1. Williamsonian modal epistemology

This paper is an exercise in broadly Williamsonian modal epistemology (WME): while I will disagree with Williamson on some important points, I share his general outlook, which I take to be characterized by two basic commitments. The first is a commitment to realism: what we know about, when we know about metaphysical modality, is an entirely objective or mind-independent phenomenon that has nothing whatsoever to do with the human mind (except, of course, where the possibilities or necessities concern the human mind). The second commitment is anti-exceptionalism Footnote ¹: in Williamson's own words,

According to anti-exceptionalism, our knowledge of metaphysical modality is continuous with our everyday knowledge about the world.

The two commitments are not entirely independent: as Williamson notes, an exceptionalist modal epistemology, with its ‘apparent cognitive isolation of metaphysically modal thought’ (Williamson Reference Williamson2007, 136) has a difficult time explaining how such isolated thought is to hook on to reality. An anti-exceptionalist has a much better chance of explaining the relation of our metaphysically modal thought to an independent metaphysically modal reality in terms of the relation between our ordinary thought to ordinary (modal and non-modal) reality.

WME, as I understand it, is intended to answer two distinct but related questions.

The first question concerns our grasp of the concepts of metaphysical modality: how do we even get to think about metaphysical modality (as opposed to some more mundane forms of modality, say practical or epistemic modality)? The second question concerns our knowledge of the extension of those concepts: how do we know what is metaphysically possible or impossible? It would appear that the two questions, and Williamson's answers to them, are closely related: knowledge of the extension of the metaphysical modalities, the subject of the second question, requires that we have – in whatever form, under whatever name – some concept of these metaphysical modalities; and if the concept of metaphysical modality is ‘the exclusive preserve of philosophers, then so is knowledge of metaphysical modality’ (Williamson Reference Williamson2007, 135). In what follows, I will take care to address both questions: the question where we get our concept of metaphysical modality, and the question how we know about its extension.

The locus classicus for WME is chapter 5 of Williamson (Reference Williamson2007). But arguably there is some reliance on WME in the methodology of Williamson's own more recent work on modality, culminating in Williamson (Reference Williamson2013) (see especially the ‘methodological afterword’). However, in what follows I will focus on Williamson (Reference Williamson2007) and some more recent papers that pick up threads from it.

Williamson's own account of modal knowledge is, of course, more specific than the broad outlines that I have sketched so far. It is his implementation of these broad outlines that I will take issue with in what follows. Section 2 presents his implementation, and some preliminary reasons for exploring the kind of alternative that I prefer. Section 3 presents my preferred implementation of WME, which I call a ‘possibility-based approach’. Sections 4–6 argue for my account by defending it against a challenge of Williamson’s, and then turning the challenge around and arguing that it is in fact a problem for Williamson's implementation, not for mine. My argument will rely to a large extent on the findings of contemporary semantics, following Williamson's dictum that ‘[p]hilosophers who refuse to bother about semantics resemble scientists who refuse to bother about the theory of their instruments’ (Williamson Reference Williamson2007, 284f).

2. Williamson's modal epistemology

Williamson's own account, as is well known, is twofold. In a first step, Williamson identifies the entry point into the relevant kind of modal thought and knowledge within our ordinary thought and knowledge about the world. In a second step, he explains how we extend modal thought and knowledge beyond that entry point to its limiting case: metaphysical modality.

First, the entry point into modal thought and knowledge, for Williamson, are counterfactual conditionals such as ‘If the bush had not been there, the rock would have ended in the lake’ (Williamson Reference Williamson2007, 142). Our knowledge of such counterfactual truths, Williamson argues, does not require any outlandish cognitive capacities. In evaluating a counterfactual, we typically use ‘offline’ the very capacities that we would use ‘online’ in perception and expectation-forming. Moreover, it is not surprising that we have the capacity to evaluate counterfactuals, since having such capacities brings with it clear evolutionary advantages.

Second, Williamson argues that given our knowledge of counterfactual conditionals, we are in a position to know about metaphysical necessity as a kind of limiting case because necessities are logically equivalent to certain counterfactual constructions:

• (V )

• (V* )

• (Q )

(And likewise for possibility, applying the standard definition in terms of necessity.)

