## Might counterfactuals

A might counterfactual is a statement of the form 'if so-and-so were the case then such-and-such might be the case'. I used to think that there are different kinds of might counterfactuals: that sometimes the 'might' takes scope over the entire conditional, and other times it does not.

For example, suppose we have an indeterministic coin that we don't toss. In this context, I'd say (1) is true and (2) is false.

(1) If I had tossed the coin it might have landed heads.
(2) If I had tossed the coin it would have landed heads.

These intuitions are controversial. But if they are correct, then the might counterfactual (1) can't express that the corresponding would counterfactual is epistemically possible. For we know that the would counterfactual is false. That is, the 'might' here doesn't scope over the conditional. Rather, the might counterfactual (1) seems to express the dual of the would counterfactual (2), as Lewis suggested in Counterfactuals: 'if A then might B' seems to be equivalent to 'not: if A then would not-B'.

On the other hand, consider the following situation. We know that the laws of nature entail either that whenever A happens then B happens or that whenever A happens then C happens; we don't know which. In the first case, if the laws of nature entail that whenever A happens then B happens (for ordinary A and B), it seems to me that (3) is true.

(3) If A had happened then B would have happened.

Similarly, in the second case, if the laws of nature entail that whenever A happens then C happens, then (4) is true.

(4) If A had happened then C would have happened.

So we know that one of (3) or (4) is true. Now consider the corresponding might counterfactuals.

(5) If A had happened then B might have happened.
(6) If A had happened then C might have happened.

Intuitively, these are both true as well. But if might counterfactuals are the dual of would counterfactuals, then (5) entails the negation of (4) and (6) entails the negation of (3), assuming B and C are logically incompatible. (By duality, (5) is equivalent to `it is not the case that if A had happened then not-B had happened'. This contradicts (4).) So the might counterfactuals (5) and (6) can't be the duals of the corresponding would counterfactuals.

Instead, the 'might' here does seem to scope over the corresponding would conditional: we don't know which of the would counterfactuals (3) and (4) is true, and that seems to be expressed by (5) and (6).

Are there also cases where 'might' takes narrow scope in the consequent of a would counterfactual? I remember that I used to think so, but sadly I can't remember any relevant example.

Over time, I changed my mind. Nowadays, I'd like to say that 'would' and 'might' are epistemic modals that are evaluated relative to a subjunctive supposition. That is, a subjunctive 'if' clause updates the information state of the utterance context by "imaging" on the antecedent; 'would' then expresses that the updated information state supports the consequent, while 'might' expresses that the updated information state is compatible with the consequent.

What does this view predict for the above two kinds of scenarios?

In the case of the indeterministic coin, the intuition that (1) is true and (2) false is vindicated. Supposing (subjunctively) that the coin is tossed, it is uncertain how it lands. So we can say that it might land heads, but not that it would land heads. In general, the new view essentially vindicates the duality of might and would counterfactuals: 'might B' is true relative to a certain subjunctive supposition A iff 'would not-B' is false relative to that supposition.

But now we run into trouble with the unknown laws scenario, where duality seems to fail.

To be sure, the intuitions here don't say that either (3) or (4) is actually assertable. Subjunctively supposing A, we can't say that B would have happened, nor that C would have happened. The subjunctive supposition A supports 'would B' only if it is evaluated under the indicative supposition that the laws of nature say 'if A then B'. But are we right when we judge that either (3) or (4) is true? Is the disjunction of (3) and (4) assertable even though neither of the disjuncts is assertable?

There are different ways to go here. One possibility is to revise the account I have sketched and argue that (would and might) counterfactuals are evaluated not relative to our subjective information state imaged on the antecedent, but relative to some more objective information state -- the (actual) objective chance function, for example. But it's not clear how that helps. One of (3) or (4) will come out as clearly true. But (5) and (6) come out false, unless 'might' scopes over the conditional. And I don't think it does. Consider (5').

