- At 07:47 PM 2/27/01 -0500, Chris Nash wrote:
> >Do any of you know the source of this theorem or a good

Like 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:

Berry's paradox:

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

contradiction.

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

originated.

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 the

The 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 Epimenides

Oh, 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....

David - 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!

anon.