The Nature of Counterfactuals

A "counterfactual" seems to be just any output of a model given by inputs that were not observed. That is, a counterfactual is conceptually almost identical to a prediction. Even in deterministic universes, being able to make predictions based on incomplete information is likely useful to agents, and ability to handle counterfactuals is basically free if you have anything resembling a predictive model of the world.

If we have a model that Omega's behaviour requires that anyone choosing box B must receive 10 utility, then our counterfactuals (model outputs) should reflect that. We can of course entertain the idea that Omega doesn't behave according to such a model, because we have more general models that we can specialize. We must have, or we couldn't make any sense of text such as "let's suppose Omega is programmed in such a way...". That sentence in itself establishes a counterfactual (with a sub-model!), since I have no knowledge in reality of anyone named Omega nor of how they are programmed.

We might also have (for some reason) near-certain knowledge that Amy can't choose box B, but that wasn't stated as part of the initial scenario. Finding out that Amy in fact chose box A doesn't utterly erase the ability to employ a model in which Amy chooses box B, and so asking "what would have happened if Amy chose box B" is still a question with a reasonable answer using our knowledge about Omega. A less satisfactory counterfactual question might be "what would happen if Amy chose box A and didn't receive 5 utility".

>Imagine trying to do physics without being able to say things like, "Imagine we have a 1kg frictionless ball...", mathematics without being able to entertain the truth of a proposition that may be false or divide a problem into cases and philosophy without being allowed to do thought experiments. Counterfactuals are such a basic concept that it makes sense to believe that they - or something very much like them - are a primitive.

In my mind, there's quite some difference between all these different types of counterfactuals. For example, consider the counterfactual question, "What would have happened if Lee Harvey Oswald hadn't shot Kennedy?" I think the meaning of this counterfactual is kind of like the meaning of the word "chair".
- For one, I don't think this counterfactual is very precisely defined. What exactly are we asked to imagine? A world that is like ours, except the laws of physics in Oswalds gun where temporarily suspended to save JFK's life? (Similarly, it is not exactly clear what counts as a chair (or to what extent) and what doesn't.)
- Second, it seems that the users of the English language all have roughly the same understanding of what the meaning of the counterfactual is, to the extent that we can use it to communicate effectively. For example, if I say, "if LHO hadn't shot JFK, US GDP today would be a bit higher than it is in fact", then you might understand that to mean that I think JFK had good economic policies, or that people were generally influenced negatively by the news of his death, or the like. (Maybe a more specific example: "If it hadn't suddenly started to rain, I would have been on time." This is a counterfactual, but it communicates things about the real world, such as: I didn't just get lost in thought this morning.) (Similarly, when you tell me to get a "chair" from the neighboring room, I will typically do what you want me to do, namely to bring a chair.)
- Third, because it is used for communication, some notions of counterfactuals are more useful than others, because they are better for transferring information between people. At the same time, usefulness as a metric still leaves enough open to make it practically and theoretically impossible to identify a unique optimal notion of counterfactuals. (Again, this is very similar to a concept like "chair". It is objectively useful to have a word for chairs. But it's not clear whether it's more useful for "chair" to include or exclude .)
- Fourth, adopting whatever notion of counterfactual we adopt for this purpose has no normative force outside of communication -- they don't interact with our decision theory or anything. For example, causal counterfactuals as advocated by causal decision theorists are kind of similar to the "If LHO hadn't shot JFK" counterfactuals. (E.g., both are happy to consider literally impossible worlds.) As you probably know, I'm partial to evidential decision theory. So I don't think these causal counterfactuals should ultimately be the guide of our decisions. Nevertheless, I'm as happy as anyone to adopt the linguistic conventions related to "if LHO hadn't shot JFK"-type questions. I don't try to reinterpret the counterfactual question as a conditional one. (Note that answers to, "how would you update on the fact that JFK survived the assassination?", would be very different from answers to the counterfactual question. ("I've been lied to all my life. The history books are all wrong.") But other conditionals could come much closer.) (Similarly, using the word "chair" in the conventional way doesn't commit one to any course of action. In principle, Alice might use the term "chair" normally, but never sit on chairs, or only sit on green chairs, or never think about the chair concept outside of communication, etc.)

