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Causation, Probability and Philosophy

Interview by Richard Marshall.

It’s important to realize that actual causation is one particular, specialized causal concept. It’s a mistake to analyze actual causation and think that you have thereby analyzed causation. The surface grammar of our language is misleading in this regard.

Do we have to worry about determinism? I guess that depends upon why you are worried. If you are worried that an indeterministic world is one without order, where things happen for no reason, and you can’t influence events, then you can stop worrying. If you are worried about free will and determinism, then I don’t think probabilistic causation makes those worries go away.

My preferred approach would be to justify one particular bit of metaphysics, by articulating some particular goal to be achieved, and showing that the bit of metaphysics is suited to that particular goal. This means-ends approach is common in epistemology: for example, James Joyce has defended probabilism — the claim that one’s degrees of belief should conform to the probability calculus — by showing that probabilistic degrees of belief minimize inaccuracy in a precise sense.

Norms provide a kind of template for how a particular situation is “supposed” to go. We then tend to focus on the exceptions, the places where norms are violated. Moreover, we can easily imagine situations that conform with norms. As a result, we are much more likely to entertain counterfactuals in which abnormal things are hypothetically rendered normal than the other way around.

Christopher Hitchcock’s research is focused on causation. He explores the kinds of causal reasoning used in the sciences, law, and everyday life, examining how causal questions in science differ from those that arise in moral or legal domains. His research makes use of formal tools for causal modeling that have been developed by philosophers, computer scientists, statisticians, and epidemiologists. In addition to causation, Hitchcock has done work in a number of other areas of the philosophy of science, including the philosophy of biology and the confirmation of hypotheses by evidence. He also works in formal epistemology, which employs mathematical tools such as probability to represent belief, inference, and evidence. He has recently undertaken a collaborative project in formal epistemology that involves modeling agreement and disagreement between individuals. Here he discusses the distinction between actual causation and causation, why norms are important in accounts of causation, why he rejects a Humean account of causation, an aside about scientific anti-realism, probabilistic causality and the worries of determinism, Kant’s ‘means-ends’ metaphysics, extended causal models, causal theories in the philosophy of mind using the fallacy of equivocation, counterfactual theories of causation, evolutionary theory as a theory of forces, defaults, typicality and normality, whether Dr Who should consult graphical causal models, probability and credences, and finally Bayes and the ‘shooting room’ paradox. Rockin’!

3:AM: What made you become a philosopher?

Christopher Hitchcock: I think I’ve always been a philosopher. I remember one incident when I was 11 or 12 years old. Somebody came to our school to administer tests for colorblindness. She asked the class if anyone had already taken such a test and knew that they were or weren’t color blind. One student said that he knew he wasn’t colorblind, because he had a box of crayons at home, and the crayon that said “red” looked red to him, the “blue” crayon looked blue to him, etc. I put up my hand and explained why that wouldn’t work. I didn’t know it at the time, but I had just discovered Wittgenstein’s Private Language Argument.

My high school offered philosophy. The teacher was eccentric; he appears as a character in two of my published papers. I don’t think I learned very much from those classes, but it was enough to pique my interest. In fact, a number of people from my small high school went on to become philosophers. One of them, Paul Bartha, was in my year; we have have been great friends since we were 12. We have co-authored two papers, and that was a lot of fun.

I went to Princeton as an undergraduate, where I expected to major in math, but I knew that I also wanted to take philosophy classes. My first philosophy class there was a big lecture class, but I was lucky to have Lisa Lloyd as my T.A. I got a C+ on my first paper in that class, because I wrote it the same way I wrote my high school philosophy papers. But I just needed that one kick in the butt, to be told how not to write a philosophy paper. I remember one day toward the end of my Freshman year, when I had math and philosophy classes back-to-back, and it struck me that my philosophy teachers seemed to be having more fun in the classroom. That’s when I decided to major in philosophy. There was a great philosophical community there: a world-class faculty, and friendly grad students who let me hang around like a kid brother.

