CS PhD student
I don't think that's exactly true. But why do you think that follows from what I wrote?
That's syntax, not semantics.
It's really not, that's the point I made about semantics.
Eh that's kind-of right, my original comment there was dumb.
You overstate your case. The universe contains a finite amount of incompressible information, which is strictly less than the information contained in . That self-reference applies to the universe is obvious, because the universe contains computer programs.
The point is the universe is certainly a computer program, and that incompleteness applies to all computer programs (to all things with only finite incompressible information). In any case, I explained Godel with an explicitly empirical example, so I'm not sure what your point is.
I agree, and one could think of this in terms of markets: a market cannot capture all information about the world, because it is part of the world.
But I disagree that this is fundamentally unrelated -- here too the issue is that it would need to represent states of the world corresponding to what belief it expresses. Ultimately mathematics is supposed to represent the real world.
No, it doesn't. There is no 1/4 chance of anything once you've found yourself in Room A1.
You do acknowledge that the payout for the agent in room B (if it exists) from your actions is the same as the payout for you from your own actions, which if the coin came up tails is $3, yes?
I don't understand what you are saying. If you find yourself in Room A1, you simply eliminate the last two possibilities so the total payout of Tails becomes 6.
If you find yourself in Room A1, you do find yourself in a world where you are allowed to bet. It doesn't make sense to consider the counterfactual, because you already have gotten new information.
That's not important at all. The agents in rooms A1 and A2 themselves would do better to choose tails than to choose heads. They really are being harmed by the information.
I see, that is indeed the same principle (and also simpler/we don't need to worry about whether we "control" symmetric situations).
I think that the philosophical questions you're describing actually evaporate and turn out to be meaningless once you think enough about them, because they have a very anthropic flavour.