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I suppose this may be an obvious quip, but according to Bayesian confirmation theory, evidence E confirms a theory A over theory B if it is more expected under theory A.

If determinism is true, and we take E to be the current state of affairs of the world, then it follows that this E is expected given a particular initial condition that leads to this E. In other words, P (E|determinism and a particular initial condition that leads to E) is 1. Now, there may be many possible initial events, but let’s assume that this initial event is necessary. Now, given any particular initial state, if the universe is indeterministic, then E is very unlikely. And if at every little moment, reality picks one of many branches as quantum mechanics seems to suggest, then P(E|indeterminism given any initial state) is exceptionally low.

So from a Bayesian perspective, would it be fair to say that determinism confirms the evidence more than indeterminism?

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  • Like most such questions, instead of asking about the world, asking about algorithms and computers is sufficient and less confusing.
    – tkruse
    Nov 14, 2023 at 5:57
  • If you have a theory that successfully duplicates the stochastic predictions of quantum mechanics, but allows deterministic predictions, hasten to a reputable physics journal and get the ball rolling on your Nobel prize. Future generations of undergrads will grumble as they memorize equations bearing your surname. If you don't have a deterministic theory that successfully duplicates the stochastic predictions of quantum mechanics, there is no theory B, so the question is irrelevant.
    – g s
    Nov 14, 2023 at 7:34
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    Surely the probability of us having ended up here is 1 regardless of which route we took. Or am I missing your point? Dec 14, 2023 at 10:07
  • @MarcoOcram the probability as calculated from BEFORE now. Probably better phrased as, the probability from the point of view of someone calculating the probability at the beginning of the universe. The probability we end up here is not 1 from that perspective in the indeterministic case.
    – TKoL
    Dec 14, 2023 at 10:13
  • Now, there may be many possible initial events, but let’s assume that this initial event is necessary. - I don't know that this is a fair assumption.
    – TKoL
    Dec 14, 2023 at 10:15

2 Answers 2

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So from a Bayesian perspective, would it be fair to say that determinism confirms the evidence more than indeterminism?

It's easier to consider a smaller scale than the world. Imagine 2 tv screens. One of the screens shows atmospheric noise, which can be regarded as indeterministic, let's say for the sake of discussion. The other tv screen shows a recording of atmospheric noise from a DVD. This means it's fully determined input.

Imagine you don't know which screen you have, but you can take a screenshot of the screen as evidence. Does this help you to determine if that screen shows the live noise or recorded noise?

In itself the screenshot is evidence for neither. Only if you knew the record that one of the screens is showing so that you could map the screenshot to a time on the DVD could you be pretty sure that that screen is the one showing a recording.

For the universe it is quite impossible to fully predict later states from initial states for multiple possible reasons (Several of which also apply to deterministic universes). So any given state cannot be compared to any predicted state with perfect accuracy to tell the universe is deterministic.

So bayesian theory is likely wrongly applied here, though I cannot tell more precisely the flaws.

However, when not making exact predictions, but rough predictions like "There is a 90% chance of rain tomorrow", we can see that the universe behaves "deterministic enough" for many purposes. Maybe this common sense can also be expressed with probability theory.

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  • Plus 1 for a lovely analogy! Dec 14, 2023 at 9:10
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Determinism is not a thing of reality. Determinism is only a theoretical idea of a system very much different from reality.

Therefore reality is indeterministic by definition, not by any conclusion.

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    That is a nice assertion but where is your proof? Secondly, the truth of determinism is irrelevant to the question I just asked if you pay attention. The question is about whether the current state of affairs is likely or unlikely given a certain theory.
    – user62907
    Nov 12, 2023 at 12:23
  • The current state of affairs is not evidence of either determinism or indeterminism. Neither is a theory. Under indeterminism the current state evolved from singularity, an initial state of zero entropy. Under determinism the current state would require one particular ready-made initial state with equal entropy, the "necessary initial event". Under determinism such an initial state cannot evolve or be created. Nov 12, 2023 at 15:09
  • The reasoning is in the right direction so +1. But you should either remove the 'therefore' (2nd para). Or add more explanation.
    – Rushi
    Nov 14, 2023 at 10:53
  • Why? If determinism ≠ reality by definition, then reality ≠ determinism by the same definition. Nov 14, 2023 at 11:25
  • Therefore reality is indeterministic by definition that's not a very good definition then.
    – TKoL
    Dec 14, 2023 at 10:16

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