A thought experiment involving a game between two players, one of whom purports to be able to predict the future. The first player has to try to maximize winnings by choosing one of two boxes of money; however, the amount won also depends on whether a prediction made about the choice by the other player proves to be true.

Alternative form of twin paradox

The phenomenon of an arrow travelling in the direction where it points when the bow is fully drawn, when it seems that the arrow would have to pass through its original position. The explanation relates to the bending of the arrow when released.

plural of paradoxical frog

(biology) The apparent paradox that additive genetic variation is maintained despite persistent female choice for particular male traits.

(linguistics) The apparent paradox that children learning English encounter many sentences amenable to dative shift (e.g. "give the book to me" → "give me the book") but apparently have no way to learn that this is not possible with certain verbs (e.g. "*donate me the book" is unacceptable), and yet rarely make this kind of error.

(economics) The apparently paradoxical observation that people's reported happiness varies directly with income both among and within nations, but over time happiness does not trend upward as income continues to grow.

plural of paradox of fiction

(philosophy) The paradox that (i) people have emotional responses to fictitious events, and (ii) one must believe that something truly exists in order to be emotionally moved by it, but (iii) nobody who considers an event to be fictitious can also believe it to be real.

(set theory) A demonstration of a surprising property of infinite sets. Some positive integers are squares while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares; yet for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other.