In what follows, I want to develop and defend a different kind of WME. Like Williamson's own approach, mine will be realist and anti-exceptionalist. It will differ from Williamson's primarily in the ‘entry point’ that it stipulates for our modal thought and knowledge: not counterfactual conditionals, but restricted possibility statements of the form ‘x can F’ and their equivalents in other languages. A different entry point will, of course, also require a different story about how we reach the limiting case of metaphysical modality (see Section 3). As will become clear later, my proposed entry point into modal thought and knowledge differs from Williamson's in two ways: it is a form of possibility, and it is an ascription of modal properties. To have labels for the two approaches, I will refer to Williamson's own modal epistemology as ‘counterfactual-based’ and mine as ‘possibility-based’.Footnote ²

Why even look for an alternative? For one thing, there is clearly room within WME for different approaches, and it should be of interest to everyone who is sympathetic to the general approach what the available implementations are. Moreover, there have been a fair amount of concerns raised about Williamson's own implementation. If those concerns do not apply to my proposed implementation, that should make it a worthwhile option to explore.

One kind of worry concerns whether the equivalences offered by Williamson are a realistic description of how we do (as opposed to how we might in principle) gain modal knowledge (see Vaidya Reference Vaidya and Summer2015; Jenkins Reference Jenkins2008).Footnote ³ Perhaps most relevant to our present purposes, Sonia Roca Royes argues that Williamson's equivalences are too demanding to provide a plausible account for our very easy knowledge of a great many de re possibilities, such as the possibility of my desk breaking or the possibility of my speaking French (Roca Royes Reference Roca Royes2011, Reference Roca Royes, Fischer and Leonforthcoming). Roca Royes herself suggests that a possibility-based modal epistemology does much better justice to the ease with which we come by some such modal knowledge. I hope it will become clear in Section 3 that this is true for my own preferred account.

A second kind of worry that has been raised about using Williamson's equivalences to explain modal knowledge is that the equivalences require the vacuous truth of counterpossibles, that is, counterfactuals with a metaphysical impossibility as their antecedent.Footnote ⁴ But of course this commitment to vacuous truth is highly controversial (see e.g. Nolan Reference Nolan1997). I myself tend to be convinced by Williamson's argument for the vacuity thesis (Williamson Reference Williamson2007, 171–175; Williamson Reference Williamson, Armour-Garb and Kroonforthcoming-a). But even so, a worry about the use of the equivalences in accounting for our modal knowledge remains. This worry is not about the truth of the vacuity claim, but about its non-obviousness. Recognition (implicit or explicit) of this non-obvious fact, the vacuous truth of counterpossibles, should not count as a precondition for knowledge of metaphysical modality – after all, the latter is presumably much more widespread than the former, and it certainly has been throughout the history of philosophy.

My own approach, it will be seen, proceeds without such a commitment. It is, I take it, less demanding, and more in line with the way in which philosophers have historically thought about metaphysical modality, than Williamson's own implementation. Nevertheless, it is firmly Williamsonian in the sense outlined in Section 1. It is time now to have a closer look at it.

3. A possibility-based approach

In recent work, Williamson (Reference Williamson, Vaidya and Prelevićms) proposes that we understand ‘metaphysical modality as the maximal objective modality’ (Williamson Reference Williamson, Vaidya and Prelevićms, 5), where objective modalities include practical and physical modality, and in general everything that is classified as ‘circumstantial’ modality in linguistics. A proposition, on this proposal, is ‘metaphysically possible if and only if it has at least one sort of objective possibility’ (Williamson Reference Williamson, Vaidya and Prelevićms, 2).

The proposal in Williamson (Reference Williamson, Vaidya and Prelevićms) is about the nature, not the epistemology, of metaphysical modality. But my claim is that it is very close to a promising version of WME. This version, which I will sketch in the present section, will deviate from Williamson's model in Williamson (Reference Williamson, Vaidya and Prelevićms) in two respects. First, Williamson thinks of metaphysical possibility as the ‘union of all types of objective possibility’ (Williamson Reference Williamson, Vaidya and Prelevićms, 3). I, on the other hand, will introduce metaphysical possibility as a gradual extension from a single kind of possibility (or, at any rate, a single kind of expression), the restricted possibility expressed by ordinary uses of the modal auxiliary ‘can’. Second, Williamson tends to use the past-tense/subjunctive form ‘could have’ as a linguistic starting point, while I use the indicative ‘can’. According to Williamson, ‘[a]lthough ‘could’ is the past tense of ‘can’, English permits us to recruit the past tense to express something more purely modal’ (Williamson Reference Williamson, Vaidya and Prelevićms, 3). Whether or not this is true, Footnote ⁵ I think that it is not a suitable entry point into modal thought and knowledge – presumably we need to already have some understanding of metaphysical modality to recruit the past tense in this way. Moreover, it is ‘can’ (in the indicative form) that is the paradigmatically circumstantial (i.e. objective) modal (see Collins Reference Collins2009; Vetter Reference Vetter2013) – a fact to which I will return below.

