Are chance and determinism incompatible?

Question

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?

Answer 1

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.

Answer 2

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?

Answer 3

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.

Answer 4

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.

Answer 5

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.