[FOM] Replacement

Bill Taylor W.Taylor at math.canterbury.ac.nz
Thu Aug 23 01:14:20 EDT 2007

A Mani wrote:

->If we want to formalize vagueness, then it makes sense to drop replacement.

Yes; but why would one want to formalize vagueness, in math, of all places?

Earlier, Roger Jones said:

> The obvious semantics for first order set theory is
> "true in the cumulative heirarchy" i.e. true in that interpretation
> of set theory which is described by the iterative conception of set.
> Unfortunately it seems to me that the supposition that the iterative
> conception can be completed and then yields a definite collection of sets
> is incoherent.  It is easy to derive a contradiction from this supposition.

I can see how one might regard the "completed cumulative hierarchy"
as incoherent; but I cannot see how one might derive a contradiction
from the supposition thereof.

You say it is easy.   Can you elaborate please?

Bill Taylor

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