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endoself comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong
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There are people working on this. EY explained his position here.
However, that is somewhat tangential. Are you proposing that decision making should be significantly altered by ignoring certain computable hypotheses - since Solomonoff induction, despite its limits, does manifest this problem - in order to make utility functions converge? That sounds horribly ad-hoc (see second paragraph of this).
I agree.
Any decision process that does not explicitly mention outcomes is only useful insofar as its outputs are correlated with our actual desires, which are about outcomes. If outcomes are not part of an AGI's decision process, they are therefore still necessary for the design of the AGI. They are probably also necessary for the AGI to know which self-modifications are justified, since we cannot foresee which modifications could at some point be considered.
If I was working on that, I could say it was being worked on. I agree that an ad-hoc hack is not what's called for. It needs to be a principled hack. :-)
Are they really? That is, about outcomes in the large-world sense we just agreed on. Ask people what they want, and few will talk about the entire future history of the universe, even if you press them to go farther than what they want right now. I'm sure Eliezer would, and others operating in that sphere of thought, including many on LessWrong, but that is a rather limited sense of "us".
Can you come up with a historical example of a mathematical or scientific problem being solved - not made to work for some specific purpose, but solved completely - with a principled hack?
I don't see your point. Other people don't care about outcomes but a) their extrapolated volitions probably do and b) if people's extrapolated volitions don't care about outcomes, I don't think I'd want to use them as the basis of a FAI.
Limited comprehension in ZF set theory is the example I had in mind in coining the term "principled hack". Russell said to Frege, "what about the set of sets not members of themselves?", whereupon Frege was embarrassed, and eventually a way was found of limiting self-reference enough to avoid the contradiction. There's a principle there -- unrestricted self-reference can't be done -- but all the methods of limiting self-reference that have yet been devised look like hacks. They work, though. ZF appears to be consistent, and all of mathematics can be expressed in it. As a universal language, it completely solves the problem of formalising mathematics.
(I am aware that there are mathematicians who would disagree with that triumphalist claim, but as far as I know none of them are mainstream.)
Being a mathematician who at least considers himself mainstream, I would think that ZFC and the existence of a large cardinal is probably the minimum one would need to express a reasonable fragment of mathematics.
If you can't talk about the set of all subsets of the set of all subsets of the real numbers, I think analysis would become a bit... bondage and discipline.
Surely the power set axiom gets you that?
That it exists, yes. But what good is that without choice?
Ok, ZFC is a more convenient background theory than ZF (although I'm not sure where it becomes awkward to do without choice). That's still short of needing large cardinal axioms.
The idea of programming ZF into an AGI horrifies my aesthetics, but that is no reason not to use it (well it is an indication that it might not be a good idea but in this specific case ZF does have the evidence on its side). If expected utility, or anything else necessary for an AGI, could benefit from a principled hack as well-tested as limited comprehension, I would accept it.