Forums → The Tavern → Paradoxes

I've been getting into paradoxes lately, to be honest they're pretty awesome.

If anyone is confused, a paradox is "

a statement or group of statements that leads to a contradiction or a situation which (if true) defies logic or reason, similar to circular reasoning.

" (wiki)

A paradox I heard awhile ago is one about a man and a turtle racing, AKA Achilles and the tortoise.

"

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.

" (wiki)

Another one that has been grabbing for my attention as of recently is Newcomb's Paradox.

"

A person is playing a game operated by the Predictor, an entity somehow presented as being exceptionally skilled at predicting people's actions. The exact nature of the Predictor varies between retellings of the paradox. Some assume that the character always has a reputation for being completely infallible and incapable of error; others assume that the predictor has a very low error rate. The Predictor can be presented as a psychic, as a superintelligent alien, as a deity, as a brain-scanning computer, etc. However, the original discussion by Nozick says only that the Predictor's predictions are "almost certainly" correct, and also specifies that "what you actually decide to do is not part of the explanation of why he made the prediction he made". With this original version of the problem, some of the discussion below is inapplicable.
The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000.
By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.

" (wiki)

At first when I saw this I thought that for sure the best way to go was to take both boxes. The Predictor, or "Supreme Being" is how I knew it, already made his choice! He can't go back now! Certainly if he predicted you to take box B and you took both you would have $1,001,000! If you took just box B you would have only $1,000,000! Same for if he thought you would take both. You still would have $1000 instead of zero!

Later my mind went into some conflicting arguments, which I tell you was not helped by advice from outside sources. Pretty soon my view changed and I thought taking only B was the way to go. Why waste a whole million dollars on just a thousand! It wouldn't be worth the risk taking both. If the Supreme Being is infallible then I'd better get the million I deserve.

My stance is basically indifferent for both sides now, but it still shifts to one direction every now and then.

The wiki article in which I got the paradox from actually is really enthralling as well. This stuff is deep, man.

Ah I could go on and on...

Anyhoo, I guess in this thread discuss paradoxes, share your own and also your views on such paradoxes.