[FOM] Concerning Ultrafinitism.
Timothy Y. Chow
tchow at alum.mit.edu
Fri Nov 3 17:10:26 EST 2006
Bill Taylor <W.Taylor at math.canterbury.ac.nz> wrote:
> 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" -
> * "In Orthodox math we derive true results by valid means;
> * in Generalized math both these restrictions are dropped!"
> Anyway, one can hardly say that Fuzzy math even died - it was
> practically still-born... math departments gave it very short shrift.
This seems to be an unnecessarily disparaging view of fuzzy logic. It may
not be particularly deep from a theoretical point of view, but this does
not prevent the idea from being successful in engineering applications.
The Wikipedia article is a pretty good introduction to the subject,
listing some "practical applications" as well as clearing up certain
misconceptions. In particular, until I see some more historical evidence,
I'm quite skeptical about any alleged historical connection between fuzzy
logic and ultrafinitism.
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