A first approximation to what I want to draw a distinction between is parts of a hypothesis that are correlated with the rest of the parts, and parts that aren't, so that and adding them decreases the probability of the hypothesis more. In the extreme case, if a part of a hypothesis is logically deduced from the other parts, then it's perfectly correlated and doesn't decrease the probability at all.
So you mean like a mind that's omniscient, omnipotent, and morally perfect?
They have always been minds. Which makes that kind of complexity-reducing correlation impossible (or greatly reduces its strength) for hypotheses with them.
Why? AIXI is very easy to specify. The ideal decision theory is very easy to specify, hard to describe or say anything concrete about, but very easy to specify.
If you're willing to allow electro-magnatism which is based on the mathematical theory of partial differential equations, I don't see why you won't allow ideal agents based on decision/game theory. Heck, economists tend to model people as ideal rational agents because ideal rational agents are simpler than actual humans.
Omniscience and omnipotence are nice and simple, but "morally perfect" is a word that hides a lot of complexity. Complexity comparable to that of a human mind.
I would allow ideal rational agents, as long as their utility functions were simple (Edit: by "allow" I mean they don't get the very strong prohibition that a human::morally_perfect agent does) , and their relationship to the world was simple (omniscience and omnipotence are a simple relationship to the world). Our world does not appear to be optimized according to a utility func...
I am about to graduate from one of the only universities in the world that has a high concentration of high-caliber analytic philosophers who are theists. (Specifically, the University of Notre Dame, IN) So as not to miss this once-in-a-lifetime opportunity, I have sent out emails asking many of them if they would like to meet and discuss their theism with me. Several of them have responded already in the affirmative; fingers crossed for the rest. I'm really looking forward to this because these people are really smart, and have spent a lot of time thinking about this, so I expect them to have interesting and insightful things to say.
Do you have suggestions for questions I could ask them? My main question will of course be "Why do you believe in God?" and variants thereof, but it would be nice if I could say e.g. "How do you avoid the problem of X which is a major argument against theism?"
Questions I've already thought of:
1-Why do you believe in God?
2-What are the main arguments in favor of theism, in your opinion?
3-What about the problem of evil? What about objective morality: how do you make sense of it, and if you don't, then how do you justify God?
4-What about divine hiddenness? Why doesn't God make himself more easily known to us? For example, he could regularly send angels to deliver philosophical proofs on stone tablets to doubters.
5-How do you explain God's necessary existence? What about the "problem of many Gods," i.e. why can't people say the same thing about a slightly different version of God?
6-In what sense is God the fundamental entity, the uncaused cause, etc.? How do you square this with God's seeming complexity? (he is intelligent, after all) If minds are in fact simple, then how is that supposed to work?
I welcome more articulate reformulations of the above, as well as completely new ideas.