How significant/relevant is the mathematical work on causality to philosophical work/discussion? If someone was talking about causality in a philosophical setting and had never heard of the relevant math, how badly would/should that reflect on them? Does it make a difference if they’ve heard of it, but didn’t bother to learn the math?
I am not up on my philosophical literature (trying to change this), but I think most analytic philosophers have heard of Pearl et al. by now. Not every analytic philosopher is as mathematically sophisticated as e.g. people at the CMU department. But I think that’s ok!
I don’t think it’s a wise social move for LW to beat on philosophers.
Which academic disciplines care about causality? (I’m guessing statistics, CS, philosophy… anything else?)
Is there anything like a mainstream agreement on how to model/establish causality? E.g. does more or less everyone agree that Pearl’s book, which I haven’t read, is the right approach? If not, is it possible to list the main competing approaches? Does there exist a reasonably neutral high-level summary of the field?
Which academic disciplines care about causality? (I’m guessing statistics, CS, philosophy… anything else?)
On some level any empirical science cares, because the empirical sciences all care about cause-effect relationships. In practice, the ‘penetration rate’ is path-dependent (that is, depends on the history of the field, personalities involved, etc.)
To add to your list, there are people in public health (epidemiology, biostatistics), social science, psychology, political science, economics/econometrics, computational bio/omics that care quite a bit. Very few philosophers (excepting the CMU gang, and a few other places) think about causal inference at the level of detail a statistician would. CS/ML do not care very much (even though Pearl is CS).
Is there anything like a mainstream agreement on how to model/establish causality? E.g. does more or less
everyone agree that Pearl’s book, which I haven’t read, is the right approach? If not, is it possible to list the main
competing approaches?
I think there is as much agreement as there can reasonably be for a concept such as causality (that is, a philosophically laden concept that’s fun to argue about). People model it in lots of ways, I will try to give a rough taxonomy, and will tell you where Pearl lies
Interventionist vs non-interventionist
Most modern causal inference folks are interventionists (including Pearl, Rubin, Robins, etc.). The ‘Nicene crede’ for interventionists is: (a) an intervention (forced assignment) is key for representing cause/effect, (b) interventions and conditioning are not the same thing, (c) you express interventions in terms of ordinary probabilities using the g-formula/truncated factorization/manipulated distribution (different names for the same thing). The concept of an intervention is old (goes back to Neyman (1920s), I think, possibly even earlier).
To me, non-interventionists fall into three categories: ‘naive,’ ‘abstract’, and ‘indifferent.’ Naive non-interventionists are not using interventions because they haven’t thought about things hard enough, and will thus get things wrong. Some EDT folks are in this category. People who ask ‘but why can’t we just use conditional probabilities’ are often in this set. Abstract non-interventionists are not using interventions because they have in mind some formalism that has interventions as a special case, and they have no particular need for the special case. I think David Lewis was in this camp. Joe Halpern might be in this set, I will ask him sometime. Indifferent non-interventionists operate in a field where there is little difference between conditioning and interventions (due to lack of interesting confounding), so there is no need to model interventions explicitly. Reinforcement learning people, and people who only work with RCT data are in this set.
Counterfactualists vs non-counterfactualists
Most modern causal inference folks are counterfactualist (including Pearl, Rubin, Robins, etc.). To a counterfactualist it is important to think about a hypothetical outcome under a hypothetical intervention. Obviously all counterfactualists are interventionist. A noted non-counterfactualist interventionist is Phil Dawid. Counterfactuals are also due to Neyman, but were revived and extended by Rubin in the 70s.
Graphical vs non-graphical
Whether you like using graphs or not. Modern causal inference is split on this point. Folks in the Rubin camp do not like graphs (for reasons that are not entirely clear—what I heard is they find them distracting from important statistical modeling issues (??)). Folks in the Pearl/SGS/Robins/Dawid/etc. camp like graphs. You don’t have to have a particular commitment to any earlier point to have an opinion on graphs (indeed lots of graphical models are not about causality at all). In the context of causality, graphs were first used by Sewall Wright for pedigree analysis (1920s). Lauritzen, Pearl, etc. gave a modern synthesis of graphical models. Spirtes/Glymour/Scheines and Pearl revived a causal interpretation of graphs in the 90s.
“Popperians” vs “non-Popperians”
Whether you restrict yourself to testable assumptions. Pearl is non-Popperian, his models make assumptions that can only be tested via a time machine or an Everett branch jumping algorithm. Rubin is also non-Popperian because of “principal stratification.” People that do “mediation analysis” are generally non-Popperian. Dawid, Robins, and Richardson are Popperians—they try to stick to testable assumptions only. I think even for Popperians, some of their assumptions must be untestable (but I think this is probably necessary for statistical inference in general). I think Dawid might claim all counterfactualists are non-Popperian in some sense.
I am “a graphical non-Popperian counterfactualist” (and thus interventionist).
Does there exist a reasonably neutral high-level summary of the field?
“Pearlian causality” is sort of like “Hawkingian physics.” (Not to dismiss the amazing contributions of both Pearl and Hawking to their respective fields).