I briefly thought about going to law school — that was what philosophy majors did. But when I looked through catalogues from various schools (you had to write letters to the schools and ask for them in those days), the only courses that sounded interesting to me were the ones that had a philosophical angle. So I decided to do graduate work in philosophy, being happily naïve about my employment prospects.

And I lived happily ever after (so far).

3:AM: Causation, counterfactuals and probability are where you ply your philosophical trade. Starting with causation, there’s a lack of consensus about what it is. Actual or token causation has taken the lion’s share of the philosophical literature but you and Josh Knobe think this might be a wrong avenue. Can you explain your thinking here and why we’d be better off examining causation in light of people’s understanding of norms?

CH: “Wrong avenue” is too strong. I have nothing against trying to analyze actual causation; I have played that game myself. But it’s important to realize that actual causation is one particular, specialized causal concept. It’s a mistake to analyze actual causation and think that you have thereby analyzed causation. The surface grammar of our language is misleading in this regard. Consider philosophers’ favorite example: “Suzy’s throwing her rock caused the bottle to smash”. This statement describes a relation of actual causation, but there is nothing in the wording to indicate that a specialized causal concept is involved. The word “caused” seems to suggest a fully general notion of causation. One of the clues that this is wrong is that many concepts that involve a causal dimension don’t involve actual causation. I have argued for this claim in detail in the specific case of causal decision theory; in particular, issues involving preemption that have dominated the literature on actual causation are irrelevant to causal decision theory. Interestingly, David Lewis’s own account of causal decision theory never makes use of his own theory of causation.

Once you recognize this, it becomes much more palatable to allow a role for norms in an account of actual causation. Here’s an analogy I have used. Consider the concept of inflation in economics. Suppose that in a given period of time, the price of beef goes up 30%, the price of pork goes down 10%, and the price of tofu stays the same. This will have different impacts on Hindus and Muslims, carnivores and vegetarians. More subtly, it will have different impacts on people depending on their willingness to make substitutions in their diet. And of course, these are just three goods out of a vast number. It is useful for economists to provide a consumer price index, a simple number that gives a general summary of whether prices have gone up or down, and by how much. But constructing such an index requires making assumptions about how people consume goods, and about how their consumption patterns will change in response to price changes. These, in turn, are influenced by people’s values — their religion, moral beliefs, dietary preferences, and so on. So the consumer price index does not just reflect objective changes in the prices of goods. Nonetheless, one shouldn’t go overboard and deny that inflation is real. The situation is similar with causation. In any given situation, there is an underlying objective causal structure. But it is very complicated. It is often useful to provide a simple, take-home message about what caused some event of interest. That is what we are reporting when we make a claim about actual causation. Norms play a role in determining what that simple take-home message is.

There has also been an awkward tension in discussions of actual causation. Non-philosophers frequently make a distinction between causes and mere background conditions. The lightning strike caused the forest fire; the oxygen in the atmosphere was a mere background condition. Starting with Mill, there has been a tradition of dismissing this distinction as philosophically meaningless. At best, it is a matter of pragmatics which of these causes one chooses to focus on. But philosophers draw distinctions, e.g., between cases of preemption where there is causation, and other cases with similar structures (such as cases of “switching” and “short circuits”) where there is not causation. That is, philosophers think that the second kind of distinction is getting at something about the metaphysics of causation, while the former is not. I think that both distinctions are on a par, and that norms play a role in both of them.

3:AM: Why don’t you like the Humean approach, roughly summarised as ‘‘In any concrete situation, there is an objective fact of the matter as to whether two events are in fact bound by the causal relation. It is the aim of philosophical inquiry to analyze this objective relation’?

CH: It was a bit of a cheat on my part to attribute this view to Hume, but I couldn’t resist the title “Of Humean Bondage”. Hume uses the language of the “cement of the universe”, but what he says is that for us, resemblance, contiguity, and cause and effect are the cement of the universe. He means that these are the three relations that connect our ideas together. J.L. Mackie then re-purposed the phrase and said that causation is the cement of the universe. I thought this metaphor aptly captured the position I reject.

