You have just been captured spying on a student council meeting, and you face dreadful consequences. You are told: “You may make one statement. If it is true, you will be dumped into a trash can in the cafeteria during the second lunch hour. If it is false, you will hang by your feet from the home basketball net during halftime of the varsity game this weekend.” What can your statement be so that you can save yourself from both of these terrifying fates?
To escape both consequences, you need a statement that cannot be labeled as either true or false. How about:
“This statement is false.”
If the statement is true, then it’s false; if the statement is false, then it’s true. So it is neither true nor false.