The tagged items are about paradoxes in general. Individual paradoxes described below may have their own individual tags.

Achilles and the tortoise

One of Zeno's paradoxes.

Achilles and the tortoise have a race. Achilles gives the tortoise a head start. Now, in order for Achilles to overtake the tortoise. he must first reach the point the tortoise was at when he began running. But, by that time, the tortoise has already moved ahead, so Achilles must now reach that point, which the tortoise has again surpassed. Thus, Achilles can never overtake the tortoise.

The arrow paradox

One of Zeno's paradoxes.

Since at any given instant, an arrow is in a particular location, it is never moving in any instant. Therefore motion is impossible.

The Berry paradox

As Russell puts it:

The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111,777. But "the least integer not nameable in fewer than nineteen syllables " is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. (Russell, 1908, p. 223)

Russell says that this contradiction "was suggested to me by Mr. G. G. Berry of the Bodleian Library."

The birthday problem

In a group of 23 people, the odds are better than even that two people share a birthday.

The Bottle Imp paradox

AKA Stevenson's Bottle.

Robert Louis Stevenson's 1891 story The Bottle Imp posits a bottle containing an imp that grants wishes. The bottle can only be sold to another at a loss, and if you die while owning it, you go to hell. The paradox is that no one should be willing to buy it for a penny, and knowing this, no one should be willing to buy it for two cents, either. By induction, no one should be willing to buy it for any price, although intuitively we feel like if the price is high enough, it should be safer to buy.


The obvious explanation is that people aren't totally rational, and people know this, so it's not irrational to expect that one might find a buyer. It occurs to me that the line of reasoning could be something like "if I buy the bottle, then it's likely that others will similarly take the risk, so it's a safe buy", or on the other hand "if I won't buy the bottle, then it's likely that others also won't, so it isn't safe to buy". Treating your own (potential, future) actions as evidence for the state of the world, and so choosing your actions based on the state you want to believe the world to be in, is akin to some variations on Newcomb's problem.

The Epimenides paradox

AKA the Liar paradox.

  • Hofstadter (1981/1985) uses this paradox as inspiration for talking about self-referential sentences.

Hempel's paradox

Also known as the raven paradox or Hempel's ravens.

If seeing a black raven supports the claim that all ravens are black, then so does seeing any non-black non-raven, such as a white shoe.

Newcomb's problem

There are two boxes, A and B. Box A contains a thousand dollars. Box B contains either a million dollars or nothing. You can take either both boxes, or just box B. The catch is that box B contains a million dollars only if a very accurate predictor has predicted that you will take box B alone. What do you do?


Hofstadter, D. R. (1985). On Self-Referential Sentences. In Metamagical Themas: Questing for the Essence of Mind and Pattern (pp. 5–24). Basic Books. (Original work published 1981)
Russell, B. (1908). Mathematical Logic as Based on the Theory of Types. American Journal of Mathematics, 30(3), 222–262.
Title Type Date Platform Names Characters Series
Paradoxes Book 2011 Marek Gensler, Piotr Łukowski