For 18 examples, just think of 3 common everyday norms having to do with each of the 6 boundaries given as example images in the post :) (I.e., cell membranes, skin, fences, social group boundaries, internet firewalls, and national borders). Each norm has the property that, when you reflect on it, it's easy to imagine a lot of other people also reflecting on the same norm, because of the salience of the non-subjectively-defined actual-boundary-thing that the norm is about. That creates more of a Schelling-nature for that norm, relative to...
To your first question, I'm not sure which particular "the reason" would be most helpful to convey. (To contrast: what's "the reason" that physically dispersed human societies have laws? Answer: there's a confluence of reasons.). However, I'll try to point out some things that might be helpful to attend to.
First, committing to a policy that merges your utility function with someone else's is quite a vulnerable maneuver, with a lot of boundary-setting aspects. For instance, will you merge utility functions multiplicatively (as in Nas...
This is cool (and fwiw to other readers) correct. I must reflect on what it means for real world cooperation... I especially like the A <-> X -> X <-> A trick.
I'm working on it :) At this point what I think is true is the following:
If ShortProof(x \leftrightarrow LongProof(ShortProof(x) \to x)), then MediumProof(x).
Apologies that I haven't written out calculations very precisely yet, but since you asked, that's roughly where I'm at :)
Based on a potential misreading of this post, I added the following caveat today:
Important Caveat: Arguments in natural language are basically never "theorems". The main reason is that human thinking isn't perfectly rational in virtually any precisely defined sense, so sometimes the hypotheses of an argument can hold while its conclusion remains unconvincing. Thus, the Löbian argument pattern of this post does not constitute a "theorem" about real-world humans: even when the hypotheses of the argument hold, the argument will not always play out...
Thanks! Added a note to the OP explaining that hereby means "by this utterance".
Hat tip to Ben Pace for pointing out that invitations are often self-referential, such as when people say "You are hereby invited", because "hereby" means "by this utterance":
That comment was like 25% of my inspiration for this post :)
I've now fleshed out the notation section to elaborate on this a bit. Is it better now?
In short, is our symbol for talking about what PA can prove, and is shorthand for PA's symbols for talking about what (a copy of) PA can prove.
- " 1+1=2" means "Peano Arithmetic (PA) can prove that 1+1=2". No parentheses are needed; the "" applies to the whole line that follows it. Also, does not stand for an expression in PA; it's a symbol we use to talk about what PA can prove.
- "" basically means the sam
Well, the deduction theorem is a fact about PA (and, propositional logic), so it's okay to use as long as means "PA can prove".
But you're right that it doesn't mix seamlessly with the (outer) necessitation rule. Necessitation is a property of "", but not generally a property of "". When PA can prove something, it can prove that it can prove it. By contrast, if PA+X can prove Y, that does mean that PA can prove that PA+X can prove Y (because PA alone can work through proofs in a Gödel encoding), but it doesn't mean that PA+...
Well, is just short for , i.e., "(not A) or B". By contrast, means that there exists a sequence of (very mechanical) applications of modus ponens, starting from the axioms of Peano Arithmetic (PA) with appended, ending in . We tried hard to make the rules of so that it would agree with in a lot of cases (i.e., we tried to design to make the deduction theorem true), but it took a lot of work in the design of Peano Arithmetic and can't be taken for gr...
It's true that the deduction theorem is not needed, as in the Wikipedia proof. I just like using the deduction theorem because I find it intuitive (assume , prove , then drop the assumption and conclude ) and it removes the need for lots of parentheses everywhere.
I'll add a note about the meaning of so folks don't need to look it up, thanks for the feedback!
I agree this is a big factor, and might be the main pathway through which people end up believing what people believe the believe. If I had to guess, I'd guess you're right.
E.g., if there's a evidence E in favor of H and evidence E' against H, if the group is really into thinking about and talking about E as a topic, then the group will probably end up believing H too much.
I think it would be great if you or someone wrote a post about this (or whatever you meant by your comment) and pointed to some examples. I think the LessWrong community is somewhat plagued by attentional bias leading to collective epistemic blind spots. (Not necessarily more than other communities; just different blind spots.)
Ah, thanks for the correction! I've removed that statement about "integrity for consequentialists" now.
Thanks for raising this! I assume you're talking about this part?
