Gödel's Second Incompleteness Theorem...

… Explained in Words of One Syllable, by George Boolos (not Boole).

If it could be proved that two plus two is five, then it could be proved that five is not five, and then there would be no claim that could not be proved, and math would be a lot of bunk. If you’ve got access to JSTOR or Mind you can get the second section: “I wish he would explain his explanation”.