Let me, then, sketch my own version of a possibility-based WME. Like Williamson's own counterfactual-based proposal, my possibility-based proposal requires two steps.

First, I need to identify an entry point into modal thought and knowledge from our ordinary thought and knowledge about the world. I have already indicated that the entry point consists in ordinary statements of the form ‘x can F’, which I will from here on call ‘can statements’.

Second, I need to show how we extend our understanding of this entry point so as to reach the limiting case of metaphysical modality. My suggestion will be that this works in much the same way as it does in other cases, such as ontology: we gradually extend the contexts of utterance, we abstract from times, and we then apply any other methods of systematic metaphysical theorizing that we have at our disposal.

The main claim that I will be defending in this paper is the claim that the entry point to thought and knowledge about metaphysical modality consists in can statements. My defence of this claim comes in Sections 4–6. In this section, I will briefly address the more immediate questions about this entry point: how do we know the truth of can statements? And how do we manage to extend from them to the limiting case of metaphysical modality?

How do we know the truth (or falsity) of can statements? As with counterfactuals (see Williamson Reference Williamson2007, 152), there is presumably no unique way of properly evaluating can statements. But it is abundantly clear that we do know, of a great many can statements, whether they are true or false, and that we must have such knowledge prior to philosophical reflection. It is crucial for practical deliberation that we know what we can do (if I cannot jump over the river, there is no point in deliberating about whether to attempt such an action), how things can be manipulated (if the stone is so heavy that it cannot be lifted, then again there is no point in deliberating about whether or not I should pick it up to use it as a tool) and how other people and animals can react (out in the wild, it may be important to know that a tiger can run faster than I can). It would not be surprising, therefore, if at least some of our ways of knowing about what objects can do were hard-wired.

Margot Strohminger (Reference Strohmingerforthcoming) argues that we can know by perception, in at least some cases, what things can do and what we can do with them: I perceive, and thereby come to know, that I can reach the mug, that the mug can shatter, and that the tomato is edible. According to a roughly Gibsonian theory of perception, such modal properties of objects are even directly represented in perception (see Nanay Reference Nanay2012, Reference Nanay2011, Reference Nanay2013).Footnote ⁶

Other ways of knowing about what can do what are certainly available, and need not consist in explicit theoretical reasoning. Imagining may well play a role here, as it does with counterfactuals (see Williamson Reference Williamson2007, Reference Williamson and Kindforthcoming-b Footnote ⁷). Sonia Roca Royes (Reference Roca Royes, Fischer and Leonforthcoming) argues that much of our knowledge of simple de re possibility claims such as ‘my desk can break’ is obtained by induction on actualized possibilities; such induction, of course, is often performed implicitly without much theoretical thought being given to the matter at all.

It may seem that my entry point into thought about metaphysical modality already is a form of knowing about metaphysical modality. It is very nearly; but not quite. Each can statement entails a metaphysical possibility;Footnote ⁸ by knowing that entailment, our knowing about the more mundane objective possibilities expressed by can statements puts us in a position to know about metaphysical possibilities as well. But in order to know about the entailment, we need to have some grasp (implicit or explicit, under this name or any other) of metaphysical possibility. And of course, since the possibilities in question are restricted, our knowledge about the falsity of a can statement does not yield knowledge of metaphysical impossibilities and necessities. What we need is some sort of grasp on metaphysical, as opposed to the more restricted forms of, possibility. Having some such grasp should enable us to turn our knowledge of restricted possibilities into knowledge of metaphysical possibilities, and it should also ensure that we do not turn knowledge of restricted impossibilities into false beliefs about metaphysical impossibilities.

This takes us to the second task of this section, an account of how we reach the limiting case that is metaphysical modality.

