I just thought of this 'cute' question and not sure how to answer it.

The sample space of an empirical statement is True or False. Then, given an empirical statement, one would then assign a certain prior probability 0<p<1 to TRUE and one minus that to FALSE. One would not assign a p=1 or p=0 because it wouldn't allow believe updating.

For example: Santa Claus is real.

I suppose most people in LW will assign a very small p to that statement, but not zero. Now my question is, what is the prior probability value for the following statement:

Prior probability cannot be set to 1.

Eliezer ruminates on foundations and wrestles with the difficulties quite a bit in the Metaethics sequence, for example:

• Where Recursive Justification Hits Bottom
• Fundamental Doubts

That kind of knowledge is not part of the human condition. By making it a presupposition of your story, you render your hypothetical inapplicable to actual human life.

That's a reason to want him to be innocent, not a reason to want to know the truth. What's her motivation for the necessary second part of the litany: "if Adam is guilty, I want to believe that Adam is guilty"?

It is a very interesting quest you have taken on. As an atheist, I am always interested in hearing good arguments in favour of God.

Why don't you start by answering: Why are you a theist? You have looked at all the evidence available to you, and arrived at a posterior where P(God exists) >> P(God does not exist). Explain your reasoning to us. If your reasoning is good enough for you, why would it not be good enough for me?

Effectiveness is desirable; effectiveness is measured by results; consistency and verifiability are how we measure what is real.

As a corollary, things that have no evidence do not merit belief. We needn't presume that we are not in a simulation, we can evaluate the evidence for it.

The central perspective shift is recognizing that beliefs are not assertions about reality, but assertions about our knowledge of reality. This what is meant by the map and the territory.

By human-granularity, I mean beliefs about macro states that can be analyzed and manipulated by human thought and expressed in reasonable amounts (say, less than a few hundred pages of text) of human language. As contrasted with pure analytic beliefs about the state of the universe expressed numerically.

For instrumental rationality, what goals are furthered by her knowing the truth of this fact? Presuming that if Adam is innocent, she wants to believe that Adam is innocent and if Adam is guilty, she wants to believe Adam is guilty, why does she want to be correct (beyond "I like being right")? What decision will she make based on it?

I understand what you are trying to say, but I am struggling to see if it is true.

It's a straightforward corollary of Bayes theorem: if P(A) = 1 (or P(A) = 0), no amount of later updating can change this value. No matter what strong contrary evidence is presented.
This is indeed a simple model of a hardcore theist: he has already set P(god(s)) to true, so he is willing to dig himself a hole of unlimited depth to account for the evidence that oppose the existence of a divinity.

As for some example, Russel's teapot is a good choice: a teapot orbiting a distant sun in other galaxy. Is it falsifiable? With our current and future technology, probably not.
Is it logically falsifiable: yes! Even if you assign a very low probability to its existence, an alien species could just transport us there and show us that there's such a teapot.
On the other hand, as I mentioned earlier, if we had put P(teapot) = 0, then we will never accept the teapot existence, even in the face of space travelling aliens that show us that the thing is actually there.

The point is that these days... and I think in the days before that, AND the days before that... ... Okay, so basically since forever, "God" has been such a loaded concept...

If you ask people where God is, some of them will tell you that "God is in everything and anything" (or something to that tune). Now, these people don't have to be right (or wrong!) but that's ... a rather broad definition to me.

One can imagine God as an entity. Like, I dunno, a space alien from an alternative universe (don't ask how that universe was created; I don't know, this is a story and not an explanation). With super advanced technology. So if we then ask "did God create the world" and we (somehow...?) went back in time and saw that, hey, this space alien was somewhere else at the time and, no, the planet formed via other means, then you'd have a definitive answer to that question.

But there are other definitions. God are the mechanics of the universe. So, what you'd call the laws of physics, no, that's just God. That's how God keeps everything going. Why, then, yes, God did create the world! But only because current scientific understanding says "we think physics did it" and then you say "Physics is God".

Anyway, if you want a sane, useful, rational answer to your third question then you must define God. I personally treated God as 1 entity in my earlier answer, which leads to the problem of having to connect events to the same entity (which, when you know very little about that entity, is pretty hard). (If you didn't connect events to that same entity then something else must have caused it, in which case you have multiple probable causes for fantastic events, and you might as well call them Gods individually?)

I don't quite grasp what you mean with the last bit...

I am a theist, but I am appalled by the lack of rational apologetic, the abundance of poor ones, and the disinterest to develop a good one. So here I am, making baby steps.

Could you clarify?

because producing new evidence is not possible anymore.

How do you claim to know that?