Mackay on counterfactual epistemic scenarios

An interesting new paper by David Mackay, Mackay (2022), raises a challenge to popular ideas about the semantics of modals. Mackay presents some data that look incompatible with classical two-dimensional semantics. But the data nicely fit classical two-dimensionalism, if we combine that with a flexible form of counterpart semantics.

Before I discuss the data, here's a reminder of some differences between epistemic modals and non-epistemic ("metaphysical") modals.

First, and most obviously, the two kinds of modals tend to quantify over different scenarios. Epistemic modals quantify over scenarios that are compatible with the evidence. Non-epistemic modals typically don't.

Second, non-epistemic modals allow for non-trivial back-reference to the actual world, while epistemic modals don't. "I could have been taller than I actually am" makes sense, "I might be taller than I actually am" does not.

Third, indexicals, names, and natural kind terms (and possibly other expressions as well) are interpreted differently when embedded under the two kinds of modals. "I could have been somewhere else now" is fine, "I might be somewhere else now" is not, even if I don't know where I am. "Hesperus and Phosphorus might be different planets" is true in a skeptical context in which we consider that the science textbooks might be full of elaborate fabrications. "Hesperus and Phosphorus could have been different planets" is false.

The problematic data now suggest that there are hybrid modals that behave like epistemic modals in some respects but like non-epistemic modals in others.

To begin, consider the following "epistemic counterfactual" from Edgington (2008).

(1) [We knew that the treasure was either in the attic or the garden. So:] If it hadn’t been in the attic, it would have been in the garden.

Here we evaluate the consequent in worlds that resemble the actual world with respect to what we knew at around the antecedent time. The domain of quantification (the "modal base") therefore appears to be epistemic.

On the other hand, we can easily refer back to the actual world in this kind of environment. For example, we might say that "if the treasure hadn't been in the attic then it would not have been where it actually was".

Finally, singular terms in conditionals like (1) do not appear to have the rigid interpretation they normally have under non-epistemic modals. Rather, they appear to undergo the kind of "epistemic shift" that characterises epistemic modals. This can't be seen directly in (1), but consider (2) and (3).

(2) [We knew that Hesperus was either Venus or Jupiter. So:] If Hesperus hadn't been Venus, it would have been Jupiter.

(3) If that [pointing at a suddenly appearing gazelle] had been a tiger, we would be dead now. Vetter (2016)

Here we don't seem to hold fixed the actual reference of 'Hesperus' and 'that' when we evaluate them in the relevant counterfactual scenarios. Intuitively, (3) does not talk about impossible worlds in which a gazelle is a tiger. It rather talks about worlds in which a tiger suddenly appeared where in fact the gazelle appeared.

Mackay infers that there is something wrong with the "two-dimensional" approach to modals. Two-dimensional accounts assume that sentences can be evaluated in two ways relative to a possible world, depending on whether the world is considered "as actual" or "as counterfactual". This is meant to explain the observed differences between the two kinds of modals.

Mackay's own account instead draws on recent "variabilist" treatments of singular terms. On standard variabilist accounts, the shift of names and indexicals under epistemic modals is captured by assuming that epistemic modals don't just shift a world parameter – as non-metaphysical modals do – but also the assignment function that interprets the names and indexicals. (We ignore kind terms.) Mackay suggests that all modals shift both a world and an assignment parameter. In effect, the worlds in Kratzer-type accounts of modals are replaced by world-assignment pairs. When we evaluate conditionals like (1)-(3), context selects an accessibility relation that shifts both the world and the assignment function based on epistemic criteria.

What about the interpretation of 'actually', which suggests that (1)-(3) are interpreted "as counterfactual"? Here things get a little complicated. In a nutshell, Mackay assumes that the logical form of modal sentences contains explicit variables for world-assignment pairs. Modals selectively bind world-assignment variables with which they are co-indexed. Material involving 'actually' simply has a different index. As a result, the relevant variables are free and get interpreted in the unshifted actual world.

On this account, the three features mentioned above are in principle independent. Context may supply a domain of worlds that is epistemic or non-epistemic. Either way, it may determine that singular terms are interpreted rigidly or non-rigidly. (These two choices combine to determine the revised modal base whose elements are world-assignment pairs.) And no matter how these choices are made, one can in principle always undo a modal shift with 'actually' type constructions whose index is not bound by the modal quantifier.

One problem with this proposal is that it seems to overgeneralise. If the three distinctions are independent, one would expect to find all eight combinations. But many of them are really hard to find. Why do almost all modal constructions fall into just two of the eight classes?

