Why not?
Because, again, you do not have access to the same evidence (if Richard is right about the conceivability of zombies, that is!). Robin's paper is unfortunately not going to avail you here. It applies to cases where Bayesians share all the same information but nevertheless disagree. To reiterate, Richard (as I understand him) believes that you and he do not share the same information.
In any case, what I want to know is how I should update my beliefs in light of Richard's statements.
Well, you shouldn't take his testimony of zombie conceivability as very good evidence of zombie conceivability. In that sense, you don't have to sweat this conversation very much at all. This is less a debate about the conceivability of zombies and more a debate about the various dialectical positions of the parties involved in the conceivability debate. Do people who feel they can "robustly" conceive of p-zombies necessarily have to found their beliefs on publicly evaluable, "third-person" evidence? That seems to me the cornerstone of this particular discussion, rather than: Is the evidence for the conceivability of p-zombies any good?
In such a dispute, there is some observation O'' that (both parties can agree) you made, which is equal to (or implies) either O or O', and the dispute is about which one of these it is the same as (or implies). But since O implies H and O' doesn't, the dispute reduces to the question of whether O'' implies H or not, and so you may as well discuss that directly.
Yes, that's the "neutral" view of evidence Richard professed to deny.
The actual values of O and O' at hand are "That one particular mental event which occurred in Richard's mind at time t [when he was trying to conceive of zombies] was a conception of zombies," and "That one particular mental event which occurred in Richard's mind at time t was a conception of something other than zombies, or a non-conception." The truth-value value of the O'' you provide has little bearing on either of these.
EDIT: Here's a thought experiment that might illuminate my argument a bit. Imagine a group of evil scientists kidnaps you and implants special contact lenses which stream red light directly into your retina constantly. Your visual field is a uniformly red canvas, and you can never shut it off. The scientists then strand you on an island full of Bayesian tribespeople who are congenitally blind. The tribespeople consider the existence of visual experience ridiculous and point to all sorts of icky human biases tainting our judgment. How do you update your belief that you're experiencing red?
EDIT 2: Looking over this once again, I think I should be less glib in my first paragraph. Note that I'm denying that you share common priors, but then appealing to different evidence that you have to explain why this can be rational. If the difference in priors is a result of the difference in evidence, aren't they just posteriors?
The answer I personally would give is that there are different kinds of evidence. Posteriors are the result of conditionalizing on propositional evidence, such as "Snow is white." But not all evidence is propositional. In particular, many of our introspective beliefs are justified (when they are justified at all) by the direct access we have to our own experiences. Experiences are not propositions! You cannot conditionalize on an experience. You can conditionalize on a sentence like "I am having experience E," of course, but the evidence for that sentence is going to come from E itself, not another proposition.
Robin's paper is unfortunately not going to avail you here. It applies to cases where Bayesians share all the same information but nevertheless disagree.
This is not correct. Even the original Aumann theorem only assumes that the Bayesians have (besides common priors) common knowledge of each other's probability estimates -- not that they share all the same information! (In fact, if they have common priors and the same information, then their posteriors are trivially equal.)
Robin's paper imposes restrictions on being able to postulate uncommon priors as ...
Part of the sequence: Rationality and Philosophy
Eliezer's anti-philosophy post Against Modal Logics was pretty controversial, while my recent pro-philosophy (by LW standards) post and my list of useful mainstream philosophy contributions were massively up-voted. This suggests a significant appreciation for mainstream philosophy on Less Wrong - not surprising, since Less Wrong covers so many philosophical topics.
If you followed the recent very long debate between Eliezer and I over the value of mainstream philosophy, you may have gotten the impression that Eliezer and I strongly diverge on the subject. But I suspect I agree more with Eliezer on the value of mainstream philosophy than I do with many Less Wrong readers - perhaps most.
That might sound odd coming from someone who writes a philosophy blog and spends most of his spare time doing philosophy, so let me explain myself. (Warning: broad generalizations ahead! There are exceptions.)
Failed methods
Large swaths of philosophy (e.g. continental and postmodern philosophy) often don't even try to be clear, rigorous, or scientifically respectable. This is philosophy of the "Uncle Joe's musings on the meaning of life" sort, except that it's dressed up in big words and long footnotes. You will occasionally stumble upon an argument, but it falls prey to magical categories and language confusions and non-natural hypotheses. You may also stumble upon science or math, but they are used to 'prove' things irrelevant to the actual scientific data or the equations used.
