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Did anyone offer an argument against the possibility of a perfect and complete prediction about a system from within that system along the following lines:

Let's imagine a machine (like a desktop computer) that had access to all of the information about a system (a universe, for the sake of argument) and knew all the physical rules governing that universe. Suppose it could make a perfect and complete prediction about the future of the universe and print it out on its screen. Consider a person sitting at that computer. To make a perfect and complete prediction, the computer would have to predict what that person would do in the future. But to do that, to predict what the person would do the moment after the computer's own prediction were to flash on the screen, the computer would have to know the output of its own prediction. In other words, it could not finish its prediction until it knew its prediction, which is impossible. More generally, if the machine's prediction were to exist in the future of the system in any consequential way, the machine would have to take its prediction into account in the creation of its prediction (I'll assume that to exist inconsequentially is impossible). Therefore, by contradiction, such a machine is impossible; a perfect and complete prediction about a system cannot be made from within that system.

Another way to think about this intuitively: whatever the computer printed out, the person could do something different. If the computer said "person will not shift in her seat in the next 5 seconds," the person could easily just shift in her seat to spite the machine.

Could such an argument be a reflection of the unmeasurability of the universe, as explained in this post? It seems unlikely to me, since this argument does not deal with any quantum mechanical properties; it seems unlikely that the source of the logical impossibility of such a theoretical device comes from the quantum mechanical properties of our universe (this could theoretically be some different universe, with different properties... I'm assuming? I am no quantum physicist so I don't know).

Could this instead be a reflection of something like Godel's incompleteness theorems (I say 'something like' because I don't want to be accused of carrying out one of the uncountably many terrible arguments that cite these theorems): some limitation that made it impossible for a set of physical rules to exist such that everything in that universe could be predicted, even with perfect and complete information?

Is such an argument sound? If so, why is such a machine logically impossible and does this have any relation to known logical/mathematical/scientific theorems or does it have any significant implications?

  • I will not vote since my votes are binding, but the review/evaluation of original work is generally considered to be off-topic here. You are free to discuss this in chat, though. – Philip Klöcking Jul 12 at 19:51
  • Is this original? If so, is there a stack exchange site that would be better suited for this question? Or should I post it on a different website altogether, like Quora or something? – Murey Tasroc Jul 12 at 20:05
  • Let me put it that bluntly: If you ask whether your argument is sound and valid, this is asking for review of your own thought, while if you ask whether an argument to that effect has been discussed in philosophy and where you could read about it, that's a reference-request and perfectly on topic – Philip Klöcking Jul 12 at 20:34
  • Well I guess I was making a reference request but also asking if the argument is even valid... is it really off topic to ask for argument validation/feedback? If so, why? It doesn't seem counterproductive to me... I will delete this question if it does really violate the rules. – Murey Tasroc Jul 12 at 21:10
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    I think what one might correctly say is that even if determinism is correct, while a third party could predict my decisions, they could not present me with this prediction in a way that I would be bound to accept it. Nor could I predict my own decisions in a way that I would be bound to accept them. There is an interesting paper on this subject from 1960. It might be behind a paywall, but have a look at D. MacKay, "On the Logical Indeterminacy of a Free Choice" Mind, Vol 59, No. 273, 1960, pp 31-40. – Bumble Jul 13 at 5:14
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I will interpret the question as suggested by Philip: whether an argument to this effect has been discussed in philosophy. It was. A philosophizing mathematician/computer scientist/physicist David Wolpert formalized just such an argument in Physical limits of inference. Wolpert formalizes measurement, observation of a phenomenon, memory of past information and prediction of a future state in terms of inference devices that are independent of the laws of physics. A yes/no question must be posed to such a device, and, based on whatever apparatus it has at its disposal, it provides an answer. There are no limits on the computational power of the device, but it must be "within" the universe it makes the predictions about, in a precise sense. As the OP suggests, the proof is a version of the Godel's incompleteness argument.

A popular exposition, without mathematical technicalities, is given by Scientific American under a catchy title Within Any Possible Universe, No Intellect Can Ever Know It All:

"Wolpert proves that in any such system of universes, quantities exist that cannot be ascertained by any inference device inside the system. Thus, the “demon” hypothesized by Pierre-Simon Laplace in the early 1800s (give the demon the exact positions and velocities of every particle in the universe, and it will compute the future state of the universe) is stymied if the demon must be a part of the universe...