They explore a pretty interesting set-up, but they don't avoid the narrowly-self-referential sentence Ψ:
So, I don't think their motivation was the same as mine. For me, the point of trying to use a quine is to try to get away from that sentence, to create a different perspective on the foundations for people that find that kind of sentence confusing, but who find self-referential documents less confusing. I added a section "Further meta-motivation (added Nov 26)" about this ...
At this point I'm more interested in hashing out approaches that might actually conform to the motivation in the OP. Perhaps I'll come back to this discussion with you after I've spent a lot more time in a mode of searching for a positive result that fits with my motivation here. Meanwhile, thanks for thinking this over for a bit.
True! "Hereby" covers a solid contingent of self-referential sentences. I wonder if there's a "hereby" construction that would make the self-referential sentence Ψ (from the Wikipedia poof) more common-sense-meaningful to, say, lawyers.
this suggests that you're going to be hard-pressed to do any self-reference without routing through the nomal machinery of löb's theorem, in the same way that it's hard to do recursion in the lambda calculus without routing through the Y combinator
If by "the normal machinery", you mean a clever application of the diagonal lemma, then I agree. But I think we can get away with not having the self-referential sentence, by using the same y-combinator-like diagonal-lemma machinery to make a proof that refers to itself (instead of a proof about sentences t...
This sentence is an exception, but there aren't a lot of naturally occurring examples.
No strong claim either way, but as a datapoint I do somewhat often use the phrase "I hereby invite you to <event>" or "I hereby <request> something of you" to help move from 'describing the world' to 'issuing an invitation/command/etc'.
Thanks for your attention to this! The happy face is the outer box. So, line 3 of the cartoon proof is assumption 3.
If you want the full (C->C) to be inside a thought bubble, then just take every line of the cartoon and put into a thought bubble, and I think that will do what you want.
LMK if this doesn't make sense; given the time you've spent thinking about this, you're probably my #1 target audience member for making the more intuitive proof (assuming it's possible, which I think it is).
ETA: You might have been asking if th...
Yes to both of you on these points:
(I'll write a separate comment on Eliezer's original question.)
That thing is hilarious and good! Thanks for sharing it. As for the relevance, it explains the statement of Gödel's theorem, but not the proof it. So, it could be pretty straightforwardly reworked to explain the statement of Löb's theorem, but not so easily the proof of Löb's theorem. With this post, I'm in the business of trying to find a proof of Löb that's really intuitive/simple, rather than just a statement of it that's intuitive/simple.
Why is it unrealistic? Do you actually mean it's unrealistic that the set I've defined as "A" will be interpretable at "actions" in the usual coarse-grained sense? If so I think that's a topic for another post when I get into talking about the coarsened variables ...
Going further, my proposed convention also suggests that "Cartesian frames" should perhaps be renamed to "Cartesian factorizations", which I think is a more immediately interpretable name for what they are. Then in your equation , you can refer to and as "Cartesian factors", satisfying your desire to treat and as interchangeable. And, you leave open the possibility that the factors are derivable from a "Cartesian partition" of the world into the "Cartesian parts" &n...
Scott, thanks for writing this! While I very much agree with the distinctions being drawn, I think the word "boundary" should be usable for referring to factorizations that do not factor through the physical separation of the world into objects. In other words, I want the technical concept of «boundaries» that I'm developing to be able to refer to things like social boundaries, which are often not most-easily-expressed in the physics factorization of the world into particles (but are very often expressible as Markov blankets in a more abstract ...
I think the boundary factorization into active and passive is wrong.
Are you sure? The informal description I gave for A and P allow for the active boundary to be a bit passive and the passive boundary to be a bit active. From the post:
the active boundary, A — the features or parts of the boundary primarily controlled by the viscera, interpretable as "actions" of the system— and the passive boundary, P — the features or parts of the boundary primarily controlled by the environment, interpretable as "perceptions" of the
Jan, I agree with your references, especially Friston et al. I think those kinds of understanding, as you say, have not adequately made their way into utility utility-theoretic fields like econ and game theory, so I think the post is valid as a statement about the state of understanding in those utility-oriented fields. (Note that the post is about "a missing concept from the axioms of game theory and bargaining theory" and "a key missing concept from utility theory", and not "concepts missing from the mind of all of humanity".)
