I confronted some research claiming that senses of agents evolved under fitness pressure systematically diverges from reality, but in the abstract they state that the standard consensus between cognitive and perceptual scientists is the other way.
In any way, I think the answer to this question is not trivial, and the idea of using a mathematical model in which there’s a universe with fixed set of laws and evolving agents to explore the possibilities seems appealing to me.
I used the expression I derived in the post, . However I didn’t notice that goes to 0 too, at least for the example I gave in my previous comment. So there seems to be no issue as long as goes to 0 since it causes the indeterminate form 0⁄0.
I think I have a more serious problem regarding these formulas. If a and b goes to 1, regardless of c, Pr(p) and Pr(q) goes to 1. So if p is the statement “q is true.” and q is the statement “p is true.” then p and q must be true, which I think is nonsense. But I cannot see where my mistake is. Could you help please?
Proving Riemann hypothesis doesn’t sound that super-human level. Instead, since IP=PSPACE, we can ask God to prove that He can solve some PSPACE-complete problem.
This is the first time I read this argument, I’m impressed and once again convinced myself that the set of all possibilities is huge and avoiding contradictions is almost always possible.
But I have some problems with this argument. Claiming that there is a finite amount of possible permutations of the perfect universe doesn’t make sense to me. I need a proof of a theorem that says something like “All big enough perfect universes are boring in the sense that they consist of repetitions of some small sub-universe whose size is at most this and that. Therefore there is no point to create perfect universes bigger than that size”. I think God can always find new interesting ways to extend the perfect universe without introducing redundancy. But then if we never run out of perfect universes God can always increase the total amount of “joy and happiness” by creating the next perfect universe.
By the way I don’t like the idea that God creates universes one after another either. I see no problem in assuming that He creates infinitely many universes at a time. Even if so the problem remains as creating all perfect universes or creating all universes where good > evil yields to the same infinite amount of happiness.
Here is what I have come up with. Think of each universe as countably infinite object. The property of being “perfect” is so strict that the set of all perfect universes is a countably infinite set, while the set of all universes where good > evil is an uncountably infinite set. Therefore God preferred the latter scenario.
Knowing (or assuming) that the value of p does not change between experiments is a different kind of knowledge than knowing the value of p.