Chris, (01)
On Fri, Jan 29, 2010 at 3:16 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
>
> ...
> ... On reflection, I will qualify my original claim that Russell's paradox
>has *nothing* to do with
> undecidability. For there is in fact a similarity between the usual argument
>given in presentations
> of Russell's paradox and the method of diagonalization in computability
>theory -- a method often
> used in proofs of undecidability. Russell's argument can be used more
>generally to show
> that, for any given set A, the set of all non-self-membered members of A
>cannot itself be a
> member of A and the proof is a clear instance of diagonalization. The
>paradox itself ensues
> from this theorem if one also assumes (or one is able to prove) that there is
>a universal set.
>
> So there is a similarity between the method of proof in Russell's paradox and
>a common
> method of proof in computability theory. But, conceptually, the paradox
>itself has nothing
> to do with undecidability/incompleteness/computability per se. (02)
I'm not sure what you mean by
"undecidability/incompleteness/computability per se." (03)
I'm happy with your agreement that "there is in fact a similarity
between the usual argument given in presentations of Russell's paradox
and the method of diagonalization in computability theory -- a method
often used in proofs of undecidability." (04)
-Rob (05)
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