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 [quote="L'lanmal"]I think it was covered with: [quote="jbvntx"][spoiler] Berry's Paradox is that the phrase "the smallest possible integer not definable in under eleven words" is a paradox. There are integers that take more than eleven words to define, [/spoiler][/quote] If the counting numbers are finite, then it wouldn't necessarily hold that [spoiler]There are integers that take more than eleven words to define[/spoiler] unless the number of integers was shown to be more than [spoiler]the number of things definable in ten words (or alternately 22 syllables).[/spoiler] This would resolve the paradox before it even got started, but is, erm, unlikely.[/quote]
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bonanova
Posted: Fri Nov 12, 2010 3:08 am    Post subject: 1

OK. I sometimes get things only on the 3rd or 4th reading and I appreciate people's forbearance on that. That's probably exactly equivalent to how I thought it through as I wrote the conversation, namely, that if "the smallest number that cannot be defined using fewer than 23 syllables" isn't 1,777,777 - or by extension any definable number, then that set has no smallest member, and by WOP must be empty. That leaves only the counting numbers that CAN be defined by fewer than 23 syllables - a finite set. Really? No - it's only a paradox.

This isn't the best puzzle I've ever written, but I enjoyed writing it, hoping it wasn't impossibly obscure. But I think that's impossible, in this forum.

I wonder whether the Russell quote was necessary...
L'lanmal
Posted: Thu Nov 11, 2010 11:09 pm    Post subject: 0

I think it was covered with:
jbvntx wrote:

Berry's Paradox is that the phrase "the smallest possible integer not definable in under eleven words" is a paradox. There are integers that take more than eleven words to define,

If the counting numbers are finite, then it wouldn't necessarily hold that There are integers that take more than eleven words to define unless the number of integers was shown to be more than the number of things definable in ten words (or alternately 22 syllables). This would resolve the paradox before it even got started, but is, erm, unlikely.
bonanova
Posted: Thu Nov 11, 2010 6:15 pm    Post subject: -1

Nice. Have we covered the finite counting numbers part?
Zag
Posted: Thu Nov 11, 2010 5:29 pm    Post subject: -2

L'lanmal wrote:
(What "and"s? There should only be an "and" if there is a decimal point or fraction.)

Just remember that the Brits can't spell, either.
L'lanmal
Posted: Thu Nov 11, 2010 3:45 pm    Post subject: -3

Ah, I was thinking letters, and couldn't figure out why not 1,373,373. Syllables should work.
(What "and"s? There should only be an "and" if there is a decimal point or fraction.)
jbvntx
Posted: Thu Nov 11, 2010 3:30 pm    Post subject: -4

I'm not sure I have it all. What I know is that ...

Berry's Paradox is that the phrase "the smallest possible integer not definable in under eleven words" is a paradox. There are integers that take more than eleven words to define, and so there must be a smallest one (well ordered principle, buried in your interview). But the phrase above only has ten words. So it's a paradox.

1,777,777 is the lowest number that takes at least 25 syllables to pronounce (I guess that must count the "and's").

I've no clue what 23-skidoo references. Unless it's the number of syllables to pronounce 1,777,777 without the "and's". Or a reference to the time period when Bertrand Russell and G.G. Berry were kicking about.

[/spoiler]
bonanova
Posted: Thu Nov 11, 2010 4:08 am    Post subject: -5

Indeed. Translate the rest?
jbvntx
Posted: Wed Nov 10, 2010 10:57 pm    Post subject: -6

Is Mr B. by chance... G. G. Berry?

bonanova
Posted: Wed Nov 10, 2010 4:45 pm    Post subject: -7

"The greatest challenge to any thinker is stating the problem in a way that will allow a solution."
bonanova
Posted: Tue Nov 09, 2010 4:32 am    Post subject: -8

Continuing the astoundingly brief CI series: See CI-1

Good evening Mr. B. What's the good word?
Thanks for inviting me. Here it is: 1,777,777

Excuse me, are you well ...
Ordered? Indeed. One more thing: the counting numbers are finite.

Really?
No.

Time for another question?
Sorry, 23 skidoo!