# Have David Wolpert's findings really “slammed the door” on scientific determinism?

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.

• Might Philosophy be better suited for this philosophy question? Oct 14 '15 at 19:43
• I'm not really clear what the question here is aside from "Do you think the universe is deterministic?", which is both too broad and primarily opinion-based since neither determinism nor non-determinism as such can ever be falsified, only specific theories can. Oct 14 '15 at 20:18
• @ACuriousMind The question is whether a particular researcher's work conclusively showed the universe is non deterministic. And the answer is not opinion based. The answer is an objective no the researcher did not show that. And the reason is because it isn't possible to show that. And the researcher just assumed an infinite universe too, another unfalsifiable claim. Oct 14 '15 at 20:28
• You can have whatever answer you want, by picking an appropriate definition of "determinism." A pretty popular definition of determinism is that determinism holds if Cauchy surfaces exist and we have the relevant wave equations (Maxwell's equations, Schrodinger equation, ...). By this definition, the answer is yes: determinism can hold (in spacetimes that have Cauchy surfaces), and it almost certainly does hold for our actual universe.
– user4552
Mar 7 '18 at 0:00

## 3 Answers

any input on whether or not this result actually demonstrates that the world can't be deterministic,

The universe can be deterministic. Full stop. And there can't be a way to show it isn't, since the determinism can itself apply to the methods you use to test it. So you shouldn't get super excited about the universe being deterministic if it is unfalsifiable.

You shouldn't get super excited about it not being deterministic either since there can't be evidence of that either.

Instead you can make much more precise theories that can be tested.

• I'm inclined to agree that determinism in general (like naturalism) is a basic axiom of science, and thus is neither a hypothesis nor falsifiable. Mar 7 '18 at 3:43

"Indeed I think true randomness is utterly absurd, as it would be almost akin to magic."

It is actually very easy to show that even on a world described by classical physics, you can have inherent randomness in the outcomes that you, as an observer, perceive

In this hypothetical classical world with no quantum uncertainty, there is teleportation technology that makes exact copies of humans by measuring the exact position of every atom in the body. For some of the discussion on the Teleporter's paradox, you can read this.

In this case, if you set up a simple experiment where you are going to be teleported to two different places rather than one, after the teleportation process is done, you will have an inherent random event in your personal account of the events; you either got teleported to place A, or either to place B

The fact that both place A and place B have a copy of you recovers a sort of ontological determinism to the events, but your perception of the events will not be able to account for what determined your particular version to land on either A or on B. Since both versions of you are indistinguishable for the rest of the universe, there is no physical uncertainty that needs to be addressed

The MWI of quantum mechanics looks very similar to this situation, since the quantum system entangles with the observer, creating a superposition of two observers that only distinguish themselves on the resulting eigenvalue they observe. Ontologically, the wavefunction evolves fully deterministically, but the inherent randomness of your observations are due to the 'branching out' of the observer

• You don't need fancy teleporters. Consider the experience of a single celled organism that divides every minute and then an hour later every bacteria on on a certain side of the petri dish gets transferred to a new petri dish with different food. The original single organism couldn't possibly predict with certainty what it will be eating in an hour. But nothing magical is going on. Oct 14 '15 at 21:04

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 $\lbrace 0,1 \rbrace$. 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 $\neg Y$: whenever $Y(u)=1$, $\neg Y(u)=0$, 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-determisim!

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