So in particular, the meaning of counterfactual claims about JFK's survival don't seem necessarily very related to the counterfactuals used in decision making. (The question, "what would happen if I don't post this comment?" that I asked myself prior to posting this comment.)

In math, meanwhile, people seem to consider counterfactuals mainly for proofs by contradiction, i.e., to prove that the claims are contrary to fact. Cf. https://en.wikipedia.org/wiki/Principle_of_explosion , which makes it difficult to use the regular rules of logic to talk about counterfactuals.

Do you agree or disagree with this (i.e., with the claim that these different uses of counterfactuals aren't very closely connected)?

The underlying thought behind both this and the previous post seems to be the notion that counterfactuals are somehow mysterious or hard to grasp. This looks like a good chance to plug our upcoming ICML paper, w

hich reduces counterfactuals to a programming language feature. It gives a new meaning to "programming Omega." http://www.zenna.org/publications/causal.pdf

In addition to self-consistency, we can also imagine agents that interact with an environment and learn about how to model the environment (thereby having an effective standard for counterfactuals - or it could be explicit if we hand-code the agents to choose actions by explicitly considering counterfactuals) by taking actions and evaluating how good their predictions are.

Interesting to read, here are a couple of comments on parts of what you say:

>the claim that all possibilities exist (ie. that counterfactuals are ontologically real)

'counterfactuals are ontologically real' seems like a bad way of re-expressing 'all possibilities exist'. Counterfactuals themselves are sentences or propositions, and even people who think there's e.g. no fact of the matter with many counterfactuals should agree that they themselves are real.

Secondly, most philosophers who would be comfortable with talking seriously about possibilities or possible worlds as real things would not go along with Lewis in holding them to be concrete. The view that possibilities really truly exist is quite mainstream and doesn't commit you to modal realism.

>what worlds should we conceive of as being possible? Again, we can make this concrete by asking what would >happen if we were to choose a crazy set of possible worlds - say a world just like this one and then a world with >unicorns and fountains of gold - and no other worlds

I think it's crucial to note that it's not the presence of the unicorns world that makes trouble here, it's the absence of all the other ones here. So what you're gesturing at here is I think the need for a kind of plenitude in the possibilities one believes in.

That is, we’re going around in circles. Suppose an agent that believes we should consider set W of worlds as possible and construct a decision theory based on this. Then this agent will evaluate agents who adopt W in order to develop their decision theory as making an optimal decision and they will evaluate agents who adopt a different set of worlds that leads to a different decision theory as making a sub-optimal decision,

Why? If agent B is has a different state of knowledge to A, B's set of (apparently) possible worlds will be different, but that doesn't mean it's worse. If B has more knowledge than A, it's ideas of possibility will be correspondingly better. In common sense terms, I should accept what an expert tells me about what is and isn't possible. An agent should not regard itself as having the best decision theory because it should not regard itself as omniscient.

You might think that the circularity is a problem, but circular epistemology turns out to be viable (see Eliezer’s Where Recursive Justification Hits Bottom).

No, the usual objections remain. If I say "you owe me a £1000 because you owe me £1000", you would not accept that as validly justified.

Edit. IE , there are an infinite number of circular arguments, most if which you still reject.

It's not clear whether Eliezer’s Where Recursive Justification Hits Bottom is supposed to be a defense of circular justification, and it's not clear how it works if it is. One could reconstruct the argument as "we have knowledge, and it's not foundationally justified, so it's circularly justified", but that depends on our having validly justified knowledge, and on circular justification being the only alternative to foundational justification. And on circular justification actually being feasible.

what worlds should we conceive of as being possible?

1. All realistic agents have finite and imperfect knowledge.

2. Therefore, for any one agent, there is a set of counterfactual claims that are crazy in the sense of contradicting what they already know.

3. Likewise, for any one agent, there is a set of counterfactual claims that are sane in the sense of not contradicting what they already know.