I am not sure what cool or insightful is for you. What seems cool to me is that proper analysis of causality and/or missing data (these two are related) in observational data in epidemiology is now more or less routine. The use of instrumental variables for getting causal effects is also routine in econometrics.
The very fact that people think about a causal effect as a formal mathematical thing, and then use proper techniques to get it in applied/data analysis settings seems very neat to me. This is what success of analytic philosophy ought to look like!
What you mention in your last paragraph is roughly what I had in mind when asking for examples. So I take it that IVs are a method inspired by causal graphs (or at least causal maths)? If so you’ve answered my question.
IVs were first derived by either Sewall Wright or his dad (there is some disagreement on this point). I don’t think they formally understood interventions in general back in 1928, but they understood causality very well in the linear model special case.
IVs can be used in more general models than linear, and the reason they work in such settings needed formal causal math to work out, yes. IVs recover interventionist causal effects.
I got into AI/ML and graphical models as an undergrad. I thought graphical models were very pretty, but I didn’t really understand them back then very well (probably still don’t..). Causal inference is the closest we have to “applied philosophy,” and that was very interesting to me because I like both philosophy and mathematics (not that I am any good at either!) Also I had an opportunity to study with a preeminent person and took it.
Are you aware of any attempts to assign a causality(-like?) structure to mathematics?
There are certainly areas of mathematics where it seems like there is an underlying causality structure (frequently orthogonal or even inverse to the proof structure), but the probability based definition of causality fails when all the probabilities are 0 or 1.
There are certainly areas of mathematics where it seems like there is an underlying causality structure (frequently
orthogonal or even inverse to the proof structure)
Can you give a simple example of/pointer to what you mean?
I don’t know if this is what Nier has in mind, but it reminds me of Cramer’s random model for the primes. There is a 100 per cent chance that 758705024863 is prime, but it is very often useful to regard it as the output of a random process. Here’s an example of the model in action.
I am aware of “logical uncertainty”, etc. However I think uncertainty and causality are orthogonal (some probabilistic models aren’t causal, and some causal models, e.g. circuit models, have no uncertainty in them).
Well, in analytic number theory, for example, there are many heuristic arguments that have a causality like flavor; however, the proofs of the statements in question are frequently unrelated to the heuristics.
Also, this is a discussion about the causal relationship between a theorem and its proof.
I don’t know much about analytic number theory, could you be more specific? I didn’t follow the discussion you linked very well, because they say things like “Pearlian causality is not counterfactual”, or think that there is any relationship between implication and causation. Neither is true.
I write about causality sometimes.
How significant/relevant is the mathematical work on causality to philosophical work/discussion? If someone was talking about causality in a philosophical setting and had never heard of the relevant math, how badly would/should that reflect on them? Does it make a difference if they’ve heard of it, but didn’t bother to learn the math?
I am not up on my philosophical literature (trying to change this), but I think most analytic philosophers have heard of Pearl et al. by now. Not every analytic philosopher is as mathematically sophisticated as e.g. people at the CMU department. But I think that’s ok!
I don’t think it’s a wise social move for LW to beat on philosophers.
Which academic disciplines care about causality? (I’m guessing statistics, CS, philosophy… anything else?)
Is there anything like a mainstream agreement on how to model/establish causality? E.g. does more or less everyone agree that Pearl’s book, which I haven’t read, is the right approach? If not, is it possible to list the main competing approaches? Does there exist a reasonably neutral high-level summary of the field?
On some level any empirical science cares, because the empirical sciences all care about cause-effect relationships. In practice, the ‘penetration rate’ is path-dependent (that is, depends on the history of the field, personalities involved, etc.)
To add to your list, there are people in public health (epidemiology, biostatistics), social science, psychology, political science, economics/econometrics, computational bio/omics that care quite a bit. Very few philosophers (excepting the CMU gang, and a few other places) think about causal inference at the level of detail a statistician would. CS/ML do not care very much (even though Pearl is CS).
I think there is as much agreement as there can reasonably be for a concept such as causality (that is, a philosophically laden concept that’s fun to argue about). People model it in lots of ways, I will try to give a rough taxonomy, and will tell you where Pearl lies
Interventionist vs non-interventionist
Most modern causal inference folks are interventionists (including Pearl, Rubin, Robins, etc.). The ‘Nicene crede’ for interventionists is: (a) an intervention (forced assignment) is key for representing cause/effect, (b) interventions and conditioning are not the same thing, (c) you express interventions in terms of ordinary probabilities using the g-formula/truncated factorization/manipulated distribution (different names for the same thing). The concept of an intervention is old (goes back to Neyman (1920s), I think, possibly even earlier).