I think that things in the world are causally connected, but there are many different ways in which they can be causally connected. And for some reason, philosophers have devoted a lot of effort to determining which of these connections are and are not cases of causation. For example, suppose I play music on my stereo. The setting of the power button and of the bass and treble knobs all affect the sound that comes out. By pressing the power button, I can cut off the sound completely, but that is all I can do. By turning the bass and treble knobs, I can exercise a more fine-grained control over the sound, but I can’t eliminate the sound completely. According to Lewis’s original counterfactual theory of causation (from 1973), the position of the power switch is a cause of the sound, but the positions of the bass and treble knobs are not. According to his later theory of causation as influence (2000), it’s the other way around. My own view is that there is no genuine issue to be resolved here. Once we understand the different ways in which the sound depends upon the buttons, there is no further issue of which buttons cause the sound.

3:AM: You’ve defended van Frassen’s causal anti-realism against Cartwright’s realism. You conclude that the anti-realist can use her anti-realist approach to causation into her vision of science in just as natural a way as the realist. Does that mean you think the issue of realist vs anti-realist isn’t important, or that by showing the strength of the anti-realist position you’ve shown how there’s no need to stick to realism if we’re wanting to use causation in an entirely natural way? Is that latter option what your causal models suggest – anti-realist theories with natural applicability – or do you see the models as idealised but realist in some way?

CH: Wow! That question goes back to the first paper I had accepted for publication (not counting a D&D monster that I published in White Dwarf when I was 14). When I was in graduate school, the scientific realism debate was ranging, and I thought about writing my dissertation on that topic. I haven’t written anything on the topic in 25 years, so I don’t have official views on the matter. Now I am less attracted to the anti-realist position than I was in graduate school. But I also think that it is a mistake to argue about scientific realism or anti-realism as global views. The issues involved in being a realist about viruses, quantum wave functions, forces of selection, and phonemes of Proto-Indo-European are just too different.

What I argued in that paper was that the issue of scientific realism is orthogonal to the issue of whether explanations are causal. In particular, inference to the best causal explanation is no better off than other forms of inference to the best explanation in arguing for scientific realism.
I haven’t really thought about the implications of my more recent work on causation for the scientific realism issue. Maybe your readers can send me some suggestions?

3:AM: What is probabilistic causality and does it mean we don’t have to worry about determinism?

CH: Probabilistic causality involves causes that raise or lower the probabilities of their effects. In particular, events can be caused even if they are not determined to occur by earlier events. For example, smoking can be a cause of lung even if the mutations that lead to cancer are truly indeterministic, since smoking increases the probability of getting lung cancer.

Do we have to worry about determinism? I guess that depends upon why you are worried. If you are worried that an indeterministic world is one without order, where things happen for no reason, and you can’t influence events, then you can stop worrying. If you are worried about free will and determinism, then I don’t think probabilistic causation makes those worries go away. I think the free will issue is (or should be) less about determinism per se, and more about the compatibility of free will with a physicalist or naturalist world view. If we are just complex physical systems, obeying the same laws as rocks, stars, and electrons, how can have free will?

3:AM: Do you see your approach a continuation of Kantian ‘means-ends metaphysics’ where one rigorously demonstrates the suitability of some conceptual framework for achieving a specified goal, and if so how does this approach help us understand causation and metaphysics – and does the model approach deal with the problem of overfitting?

CH: There has been an explosion of work in analytic metaphysics recently, but also a backlash of criticism. My own attitude to metaphysics is mixed. I don’t object to metaphysics per se, but I often find metaphysicians’ characterization of their projects puzzling. I don’t put much stock in the rationalist project of trying to understand the fundamental nature of reality using a priori methods. But let’s suppose that I wanted to build a database of the objects on my desk. Moreover, I want to be able to query the database. There is a philosophy journal and a Starbucks cup on my desk. When I ask the database: Are there at least two paper objects on my desk? I want it to answer “yes”. How could I structure the information in the database to permit it to draw this kind of inference? It seems to me that a metaphysical theory of constitution would be really useful for this kind of project. So I think that a lot of metaphysics would make sense if we re-consider the goal of the enterprise.

