A fallacy is an incorrect result—in this case, one arrived at through misleading reasoning when examining a logical argument. One of the more common fallacies in logic is thinking incorrectly that if “p implies q” is true, “then q implies p” is also true. The idea of such invalid arguments was well-known in the past: With Greek mathematician Aristotle’s syllogisms, an argument was valid if it adhered to all the laws; to be false, it only needed to break one law. Euclid, another Greek mathematician, was known to have written an entire book on fallacies in geometry, but the book has since been lost.

English logician, philosopher, and mathematician Bertrand Russell came up with a puzzling paradox involving sets.