This sounds like we're talking past each other somehow. Your point (a) is not clear to me - I was saying that to learn a sufficiently high-probability causal model from non-intervention data, you need to have observed the data in sufficient detail to rule out confounders (except at some low probability) (via simplicity priors, which otherwise can't drive down the probability of an untestable invisible confounder by all that far). This can certainly be done in principle, e.g. if you put the system under a microscope with a higher resolution than the system, and verified there were only X kinds of stuff in it and no others.
Your point (b) sounds just plain wrong to me. If you have a simplicity prior over causal models, and you can derive testable probable predictions from causal models, then you can do Bayesian updating and get a posterior over causal models. Substituting the word "flammable fizzbins" for "causal models" in the preceding sentence will produce another true sentence. I think you mean something different by "Bayesian" and "Occam's Razor" than I do.
By (a) I mean that you can sometimes get the true graph exactly even without having to observe confounders. Actually this was sort of known already (see the FCI algorithm, or even the IC* algorithm in Pearl's book), but we can do a lot better than that. For example, if we have the true graph:
a -> b -> c -> d, with a <- u1 -> c, and a <- u2 -> d, where we do not observe u1,u2, and u1,u2 are very complicated, then we can figure out the true graph exactly by independence type techniques without having to observe u1 and u2. Note: the ma...
Part of the sequence: Rationality and Philosophy
Thomas Kelly
Jason Brennan
After millennia of debate, philosophers remain heavily divided on many core issues. According to the largest-ever survey of philosophers, they're split 25-24-18 on deontology / consequentialism / virtue ethics, 35-27 on empiricism vs. rationalism, and 57-27 on physicalism vs. non-physicalism.
Sometimes, they are even divided on psychological questions that psychologists have already answered: Philosophers are split evenly on the question of whether it's possible to make a moral judgment without being motivated to abide by that judgment, even though we already know that this is possible for some people with damage to their brain's reward system, for example many Parkinson's patients, and patients with damage to the ventromedial frontal cortex (Schroeder et al. 2012).1
Why are physicists, biologists, and psychologists more prone to reach consensus than philosophers?2 One standard story is that "the method of science is to amass such an enormous mountain of evidence that... scientists cannot ignore it." Hence, religionists might still argue that Earth is flat or that evolutionary theory and the Big Bang theory are "lies from the pit of hell," and philosophers might still be divided about whether somebody can make a moral judgment they aren't themselves motivated by, but scientists have reached consensus about such things.
In its dependence on masses of evidence and definitive experiments, science doesn't trust your rationality:
Sometimes, you can answer philosophical questions with mountains of evidence, as with the example of moral motivation given above. But or many philosophical problems, overwhelming evidence simply isn't available. Or maybe you can't afford to wait a decade for definitive experiments to be done. Thus, "if you would rather not waste ten years trying to prove the wrong theory," or if you'd like to get the right answer without overwhelming evidence, "you'll need to [tackle] the vastly more difficult problem: listening to evidence that doesn't shout in your ear."
This is why philosophers need rationality training even more desperately than scientists do. Philosophy asks you to get the right answer without evidence that shouts in your ear. The less evidence you have, or the harder it is to interpret, the more rationality you need to get the right answer. (As likelihood ratios get smaller, your priors need to be better and your updates more accurate.)
Because it tackles so many questions that can't be answered by masses of evidence or definitive experiments, philosophy needs to trust your rationality even though it shouldn't: we generally are as "stupid and self-deceiving" as science assumes we are. We're "predictably irrational" and all that.
But hey! Maybe philosophers are prepared for this. Since philosophy is so much more demanding of one's rationality, perhaps the field has built top-notch rationality training into the standard philosophy curriculum?
Alas, it doesn't seem so. I don't see much Kahneman & Tversky in philosophy syllabi — just light-weight "critical thinking" classes and lists of informal fallacies. But even classes in human bias might not improve things much due to the sophistication effect: someone with a sophisticated knowledge of fallacies and biases might just have more ammunition with which to attack views they don't like. So what's really needed is regular habits training for genuine curiosity, motivated cognition mitigation, and so on.
(Imagine a world in which Frank Jackson's famous reversal on the knowledge argument wasn't news — because established philosophers changed their minds all the time. Imagine a world in which philosophers were fine-tuned enough to reach consensus on 10 bits of evidence rather than 1,000.)
We might also ask: How well do philosophers perform on standard tests of rationality, for example Frederick (2005)'s CRT? Livengood et al. (2010) found, via an internet survey, that subjects with graduate-level philosophy training had a mean CRT score of 1.32. (The best possible score is 3.)
A score of 1.32 isn't radically different from the mean CRT scores found for psychology undergraduates (1.5), financial planners (1.76), Florida Circuit Court judges (1.23), Princeton Undergraduates (1.63), and people who happened to be sitting along the Charles River during a July 4th fireworks display (1.53). It is also noticeably lower than the mean CRT scores found for MIT students (2.18) and for attendees to a LessWrong.com meetup group (2.69).
Moreover, several studies show that philosophers are just as prone to particular biases as laypeople (Schulz et al. 2011; Tobia et al. 2012), for example order effects in moral judgment (Schwitzgebel & Cushman 2012).
People are typically excited about the Center for Applied Rationality because it teaches thinking skills that can improve one's happiness and effectiveness. That excites me, too. But I hope that in the long run CFAR will also help produce better philosophers, because it looks to me like we need top-notch philosophical work to secure a desirable future for humanity.3
Next post: Train Philosophers with Pearl and Kahneman, not Plato and Kant
Previous post: Intuitions Aren't Shared That Way
Notes
1 Clearly, many philosophers have advanced versions of motivational internalism that are directly contradicted by these results from psychology. However, we don't know exactly which version of motivational internalism is defended by each survey participant who said they "accept" or "lean toward" motivational internalism. Perhaps many of them defend weakened versions of motivational internalism, such as those discussed in section 3.1 of May (forthcoming).
2 Mathematicians reach even stronger consensus than physicists, but they don't appeal to what is usually thought of as "mountains of evidence." What's going on, there? Mathematicians and philosophers almost always agree about whether a proof or an argument is valid, given a particular formal system. The difference is that a mathematician's premises consist in axioms and in theorems already strongly proven, whereas a philosopher's premises consist in substantive claims about the world for which the evidence given is often very weak (e.g. that philosopher's intuitions).
3 Bostrom (2000); Yudkowsky (2008); Muehlhauser (2011).