(5') What if A had happened? It might be that B had happened.

This seems to me to say the same thing as (5). But it's not plausible that the 'might' in the second sentence somehow scopes over the 'if' in the first.

I'd rather stick with the idea that counterfactuals are evaluated relative to subjective information states. The problem raised by the laws case is then related to a more general problem: to explain why counterfactuals intuitively seem to describe objective and possibly unknown facts about the world.

Let's have a closer look at the "imaging" function that defines subjunctive supposition. Roughly speaking, when we subjunctively suppose A, we shift the (subjective) probability of any world w to the A-world closest to w. Which A-world is closest to w is determined by intrinsic facts about w: the laws, the past, or whatever. Some worlds are such that the closest A-worlds are B-worlds, others are not. On the view I sketched, 'if A then would B' is assertable only if the worlds in our subjective information state are all of the first kind. That's how counterfactuals appear to describe an objective feature of the world (and that's how the Lewis-Stalnaker account comes out almost right on the new account).

In the scenario with the unknown laws, we know that the world is one of two ways: the laws either say 'if A then B' or 'if A then C'. On the supposition that it is the first way, (3) is assertable; on the supposition that it is the second way, (4) is assertable. If we read 'S is true at w' as 'S is assertable on the supposition w', then (3) is true at some worlds in our information state and (4) is true at the remaining worlds. If 'A or B' is true at w iff one (or more) of A and B is true at w, the disjunction of (3) and (4) comes out true at all worlds in our information state. The disjunction is true even though neither disjunct is assertable.

That looks promising to me. But it all needs to be spelled out more carefully.

Someday.

# on 13 May 2018, 19:18

Hi Woâ€”really interesting post!

The idea that might-counterfactuals are epistemic is very interesting, and I think it's definitely correct in *some* cases. At the same time, I think there are reasons to resist it if it's taken as a blanket theory of might-counterfactuals. Let me mention two.

The first reason is that "might have" statements seem to have a clear non-epistemic reading. That reading should carry over to conditionals. Forget for a second about conditionals, and consider unembedded occurrences of "might" in combination with the perfect, as in (i):

(i) It might have rained in San Diego yesterday.

(i) is normally considered ambiguous between an epistemic reading ("For all we know, yesterday it rained in San Diego") and a reading that is normally called "historical" or "metaphysical" ("There is a close rain-in-San-Diego possibility"). To see that this second reading is needed, notice that (i) can be felicitously conjoined with a clause incompatible with its prejacent.

(ii) It didn't rain in San Diego yesterday, but it might have rained in San Diego yesterday.

This is unexpected if "might have" in (ii) is epistemic. In that case (ii) would be of the form "not p and might p" (or close enough) and hence should be infelicitous. Conversely, we fully expect the consistency of (ii) if the "might" is read non-epistemically.

Now, back to conditionals. Given that unembedded "might have" has a non-epistemic reading, the default expectation is that conditionals where "might have" is the main modal will also have a non-epistemic reading. This is a straightforward prediction on Kratzer's view, on which if-clauses have no quantificational force of their own and hence cannot introduce a new modal flavor. But also other mainstream views should reproduce this prediction. In any case, the idea that "might have" can have non-epistemic readings by itself, but is forced to have epistemic readings when it appears in a conditional, seems to need further motivation.

The second reason is that, once we recognize that "might have" statements and conditionals are ambiguous, we have a good explanation of your examples that doesn't require that we go epistemic across the board.

Claiming ambiguity is generally undesirable. But for the case of "might have" phrases we can predict it in a principled way: we can trace it to a difference in scope between the perfect and the "might". (If I remember correctly, this is what Condoravdi suggests in a 2002 paper.) On the epistemic reading, the modal scopes over the perfect in logical form:

(iii) might [PERFECT [rain in San Diego]]

On the non-epistemic reading, the modal takes lower scope:

(iv) PERFECT [might [rain in San Diego]]

Interestingly, the difference between (iii) and (iv) is visible in some languages that have richer morphology than English. For example, in Italian a verb phrase like "might have been" can be translated as "potrebbe essere stato" (might [PERFECT [be]]) or "avrebbe potuto essere" (PERFECT [might [be]]). The first tends to be read epistemically, the second non-epistemically. (The correlation is not perfect, and I have to admit that my intuitions are somewhat unclear when I try to translate (5) and (6). But the basic point is that this ambiguity exists at LF.)

