kaleido wrote: ↑October 23rd, 2022, 1:25 pm- deterministic: If you take action A then consequence B will occur. Always.This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[8] and is fully determined by their initial conditions, with no random elements involved.[9] In other words, the deterministic nature of these systems does not make them predictable.What is the use of calling a system deterministic if you can't determine its action? But OK, I'll go with this definition.
- unpredictable: If event C takes place, it is not possible to determine what action caused it.
Such system is deterministic but largely unpredictable, i.e. chaotic.
The truth about natural numbers is exactly like that, i.e. chaotic:
- theorem of soundness: If you can prove proposition P from arithmetic theory, then P is true in the natural numbers.
- theorem of incompleteness: There exist true propositions in the natural numbers that cannot be proved from arithmetic theory.
You will find that the theorem of incompleteness dominates the theorem of soundness, i.e. most truth about the natural numbers cannot be proven in arithmetic theory.
kaleido wrote: ↑October 23rd, 2022, 1:25 pm You could argue the same happens to the universe but, likewise, you wouldn't be able to prove it.It requires proving that the theory of the universe (=theory of everything, ToE) contains a copy of Robinson's fragment Q of arithmetic theory. In that case, the universe is a deterministic but chaotic system, on the condition that the ToE does not contain the definition of a true random number generator too, because in that case, it is not necessarily clear what is going on.
kaleido wrote: ↑October 23rd, 2022, 1:25 pm This brings us back to Zarathustra's dice-throwers and probability. Even if there is only one possible fate, you won't be able to determine it, hence it wouldn't be, from our point of view, deterministic. You could say that from the point of view of the universe everything is already determined, but we can't place ourselves on this point of view. Hence determinism as the idea that you can calculate and determine with 100% certainty the future is wrong.Yes. It's like using a cryptographical PRNG (Pseudo Random Number Generator). The next number is perfectly deterministic if you know what PRNG it is, as well as the initial seed, but for someone who does not have that information, it looks indistinguishable from random.
kaleido wrote: ↑October 23rd, 2022, 1:25 pm Consider that just by the very act of measuring we already affect the outcome. We can never determine with 100% certainty the future, because we ourselves are included in the universe and affect it with our own actions.If we truly have free will, then the theory of the universe cannot predict our actions. Otherwise, it can.
kaleido wrote: ↑October 23rd, 2022, 1:25 pm You would have to be situated "outside" the universe to be able to tell the outcome of the universe at any given point in time, but to be "outside" the universe is non-sensical. The universe is everything, you can't be "outside" everything.If we have free will, then our action cannot be predicted from the theory of the universe. Hence, in that case, our actions are true propositions in the universe but not provable from its theory.
Since the universe expands, and on the condition that the theory of the universe is not able to predict the precise end of the universe, the Lowenheim-Skolem theorem will be provable from the theory of the potentially infinite universe. In that case, it is a multiverse. Under those conditions, there are an unlimited number of universes that interpret the theory of the universe.
Hence, the existence of free will almost surely implies that our universe is part of a multiverse. That is exactly what religion says: there is also a heaven and a hell.
kaleido wrote: ↑October 23rd, 2022, 1:25 pm It's in this sense that I say that the universe isn't deterministic.A free-will containing Lowenheim-Skolem multiverse is still perfectly deterministic, but again chaotic.
kaleido wrote: ↑October 23rd, 2022, 1:25 pm Though, from the perspective of the universe, everything may already be determined—we just won't ever be able to determine it ourselves.If we had a copy of the theory of the universe, then according to the theorem of soundness, every proposition about the universe that is provable from this theory, would still be true in the universe, but also in every other universe of the entire multiverse. So, it is would be deterministic. However, since the theorem of incompleteness would also be provable from this theory, there will be numerous true propositions about the universe that are unprovable from its theory. Hence the universe would also be chaotic.
kaleido wrote: ↑October 23rd, 2022, 1:25 pm The use of the words "determinism" and "deterministic" simply vanishes at this point.No, they don't.
The theorem of incompleteness will massively dominate the theorem of soundness, but the theorem of soundness will still be perfectly provable and therefore true across the entire multiverse.
Soundness never vanishes. It just gets dominated by chaos.