Analytic philosophy is clearer, more rigorous, and better with math and science, but only does a slightly better job of avoiding magical categories, language confusions, and non-natural hypotheses. Moreover, its central tool is intuition, and this displays a near-total ignorance of how brains work. As Michael Vassar observes, philosophers are "spectacularly bad" at understanding that their intuitions are generated by cognitive algorithms.
A diseased discipline
What about Quinean naturalists? Many of them at least understand the basics: that things are made of atoms, that many questions don't need to be answered but instead dissolved, that the brain is not an a priori truth factory, that intuitions come from cognitive algorithms, that humans are loaded with bias, that language is full of tricks, and that justification rests in the lens that can see its flaws. Some of them are even Bayesians.
Like I said, a few naturalistic philosophers are doing some useful work. But the signal-to-noise ratio is much lower even in naturalistic philosophy than it is in, say, behavioral economics or cognitive neuroscience or artificial intelligence or statistics. Why? Here are some hypotheses, based on my thousands of hours in the literature:
Of course, there is mainstream philosophy that is both good and cutting-edge: the work of Nick Bostrom and Daniel Dennett stands out. And of course there is a role for those who keep arguing for atheism and reductionism and so on. I was a fundamentalist Christian until I read some contemporary atheistic philosophy, so that kind of work definitely does some good.
But if you're looking to solve cutting-edge problems, mainstream philosophy is one of the last places you should look. Try to find the answer in the cognitive science or AI literature first, or try to solve the problem by applying rationalist thinking: like this.
Swimming the murky waters of mainstream philosophy is perhaps a job best left for those who already spent several years studying it - that is, people like me. I already know what things are called and where to look, and I have an efficient filter for skipping past the 95% of philosophy that isn't useful to me. And hopefully my rationalist training will protect me from picking up bad habits of thought.
Philosophy: the way forward
Unfortunately, many important problems are fundamentally philosophical problems. Philosophy itself is unavoidable. How can we proceed?
First, we must remain vigilant with our rationality training. It is not easy to overcome millions of years of brain evolution, and as long as you are human there is no final victory. You will always wake up the next morning as homo sapiens.
Second, if you want to contribute to cutting-edge problems, even ones that seem philosophical, it's far more productive to study math and science than it is to study philosophy. You'll learn more in math and science, and your learning will be of a higher quality. Ask a fellow rationalist who is knowledgeable about philosophy what the standard positions and arguments in philosophy are on your topic. If any of them seem really useful, grab those particular works and read them. But again: you're probably better off trying to solve the problem by thinking like a cognitive scientist or an AI programmer than by ingesting mainstream philosophy.
However, I must say that I wish so much of Eliezer's cutting-edge work wasn't spread out across hundreds of Less Wrong blog posts and long SIAI articles written in with an idiosyncratic style and vocabulary. I would rather these ideas were written in standard academic form, even if they transcended the standard game of mainstream philosophy.
But it's one thing to complain; another to offer solutions. So let me tell you what I think cutting-edge philosophy should be. As you might expect, my vision is to combine what's good in LW-style philosophy with what's good in mainstream philosophy, and toss out the rest:
Note that this is not just my vision of how to get published in journals. It's my vision of how to do philosophy.
Meeting journals standards is not the most important reason to follow the suggestions above. Write short articles because they're easier to follow. Open with the context and goals of your article because that makes it easier to understand, and lets people decide right away whether your article fits their interests. Use standard terms so that people already familiar with the topic aren't annoyed at having to learn a whole new vocabulary just to read your paper. Cite the relevant positions and arguments so that people have a sense of the context of what you're doing, and can look up what other people have said on the topic. Write clearly and simply and with much organization so that your paper is not wearying to read. Write lots of hand-holding sentences because we always communicate less effectively then we thought we did. Cite the relevant literature as much as possible to assist your most careful readers in getting the information they want to know. Use your rationality training to remain sharp at all times. And so on.
That is what cutting-edge philosophy could look like, I think.
Next post: How You Make Judgments
Previous post: Less Wrong Rationality and Mainstream Philosophy