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
On Jan 28, 2008 3:44 PM, <matthew.west@shell.com> wrote:
> Dear Rob,
>
> > Russell's example was the set of all sets which don't contain
> > themselves.
> >
> > What about Russell's set? Can it be thought? If so, is it contained in
> > your label.
>
> MW: Russell's paradox is an example of a description that does not point
> to anything (and logically cannot). It is literally non-sense.
>
> MW: The problem was that there was at the time a version of set theory
> that claimed that there was always something referred to by any
> description.
>
> MW: It is an interesting historical note to see how this was dealt with,
> preferring to keep the principle that everything had a description, but
> descriptions were not allowed to be self-referrential, rather than simply
> not insisting that all descriptions had to refer to something. A mistake
> in my view. But so it goes.
>
> Regards
>
> Matthew West
> Reference Data Architecture and Standards Manager
> Shell International Petroleum Company Limited
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