[FOM] Fwd: Re: Replacement
A. Mani
a_mani_sc_gs at yahoo.co.in
Wed Aug 22 09:31:39 EDT 2007
On Monday 20 August 2007 15:33, Alex Simpson wrote:
> Two further comments on Replacement.
> One can give many reasons for questioning the axioms of set theory,
> but Replacement need not necessarily be the first target.
> Constructive mathematics, for example, provides an interesting view on
> which axioms of set theory are unreasonable.
<snip>
> So, indeed, why doubt Replacement?
If we want to formalize vagueness, then it makes sense to drop replacement. In
generalized forms of rough set theory, I can define a map from which I cannot
get its image in a exact way, while in classical rough set theory the image
may not be crisp (a set).
(An introduction to rough sets is
http://logic.mimuw.edu.pl/prace/1999/D5/Tutor06_09.ps
The site has a lot more material on rough sets.
The rough set homepage is at
http://www.roughsets.org )
Best
A. Mani
--
A. Mani
Member, Cal. Math. Soc
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