I recently read an article describing how mathematician/physicist David Wolpert's research closed the door on scientific determinism. I have huge doubts about the implied conclusion, considering the fact that a result like this would have significant implications philosophically, but I haven't seen his work discussed in philosophical circles (Wolpert first demonstrated this in 2008). His work is also cited in the Wikipedia entry for "Laplace's Demon."

If anything, I could see this result as having implications for the epistemology of determinism, as we might never be able to "know" that the world was indeed deterministic. But that is completely independent of whether or not the universe is ontologically deterministic. I'll mention that I am a strong proponent of causal determinism. Indeed I think true randomness is utterly absurd, as it would be almost akin to magic.

If anyone has any input on whether or not this result actually demonstrates that the world can't be deterministic, I'd be happy to listen and further question my own worldview. But at first blush I am taking this to be a wild exaggeration. I will crosspost this to the physics and mathematics stack-exchanges as well (in consideration of Wolpert's background).

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    Ontological determinism has been obsolete already at the time of Laplace, As Poisson already knew in 1806, to get determinism even in classical mechanics one needs technical assumptions, that are not met by the gravitational force among others conferences.phs.uoa.gr/andhps/Files/Abstracts/van%20Strien.pdf General relativity is notoriously indeterministic plato.stanford.edu/entries/determinism-causal/#GenRelGTR, and in a different way so is quantum field theory. While determinism can not be "refuted" the reasons that suggested it in the first place proved to be fallacious.
    – Conifold
    Aug 2, 2015 at 22:47
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    @Pete1187 cross-posting is largely disallowed. If you feel the need to post similar questions, then you should vary them sufficiently to avoid cross-posting. See meta.stackexchange.com/questions/64068/…
    – virmaior
    Aug 2, 2015 at 23:23
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    @Conifold I'm not convinced at all by Norton's dome or the "Hole" and singularity objections to determinism in General Relativity, which I remember being discussed at length back in the undergrad years in Philosophy of Physics. In addition, there are several different interpretations of quantum mechanics that are fully deterministic, so I'm very surprised to hear you say "ontological determinism has been obsolete..at the time of Laplace." The fact that you make that assertion with certainty is pretty striking.
    – Pete1187
    Aug 3, 2015 at 4:57
  • @virmaior Thanks for letting me know. I have kept the question to this forum for now
    – Pete1187
    Aug 3, 2015 at 4:57
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    Objections are made to established doctrines, but physical theories were used by mechanistic philosophy to establish Laplacian determinism as "supported by science" in the first place. It is clearly not the case anymore (even Bohmian and many worlds interpretations of QM are so far inconsistent with QFT), determinism is useless in biology and other sciences even as a structural principle, and it creates all sorts of unnecessary problems in ethics (free will, responsibility, etc.). Determinism can certainly be "saved" with various contrivances, but there is simply no point to it anymore.
    – Conifold
    Aug 3, 2015 at 17:14

2 Answers 2


The idea of the proof is simple: assume we have a prediction device which answers "yes or no" questions, then show that there is a Boolean function of the state of the universe that the prediction device cannot predict.

What is this function? It is the negation of the answer given by the prediction device! This is considered a function of the state of the universe because the prediction device exists within the universe. Stripped of all its complex notation and jargon, the proof is a restatement of a logic puzzle: if there is a computer that gives "yes or no" answers and knows everything, what question can you ask that it will not be able to answer?

"Will your answer to this question be 'no'?"

Does this really refute determinism?

Wolpert's model of a prediction device is defined as a pair C of functions (X,Y) with domain the possible wordlines (in philosophy jargon, nomologically possible worlds) u of the Universe U, where X is the 'setup function' (with no codomain defined in the paper) and Y is the 'answer functon' with codomain {0,1}. The setup function X maps to initial states of the prediction device--X(u) is the initial state of the prediction device in the worldline u of the Universe, including its input.

Then the proof simply shows that the device C = (X,Y) cannot predict the function ~Y: whenever Y(u)=1, ~Y(u)=0, and obversely.

