Paradoxes

From the cool list of paradoxes on wikipedia:

• Raven paradox (or Hempel's Ravens): Observing a red apple increases the likelihood of all ravens being black.
• Unexpected hanging paradox: The day of the hanging will be a surprise, so it cannot happen at all, so it will be a surprise. The Bottle Imp paradox uses similar logic.
• Drinker paradox: In any non-empty pub, there is a customer such that, if he or she drinks, everybody in the pub drinks.
• Curry's paradox: "If this sentence is true, the world will end in a week."
• Epimenides paradox: A Cretan says "All Cretans are liars".
• Exception paradox: "If there is an exception to every rule, then every rule must have at least one exception, excepting this one" ...is there an exception to the rule that states that there is an exception to every rule?
• Fazzini paradox : I always lie.
• Liar paradox: "This sentence is false." This is the canonical self-referential paradox.
• Russell's paradox: Does the set of all those sets that do not contain themselves contain itself? Russell popularized it with the Barber paradox: The adult male barber who shaves all men who do not shave themselves, and no-one else.
• Shaynes Paradox: The following sentence is true. The previous sentence is false.
• Don't read this: There is no possible way to obey the statement because by the time the command is given to you it has already been contradicted.
• Drasin's Paradox: "Everything is biased. If you disagree with me, it is due to a bias of your own self."
• Ordering a servant not to serve you. By not serving you he disobeys the order, as he is obeying the order not to serve you.
• Ship of Theseus (a.k.a. George Washington's or Grandfather's old axe): When every component of the ship has been replaced at least once, is it still the same ship?
• Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement.
• Boy or Girl: If in a two-child family, one child is a boy, what is the probability that the other child is a girl?
• Sleeping Beauty problem: A probability problem that can be correctly answered as one half or one third depending on how the question is approached.
• Two-envelope paradox: You are given two indistinguishable envelopes and you are told one contains twice as much money as the other. You may open one envelope, examine its contents, and then, without opening the other, choose which envelope to take.

Robert Boyle's self-flowing flask fills itself in this diagram, but perpetual motion machines do not exist.

• Archimedes Paradox: A massive battleship can float in a few litres of water.
• Schrödinger's cat paradox: A quantum paradox - Is the cat alive or dead before we look?
• Epicurean paradox, or Problem of evil: The existence of evil seems to be incompatible with the existence of an omnipotent and caring God.
• Free will and omniscience paradox: If there is an omniscient being then it is impossible to have free will, for the omniscient being already knows what you are going to decide, therefore you can't decide because the decision has already been made.
• Grandfather paradox: You travel back in time and kill your grandfather before he meets your grandmother which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather.
• Hutton's Paradox: If asking oneself "Am I dreaming?" in a dream proves that one is, what does it prove in waking life?
• Paradox of thrift: If everyone saves more money during times of recession, then aggregate demand will fall and will in turn lower total savings in the population.
• Parrondo's paradox: It is possible to play two losing games alternately to eventually win.
• Productivity paradox, Solow computer paradox Worker productivity may go down, despite technological improvements...
• St. Petersburg paradox: People will only offer a modest fee for a reward of infinite value.
• Buttered cat paradox, a humorous example of a paradox from contradicting folk tales
• Impossible object
• Proof that 0.999... equals 1

More paradoxes.