Every number can be defined by a sentence in natural language.
Let $n$ be an integer such that $n \ge 15$.
Consider the integer that is defined as:
- the smallest integer which cannot be defined by a sentence of at most fifteen words.
Let this number be $N$.
That is $N$ cannot be defined by a sentence of at most fifteen words.
But that very sentence itself has fifteen words.
So $N$ has been demonstrated to be definable in a fifteen-word sentence.
So: can it or can't it?
Also known as
Some sources cite this as Berry's paradox.
Source of Name
This entry was named for George Godfrey Berry.