Mackay holds that conditionals like (1)-(3), at least, are an exception. The modals here quantify over epistemically accessible worlds, singular terms undergo epistemic shift, and yet we can non-trivially refer back to the actual world.

But is that true?

Let's begin with the first issue. What are the worlds to which (1)-(3) direct us? Standard epistemic modals direct us to worlds compatible with our evidence. None of (1)-(3) do that. When we utter (1), we know that the treasure is in the attic. When we utter (3), we know that the relevant animal is not a tiger. Worlds where a tiger suddenly appeared are not epistemically accessible. Perhaps they were accessible relative to our earlier evidence. But even that may be false. (3) can be true even if we knew all along that there are no tigers around.

So I don't think it's true that "epistemic conditionals" like (1)-(3) have an epistemic modal base. They direct us towards scenarios of which we know that they don't obtain. What's special about at least (1) and (2) is how the counterfactual scenarios are selected. In general, the domain of non-epistemic modals is selected by holding fixed some actual circumstances, perhaps determined by a "modal anchor". Which circumstances are held fixed is highly context-dependent. In (1) and (2), the modal anchor happens to be our earlier state of knowledge. As I mentioned above, the conditionals direct us to worlds that resemble the actual world with respect to the facts that we knew before we made the relevant discoveries. That doesn't turn the conditionals into epistemic modals. We're still holding fixed salient circumstances.

What about the second issue? Do "epistemic conditionals" involve an epistemic shift of singular terms? Again, the answer is no. There are strong constraints on how the reference of singular terms normally shifts under epistemic modals. 'I' always refers to the individual at the centre of the scenario under consideration, 'you' (singular) refers to an individual with which the individual at the centre is currently engaging, demonstrative 'that' refers to whatever individual is pointed at in the scenario, and so on. If (3) involves this kind of shift then the worlds we should be considering are worlds at which I (or rather, the individual at the centre) am pointing at a tiger. But I would hardly be pointing at a tiger if I were dead. So (3) would come out as false.

Or consider a variant of (1): 'If the treasure hadn't been in the attic, we would never have met you/Frank/this guy'. In the consequent of the conditional, 'you' clearly refers to the person I'm actually talking to, not to whomever I might be talking to in the counterfactual scenario.

In sum, we don't see the kind of shift that characterises epistemic modals.

But we also don't see the kind of rigid interpretation that is often thought to characterise non-epistemic modals. So what's going on with these terms?

Counterpart theory provides an attractive answer. According to counterpart theory, even non-epistemic modals shift the reference of singular terms. The reference is shifted to a counterpart of their original referent. Counterparthood is a flexible and context-sensitive matter. That's why we can make sense of both 'if a billion tons of sand were dropped onto Mt Everest then Mt Everest would be submerged' and 'if a billion tons of sand were dropped onto Mt Everest then Mt Everest would be even taller'. In the first case, we treat the submerged mountain consisting of the original Mt Everest material as a counterpart of Mt Everest. In the second, the larger structure created by adding the sand is treated as a counterpart. Famously, counterpart theory also makes sense of contingent identity and distinctness. "If the two islands had merged they would have been a single island".

On this background, it is not hard to see what is going on with (2) and (3). Here we simply have an unusual counterpart relation. As Mackay himself points out, the reference of the relevant terms appears to shift by the acquaintance-type counterpart relations discussed in Lewis (1983). In (3), for example, the relevant counterparts of the gazelle are individuals that stand to us in a similar acquaintance relation as the gazelle does in the actual world: We just saw them suddenly appear over there.

I hadn't realised that such counterpart relations are available for non-epistemic modals. And they only appear to be available under very specific conditions. Imagine we're in the context of (3) and I utter, "if a tiger had just appeared then that [pointing at the gazelle] would have killed us". I can't hear a reading of this on which 'that' denotes the counterfactual tiger. Similar puzzles arise in counterpart-theoretic interpretations of attitude ascriptions. I don't fully understand the mechanisms at work here.

But I don't see a good reason here to give up the classical 2D picture of how modals pattern into two distinct classes.

Edgington, Dorothy. 2008. “Counterfactuals.” Proceedings of the Aristotelian Society 108: 1–21.
Lewis, David. 1983. “Individuation by Acquaintance and by Stipulation.” The Philosophical Review 92: 3–32.
Mackay, John. 2022. “Counterfactual Epistemic Scenarios.” Noûs, no. n/a.
Vetter, Barbara. 2016. “Williamsonian Modal Epistemology, Possibility-Based.” Canadian Journal of Philosophy 46 (4-5): 766–95.


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