Sorry, I understand the technical point about causal graphs you are refering to, but I do not understand the argument you're trying to make with it in this context.
Suppose it's the year 2100, and we have figured out the true underlying laws of physics, and it turns out that we run on a cellular automaton, and we have some very large and energy-intensive instruments that allow us to set up experiments where we can precisely set up the states of individual primitive cells. Now we want to use probabilistic reasoning to examine the time evolution of a cluster of such cells if we have only probabilistic information about the boundary conditions. Since this is a completely ordinary cellular automaton, we can describe it using a causal model, where the state of a cell at time t+1 is caused by its own state and the state of its neighbours at time t.
In this case, causality is really fundamentally there in the laws of physics (in a discrete analog of what we suspect for our actual laws of physics). And though you can't reach in from the outside of the universe, it's possible to imagine scenarios where you could do the equivalent of do() on some of the cells in your experiment, though it wouldn't really be done by acausally changing what happens in the universe -- one way to imagine it is that your experiment runs only in a two-dimensional slice surrounded by a "vacuum" of cells in a "zero" state, and you can reach in through that vacuum to change one of the cells in the two-dimensional grid.
But when it comes to how to model this inside a computer, it seems that you can reach all the conclusions you need by "ordinary" probabilistic reasoning: For example, you could start with say a uniform joint probability distribution over the state of all cells in your experiment at all times; then you condition on the fact that they fulfill the laws of physics, i.e. the time evolution rule of the cellular automaton; then you condition again on what you know about the boundary conditions, e.g. the fact that your experimental apparatus reaches in through the third dimension at some point to change the state of some cells. It's extraordinarily inefficient to represent the joint distribution as a giant look-up table of probabilities, but I do not see what inferences you want but are going to lose by doing the calculations that way.
(All of this holds even if the true laws happen to be deterministic in only one direction in time, so that in your experiment you can distinguish a -> b -> c from c -> b -> a by reaching in through the third dimension at time b.)
It depends on granularity. If you are talking about your game of life world on the level of the rules of the game, that is equivalent to talking about our Universe on the level of the universal wave function. In both cases there are no more agents with actuators and no more do(.), as a result. That is, it's not that your factorization will be causal, it's that there is no causality.
But if you are taking a more granular view of your game of life world, similar to the macroscopic view of our Universe, where there are agents that can push and prod their en...
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).