‘What I am saying cannot be proved.’
Suppose this statement can be proved. Then what it says must be true. But it says it cannot be proved. If we assume it can be proved, we prove it cannot be proved. So our supposition that it was provable is wrong. With that road closed to us, let’s try the only other one available — let’s suppose it cannot be proved. Since that is precisely what it says, then it is true after all. And this ends our proof of the above statement!
— Gary Hayden and Michael Picard, This Book Does Not Exist, 2009