8. (Unscoped) Consequentialism — the problem that an AI system engaging in consequentialist reasoning, for many objectives, is at odds with corrigibility and containment (Yudkowsky, 2022, no. 23).
7. Preference plasticity — the possibility of changes to the preferences of human preferences over time, and the challenge of defining alignment in light of time-varying preferences (Russell, 2019, p.263).
6. Mesa-optimizers — instances of learned models that are themselves optimizers, which give rise to the so-called inner alignment problem (Hubinger et al, 2019).
5. Counterfactuals in decision theory — the problem of defining what would have happened if an AI system had made a different choice, such as in the Twin Prisoner's Dilemma (Yudkowsky & Soares, 2017).
4. Impact regularization — the problem of formalizing "change to the environment" in a way that can be effectively used as a regularizer penalizing negative side effects from AI systems (Amodei et al, 2016).
3. Mild optimization — the problem of designing AI systems and objective functions that, in an intuitive sense, don’t optimize more than they have to (Taylor et al, 2016).
2. Corrigibility — the problem of constructing a mind that will cooperate with what its creators regard as a corrective intervention (Soares et al, 2015).
1. AI boxing / containment — the method and challenge of confining an AI system to a "box", i.e., preventing the system from interacting with the external world except through specific restricted output channels (Bostrom, 2014, p.129).
In Part 3 of this series, I plan to write a shallow survey of 8 problems relating to AI alignment, and the relationship of the «boundary» concept to formalizing them. To save time, I'd like to do a deep dive into just one of the eight problems, based on what commenters here would find most interesting. If you have a moment, please use the "agree" button (and where desired, "disagree") to vote for which of the eight topics I should go into depth about. Each topic is given as a subcomment below (not looking for karma, just agree/disagree votes). Thanks!
> First, great news on founding an alignment organization on your own.
Actually I founded it with my cofounder, Nick Hay!
Thanks for signal-boosting the coco solution! I'm actually planning workshop near CMU this fall with Adam Kalai :)
Eliezer, thanks for sharing these ideas so that more people can be on the lookout for failures. Personally, I think something like 15% of AGI dev teams (weighted by success probability) would destroy the world more-or-less immediately, and I think it's not crazy to think the fraction is more like 90% or higher (which I judge to be your view).
FWIW, I do not agree with the following stance, because I think it exposes the world to more x-risk:
So far as I'm concerned, if you can get a powerful AGI that carries out some pivotal superhuman engineering
John, it seems like you're continuing to make the mistake-according-to-me of analyzing the consequences of a pivotal act without regard for the consequences of the intentions leading up to the act. The act can't come out of a vacuum, and you can't built a project compatible with the kind of invasive pivotal acts I'm complaining about without causing a lot of problems leading up to the act, including triggering a lot of fear and panic for other labs and institutions. To summarize from the post title: pivotal act intentions directly have negative consequences fox x-safety, and people thinking about the acts alone seem to be ignoring the consequences of the intentions leading up to the act, which is a fallacy.
I see the argument you're making there. I still think my point stands: the strategically relevant question is not whether unilateral pivotal act intentions will cause problems, the question is whether aiming for a unilateral pivotal act would or would not reduce the chance of human extinction much more than aiming for a multilateral pivotal act. The OP does not actually attempt to compare the two, it just lists some problems with aiming for a unilateral pivotal act.
I do think that aiming for a unilateral act increases the chance of successfully executing the pivotal act by multiple orders of magnitude, even accounting for the part where other players react to the intention, and that completely swamps the other considerations.
Eliezer, from outside the universe I might take your side of this bet. But I don't think it's productive to give up on getting mainstream institutions to engage in cooperative efforts to reduce x-risk.
A propos, I wrote the following post in reaction to positions-like-yours-on-this-issue, but FYI it's not just you (maybe 10% you though?):
> Failure mode: When B-cultured entities invest in "having more influence", often the easiest way to do this will be for them to invest in or copy A'-cultured-entities/processes. This increases the total presence of A'-like processes in the world, which have many opportunities to coordinate because of their shared (power-maximizing) values. Moreover, the A' culture has an incentive to trick the B culture(s) into thinking A' will not take over the world, but eventually, A' wins.
> In other words, the humans and human-aligned institutions no
> My prior (and present) position is that reliability meeting a certain threshold, rather than being optimized, is a dominant factor in how soon deployment happens.
