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Re: [ontolog-forum] Can Syntax be Semantic?

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Rob Freeman <lists@xxxxxxxxxxxxxxxxxxx>
Date: Fri, 29 Jan 2010 12:30:03 +1300
Message-id: <7616afbc1001281530v58970727p583010ba4a5e47ed@xxxxxxxxxxxxxx>
On Thu, Jan 28, 2010 at 4:52 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
> Russell's paradox has nothing whatever to do with decidability or 
>irreducibility (whatever you think that means).  Do you even know what 
>Russell's paradox is?    (01)

There's one particular talk by Chaitin on the history of this which I
always like:    (02)

"So there was a problem with set theory --- that became increasingly
clear. I think Russell helped to make it be recognized by everybody
that we had a serious crisis and that methods of reasoning that seemed
at first sight perfectly legitimate in some cases led to obvious
disaster, to contradictions. There were a whole bunch of paradoxes
that Russell advertised: the Berry paradox, the one I just mentioned
is called the Russell paradox, and there's another paradox, the
Burali-Forti paradox.    (03)

A lot of these paradoxes in fact were really brought to the attention
of the world by Russell. Russell would typically have a footnote
saying this paradox occurred to me while I was reading a paper by
Burali-Forti, so everyone calls it the Burali-Forti paradox.
Burali-Forti I think spent his whole life trying to live down this
attribution because he didn't believe that mathematics was in
trouble!"    (04)

"So what happens when you start playing with this idea? What happens
is, everywhere you turn, you get incompleteness and undecidability..."    (05)

http://arxiv.org/html/nlin/0004007    (06)

-Rob    (07)

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