Note that there is no dependence of the answer function on the setup function. For distinct answer functions Y, Y', prediction devices with identical setups C=(X,Y) and C'=(X,Y') give different answers. To prove non-determinism, Wolpert has assumed non-determinism!

This has the strange consequence that if we built a machine C = (X,Y), and found that there were a function of the universe ~Y that our machine could not predict, there would be a machine C' = (X,~Y), physically indistinguishable in its initial state from C in all possible worlds (since the setup function is the same) which predicted the "unpredictable" function ~Y perfectly!

To remove this circularity, could we use this argument as a reductio, i.e., assume determinism, so that any machines with distinct answer functions Y, Y' must have distinct setup functions, and then derive a contradiction from the assumption that some machine predicts the negation of its answer function? No: the argument becomes completely trivial--of course the machine (X,Y) doesn't predict the function ~Y, because our assumption of determinism implies that for each u, the initial state X(u) determines the output Y(u).

In other words, if Y is not determined by X, then although it is trivial that a machine with answer function Y cannot predict the function ~Y, we can at least claim that "No matter how the device is set up, there is a function of the state of the universe it cannot predict"--as Wolpert says in the paper, even if the device is given the correct answer in its input, it cannot predict the output of the function correctly. This sounds impressive, until we realize that this is because we've already assumed non-determinism.

But if we assume that the initial state of the device determines its output, then the proof result reduces to "If a machine is set up to output some values, then the values it is set up to output are not equal to the negation of these values."

We have either circularity or triviality.

The door to determinism remains open.


The article did not say much that is new. The idea that science can define what is ontologically true has always been a faith belief, just like everything which claims to be able to make ontological claims of truth or falsehood. Combine this with quantum physics, which challenges determinism naturally, and it is natural to see the claims he makes. I can only assume that his actual work is more profound than this article makes it seem.

It seems his biggest issue is that there must be some limit on omnipotent, omniscient deities a. la. Abrahamic tradition. This sort of issue has been known for centuries, at least as far back as the first time someone asked "Can God create a rock so heavy even he cannot lift it." He seems to have simply come across a new one.

I think the big thing he is trying to point out is that, if we assume all of reality is modeled with these "inference engines," that we have to be ready for science to fail to describe at least 1 bit of state in the universe, for no reason other than our current science finds itself naturally organized into inference engine notations.

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    I think there is a misunderstanding of his conclusion - it requires the entity to exist as a part of the universe. Therefore we humans, being a part of the universe, cannot know the state of everything in the universe, and therefore cannot definitively prove determinism. The "deity" of the Abrahamic tradition, is understood to exist outside of our reality/universe, and therefore would not be affected by Wolpert's proof.
    – LightCC
    Dec 27, 2015 at 20:05
  • @LightCC That seems like a reasonable line of thinking that is rational and consistent with the general direction the author's math goes, but I do not believe the article suggests in the slightest that that's actually what the author is saying. In fact, there's textual evidence to suggest the exact opposite. Consider the final line of the conclusion, "Deism is allowed, he says, but not the traditional Abrahamic God." It's pretty hard to believe that would be the conclusion if the intended conclusion was "Abrahamic Gods are totally admissible because they're not included in the proof."
    – Cort Ammon
    Dec 27, 2015 at 20:18
  • (I actually prefer the direction you took it, myself. I think Wolpert is narrowing his focus more than is absolutely necessary)
    – Cort Ammon
    Dec 27, 2015 at 20:19
  • Sorry Cort, I missed the article link, I was going off of this article from Scientific American (5th paragraph): scientificamerican.com/article/limits-on-human-comprehension. Reading the Wolpert quote it's obvious he is limiting God to naturalistic investigation only (no supernatural powers to affect anything outside the laws of nature). He may be a good mathematician, looks to be sketchy on the philosophy side, and is definitely not a very good theologian.
    – LightCC
    Dec 27, 2015 at 20:26
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    @LightCC Ah, that makes sense. Personally, I find it to be great fun to dive into a strict mathematical system (like Wolpert's), and then say "what if this is not everything? What if there's something more? What would that something have to look like in scenario A or class of scenarios B"
    – Cort Ammon
    Dec 27, 2015 at 20:50

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