Re: Is a function a relation?
Date: Tue, 23 Jun 2009 20:27:42 -0700 (PDT)
On Jun 23, 3:33 am, David BL <davi..._at_iinet.net.au> wrote:
> It's not clear that type systems particularly help in this purist
> mathematical endeavour.
My sense is that it doesn't.
> I note that the usual axioms of set theory
> completely ignore any concept of type. I'd be interested to know
> whether modern mathematicians that have researched type theory believe
> it's important to mathematical foundations. My understanding is that
> Russell only investigated type theory with the aim to avoid paradoxes
> by preventing loops, but his work was made redundant by axiomatic
> systems like ZFC which is believed to be free of paradoxes.
Certainly Russel's paradox is easily avoided by using a restricted form of comprehension. However every time I see it suggested that that was a particular motivation for Russel's work, it gets laughed at by those more in the know about math history.
An interesting paper on the question, which I bet you will
Anything by Leslie Lamport is worth reading. Even if he
often flies way over my head.
Anything by Leslie Lamport is worth reading. Even if he often flies way over my head.
Marshall Received on Wed Jun 24 2009 - 05:27:42 CEST