As an apt comment on this and other, similar, threads, I recommend (01)
http://xkcd.com/675/ (02)
Pat

On Jan 29, 2010, at 6:20 PM, Christopher Menzel wrote: (03)
> On Sat, 20100130 at 12:28 +1300, Rob Freeman wrote:
>> Chris,
>>
>> 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 nonselfmembered
>>> 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.
>>
>> I'm not sure what you mean by
>> "undecidability/incompleteness/computability per se."
>
> It means the paradox has nothing to do with the concepts themselves.
> Russell's paradox is a paradox of set theory; it was discovered
> decades
> before computability theory was even formulated and none of the
> concepts
> of computability theory are presupposed by the paradox in any way.
> Nor
> does it have any implications for them. The only connection, as I
> pointed out, is that the *structure* of the usual proof of Russell's
> paradox (more accurately, the usual proof of a proposition that, with
> the assumption of a universal set, entails Russell's paradox) is
> similar
> to the structure of some proofs of undecidability.
>
>> 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."
>
> My agreement?? Again you are being entirely disingenuous. For X to
> agree with Y about A implies that Y has asserted A; and it typically
> presupposes that Y also understands A. So to characterize my
> observation about diagonalization in the proof of Russell's paradox as
> something I have *agreed* with you about suggests that it is something
> that you yourself have asserted and that you understand. You've
> certainly not asserted it, and the numerous confusions and errors
> about
> logic and computability in your own posts lead one, at the least, to
> be
> suspicious of whether you understand it.
>
> cm
>
>
>
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontologforum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontologforum/
> Unsubscribe: mailto:ontologforumleave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgibin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontologforum@xxxxxxxxxxxxxxxx
>
> (04)

IHMC (850)434 8903 or (650)494 3973
40 South Alcaniz St. (850)202 4416 office
Pensacola (850)202 4440 fax
FL 32502 (850)291 0667 mobile
phayesATSIGNihmc.us http://www.ihmc.us/users/phayes (05)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontologforum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontologforum/
Unsubscribe: mailto:ontologforumleave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgibin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontologforum@xxxxxxxxxxxxxxxx (06)
