All of fryolysis's Comments + Replies

Knowing (or assuming) that the value of  does not change between experiments is a different kind of knowledge than knowing the value of .

-1l8c
OK. But if you yourself state that you "certainly know" -- certainly -- that p is fixed, then you have already accounted for that particular item of knowledge. If you do not, in fact, "certainly know" the probability of p -- as could easily be the case if you picked up a coin in a mafia-run casino or whatever -- then your prior should be 0.5 but you should also be prepared to update that value according to Bayes' Theorem. I see that you are gesturing towards assigning also the probability that the coin is a fair coin (or generally such a coin that has a p of a certain value). That is also amenable to Bayes' Theorem in a normal way. Your prior might be based on how common biased coins are amongst the general population of coins, or somewhat of a rough guess based on how many you think you might find in a mafia-run casino. But by all means, your prior will become increasingly irrelevant the more times you flip the coin. So, I don't think you need to be too concerned about how nebulous that prior and its origins are! 

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?

1JBlack
If a=b=1 then Pr(p & q) / Pr(p) = P(p & q) / Pr(q) = 1 so that Pr(p) = Pr(q) = Pr(p & q). That doesn't require that Pr(p), Pr(q), or Pr(p & q) goes to 1. It just means that in a Venn diagram, p and q coincide (or in popular parlance, "are a circle"). How did you get Pr(p) = Pr(q) = 1?

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. Therefor... (read more)