Category:Berry Paradox
This category contains pages concerning Berry Paradox:
Every number can be defined by a sentence in natural language.
For the purpose of this argument, let that natural language be English.
It is assumed without proof that English has a finite number of words.
Let $n$ be an integer such that $n \ge 15$.
Then the cardinality of the set of integers that can be defined in no more than $n$ words is finite.
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?
Source of Name
This entry was named for George Godfrey Berry.
Pages in category "Berry Paradox"
The following 3 pages are in this category, out of 3 total.