[FOM] Another easy solution does not work
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.
More information about the FOM