Richard's Paradox

[jesternl]

(If nothing else, I like the name )

Clearly there are integers so huge they can't be described in fewer than 22 syllables. Put them all in a big pile and consider the smallest one. It's "the smallest integer that can't be described in fewer than 22 syllables."

That phrase has 21 syllables.

[Chuck]

If I make a list of all the integers that I claim are not describable in fewer than 22 syllables, you can then point to the lowest number on the list and claim that it is describable in fewer than 22 syllables. But then if I remove it from the list then that definition no longer describes it, so I have a number that's not describable in fewer than 22 syllables that's not on my list, so I have to put it back. Since the 21 syllable description cannot reliably identify this number, it is not a description of it, so it must be on the list of numbers that aren't describable in fewer than 22 syllables.

[CzarJ]

How much wood could a woodchuck, Chuck?

[Chuck]

All of it.

[Beartalon]

All integers can be described in two syllables: "Number."

[Chuck]

We want descriptions of individual integers so we can tell them apart.

[Beartalon]

Number one
Number two
Number three
...

[Poisonium]

[jesternl]

[Poisonium]

Not necessarily. As this is a paradox, there are many ways of understanding it, and I see it as though that you basically conclude they can be described in less than 22 syllables.


Say for example we have found the lowest 10 numbers that cannot be described in less than 22 syllables. We run the line "the smallest integer that can't be described in fewer than 22 syllables." on the lowest of them. That way we can cross that one out. Seeing as we have just described that one, the next number can also be described, and so on and so forth. But then again, it is a paradox, so there is no final solution.

PS: The actual name of this is "Berry's Paradox".[/spoiler]

[Bicho the Inhaler]