[FOM] PoV on Ultrafinitism

[A. MANI]

On Wednesday 11 February 2009 01:01:36 Vaughan Pratt wrote:
> jean paul van bendegem wrote:
> > And that seems odd. This kind of paradoxical reasoning is related to the
> > analysis of vague concepts, so rather than "fuzzy" I would prefer to use
> > the term "vague".
>
> What you are calling "vague" here is not mathematics but English, which
> suffers from what one might call in this case JIS, Jumpy-In Syndrome.
> The English sentence "I can write down all numerals" is vague in that it

I think you are taking it to a very different semantic domain. The argument (if 
'writing down' is 'abstracted')  is all right in many suitable mathematical/ 
semantic domains (possibly placed with in the usual classicalist mathematical 
domain or without). The distinction between 'fuzzy' and 'vague' is a good one 
as models assuming the former always carry a lot of justified/unjustified/poorly 
justified gradation theory. 

The exact reasons for calling it 'vague' would be more interesting. Ultimately 
I expect to see a situation in which we have sufficient classification of the 
possible theories for easy application.    

Best

A. Mani

-- 
A. Mani
Member, Cal. Math. Soc