on this.
However, Randall is not a replacement-denier. His point is that the
arguments for replacement (along the lines that it is obviously true
in the cumulative hierarchy) are in fact merely arguments for Sigma-2
replacement. (He has convinced me, for one.) The significance of
this observation of his is that should anyone (per impossibile) find
a proof of an inconsistency inside ZF then the usual arguments could
nevertheless still be put to good use - this time justifying Sigma-2
replacement. There is all the difference in the world between
repudiating replacement and cocking an eye at the arguments that
replacement is obviously true in the cumulative hierarchy. Those look
*extremely* dodgy to me, but there are plenty of other reasons to adopt
replacement. And, as i say, what i am intruiged by is the thought
processes of the people who repudiate it.
On Fri, 17 Aug 2007, Robert M. Solovay wrote:
> Randall Holmes has expressed support for the view that Sigma_2 replacement
> is more reasonable than full replacement. [I don't have a cite for this.
> Perhaps this view was only expressed in correspondence.] Randall reads
> this list and perhaps can shed more light on his views.
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