I don't think we can get to convergence on many of these discussions, so I'm happy to just leave it here for the reader to think through.
Yeah I agree we probably can't reach convergence on how alignment affects deployment time, at least not in this medium (especially since a lot of info about company policies / plans / standards are covered under NDAs), so I also think it's good to leave this...
> Both [cultures A and B] are aiming to preserve human values, but within A, a subculture A' develops to favor more efficient business practices (nihilistic power-maximizing) over preserving human values.
I was asking you why you thought A' would effectively outcompete B (sorry for being unclear). For example, why do people with intrinsic interest in power-maximization outcompete people who are interested in human flourishing but still invest their money to have more influence in the future?
Ah! Yes, this is really getting to the crux of thing...
Failure mode: When B-cultured entities invest in "having more influence", often the easiest way to do this will be for them to invest in or copy A'-cultured-entities/processes. This increases the total presence of A'-like processes in the world, which have many opportunities to coordinate because of their shared (power-maximizing) values. Moreover, the A' culture has an incentive to trick the B culture(s) into thinking A' will not take over the world, but eventually, A' wins.
I'm wondering why the easiest way is to copy A'---why was A' better at...
Thanks for the pointer to grace2020whose! I've added it to the original post now under "successes in our agent-agnostic thinking".
But I also think the AI safety community has had important contributions on this front.
For sure, that is the point of the "successes" section. Instead of "outside the EA / rationality / x-risk meme-bubbles, lots of AI researchers think about agent-agnostic processes" I should probably have said "outside the EA / rationality / x-risk meme-bubbles, lots of AI researchers think about agent-agnostic processes, and to my ...
Thanks for this synopsis of your impressions, and +1 to the two points you think we agree on.
I also read the post as also implying or suggesting some things I'd disagree with:
As for these, some of them are real positions I hold, while some are not:
- That there is some real sense in which "cooperation itself is the problem."
I don't hold that view. I the closest view I hold is more like: "Failing to cooperate on alignment is the problem, and solving it involves being both good at cooperation and good at alignment."
- Relatedly, that cooperation plays a qual
Failing to cooperate on alignment is the problem, and solving it involves being both good at cooperation and good at alignment
Sounds like we are on broadly the same page. I would have said "Aligning ML systems is more likely if we understand more about how to align ML systems, or are better at coordinating to differentially deploy aligned systems, or are wiser or smarter or..." and then moved on to talking about how alignment research quantitatively compares to improvements in various kinds of coordination or wisdom or whatever. (My bottom line from doing ...
The previous story tends to frame this more as a failure of humanity’s coordination, while this one frames it (in the title) as a failure of intent alignment. It seems like both of these aspects greatly increase the plausibility of the story, or in other words, if we eliminated or made significantly less bad either of the two failures, then the story would no longer seem very plausible.
Yes, I agree with this.
A natural next question is then which of the two failures would be best to intervene on, that is, is it more useful to work on intent alignment, or wo
For some reason when I express opinions of the form "Alignment isn't the most valuable thing on the margin", alignment-oriented folks (e.g., Paul here) seem to think I'm saying you shouldn't work on alignment
In fairness, writing “marginal deep-thinking researchers [should not] allocate themselves to making alignment […] cheaper/easier/better” is pretty similar to saying “one shouldn’t work on alignment.”
(I didn’t read you as saying that Paul or Rohin shouldn’t work on alignment, and indeed I’d care much less about that than about a researcher at CHAI argui...
Perhaps I should start saying "Guys, can we encourage folks to work on both issues please, so that people who care about x-risk have more ways to show up and professionally matter?", and maybe that will trigger less pushback of the form "No, alignment is the most important thing"...
I think that probably would be true.
For some reason when I express opinions of the form "Alignment isn't the most valuable thing on the margin", alignment-oriented folks (e.g., Paul here) seem to think I'm saying you shouldn't work on alignment (which I'm not), which trigg
I think that the biggest difference between us is that I think that working on single-single alignment is the easiest way to make headway on that issue, whereas you expect greater improvements from some categories of technical work on coordination
(my sense is that I'm quite skeptical about most of the particular kinds of work you advocate
That is also my sense, and a major reason I suspect multi/multi delegation dynamics will remain neglected among x-risk oriented researchers for the next 3-5 years at least.
If you disagree, then I expect the main disagr
From the OP:
I.e., I agree.... (read more)