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You play a game with a fortune teller. There are two cards with the face down on the table; he wins if you raises the card's suit he foresees, you win if his prediction turns out to be wrong. Suppose he's a true clairvoyant and he knows which card you're going to pick. You know that the magician can't lie, and he says: «You're going to lift this one». Whichever card the clairvoyant will say that you'll pick, you'll pick the other one; therefore, the clairvoyant cannot correctly say to you which card you will pick – even if he wants to (or you are compelled to lose against your reason).

Edit: I found interesting similarities with the Newcomb Paradox

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    This isn't spelled out correctly. First you say "he wins if he raises the card he foresees" then you say "he knows which card you're going to lift." So, who is lifting the cards? Also, it isn't clear what you mean by choosing a card, do you mean he predicts which card, on the left or on the right, will be chosen? Or he predicts what will be on the face of the card that is chosen? – Not_Here Sep 12 '18 at 17:19
  • But, assuming a non problematic interpretation of your thought experiment, basically what you're asking is "if you know the future, you can do something to change the outcome, and then the future won't be what was predicted", correct? This is one of the oldest puzzles about time travel and fatalism and determinism. – Not_Here Sep 12 '18 at 17:21
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    A true clairvoyant will know not only what card you will pick but also how what they say will affect your action. So if they know saying "card A" will cause you to pick B, they wouldn't say it. Instead they should say "B", while knowing it will make you pick A. So maybe your argument shows that they can't say what you'll pick, but not that they can't know it. – Eliran Sep 12 '18 at 19:02
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    If the clairvoyant is required to tell you which card you're going to pick prior to picking it, and can't lie about it -- why then would he also be required to write it down on a hidden sheet of paper? – Bread Sep 12 '18 at 21:49
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    @Bread You're right, thank you, it's an useless detail, I edited the question. – Francesco D'Isa Sep 12 '18 at 22:02
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Your argument rests on an ambiguity in the word tell: an ambiguity between saying (as in telling a story) and knowing (as in telling the future).

So a valid version of your argument is:

Whichever card the clairvoyant will say that you'll pick, you'll pick the other one; therefore, the clairvoyant cannot correctly say to you which card you will pick.

But there is no paradox here, at least not in the sense that the clairvoyant cannot know what the future is (and thus not be a clairvoyant). All that has been shown is that they cannot truthfully say it to you. Saying is not a requirement for knowing. Perhaps it is a requirement for this type of game, in which case you've shown that it's an impossible one.

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  • Thank you, I corrected the word (I missed that nuance between say and tell). And you are right, there's no paradox, technically speaking: my astonishment was for that mysterious force that prevent the c. to tell the truth – Francesco D'Isa Sep 12 '18 at 19:42
  • Moreover, if you know that he can't tell the truth, you should always pick the other card. But this would made it true – Francesco D'Isa Sep 12 '18 at 19:53
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Nearly all of life's questions, and most of the suggested answers, can be found in science fiction movies.

Oracle: "I'd ask you to sit down, but, you're not going to anyway. And don't worry about the vase."

Neo: "What vase?" [Neo knocks over a vase of flowers, which shatters on the floor.]

Oracle: "That vase."

Neo: "I'm sorry..."

Oracle: "I said don't worry about it. I'll get one of my kids to fix it."

Neo: "How did you know?"

Oracle: "Ohh, what's really going to bake your noodle later on is, would you still have broken it if I hadn't said anything?"

There is no contradiction in predicting the future in certain circumstances. Certain things are deterministic. If you have adequate information you can predict certain things with great accuracy. This includes brain structure and activity within limits. The brain is a material structure that obeys physical laws.

Ordinarily it is difficult to get adequate information to make the sort of prediction your question implies. Even to get an edge where you could predict accurately enough to make some money would probably require some kind of brain scanning headgear, and a lot of practice and tuning of a very sophisticated model.

But to get it once is not a problem. Mentalist acts have many variations on this.

"LOOK! What's that over there!" (Switches cards.)

"What? What's over there?"

"I'll tell you later. But first, choose your card."

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  • yep, I forgot that one from Matrix, it fits well :) In the case of the vase by the way, it is fair to assume that Neo would have broken it anyway (or that the lady hated the vase). In the case of the game, the mentalist CAN'T say the truth even if he wants to. If he does, you'll change the card. A force prevent him to tell the truth? – Francesco D'Isa Sep 12 '18 at 19:38
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    @FrancescoD'Isa Whether or not he would have broken it anyways is a very interesting line of questioning. There was an obvious cause-and-effect between her saying "don't worry about the vase," and him looking around for a vase, which cased him to tip it over. Whether there was another world-line which lead him to knocking it over on his own is a fascinating question actually explored by real physicists in dealing with the Novikov Consistency Principle – Cort Ammon Sep 13 '18 at 15:38

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