Kant’s approach to metaphysics is broadly along these lines. He claimed that metaphysics does not concern the nature of things in themselves. Rather, it concerns the concepts that we impose on the world of experience in order to make it intelligible. But I think Kant’s project was way too ambitious. He wanted to justify all of metaphysics (as he understood it) as a precondition for any empirical knowledge.

My preferred approach would be to justify one particular bit of metaphysics, by articulating some particular goal to be achieved, and showing that the bit of metaphysics is suited to that particular goal. This means-ends approach is common in epistemology: for example, James Joyce has defended probabilism — the claim that one’s degrees of belief should conform to the probability calculus — by showing that probabilistic degrees of belief minimize inaccuracy in a precise sense. I have tried to illustrate this approach in metaphysics using the question of whether the time at which an event occurs is an essential property of that event. Framed baldly as a question about the nature of events, it is hard to see how to get any purchase on this problem. But I show that if you want to accurately represent the possible interventions on a system, you have to represent events in one way rather than another. For this particular purpose, one needs to distinguish possible events that happen at different times.

3:AM: What is an extended causal model and why does yours offer a definition of causality with information about both causal structure and normality?

CH: As you say, an extended causal model is a structure that incorporates information both about causal structure, and about normality. Causal models provide a logic of interventions and counterfactuals that differs somewhat from logics of counterfactuals descended from Lewis. Default logics capture non-monotonic inferences governed by default rules (e.g. birds fly) that can be overridden by exceptions (penguins don’t fly). In my work with Joe Halpern, we sought to provide a semantic structure that could combine these ideas. We were motivated by our interest in actual causation (which involves both counterfactuals and normality). One problem we encountered was that extended causal models are incredibly complex structures — there is a kind of combinatorial explosion. So we sought to find ways in which these extended causal models could be represented more compactly. The idea is to use the causal structure to generate the normality structure, so that the normality structure could be specified by setting just a few parameters.

3:AM: When looking at the variety of causal theories available to philosophers of mind, you’ve argued that there’s something wrong with any argument whose premises can only be made true by shifting between different theories. Why is that such a problem? What should philosophers do instead?

CH: It’s a problem because it involves a fallacy of equivocation. Suppose I argue as follows: “Every river has two banks. A bank is a financial institution. Therefore, every river has two financial institutions.” This argument is unsound because the word “bank” means something different in each premise.I think that something similar is at work in the familiar causal exclusion argument. (This argument purports to show that certain otherwise attractive theories about the relationship between the mental and the physical have an unpalatable consequence: that mental properties are causally inert.) This argument has a number of premises involving causation. Each premise is plausible on some conception of causation. But there is no one conception of causation on which they are all true. What philosophers should do instead is be much more explicit about what conception of causation they are employing. I don’t think it even matters whether they use the “right” conception of causation. They will at least prove something that is true about the thing they are calling “causation” (whether it deserves the name or not).

3:AM: Are counterfactual theories of causation barking up the wrong tree?

CH: Not at all! NASA sometimes justified the tremendous expense of the Apollo missions by citing the “spinoff” technology that resulted from the project: microchips, freeze-dried food, memory foam, and so on. I think the situation is similar in the study of causation. Going back to Lewis (and a few predecessors), people have been trying to analyze causation (or more specifically, actual causation) in terms of counterfactuals. No one has produced an analysis that has been widely accepted. But in the process, a lot of good philosophy has spun off. We have recognized a wide variety of different kinds of causal structure, cases of early and late preemption, overdetermination, trumping, double prevention, and so on. We have also recognized different kinds of causal relationship: on-off control vs. fine-grained influence (as discussed in response to question 3), net effects vs. path-specific effects, and so on. And counterfactual theories have proven to be very useful tools for characterizing all of these different things. They have also influenced formal developments in causal modeling in statistics and computer science.

