Q&A: The Berry Paradox
The Berry Paradox
Question
Hello Rabbi.
I started reading the first book in the trilogy. And it’s difficult.
The Rabbi surely knows the following sentence:
“the smallest positive integer not definable in fewer than twenty words”
For example, to express 1, 100, 20, 100000, a single word is enough (one, one hundred, twenty, million). By contrast, 123 requires three words: “one hundred twenty-three.”
One can assume that there are numbers that require more than twenty words to express.
But in every set of integers there is a smallest number, so the sentence above, whose length is fewer than twenty words, expresses a number that cannot be expressed in fewer than twenty words. And that is a contradiction.
Therefore the expression “that cannot be expressed in fewer than twenty words” is meaningless or not well-defined.
And it seems to me that the expression “a greatest being that cannot be conceived” is also meaningless, and therefore that priest’s argument is meaningless too.
I would be happy for an explanation
Answer
Hello M.,
Regarding the Berry 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, that expression has no meaning, because there is no such number. But you compare it to the expression “the most perfect being that can be conceived,” and I do not see any justification for that. Unlike Berry’s expression (the smallest number describable in fewer than a hundred words), that expression does not lead to a paradox, so I do not see any basis for your claim that it has no meaning. Anselm’s claim is that by way of reductio he arrives at the conclusion that this being exists. That is not a paradox but a proof by contradiction.