# FOM: Iterative conception of set

Moshe' Machover moshe.machover at kcl.ac.uk
Fri Jan 23 06:26:23 EST 1998

>	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.

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.

Moshe'