Determinism, Free Will and Paradox

[Alex K]

Concerning your third paragraph: yes, from a maths point of view I'd say the whole history of the universe would be equivalent to the initial conditions plus the fundamental laws of physics. Deep philosophical question: does time even exist in this case?

Saying that subsequent conditions are a product of initial conditions and the laws of physics seems to imply that time does exist. But I think the directionality is less clear-- given that all states, from beginning to end, are set in stone, then why wouldn't we argue that the initial conditions are a product OF subsequent events?

Ohh, my favourite topic, about which I can go on for days. No, directionality in this case is not clear at all! The laws of classical (non quantum) physics are identical under time reversal. If you look at a simulation of several mass points attracting each other, there is no way to tell whether you are watching it forward or backwards, save for one thing: if you're watching it forward, one tends to, statistically, observe less likely configurations to go towards more likely ones. If one has many many particles, this becomes the second law of thermodynamics. If, on the other extreme, you have just two particles, there is no notion of direction of time in principle.

In ypur deterministic pet universe, one could identify regions in time evolution where one can use entropy to assign a direction, and this would coincide with our subjective notion of an arrow of time. Towards heat death, this becomes less and less pronounced.

In any case, there currently aren't good reasons to think the universe is deterministic, so this discussion is interesting mainly as a thought experiment.

I've often agreed with you on this. However, how would one collect evidence on either side of this question?

Quantum measurements look perfectly random, and if there are hidden variables which guide this observed randomness in a deterministic way, we do not have evidence for them. This to me is evidence against determinism - we can discuss how strong. If there is a many worlds multiverse, it is deterministic as a whole, but the subjective path through it for any observer is truly random if the observer we follow is chosen randomly.