[FOM] Another easy solution does not work

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Mon Sep 16 04:56:19 EDT 2002

Fri, 13 Sep 2002 08:28:30 -0400, Harvey Friedman wrote:

> Whereas in the case of the liar paradox, there is no appearance of 
> doing something particularly mathematical, and given Kripke's 
> Watergate example and other related examples, even involving Nixon's 
> "I am not a crook", it has all the appearance of doing something that 
> ordinary people do. So simply declaring that there shall be no self 
> referential statements is not a satisfactory solution.

> Put another way, the Liar Paradox is a very special and fundamental 
> situation, unlike general recursion along non well founded orders, 
> which explicitly involves, e.g., infinitely many objects.

I am not really disagreeing. But still: I argued, in my funny little 
paper "The concept of truth in a finite universe" (Journal of Philosophical 
Logic 29, 617-633 (2000); see esp. Section 9), that *in the formalized 
setting*, self-reference, or more exactly diagonalization, and consequently 
Liar, require an axiom of infinity. 

Panu Raatikainen

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