[FOM] Fwd: Re: Replacement

[A. Mani]

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