The theorem’s proof, similar to the results of Gödel’s incompleteness theorem and Turing’s halting problem, relies on a variant of the liar’s paradox—ask Laplace’s demon to predict the following yes/no fact about the future state of the universe: “Will the universe not be one in which your answer to this question is yes?” For the demon, seeking a true yes/no answer is like trying to determine the truth of “This statement is false.” Knowing the exact current state of the entire universe, knowing all the laws governing the universe and having unlimited computing power is no help to the demon in saying truthfully what its answer will be.

The proof is mathematically impeccable, but there is a catch, already discussed in austinlorenz's answer to Have David Wolpert's findings really “slammed the door” on scientific determinism? The "within" stipulation turns out to be a way of allowing self-reference, and the "question" is no more meaningful than the Liar sentence with the question mark at the end. There is a state of the universe that an inference device cannot predict, yes, because the answers it is designed to give can not also be their negations.

There is an alternative interpretation of the OP question suggested by the remark "whatever the computer printed out, the person could do something different". This is more or less the key ingredient of libertarian free will: the freedom to do otherwise in identical circumstances. Whatever else it means or entails, it certainly entails indeterminism. And if we stipulate indeterminism we can certainly infer it: no accurate prediction is possible by stipulation. But the contrapositive is equally valid: if we do not assume indeterminism then determinism is not ruled out, and accurate prediction is possible.

This is similar to Novikov's self-consistency principle for time travelers: one can go to the past as long as the present already incorporates what they "caused" there. In a popular illustration, a time traveler, who went to the past to kill her own grandfather, slips on a banana peel strategically "placed" by the deterministic universe at the critical moment, and fails.

This is why the inside/outside distinction (we can only do otherwise if we "know" the prediction) either does not work, or introduces the same sort of circularity as in Wolpert's argument. It is not that the prediction has to stay idle, and not "cause" anything "inside", in which case it will be "outside". It can "cause" things around at leisure, the point is that all of its "causing" is incorporated into what it predicted anyway. There is no need to "know" it, or refrain from acting on such knowledge, the only question is whether the universe is deterministic or not. If it is indeterministic the impossibility conclusion is baked into the premise. And in a deterministic universe things will happen the predicted way regardless: trying to make it not happen will cause it to happen.

Finally, there is a valid argument in the vicinity along the lines of computational complexity. There are pseudorandom sequences so "unpredictable" that any way of generating them is as complex as listing the terms one by one. If we assume that "within a system" means a limitation on computational capacity, and the universe evolves along such a sequence, there is no way to predict its evolution other than to wait and see it play out. If any simulation would take just as long then there is no way of predicting an outcome in advance of it happening.

  • The first half was exactly what I was looking for, and that last paragraph is very interesting. Thank you. I do want to press further on your point that "whatever the computer printed out, the person could do differently" implies free will. This only conflicts with determinism if we assume the computer's printout is a perfect and complete prediction (which I was arguing could not be made). For any prediction made could be disobeyed, and thus could not be perfect and complete. I think this is a different version of the argument made in the quote (and of that demon proof). – Murey Tasroc Jul 13 at 19:03
  • Say the machine said that someone was going to eat a bagel in 10 hours. I find it far fetched that, even if that person avoided bagels at all cost, they would be forced to eat the bagel somehow. The only reason why determinism is believable is because one does not know their destiny -- we think we have free will because we make decisions all the time in everyday life. Determinists think that these decisions have already decided. Even if you switch your decision, it has already been decided that you would do that. If you are told your destiny, however, you could easily do differently. – Murey Tasroc Jul 13 at 19:07
  • So even in a deterministic world, it is impossible to tell someone their destiny (that is an implication of the above argument) – Murey Tasroc Jul 13 at 19:08
  • @MureyTasroc I am afraid people's confidence in their ability to do otherwise is generally misplaced. There are many experiments where people report intention to do something only after automatic mechanisms are already in the process of doing it, in other words they fabricate the "intention". This does not mean that this is always the case, and we do not have such an ability, but it does mean that our reasons for believing we do are no good. It is not at all far fetched that a person fulfills their "destiny" absent mindedly, or are induced/coerced into it, whether they are told it or not. – Conifold Jul 15 at 19:13

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