FOM: Re: Iterative conception of set
csilver at sophia.smith.edu
Sat Jan 24 08:10:54 EST 1998
On Fri, 23 Jan 1998, Moshe' Machover wrote:
> > 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.
That seems right to me.
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