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Bill Taylor wrote:
> Is the following a reasonable point of view, do people think?
>
> I'm still kind of wondering where Yessenin-Volpin, Edward Nelson,
> and other ultrafinitists are coming from.
>
> They purport to find, or rather take the public stance of finding,
> that the concept of "all the naturals" is confusing and vague,
> whereas it is indeed *crystal-clear* to the rest of us.
To be fair, for example, I just read an essay by Abraham Robinson in
which he denies that he can conceive of an infinite set. He does endose
working with infinite sets as ideal objects in a formal theory, but he
makes crystal clear that to him the concept of an infinite set is
meaningless otherwise.
> Some time ago, back in the late seventies to early eighties,
> there was a brief flurry of interest from fringe mathematicians
> in "fuzzy math". It was never quite clear what this was, but it
> still has a small amount of library shelf space, though perhaps
> little or no presence in math departments in academia.
> It seemed to be (AFAICT), basically, that joke that
> used to go around about "Generalized Mathematics" -
Yet I see more and more new books on the shelves every time I visit the
library that have titles with the word 'fuzzy' in them, and these are
usually Springer Verlag books, including textbooks and collections of
articles and reportings of conference proceedings. Some of the material
seems to be computer science, but plenty of it is categorized as
mathematics. Well, my just saying that there are a lot of new books,
written by professional mathematicians, with the words 'fuzzy' in the
title is not an argument that fuzzy is an important area of study, but
it at least gives me some reason to doubt claims that it is not
currently an important area of study.
MoeBlee
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