3:AM: Why do you think it fruitful to understand evolutionary theory as a theory of forces analogous to Newton’s mechanics? And are causes forces?

CH: It is fairly common to present evolutionary theory, or more specifically population genetics, as a theory of forces analogous to Newtonian mechanics. I think this is a useful analogy. But critics have attacked this analogy. In the paper that I wrote with Joel Velasco, we argue that these criticisms are based on an overly narrow conception of Newtonian forces. Forces in Newtonian mechanics are heterogeneous: gravity is very different from friction. Evolutionary forces are also heterogeneous: natural selection is very different from mutation pressure. Most participants in the debate seemed to assume that if evolutionary forces are like Newtonian forces, then natural selection must be like gravity. But it turns out that natural selection is more like friction, and gravity is more like mutation pressure. So I think the analogy works. But because Newtonian forces are so heterogeneous, saying that something is like a Newtonian force is a much weaker claim than people had realized.

3:AM: You’ve looked at the data about judgments of actual causation coming out of psychology ad experimental philosophy. Defaults, typicality and normality are important influences on such judgments according to the sources. So can you sketch what these are and then say why you think it useful to incorporate them into an account of actual causation, leaving us with a notion of actual causation as being both graded and comparative?

CH: Defaults, typicality, and normality are all slightly different things. Typicality means something like statistical frequency. Typically, humans are right-handed (about 90% are). But “typical” also carries a connotation of something like “stereotypical”, something that we think of as characterizing a type. In this sense, a typical Bavarian wears lederhosen, although the actual frequency is not very high. “Default” is what is assumed in the absence of any further specification. In Newtonian mechanics, the default behavior of a body is to travel in a straight line with uniform velocity. Literally nothing in the universe does this: everything is affected by the force of gravity. But it is nonetheless crucial to the theory to begin by saying what happens when no forces are acting. A “norm” can be a statistical norm, but more often (in philosophy at least), we use “norm” to mean a prescriptive norm. This can be a moral norm, a social norm (such as a rule of etiquette), a law, or a policy adopted by an institution. There are also norms of proper functioning governing biological organisms and machines. I like to use “norm”, “normal”, and “normality” as an umbrella term covering all of these notions.

These things are all different, and as philosophers, we naturally want to make distinctions. And real harm results from conflating them. Many people believe that homosexuality is morally wrong, and I think they do this in part because it is statistically infrequent and it violates a biological norm of reproductive fitness. That is just sloppy thinking. But I think that norms of all these different kinds play a similar role in certain aspects of our thinking. They provide a kind of template for how a particular situation is “supposed” to go. We then tend to focus on the exceptions, the places where norms are violated. Moreover, we can easily imagine situations that conform with norms. As a result, we are much more likely to entertain counterfactuals in which abnormal things are hypothetically rendered normal than the other way around.

There is now a large body of empirical literature showing that normality in all of these forms influences subjects’ judgments of actual causation. Not only does the normality of an event affect our willingness to judge that it is a cause, it also affects our judgments about other events. (This is one of the ways in which judgments of actual causation are comparative.) So if you want to provide an account of actual causation that accords with the judgments of actual subjects, it will need to incorporate normality. And it is not just naïve subjects who make these judgments. When Josh Knobe and I ran an online survey, we had over 300 philosophers participate, and their judgments were sensitive to normality in the same way that other subjects’ judgments were.

Since normality is a matter of degree, it is natural to think of actual causation coming in degrees. And if you give subjects’ a numerical scale, they are often happy to assign intermediate ratings to causal claims.

3:AM: If the Time Lord time traveller Dr Who has to make an intervention, should he consult graphical causal models?

