>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)?
I agree with almost everything you’ve written in this comment.
I think you’re right that I am brushing over some differences between different kinds of counterfactuals a bit too much here. If you know of any articles that do a good job of separating out the different kinds of counterfactuals, then that’s something I’d really appreciate having.
Thinking over this again, it might have been better if I had written that (1) humans seem to have some kind of inner simulator and that (2) one of its main properties is that it is able to simulate situations that aren’t actually true. In fact, if this simulator only worked for simulating the actual world, it’d be pretty useless as we are mistaken about some facts, and for other facts, we need to use our best guess.
Further, I could claim that (3) this simulator plays an incredibly fundamental and core part of human thought as opposed to say, our understanding of music or Russian history, such that it’s difficult to talk about this simulator without “using its own language” so to speak.
I’m open to the possibility that we might have multiple simulators, such as counterfactual mathematical statements being handled by a different system than counterfactual statements of the world. In fact, these days I tend to make a distinction between our evolved intuitions regarding counterfactuals and the higher-level cognitive concept of counterfactuals that we’ve built up from these intuitions.
I also like your almost Wittgenstenian-language game model of counterfactuals. I agree that there are a lot of social conventions around how counterfactuals are constructed and that in a lot of circumstances, people aren’t really aiming to produce a consistent counterfactual. Hmm… I probably needed to engage with that more for one of my most recent posts on counterfactuals. In that post, I provided an argument for consistent counterfactuals, but I’m now thinking that I need to think more about what circumstances we actually want consistency and in which circumstances we don’t really care.
All this said, I don’t agree with the claim that these definitions don’t have very much to do with each other, although maybe you meant this in a sense other than I’m taking it here. I believe that different notions of counterfactual are likely built upon the same underlying intuitions, such that these definitions are likely to be very closely related.
>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)?
I agree with almost everything you’ve written in this comment.
I think you’re right that I am brushing over some differences between different kinds of counterfactuals a bit too much here. If you know of any articles that do a good job of separating out the different kinds of counterfactuals, then that’s something I’d really appreciate having.
Thinking over this again, it might have been better if I had written that (1) humans seem to have some kind of inner simulator and that (2) one of its main properties is that it is able to simulate situations that aren’t actually true. In fact, if this simulator only worked for simulating the actual world, it’d be pretty useless as we are mistaken about some facts, and for other facts, we need to use our best guess.
Further, I could claim that (3) this simulator plays an incredibly fundamental and core part of human thought as opposed to say, our understanding of music or Russian history, such that it’s difficult to talk about this simulator without “using its own language” so to speak.
I’m open to the possibility that we might have multiple simulators, such as counterfactual mathematical statements being handled by a different system than counterfactual statements of the world. In fact, these days I tend to make a distinction between our evolved intuitions regarding counterfactuals and the higher-level cognitive concept of counterfactuals that we’ve built up from these intuitions.
I also like your almost Wittgenstenian-language game model of counterfactuals. I agree that there are a lot of social conventions around how counterfactuals are constructed and that in a lot of circumstances, people aren’t really aiming to produce a consistent counterfactual. Hmm… I probably needed to engage with that more for one of my most recent posts on counterfactuals. In that post, I provided an argument for consistent counterfactuals, but I’m now thinking that I need to think more about what circumstances we actually want consistency and in which circumstances we don’t really care.
All this said, I don’t agree with the claim that these definitions don’t have very much to do with each other, although maybe you meant this in a sense other than I’m taking it here. I believe that different notions of counterfactual are likely built upon the same underlying intuitions, such that these definitions are likely to be very closely related.