dilemma; was Re: Axiomatic ontology
> Matthew,
>
> What you write sounds like the way Russell himself tried to deal with
> the problem. I didn't realize anyone still adhered to that.
>
> Last time I checked this was still a dilemma in mathematics. Axiomatic
> formulations of maths appear to be irreducibly multiple. As I
> understand it modern mathematics is trying to deal with this by
> seeking a philosophical basis in relationships, called Category Theory
> (a so called "geometric model", which bears a striking resemblance to
> my mind to the the way 20th century physics tried to deal with its own
> frame of reference issues.)
>
> Whatever else you might say about them, I don't think you can
> trivialize the consequences of Russell's paradox as "an interesting
> historical note."
>
> -Rob
>
Sorry Rob, this is no more 'a dilemma in mathematics' -- cf eg
Grothendieck's Universes
(say SGA4, Springer Lecture Notes in Maths 269; MacLane Categories for
the Working Mathematician; etc., etc.) or Feferman in Butts&Hintikka
(eds.), Logic, Foundations of Mathematics and Computability Theory,
Reidel 1977. And many, many more references...
IMHO the above characterization of Category Theory is somewhat short,
but this is not the place for a discussion of that subject.
Cheers
˜=michel
--
Michel Eytan
eytan@umb.u-strasbg.fr
I
say what I mean and mean what I say