CH: Absolutely! He needs to know what kind of time travel story he is in. Is it one of those “cheat” time travel stories where the actions of the time traveler create a new time line (like Back to the Future, and the Star Trek reboot)? Or is it an honest time travel story where all of the events take place in one consistent time line (like Twelve Monkeys and Bill and Ted’s Excellent Adventure)? This will influence the way in which he uses information he has about the future. Is it information about what will, in fact, happen as a result of his intervention? Or is it information about what would happen if he didn’t intervene? Graphical causal models provide methods for incorporating both kinds of information. Other versions of causal decision theory don’t provide this flexibility.

3:AM: Probability is another of your philosophical targets. A Bayesian approach substitutes ‘belief’ talk with ‘credence’ talk in some way (I think!). Can you sketch what credences are and why they might be an improvement on belief talk?

CH: Credences are degrees of belief, that have numerical values satisfying the probability calculus. So if I have a credence of .39 that Trump will be impeached, I have to have a credence of .61 that he will not be impeached (since probabilities must add to 1). It’s obviously an idealization that people will have numerically precise degrees of belief. But I find the idea that people believe some things more or less strongly, and that these degrees of belief can lie somewhere between full belief and disbelief, very natural. I actually find it kind of liberating that I don’t need to make up my mind about whether something is true; I can weigh the evidence, believe it to a greater or lesser degree, and still use that partial belief to make reasoned decisions. There’s a lot that you can do once you have the formalism of probability theory on board. For instance, you can use decision theory to provide an account of rational decision-making, and you can provide an account of belief revision using conditionalization.

3:AM: [For the reader, the ‘Shooting Room’ paradox, here taken from Richard Yetter Chappell: ‘… here’s the set up: a group of people are sent into a room. Two dice are rolled, and if they land double sixes then everyone in the room gets shot. Otherwise, they’re released and the whole procedure is repeated again with a new group of ten times as many people. (And so on, until a group gets shot.) You’re sent into the room. What is your chance of being shot?

Well, obviously 1/36, right? That’s the chance of double sixes being rolled. But note that the vast majority (~90%) of people who enter the room get shot. (This is stipulated — assume there is an unlimited stock of people, ammo, etc. There’s no risk of “running out”, no matter how many rounds the game goes on for.) You have no reason to consider yourself one of the lucky 10%. You have the same chance of being shot that anyone else who enters the room does. So you must all have a 9/10 chance of being shot.

Very puzzling.’]

According to Bayes, can we calculate the hour of our death given that we exist now – and does this connect with John Leslie’s ‘Shooting Room’ paradox?

CH: No and yes. To my knowledge, Bayes himself never wrote about this topic. Paul Bartha came up with the title for our paper on the doomsday paradox. It includes a quote from the book of Revelation, and refers to Bayes by his religious title. I thought this made a nice juxtaposition. From the fact that we exist now, we can infer that we are not dead yet, and that’s about all that we can conclude about the time of our death. So I basically reject any kind of doomsday reasoning.

The shooting room paradox is closely related to the doomsday paradox, but the mechanism underwriting the probabilities is much more explicit, and this makes it easier to grapple with in a rigorous fashion. It turns out to be a subtle problem. For example, the correct solution depends upon whether your credences are countably additive or only finitely additive. (This concerns the way in which you assign credences to certain infinite disjunctions.)

3:AM: And for the readers at 3:AM, are there five books other than your own that you can recommend that will take us further into your philosophical world?

CH: I would say the five most important books are (in chronological order):

David Lewis, Philosophical Papers, Volume II

Peter Spirtes, Clark Glymour, and Richard Shceines, Causation, Prediction and Search.

Judea Pearl, Causality: Models, Reasoning, and Inference.

James Woodward, Making Things Happen: A Theory of Causal Explanation

Joseph Halpern, Actual Causality

But some of these books are quite technical. So if I can cheat, I would recommend that beginners start with the Oxford Handbook of Causation. I am a co-editor (with Helen Beebee and Peter Menzies) and I wrote one of the chapters. So perhaps to comply with the letter of your request I should advise readers to only read the other 36 chapters.

Richard Marshall is still biding his time.

Buy his new book here or his first book here to keep him biding!

First published in 3:AM Magazine: Monday, August 14th, 2017.