[FOM] PoV on Ultrafinitism
a_mani_sc_gs at yahoo.co.in
Wed Feb 11 10:30:08 EST 2009
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.
Member, Cal. Math. Soc
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