I'm not familiar with those concepts (like Wiener Process), but I don't think notions of predictability should be mixed up with notions of determinism. Whether something is predictable or not does not change how deterministic it is.
I think what I have to say, then, is welcome to quantum mechanics. Or, in fact, welcome to probability theory. Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world.
An interesting question is: how could a fully deterministic ontology give rise to beings capable of having probabilistic beliefs? Worse, how can a fully deterministic ontology give rise to truly random mathematical entities like Chaitin's Omega? In fact, in such a universe, where do the bits for atomic random-number generators come from? After all, if they're not really random, there should be some deterministic model capable of predicting them, and yet, quantum mechanics tells us precisely that such a thing is impossible.
You can try to have a Bayesian epistemology with a nonstochastic ontology, but it doesn't really make sense. Just let your ontology be stochastic: then and only then you can physically account for both physical randomness and probabilistic belief.
> I think what I have to say, then, is welcome to quantum mechanics. Or, in fact, welcome to probability theory. Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world.
I'm not talking about randomness. I'm talking about determinism, and as far as I can see what you're saying says nothing about determinism or differing degrees of determinism.
> An interesting question is: how could a fully deterministic ontology give rise to beings capable of having probabilistic beliefs?
I don't see that as a problem at all. It fits completely fine with the idea that probability is a matter of lack of knowledge.
> Worse, how can a fully deterministic ontology give rise to truly random mathematical entities like Chaitin's Omega? In fact, in such a universe, where do the bits for atomic random-number generators come from? After all, if they're not really random, there should be some deterministic model capable of predicting them, and yet, quantum mechanics tells us precisely that such a thing is impossible.
You're talking like it's already a settled matter as to whether reality is fundamentally deterministic or not. Are you saying that there's definitive proof that deterministic accounts of QM are incorrect?
The person I was replying to said "Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world."
This is because randomness can be seen as a matter of incomplete knowledge. Determinism is independent of our knowledge.
Now, perhaps there is randomness that is independent of our knowledge. But I was talking about randomness/determinism in the context of the quoted statement, which was a matter of knowledge.
> This is because randomness can be seen as a matter of incomplete knowledge. Determinism is independent of our knowledge.
I'm not sure there's a meaningful difference. "Determinism" as you're describing it is an interpretation with no practical implications.
You can imagine a god controlling every "random" event in our universe by selecting the outcome from "the big book of outcomes" and claim that everything is deterministic. You can also imagine the god consulting a D20 instead, and claim that everything is non-deterministic. The former makes randomness a function of our lack of knowledge and the latter makes it truly random. These two scenarios are equivalent and neither is falsifiable, though, making the distinction meaningless. From your perspective, random events are still non-deterministic.
You're just making up scenarios that fit your point of view, without arguing that these correspond to the actual options.
Are you arguing that there cannot be any distinction between determinism and non-determinism?
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The scenarios are ones involving a god choosing and performing actions, and the supposed randomness of their dice. What are they meant to translate to?
> I'm arguing that your "deterministic randomness" is indistinguishable from "nondeterministic randomness". You're trying to define a class of "randomness" to be "deterministic but unknown
> You're just making up scenarios that fit your point of view, without arguing that these correspond to the actual options.
No, I gave scenarios that demonstrate why your distinction is not meaningful. If you have a scenario that changes this, can you please explain it?
> Are you arguing that there cannot be any distinction between determinism and non-determinism?
No, I'm arguing that your "deterministic randomness" is indistinguishable from "nondeterministic randomness". You're trying to define a class of "randomness" to be "deterministic but unknown". Near as I can tell, this is a distinction without a difference.
