CS PhD student
Abhimanyu Pallavi Sudhir
Karma: 73
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.
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 don’t think this is right. A superrational agent exploits the symmetry between A1 and A2, correct? So it must reason that an identical agent in A2 will reason the same way as it does, and if it bets heads, so will the other agent. That’s the point of bringing up EDT.
Wait, but can’t the AI also choose to adopt the strategy “build another computer with a larger largest computable number”?
I don’t understand the significance of using a TM—is this any different from just applying some probability distribution over the set of actions?
Suppose the function U(t) is increasing fast enough, e.g. if the probability of reaching t is exp(-t), then let U(t) be exp(2t), or whatever.
I don’t think the question can be dismissed that easily.
It does not require infinities. E.g. you can just reparameterize the problem to the interval (0, 1), see the edited question. You just require an infinite set.
Infinite t does not necessarily deliver infinite utility.
Perhaps it would be simpler if I instead let t be in (0, 1], and U(t) = {t if t < 1; 0 if t = 1}.
It’s the same problem, with 1 replacing infinity. I have edited the question with this example instead.
(It’s not a particularly weird utility function—consider, e.g. if the agent needs to expend a resource such that the utility from expending the resource at time t is some fast-growing function f(t). But never expending the resource gives zero utility. In any case, an adverserial agent can always create this situation.)
I see. So the answer is that it is indeed true that Godel’s statement is true in all models of second-order PA, but unprovable nonetheless since Godel’s completeness theorem isn’t true for second-order logic?
This seems to be relevant to calculations of climate change externalities, where the research is almost always based on the direct costs of climate change if no one modified their behaviour, rather than the cost of building a sea wall, or planting trees.
Disagree. Daria considers the colour of the sky an important issue because it is socially important, not because it is of actual cognitive importance. Ferris recognizes that it doesn’t truly change much about his beliefs, since their society doesn’t have any actual scientific theories predicting the colour of the sky (if they did, the alliances would not be on uncorrelated issues like taxes and marriage), and bothers with things he finds to be genuinely more important.
conditionalization is not the probabilistic version of implies
Resolution logic for conditionalization:
Resolution logic for implies: