Paradox Theorems

By in Bizaare, Confusing, Paranormal

This is some of the craziest stuff you will ever try get your head around. Sam showed a couple of these to me a while back, and they’re just insane.

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Curry’s paradox: “If this sentence is true, the world will end in a week.”

Epimenides paradox: A Cretan says “All Cretans are liars”. Are all Cretans, therefore liars?

Exception paradox: “If there is an exception to every rule, then every rule must have at least one exception, the exception to this one being that it has no exception.”

Grelling-Nelson paradox: Is the word “heterological”, meaning “not applicable to itself,” a heterological word?

Intentionally blank page: Many documents contain pages on which the text “This page is intentionally blank” is printed, thereby making the page not blank.

Liar paradox: “This sentence is false.” This is the canonical self-referential paradox. Also “Is the answer to this question no?”

Petronius’ paradox: “Moderation in all things, including moderation.”

Quine’s paradox: “yields a falsehood when appended to its own quotation” yields a falsehood when appended to its own quotation.

Paradox of the Court: A law student agrees to pay his teacher after winning his first case. The teacher then sues the student (who has not yet won a case) for payment.

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.

Zeno’s paradoxes: “You will never reach point B from point A as you must always get half-way there, and half of the half, and half of that half, and so on….” (This is also a physical paradox.)

Fitch’s paradox: If all truths are knowable, then all truths must in fact be known.

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?

Nihilist paradox: If truth does not exist, the statement “truth does not exist” is a truth, thereby proving itself incorrect.

Omnipotence paradox: Can an omnipotent being create a rock too heavy to lift?

Paradox of hedonism: In seeking happiness, one does not find happiness.

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.

Raven paradox (or Hempel’s Ravens): Observing a green apple increases the likelihood of all ravens being black. http://en.wikipedia.org/wiki/Raven_paradox

Horse paradox: All horses are the same color. http://en.wikipedia.org/wiki/All_horses_are_the_same_color

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By the way, if you ever get asked the omnipotent paradox “Can an omnipotent being (namely God) create a stone too heavy for Him to lift?”, C.S. Lewis has a very well worded retort for it.

C.S. Lewis in his book “The Problem of Pain” holds that the nature of the paradox is internal to the statement. To quote: “This is no limit to His power. If you choose to say God can give a creature free will and at the same time withhold free will from it’, you have not succeeded in saying anything about God: meaningless combination of words do not suddenly acquire meaning simply because we prefix to them to other words ‘God can’” (p. 18). In the end, “not because His power meets an obstacle, but because nonsense remains nonsense even when we talk it about God”.


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