Re: [PrimeNumbers] A classic [s]p[r]oof; Answered.
- At 07:47 PM 2/27/01 -0500, Chris Nash wrote:
> >Do any of you know the source of this theorem or a goodLike Chris, I thought these were rather old, but I spent some time in
> >reference that discusses the error in the proof?
>It is indeed classical, and probably goes back a long long way (long
>before Russell's formulation). These sort of self-referential
the library and it turns out that perhaps they are not. The "originator"
seems to be G. G. Berry of the Bodleian library who wrote the
paradox (in a messier form) to Russel 21 December 1904. So this
indeed came after the big set of all sets paradox (and the largest
cardinal paradox, Richard's least undifinable cardnal paradox and
the rest). Russel was the first to publish it in 1906 (Berry never
did). In 1908 Russel published it in this simplified form:
Hence "the least integer not nameable in fewer
than nineteen syllables" must denote a definite
integer; in fact, it denotes 111,777. But "the
least integer not nameable in fewer than
nineteen syllables" is itself a name consisting
of eighteen syllables; hence the least integer
not nameable in fewer than nineteen syllables
can be named in eighteen syllables, which is a
Berry introduced himself to Russell with a card that on one side
said "the statement on the other side of this card is false" and
on the other side said "the statement on the other side of this
card is true"--another (now) well known paradox that he also
Berry's paradox is not isomorphic to the Curios (or interesting)
paradox, but looks to me like the forerunner.
>statements get a lot of treatment in G\"odel, and so the "error in theThe Berry type of paradox is a "semantic paradox," and unlike
>proof" is that incompleteness allows us to construct the statement in
>the first place.
Russell's set of all sets and the various diagonal arguments
(Richards, G\"odel, ...) in that they can not be directly
expressed within logic. And indeed forms of them are old
(so the Chris' weren't completely off base!) The first is
perhaps Epimenides the Cretan's all Cretan's are liars...
- Chris Caldwell wrote:
> The first is perhaps EpimenidesOh, I bet long before some hunter-gather's grunted along
these lines round a fire:
Ugg: Caught summat?
Glugg: Two no-names!
Can't see that the curios thing is much different from
the self-contradictory "Anon" appended to a pome....
- At 01:35 AM 3/7/01 +0000, d.broadhurst@... wrote:
>Chris Caldwell wrote:No doubt. But my context is simpler, I was looking for references;
> > The first is perhaps Epimenides
>Oh, I bet long before some hunter-gather's grunted along
>these lines round a fire:
and the first seems to be Epimenides. But I'd be glad to reference
the hunter gatherers if you know of a cave wall I can cite!