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Berry’s paradox

שו”תCategory: generalBerry’s paradox
asked 5 years ago

Hello Rabbi.

I started reading the first book in the trilogy. And it’s hard.
The rabbi probably knows the following sentence.
“The smallest whole number that cannot be expressed in fewer than twenty words”
For example, to pronounce 1, 100, 20, 100000, only one word is enough (one, one hundred, twenty, one million). On the other hand, 123 requires three words: “one hundred twenty-one.”
It can be assumed that there are numbers that require more than twenty words to express.
But in every group of integers there is a smallest number among them, and therefore the above expression, which is less than twenty words long, expresses a number that cannot be expressed in less than twenty words. This is a contradiction.
Therefore, the phrase “which cannot be expressed in less than twenty words” is meaningless or ill-defined.
And it seems to me that the phrase “something unimaginably great” is also meaningless, and therefore that priest’s argument is meaningless.

I would be happy to explain.


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0 Answers
מיכי Staff answered 5 years ago
Hello M. Regarding Berry’s paradox https://he.wikipedia.org/wiki/%D7%94%D7%A4%D7%A8%D7%93%D7%95%D7%A7%D7%A1_%D7%A9%D7%9C_%D7%91%D7%A8%D7%99 Indeed, this expression has no meaning because there is no such number. But you compare it to the expression “the most complete being imaginable,” and I see no reason for that. Unlike Berry’s expression (the smallest number that can be described in less than a hundred words), this expression does not lead to a paradox, and therefore I see no basis for your claim that it has no meaning. Anselm’s claim is that it leads by way of negation to the conclusion that this being exists. This is not a paradox but a proof by way of negation.

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