Now, once we have established that "might have" is ambiguous, we can say simply that (1)/(2) and (5)/(6), on their natural interpretations, have different LFs and hence different flavors. The natural reading of (1)/(2) is metaphysical, the natural reading of (5)/(6) epistemic.

Very interesting stuff!

# on 14 May 2018, 12:18

Hi Paolo, thanks! Good points. Two quick initial thoughts in response.

1. I think I could have said everything with 'might' rather than 'might have'. For example, in the unknown law case, one of (3') and (4') is intuitively true, and so are both of (5') and (6').

(3') If A were to happen B would happen.
(4') If A were to happen C would happen.
(5') If A were to happen B might happen.
(6') If A were to happen C might happen.

2. I agree that 'might have' has an apparently non-epistemic reading, but couldn't this, too, come about through embedding an epistemic 'might'? My thought is that just as might counterfactuals evaluate the 'might' clause under a subjunctive supposition, so unembedded 'might have' statements could evaluate the 'might' clause under a shift of the original information state. An obvious idea would be that the shift is brought about by the perfect, which moves every world some distance into the past. (As it stands, that doesn't seem to yield the right results though.)

# on 15 May 2018, 18:23

Hi Wo, just some quick thoughts in response:

1. Yes, that's true. I think here there are two alternative responses here.

On the first, there is simply a difference between "might" and "might have". The former is always epistemic, but the latter is not. This still leaves you with some cases where might-have counterfactuals are historical.

On the second (which I would prefer), "might" without a perfect is similarly ambiguous between a historical and an epistemic reading. Perhaps one argument for this view is that, once certain possibilities are foreclosed, it's easy to switch from a simple might counterfactual to a might+perfect counterfactual:

A: If you tossed the coin, it might land tails.
B: I won't toss it though.
A: Okay. But still, if you had tossed it, it might have landed tails.

A similar switch is not as easy for epistemic modals. (There is controversy about whether it happens at all, but even if it does it's much more marginal.)

2. In a way, what you're suggesting is not dissimilar from what Condoravdi suggests in her 2002 paper. The worry is that you can have a true might-have historical statement even if at no point anyone thought the prejacent was an open epistemic possibility. For example, (i) is true, even though the corresponding epistemic claim is self-defeating, and presumably no one ever took it to be an epistemic possibility.

(i) I might have been taller than I am.

But maybe you have in mind a kind of idealized notion of knower/knowability? That actually seems an interesting idea to me, and it might be a plausible way of understanding what "historical" modality amounts to.

# on 18 May 2018, 13:48

Hi Paolo,

Re 2: my idea wasn't that 'might have p' is true iff there was a time in the past at which p was compossible with the then available evidence. That doesn't look promising to me. (After all, it might have been that there are no sentient beings, and so nobody had any evidence for anything.) Rather, the idea was that 'might have p' evaluates p relative to our actual information state, but shifting all worlds in the state into the past. This would be analogous to my proposal in the post about might counterfactuals. The problem is that if all worlds in the current state are (say) worlds where some coin landed tails, then all temporal predecessors of these worlds are worlds where the coin is going to land tails. So this idea probably doesn't work either. In any case, I don't have any real view about 'might have'.

Re 1: Bare 'might's do always seem epistemic to me. In your example ('if you had tossed it, it might have landed tails'), I think the 'might have' is naturally interpreted as an epistemic 'might' with a past-tense/subjunctive prejacent, in which case the switch would be unsurprising.