[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.


Tim Chow

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