When one person says “I guess we’ll have to agree to disagree” and the second person says “Actually according to Aumann’s Agreement Theorem, we can’t” is the second person making a type error?
Note: I confess to being a bit surprised that you picked this example. I’m not quite sure whether you picked a bad example for your point (possible) or whether I’m misunderstanding your point (also possible), but I do think that this question is interesting all on its own, so I’m going to try and answer it.
Here’s a joke that you’ve surely heard before—or have you?
Three mathematicians walk into a bar. The bartender asks them, “Do you all want a beer?”
The first mathematician says, “I don’t know.”
The second mathematician says, “I don’t know.”
The third mathematician says, “I don’t know.”
The lesson of this joke applies to the “according to Aumann’s Agreement Theorem …” case.
When someone says “I guess we’ll have to agree to disagree” and their interlocutor responds with “Actually according to Aumann’s Agreement Theorem, we can’t”, I don’t know if I’d call this a “type error”, precisely (maybe it is; I’d have to think about it more carefully); but the second person is certainly being ridiculous. And if I were the first person in such a situation, my response might be something along these lines:
“Really? We can’t? We can’t what, exactly? For example, I could turn around and walk away. Right? Surely, the AAT doesn’t say that I will be physically unable to do that? Or does it, perhaps, say that either you or I or both of us will be incapable of interacting amicably henceforth, and conversing about all sorts of topics other than this one? But if not, then what on Earth could you have meant by your comment?
“I mean… just what, exactly, did you think I meant, when I suggested that we agree to disagree? Did you take me to be claiming that (a) the both of us are ideal Bayesian reasoners, and (b) we have common knowledge of our posterior probabilities of the clearly expressible proposition the truth of which we are discussing, but (c) our posterior probabilities, after learning this, should nonetheless differ? Is that what you thought I was saying? Really? But why? Why in the world did you interpret my words in such a bizarrely technical way? What would you say is your estimate of the probability that I actually meant to make that specific, precisely technical statement?”
And so on. The questions are rhetorical, of course. Anyone with half an ounce of common sense (not to mention anyone with an actual understanding of the AAT!) understands perfectly well that the Theorem is totally inapplicable to such cases.
(Of course, in some sense this is all moot. The one who says “actually, according to the AAT…” doesn’t really think that his interlocutor meant all of that. He’s not really making any kind of error… except, possibly, a tactical one—but perhaps not even that.)
Firstly, I hadn't heard the joke before, and it made me chuckle to myself.
Secondly, I loved this comment, for very accurately conveying the perspective I felt like ricraz was trying to defend wrt realism about rationality.
Let me say two (more) things in response:
Firstly, I was taking the example directly from Eliezer.
I said, "So if I make an Artificial Intelligence that, without being deliberately preprogrammed with any sort of script, starts talking about an emotional life that sounds like ours, that means your religion is wrong."
He said, &... (read more)
Epistemic status: trying to vaguely gesture at vague intuitions. A similar idea was explored here under the heading "the intelligibility of intelligence", although I hadn't seen it before writing this post. As of 2020, I consider this follow-up comment to be a better summary of the thing I was trying to convey with this post than the post itself. The core disagreement is about how much we expect the limiting case of arbitrarily high intelligence to tell us about the AGIs whose behaviour we're worried about.
There’s a mindset which is common in the rationalist community, which I call “realism about rationality” (the name being intended as a parallel to moral realism). I feel like my skepticism about agent foundations research is closely tied to my skepticism about this mindset, and so in this essay I try to articulate what it is.
Humans ascribe properties to entities in the world in order to describe and predict them. Here are three such properties: "momentum", "evolutionary fitness", and "intelligence". These are all pretty useful properties for high-level reasoning in the fields of physics, biology and AI, respectively. There's a key difference between the first two, though. Momentum is very amenable to formalisation: we can describe it using precise equations, and even prove things about it. Evolutionary fitness is the opposite: although nothing in biology makes sense without it, no biologist can take an organism and write down a simple equation to define its fitness in terms of more basic traits. This isn't just because biologists haven't figured out that equation yet. Rather, we have excellent reasons to think that fitness is an incredibly complicated "function" which basically requires you to describe that organism's entire phenotype, genotype and environment.
In a nutshell, then, realism about rationality is a mindset in which reasoning and intelligence are more like momentum than like fitness. It's a mindset which makes the following ideas seem natural:
To be clear, I am neither claiming that realism about rationality makes people dogmatic about such ideas, nor claiming that they're all false. In fact, from a historical point of view I’m quite optimistic about using maths to describe things in general. But starting from that historical baseline, I’m inclined to adjust downwards on questions related to formalising intelligent thought, whereas rationality realism would endorse adjusting upwards. This essay is primarily intended to explain my position, not justify it, but one important consideration for me is that intelligence as implemented in humans and animals is very messy, and so are our concepts and inferences, and so is the closest replica we have so far (intelligence in neural networks). It's true that "messy" human intelligence is able to generalise to a wide variety of domains it hadn't evolved to deal with, which supports rationality realism, but analogously an animal can be evolutionarily fit in novel environments without implying that fitness is easily formalisable.
Another way of pointing at rationality realism: suppose we model humans as internally-consistent agents with beliefs and goals. This model is obviously flawed, but also predictively powerful on the level of our everyday lives. When we use this model to extrapolate much further (e.g. imagining a much smarter agent with the same beliefs and goals), or base morality on this model (e.g. preference utilitarianism, CEV), is that more like using Newtonian physics to approximate relativity (works well, breaks down in edge cases) or more like cavemen using their physics intuitions to reason about space (a fundamentally flawed approach)?
Another gesture towards the thing: a popular metaphor for Kahneman and Tversky's dual process theory is a rider trying to control an elephant. Implicit in this metaphor is the localisation of personal identity primarily in the system 2 rider. Imagine reversing that, so that the experience and behaviour you identify with are primarily driven by your system 1, with a system 2 that is mostly a Hansonian rationalisation engine on top (one which occasionally also does useful maths). Does this shift your intuitions about the ideas above, e.g. by making your CEV feel less well-defined? I claim that the latter perspective is just as sensible as the former, and perhaps even more so - see, for example, Paul Christiano's model of the mind, which leads him to conclude that "imagining conscious deliberation as fundamental, rather than a product and input to reflexes that actually drive behavior, seems likely to cause confusion."
These ideas have been stewing in my mind for a while, but the immediate trigger for this post was a conversation about morality which went along these lines:
I had a lot of difficulty in figuring out what I actually meant during that conversation, but I think a quick way to summarise the disagreement is that O is a rationality realist, and I’m not. This is not a problem, per se: I'm happy that some people are already working on AI safety from this mindset, and I can imagine becoming convinced that rationality realism is a more correct mindset than my own. But I think it's a distinction worth keeping in mind, because assumptions baked into underlying worldviews are often difficult to notice, and also because the rationality community has selection effects favouring this particular worldview even though it doesn't necessarily follow from the community's founding thesis (that humans can and should be more rational).