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IlyaShpitser comments on Philosophy Needs to Trust Your Rationality Even Though It Shouldn't - Less Wrong
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Well, this is very rapidly getting us into complex territory that future decision-theory posts will hopefully explore, but a very brief answer would be that I am unwilling to define anything fundamental in terms of do() operations because our universe does not contain any do() operations, and counterfactuals are not allowed to be part of our fundamental ontology because nothing counterfactual actually exists and no counterfactual universes are ever observed. There are quarks and electrons, or rather amplitude distributions over joint quark and lepton fields; but there is no do() in physics.
Causality seems to exist, in the sense that the universe seems completely causally structured - there is causality in physics. On a microscopic level where no "experiments" ever take place and there are no uncertainties, the microfuture is still related to the micropast with a neighborhood-structure whose laws would yield a continuous analogue of D-separation if we became uncertain of any variables.
Counterfactuals are human hypothetical constructs built on top of high-level models of this actually-existing causality. Experiments do not perform actual interventions and access alternate counterfactual universes hanging alongside our own, they just connect hopefully-Markov random numbers into a particular causal arrow.
Another way of saying this is that a high-level causal model is more powerful than a high-level statistical model because it can induct and describe switches, as causal processes, which behave as though switching arrows around, and yields predictions for this new case even when the settings of the switches haven't been observed before. This is a fancypants way of saying that a causal model lets you throw a bunch of rocks at trees, and then predict what happens when you throw rocks at a window for the first time.
I would be interested in reading about this. A few points:
(a) I agree that causality is a "useful fiction" (like real numbers or derivatives).
(b) If you are going to be writing posts about "causal diagrams" you need to be clear about what you mean. Usually by causal diagrams people mean Pearl's stuff, or closely related stuff (agnostic causal models, minimal causal models, etc.) All these models are defined via either do(.) or stronger notation. If you do not mean that by causal diagrams, that's fine! But please explain what you do mean to avoid confusing people. You have a paper on TDT that seems to use causal diagrams. Which ones did you mean in there?
edit: I should say that if your project has "defining actual cause" as a special case, it's probably a black hole from which no one returns (it's the analytic philosophy version of the P/NP problem).
edit 2: I think the derivation of "do(.)" ought to be not dissimilar to the derivation of "+", if you worry about induction problems. "+" is a mathematical fiction very useful for representing regularities with handling objects, "do(.)" is a mathematical fiction very useful for representing regularities involved with algorithms with actuators running around.
If causality is' useful fiction, it's conjugate to some useful nonfiction; I should like to know what the latter is.
I don't think Pearl's diagrams are defined via do(). I think I disagree with that statement even if you can find Pearl making it. Even if do() - as shorthand for describing experimental procedures involving switches on arrows - does happen to be a procedure you can perform on those diagrams, that's a consequence of the definition, it is not actually part of the representation of the actual causal model. You can write out causal models, and they give predictions - this suffices to define them as hypotheses.
More importantly: How can you possibly make the truth-condition be a correspondence to counterfactual universes that don't actually exist? That's the point of my whole epistemology sequence - truth-conditions get defined relative to some combination of physical reality that actually exists, and valid logical consequences pinned down by axioms. So yes, I would definitely derive do() rather than have it being primitive, and I wouldn't ever talk about the truth-condition of causal models relative to a do() out there in the environment - we talk about the truth-condition of causal models relative to quarks and electrons and quantum fields, to reality.
I'm a bit worried (from some of his comments about causal decision theory) that Pearl may actually believe in free will, or did when he wrote the first edition of Causality. In reality nothing is without parents, nothing is physically uncaused - that's the other problem with do().
Well, the author is dead, they say.
There are actually two separate causal models in Pearl's book: "causal Bayesian networks" (chapter 1), and "functional models" aka "non-parametric structural equation models" (chapter 7). These models are not the same, in fact functional models are a lot stronger logically (that is they make many more assumptions).
The first is defined via do(.), you can check the definition. The second can be defined either via a set of functions, or via a set of axioms. The two definitions are, I believe, equivalent. The axiomatic approach is valuable in statistics, where we often cannot exhibit the functions that make up the model, and must resort to enumerating assumptions. If you want to take the axiomatic approach you need a language stronger than do(.). In particular you need to be able to express counterfactual statements of the form "I have a headache. Would I have a headache had I taken an aspirin one hour ago?" Pearl's model in chapter 7 actually makes assumptions about counterfactuals like that. If you think talking about counterfactual worlds that don't actually exist is dubious, then you join a large chorus of folks who are critical of Pearl's functional models.
If you want to learn more about different kinds of causal models people look at, and the criticisms of models that make assumptions on counterfactuals, the following is a good read:
http://events.iq.harvard.edu/events/sites/iq.harvard.edu.events/files/wp100.pdf
Some folks claim that a model is not causal unless it assumes consistency, which is an axiom stating that if for a person u, we intervene on X and set it to a value x that naturally occurs in u, then for any Y in u, the value of Y given that intervention is equal to the value of Y in that same person had we not intervened on X at all. Or, concisely:
Y(x,u) = Y(u), if X(u) = x
or even more concisely:
Y(X) = Y
This assumption is actually counterfactual. Without this assumption it's not possible to do causal inference.