Question

As strange as it may seem, it is possible to give a precise-looking verbal definition of an integer that, in fact, is not a definition at all. The following was devised by an English librarian, G. G. Berry, and reported by Bertrand Russell. Explain how it leads to a contradiction. Let $n$ be “the smallest integer not describable in fewer than $12$ English words.” (Note that the total number of strings consisting of $11$ or fewer English words is finite.)
Worth 10 points.
YOUR ANSWER MUST BE UNIQUE

Answer 1

The statements hold the contradiction, just by confusion in keep meaning of statements and get confused with "12" which is string in quotes

Let  be “the smallest integer not describable in fewer than  English words.” (Note that the total number of strings consisting of  or fewer English words is finite.)

What do you mean by contradiction?
Contradiction means that couple of statements that opposes each other.

Here,
The statement says let n be  “the smallest integer not describable in fewer than  English words.” which implies that n is connected with string mentioned in "" quotes, which is not a definition but contain 11 words in the quotes.
and another statement -  Note that the total number of strings consisting 11  or fewer English words is finite which implies that:
the limit of words inside the quotes ≤ 11 words

Thus, strings implies in quotes is simple meaning with 11 word in it
While in statement in brackets implies the limit of words as a string should be ≤ 11. the string "12" create the contradiction in minds.

Learn more about contradiction here:
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