[FOM] Replacement

Thomas Forster 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.

Home page: www.dpmms.cam.ac.uk/~tf; dpmms phone +44-1223-337981. 
In NZ until october work ph +64-3367001 and ask for extension 8152.
Mobile in NZ +64-21-0580093 (Mobile in UK +44-7887-701-562).

More information about the FOM mailing list