# FOM: Re: Iterative conception of set

Charles Silver csilver at sophia.smith.edu
Sat Jan 24 08:10:54 EST 1998


On Fri, 23 Jan 1998, Moshe' Machover wrote:

C. Silver:
> >	Boolos's conception is much weaker than Shoenfield's.  Shoenfield
> >gives a kind of "proof" of replacement, but it relies on his 'principle of
> >cofinality', which in turn relies on being able to "visualize" the
> >completion of various stages of set construction.  I suspect that what you
> >are not convinced of is "visualization".  At least, that's the part that
> >bothers me.

Moshe' Machover:
> Yes. In my view his key statement 'Since we can visualize the collection A
> as a single object ... we can also visualize the collection of stages
> S-\alpha as a single object...' is a surreptitious invocation of the
> conception of limitation of size.

That seems right to me.

Charlie Silver
Smith College