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I was just watching this video about reconciling free will and physical laws. The video begins with the following premises

  • It is possible for a human being to create a machine that, given the intial state of the universe, can predict the future state of the universe at any time, and present that future in a human-understandable form
  • A human could then read their own future and perform some action not predicted by the machine

This would then create a contradiction since the machine would then have incorrectly predicted the future. Since assuming both premises led to a contradiction, this must mean one of the premises was incorrect. This would seem to lead to the conclusion that either

  • It is impossible for humans to construct a machine to predict the future with perfect accuracy, or
  • Humans are incapable of making the choice to not follow the prediction

Both of these potential conclusions have very profound consequences, one annihilating the very concept of free will and the other placing fundamental limits on our capacity to understand the universe.

How has this paradox been addressed, and what are the canonical views of its implications?

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    Premise 1 is known to be false. The underlying idea (determinism) may still be valid, but it is hard to satisfactorily reconcile it with the most widely accepted interpretations of quantum physics. – Era Jun 13 '16 at 19:33
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    "It is possible for a human being to create a machine that, given the intial state of the universe, can predict the future state of the universe at any time," -- No it's not. Chaos and rounding errors make it impossible. In other words the universe might be completely deterministic yet totally unpredictable. As a striking example, we don't even know if the solar system is stable under deterministic Newtonian gravity. amazon.com/Newtons-Clock-Chaos-Solar-System/dp/0716727242 – user4894 Jun 13 '16 at 20:32
  • Premise 1 is false not just because of quantum indeterminacy, but because it implies an infinite regress. If you can simulate precisely the universe, the simulation itself contains a full simulation, which also contains a full simulation, et cetera. You can simulate a different, simpler universe, or part of a universe, but not the full. – kbelder Jun 27 '17 at 18:32
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How has this paradox been addressed, and what are the canonical views of its implications?

This paradox is directly addressed by mathematician David Wolpert, in a theorem named after him (Wolpert's theorem) and the answer is:

  • It is impossible for humans to construct a machine to predict the future with perfect accuracy,

More generally, it impossible for any sentient being (human, demon, super-AI,...) to perfectly predict events in a universe of which it is part of. To be able to perfectly predict future events in the universe, it has to do so from outside of that universe. The very fact that it is part of it (i.e. inside it) prevents it from performing such predictions.

Wolpert's result was published as a refutation of the idea of Laplace's demon: Laplace proposed that a demonic being with absolute knowledge of every particle's current position and current speed in the universe, should be able to infer all the past states and all of the future states of the universe from that information. Wolpert arrived at his results using a method similar to Turing's result with regards to undecidability and the limits of Turing machines. The result is also closely connected to Gödel's incompleteness theorem. Gödel proved that no theory can prove it's own consistency, and using a similar approach, Wolpert proved that no universe (an any intelligent inhabitants of that universe are considered part of it) can predict itself.

Note that Wolpert's result applies to any universe, regardless of the laws of physics that govern it - i.e. quantum mechanics, or relativity, etc...don't have anything to do with his result.

See here for Wolpert's original paper and for an article on his result.

As to whether this counts as "canonical" or not I don't know. As far as I know, Wolpert is the only person to address this issue directly. Most people consider that Quantum Mechanics puts an inherent limit on the predictability of the universe, regardless of whether humans are trying to predict anything in it or not, so the paradox you mention isn't of much interest to philosophers.

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The first premise is false because no such machine is conceivable, and the second premise is an unjustified assumption. The human may think that he can perform some action not predicted by such a machine (if it did exist), but how could he possibly know that? Whatever he chooses may be exactly what the computer predicted, thus resolving the paradox.

I also don't agree that it would annihilate free will. Just because you're predictable, doesn't mean that you are not free to follow the inclinations of your nature. On the contrary, true freedom is when your actions are fully determined by your own inclinations as opposed to some factor that operates in conflict with what you may have otherwise wanted. As Jonathan Edwards said:

"Now, who ever imagined such a liberty as this, a higher sort or degree of freedom, than a liberty of following one's own views and purposes and acting agreeable to his own inclinations and passions!" (Freedom of the Will)

That also implies that true freedom will at times entail that our actions will be characterized as being extremely predictable. When the most pressing matters arise, I believe that all of us would want to be found acting in conformity with our good character (assuming that we have such a thing). What parent, for example, wouldn't rush to help their child when in immediate need or danger?

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These conclusions do come from the idea that the computer has to be 100% correct, if it has some degree of improbability then it is conceivable that we change our future that the robot incorrectly foresaw. This is also under the axiom that the future is rectilinear, if it has a degree of flexibility then unknowable futures with the ability of some sort of future perception can be possible. Maybe.

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