To me, non-interventionists fall into three categories: ‘naive,’ ‘abstract’, and ‘indifferent.’ Naive non-interventionists are not using interventions because they haven’t thought about things hard enough, and will thus get things wrong. Some EDT folks are in this category. People who ask ‘but why can’t we just use conditional probabilities’ are often in this set. Abstract non-interventionists are not using interventions because they have in mind some formalism that has interventions as a special case, and they have no particular need for the special case. I think David Lewis was in this camp. Joe Halpern might be in this set, I will ask him sometime. Indifferent non-interventionists operate in a field where there is little difference between conditioning and interventions (due to lack of interesting confounding), so there is no need to model interventions explicitly. Reinforcement learning people, and people who only work with RCT data are in this set.
Counterfactualists vs non-counterfactualists
Most modern causal inference folks are counterfactualist (including Pearl, Rubin, Robins, etc.). To a counterfactualist it is important to think about a hypothetical outcome under a hypothetical intervention. Obviously all counterfactualists are interventionist. A noted non-counterfactualist interventionist is Phil Dawid. Counterfactuals are also due to Neyman, but were revived and extended by Rubin in the 70s.
Graphical vs non-graphical
Whether you like using graphs or not. Modern causal inference is split on this point. Folks in the Rubin camp do not like graphs (for reasons that are not entirely clear—what I heard is they find them distracting from important statistical modeling issues (??)). Folks in the Pearl/SGS/Robins/Dawid/etc. camp like graphs. You don’t have to have a particular commitment to any earlier point to have an opinion on graphs (indeed lots of graphical models are not about causality at all). In the context of causality, graphs were first used by Sewall Wright for pedigree analysis (1920s). Lauritzen, Pearl, etc. gave a modern synthesis of graphical models. Spirtes/Glymour/Scheines and Pearl revived a causal interpretation of graphs in the 90s.
“Popperians” vs “non-Popperians”
Whether you restrict yourself to testable assumptions. Pearl is non-Popperian, his models make assumptions that can only be tested via a time machine or an Everett branch jumping algorithm. Rubin is also non-Popperian because of “principal stratification.” People that do “mediation analysis” are generally non-Popperian. Dawid, Robins, and Richardson are Popperians—they try to stick to testable assumptions only. I think even for Popperians, some of their assumptions must be untestable (but I think this is probably necessary for statistical inference in general). I think Dawid might claim all counterfactualists are non-Popperian in some sense.
I am “a graphical non-Popperian counterfactualist” (and thus interventionist).
We are working on it.
Can you point out some cool/insightful applications of broadly Pearlian causality ideas to applied problems in, say, epidemiology or econometrics?
“Pearlian causality” is sort of like “Hawkingian physics.” (Not to dismiss the amazing contributions of both Pearl and Hawking to their respective fields).
I am not sure what cool or insightful is for you. What seems cool to me is that proper analysis of causality and/or missing data (these two are related) in observational data in epidemiology is now more or less routine. The use of instrumental variables for getting causal effects is also routine in econometrics.
The very fact that people think about a causal effect as a formal mathematical thing, and then use proper techniques to get it in applied/data analysis settings seems very neat to me. This is what success of analytic philosophy ought to look like!
What you mention in your last paragraph is roughly what I had in mind when asking for examples. So I take it that IVs are a method inspired by causal graphs (or at least causal maths)? If so you’ve answered my question.
IVs were first derived by either Sewall Wright or his dad (there is some disagreement on this point). I don’t think they formally understood interventions in general back in 1928, but they understood causality very well in the linear model special case.
IVs can be used in more general models than linear, and the reason they work in such settings needed formal causal math to work out, yes. IVs recover interventionist causal effects.
Why?
It’s his job.
Nobody gets my jokes...
What caused your interest in the topic? What was the arc of your career leading up to that?
Thanks for your question.
I got into AI/ML and graphical models as an undergrad. I thought graphical models were very pretty, but I didn’t really understand them back then very well (probably still don’t..). Causal inference is the closest we have to “applied philosophy,” and that was very interesting to me because I like both philosophy and mathematics (not that I am any good at either!) Also I had an opportunity to study with a preeminent person and took it.
Are you aware of any attempts to assign a causality(-like?) structure to mathematics?
There are certainly areas of mathematics where it seems like there is an underlying causality structure (frequently orthogonal or even inverse to the proof structure), but the probability based definition of causality fails when all the probabilities are 0 or 1.
Can you give a simple example of/pointer to what you mean?
I don’t know if this is what Nier has in mind, but it reminds me of Cramer’s random model for the primes. There is a 100 per cent chance that 758705024863 is prime, but it is very often useful to regard it as the output of a random process. Here’s an example of the model in action.
I am aware of “logical uncertainty”, etc. However I think uncertainty and causality are orthogonal (some probabilistic models aren’t causal, and some causal models, e.g. circuit models, have no uncertainty in them).
Well, in analytic number theory, for example, there are many heuristic arguments that have a causality like flavor; however, the proofs of the statements in question are frequently unrelated to the heuristics.
Also, this is a discussion about the causal relationship between a theorem and its proof.
I don’t know much about analytic number theory, could you be more specific? I didn’t follow the discussion you linked very well, because they say things like “Pearlian causality is not counterfactual”, or think that there is any relationship between implication and causation. Neither is true.