What is a Paradox?

A paradox is an argument that seems contradictory and doesn't seem to make sense within logic or common sense. Paradoxes are known to be invalid arguments but are still valuable ideas of which to be thought about. Some have revealed errors in existing logic and have caused the rules of logic to be rewritten.

Examples:

Logic:

Crocodile dilemma: If a crocodile steals a child and promises its return if the father can correctly guess what the crocodile will do, how should the crocodile respond in the case that the father correctly guesses that the child will not be returned?

Catch-22 : A situation in which someone is in need of something that can only be had by not being in need of it.

Self Reference:

Socratic paradox: "I know that I know nothing at all."

Vagueness:

Sorites paradox: One grain of sand is not a heap. If you don't have a heap, then adding only one grain of sand won't give you a heap. Then no number of grains of sand will make a heap. Similarly, one hair can't make the difference between being bald and not being bald. But then if you remove one hair at a time, you will never become bald. Also similar, one dollar will not make you rich, so if you keep this up, one dollar at a time, you will never become rich.