[FOM] Replacement

[Rupert McCallum]

--- Bill Taylor <W.Taylor at math.canterbury.ac.nz> wrote:

> Thomas Forster did not ask for examples of theorems that can be
> proved
> only with replacement, as many people have been given.  I'm sure he
> is
> fully familiar with them already.
> 
> He asked, specifically, if there were any people who accepted
> some sort of Platonic reality for sets, but who actually thought
> the Axiom of Replacement was FALSE, not merely inappropriate
> to classical mathematics, but actually false.
> 
> Are there any people here in that category, or that have colleagues
> etc
> of that type?
> 
> Bill Taylor
> 

I once found a paper online arguing that only predicative replacement
should be allowed, that the range of a function can be assumed to be a
set only if that function is definable by means of a formula with
quantifiers relativized to a set already known to exist. I'm having
trouble finding it at the moment.



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