Re: Isomorphism between Mereology and Boolean algebra without least element
Thus spake John F. Sowa at 2:39 pm -0400 on 10/7/05 re Re: Isomorphism
between Mereology and Boolean algebra witho:
> The Bourbaki are an excellent example of brilliant
> mathematicians with an interesting point of view, which
> was useful as far as it went. In some respects, they
> did a lot of good, but in other respects, they also did
> a lot of harm by stifling other points of view.
>
> Three of their worst influences were (1) to ignore category
> theory, (2) to ignore the importance of diagrams, and (3) to
> ignore the importance of applications, especially to physics
> and now to computer science.
>
> I recommend an interview with Pierre Cartier, one of the
> later members of the Bourbaki
At some time in the 70s there were rumours that Bourbaki was writing a volume
on Category Theory, but it came to nothing. [I believe I have told another
list (FOM, probably) that Chevalley was supposed to have written a definitive
treatise on Categories that he lost on a trip by ship to the USA -- he had no
backup: that did not exist at that time, when manuscripts were what they mean
in Latin.] There was a severe "psychological" problem IMHO: they had invented
the notion of universal construction which is *more general* than the notion
of a left adjoint to a functor (*the* important one in Category Theory) but
it's *too* general. As MacLane puts it in Categories for the Working
Mathematician "good general theory does not search for the maximum generality
but for the right generality".
As for Cartier, he gave several lectures on Topos Theory some of which it was
my good fortune to hear at the Seminaire Bourbaki in the late '70s.
BTW I strongly dissent with his explanation about the lack of diagrams. I
dunno about Puritans but the "Old Testament" does not forbid pictorial
representation of truth (what could that be?) but only of God. Anyway,
considering the vast number of Jewish painters in the 20th century I believe
it applies no longer anyway...
Cheers
~=michel
--
Michel Eytan
eithn@free.fr
I say what I mean and mean what I say