Are chance and determinism incompatible?

In an “objectively” chancy world such as the one proposed by some interpretations of quantum mechanics, we can only probabilistically but not fully determine measurements.

So, A and B may have a 50% probability of each occurring, but there is no reason as to why A occurs instead of B. But what does probability mean here? Presumably, it means that given enough trials, 50% of the measurements would be A and 50% of the measurements would be B. But each measurement is fundamentally unpredictable, even in principle. In this case, we decide to define our sample space in such a way that it includes A, B, and nothing else.

Now, suppose that our world is deterministic. In this case, we now have a cause that determines each measurement to either be A or B. In this case, the notion of chance seems to evaporate.

However, what would be the reason for why there exists a law that determines the next measurement to be A, instead of B? Presumably, none. The law would just exist. If so, why can’t one define another sample space of outcomes where the outcomes are the laws themselves?

For example, one might say that there could have been a law that determines the next measurement to be A instead of B but that didn’t happen. In this case, you could still have a sort of “epistemic” probability with respect to an outcome such as A or B even if it’s determined.

One might object to this by stating that there is no real sense in which the next measurement could have been anything else in the case of a deterministic universe. But what reason do we have to suppose that the next measurement could have been anything else in the case of an indeterministic universe either?

“There is no reason or sufficient cause as to why A occurred instead of B” does not imply “B, instead of A, could have occurred”. The very notion of possibility is epistemic in nature. It is a mental construct and doesn’t occur in reality. If it did, it would simply be referred to as an actuality, not a possibility.

But if possibility is only epistemic, then what difference is there between possibilities of outcomes in an indeterministic universe and possibilities of laws in a deterministic universe?

• On this topic I recommend "Interpretations of probability" by Alan Hájek
– Stef
Dec 19, 2023 at 14:19
• Note that the term determinism can be used more generally than the typical meaning of causal determinism. If everything that happens could not have happened any other way, that is still determinism, even if gods decided the events. Non-causal determinism and indeterminism can appear the same to an observer. Yet a random distribution of outcomes makes indeterminism a little more believable than non-causal determinism. Dec 23, 2023 at 8:42

But if possibility is only epistemic, then what difference is there between possibilities of outcomes in an indeterministic universe and possibilities of laws in a deterministic universe?

A very odd question, honestly. That's tortured thinking, tortured language. You may wish to remember that the difference between determinism and undeterminism depends on the concept of possibility.

Determinism says that given certain initial conditions, only one outcome is possible, while undeterminism states that several outcomes may be possible. Without this notion, there is no difference between determinism and undeterminism.

The problem is that you cannot meaningfully define the sample space of outcomes for the laws being as they are. Ours is the only universe we know about, so we have a sample of one. You could, if you liked, imagine other possible universes with different laws in order to posit a bigger sample set, but it would all be unprovable guesswork so why bother?

• I agree, but why is it any more meaningful to talk about different outcomes given the same laws? It seems that this is more of a matter of comfort than something based in reality. There is no evidence that the universe could have played out differently, even without determinism. There is always a sample space of one
– user62907
Dec 21, 2023 at 10:27
• Agreed. The point is that chance is a matter of perspective. If I have a completely clockwork robot that picks cards out of a deck in a completely deterministic way, and asks you to guess which card it's holding, you will consider it a matter of chance whether you guess correctly. Dec 21, 2023 at 13:06
• Don't be too quick to discount the predictive possibilities of guesses about the state of regions to which no spacetime trajectory can lead from our reference frame and which therefore are not, were not, and never will be. The insides of black holes are a useful example.
– g s
Dec 21, 2023 at 19:12
• @gs cheers! Given the lateness of the hour and the fact that I have eaten an exceptionally heavy dinner, I am afraid that your comment has by a considerable margin passed over my nodding old head. Maybe I'll stand a chance of understanding it in the morning! Sleep well. Dec 21, 2023 at 20:12

This problem goes away by phrasing determinism in terms of predictability instead of possible worlds, as you too have noticed.

The only physically meaningful difference between a deterministic and an non deterministic world is that the current state of the universe allows you to predict the future. The does not hold in a non deterministic universe.

Questions like "Could something else have happened?" are equally meaningless in either universe, like you said. This question is meaningless also in a many worlds theory, as all the outcomes become real in those theories.

Si, chance and determinism are incompatible.

However ... how do we understand chance? Did you just imagine a coin doing flips in the air or a die rolling on a board? These are events in classical physics, a fully deterministic (pace Hume and his problem of induction and an honorable mention to an English physicist who would've laughed at USA's and Russia's so-called guided missiles, and all precision munitions in general) environment, and yet when you perform experiments with coins/dice, they mimic, to a T, true randomness. Daniel Dennett should be most pleased.

• There is no "fully deterministic" environment in reality. Chance is a fully understood concept. A chance is an outcome that no-one has deliberately decided. Dec 22, 2023 at 4:01
• Danke for the correction. I shall edit my answer. Dec 22, 2023 at 4:10

Yes, they are incompatible.

The definition of determinism makes it clear: When every event is completely determined by the previous event, there is absolutely no wiggle room for any probabilistic variation.

Hidden variables cannot explain probabilistic inaccuracies away, as there must be something that makes the hidden variables vary. In determinism there are no variables.

• Does chance require the notion of counterfactuals? In other words, does it require that the world could have been a different way? If so, even if the universe is not deterministic, how can we know that the events in it could have been otherwise?
– user62907
Dec 19, 2023 at 11:43
• @thinkingman Surely, we can imagine things a different way from the way they are, even if the universe is deterministic. Isn't that enough for a counter-factual? Dec 19, 2023 at 11:50
• @thinkingman Chance is the very opposite of choice. Both mean the occurrence of one outcome out of multiple possibilities. Chance no-one selects, choice is deliberately selected by someone. Both chance and choice are excluded from determinism. In reality we have both. The future may turn out in multiple different ways by choice and by chance. We have no reason to assume that this was not the case in the history. Dec 19, 2023 at 15:09