Re: Isomorphism between Mereology and Boolean algebra without least element
Thus spake John F. Sowa at 7:07 pm -0400 on 6/7/05 re Re: Isomorphism between
Mereology and Boolean algebra witho:
> Category theory is an alternative foundation for
> mathematics, and many mathematicians say that category
> theory is much more powerful as a foundation for math
> than any version of set theory. (In fact, category
> theory has a great deal of usefulness for working
> mathematicians, and it would therefore qualify as
> a better foundation than any version of set theory.)
To be more precise it's Topos Theory (a la Lawvere, not a la Grothendieck),
that provides an alternative foundation.
However most Working Mathematicians (except the ones doing Algebraic
Geometry, Homotopy,Fibrations and closely related domains) reject it,
MacLane's book title notwithstanding, calling Category Theory "Abstarct
non-sense". Even worse, the underlying logic of Topos Theory is
Intuitionnistic Logic, which is a dirty word, nay blasphemous to the
Platonistic Weltanschaung of the majority...
Of course I agree with your point of view -- it goes without saying ;-)
Cheers
~=michel
--
Michel Eytan
eithn@free.fr
I say what I mean and mean what I say