From: Andr�s Silva
Subject: Kleene-Rosser paradox ?
Date: Mon, 25 Nov 1996 00:00:00 +0000
Message-ID: <57ci2n$atg@panoramix.fi.upm.es>

Hello. In the book "Object Oriented Methods (2nd ed)" by Ian Graham
I found this (p. 71) :

"Church's original theory [he refers to lambda calculus] was shown to be
inconsistent by the discovery of the Kleene-Rosser paradox..."

and he says nothing more about that paradox (not even bibl. ref.). Well, I've
never heard of the Kleene-Rosser paradox. Please, could you give me some 
information about it and its implications???

Thanks in advance

-----------------------
Andr=E9s Silva
Universidad Polit=E9cnica de Madrid

From: Marty Hall
Subject: Re: Kleene-Rosser paradox ?
Date: Tue, 26 Nov 1996 00:00:00 +0000
Message-ID: <x53exxt2iv.fsf@rsi.jhuapl.edu>

"Andr�s Silva" <······@zape.fi.upm.es> writes:

> 
> Hello. In the book "Object Oriented Methods (2nd ed)" by Ian Graham
> I found this (p. 71) :
> 
> "Church's original theory [he refers to lambda calculus] was shown to be
> inconsistent by the discovery of the Kleene-Rosser paradox..."
> 
> and he says nothing more about that paradox (not even bibl. ref.). Well, I've
> never heard of the Kleene-Rosser paradox. Please, could you give me some 
> information about it and its implications???

The paper is Kleene, S.C., and J.B. Rosser, "The Inconsistency of
Certain Formal Logics," Annals of Math. 36, 2nd series, 63-636, 1935.
It was a variation of Russel's paradox. Curry later had a simpler
proof, so this is usually called "Curry's Paradox".

This information (and a sketch of the proof itself) is in
section 2 of Rosser, J.B. "Highlights of the History of the Lambda
Calculus," Annals of the History of Computing, Vol 6 No 4, Oct 1984.
(I hadn't looked at *that* paper in a long time :-).

						- Marty

Lisp Resources: <http://www.apl.jhu.edu/~hall/lisp.html>