Re: Is a function a relation?

From: Marshall <>
Date: Tue, 23 Jun 2009 20:27:42 -0700 (PDT)
Message-ID: <>

On Jun 23, 3:33 am, David BL <> 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 like:

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

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