My proposed response is this. We begin with can statements such as the ones that I have mentioned above: I can reach the mug, I can speak French, the desk can break, the tomato can be eaten. Can statements are our paradigmatic forms of expression for objective, or in linguistic terms: circumstantial modality. (See Kratzer (Reference Kratzer, von Stechow and Wunderlich1991), and the corpus-linguistic surveys Coates (Reference Coates1983) and Collins (Reference Collins2009); according to Collins, ‘can’ is used circumstantially in 81 of its uses, which is far more than any other modal auxiliary.) In order to get from ordinary can statements to metaphysical modality we do what we generally do when we go from ordinary thought to thought in metaphysics: we generalize. In particular, we generalize away from times and from contextual restrictions.

Here is an analogous case. When we make or consider existence claims (in the present tense) in ordinary contexts, we talk about what there is in some relevant domain and at the time of the utterance. When we think about existence claims in metaphysics (also usually phrased in the present tense), we want to speak timelessly and unrestrictedly. If our theories about existence and about existents did not cover dinosaurs because they no longer exist, Footnote ⁹ or if they did not cover distant stars or elementary particles because those are not generally relevant to us, then that would constitute a problem for those theories; metaphysics is about all there is, at any time, whatever our interests.Footnote ¹⁰

Likewise, when we make or consider possibility claims, in particular can statements (in the present tense) in ordinary contexts, we talk about relevant possibilities obtaining at the time of the utterance. When we think about possibility claims in metaphysics (also usually phrased in the present tense), we want to speak timelessly and unrestrictedly. A metaphysics of modality is about all possibilities whatsoever, at any time, whatever our interests. Let's see how we might implement this thought.

First, times. When we think about metaphysical possibility, we don’t just ask ourselves whether this can be or that can be. We think (metalinguistically) about whether a sentence of the form ‘x can F’ is, was or will ever be true; or we think (in object language) about whether it is, was, or ever will be the case that x can F. This idea is nicely captured by Dorothy Edgington:

Second, contexts. Can statements, like modal statements in general, are notoriously context-sensitive (Kratzer Reference Kratzer1977, Reference Kratzer, Eikmeyer and Rieser1981). Take a well-known example from Lewis Reference Lewis1976: compared to an ape, I can speak Finnish; I have the requisite larynx, brain and nervous systems. An ape can’t speak a human language such as Finnish; but I can. However, don’t expect me to speak Finnish. I can’t speak Finnish; I’ve never learned it. Many more examples of this kind can be constructed. Fortunately, it is the very context-sensitivity of can statements that allows us to overcome their restricted nature and ultimately reach an unrestricted notion of metaphysical possibility.

Lewis's example points the way. My friend Mari can speak Finnish, but I can’t; or so we would say in one context. Compared to an ape, of course, I can speak Finnish – I have the requisite physiological and neural make-up. And what about the ape? He doesn’t have the right larynx or neural wiring to speak a human language such as Finnish. But with surgical alteration, he could in principle be changed in those respects (I think) and become able to speak. He contrasts with, say, a rock: no amount of surgery could make a rock able to speak. Compared to a stone, the ape can speak – it just takes more changes for him to realize that possibility than it does for me.Footnote ¹¹

Can statements made in ordinary language are context-sensitive; with a little work on the context, we can generally extend the realm of true possibility statements. It seems, though, that this ends somewhere. I cannot think of a context that would make me assent to ‘Mount Everest can speak Finnish’ (and if you can, then try ‘the number two can speak Finnish’). The concept of metaphysical possibility simply marks the result of the extension, whatever exactly it may be; the concept of metaphysical necessity marks the limits of such an extension, whatever they may be.

We do not, of course, always actually go through some such process of gradual extension. We use terms such as ‘absolutely’ (as in Edgington's passage above) to mark the end-point of such extensions directly; sometimes the work is done simply by the fact that we are using modal terms while doing metaphysics. (Compare again the case of existence: we could, but we do not usually, extend the context for our quantificational statements gradually; rather, we tend to use adverbs such as ‘simpliciter’ to mark the end-point of such an extension.) The important point for present purposes is that there are natural limits to contextual extension, though it is not always easy, and almost never uncontroversial, to state where they are located.

Note that all this is not intended as a definition or an analysis of metaphysical possibility or our concept of it, but simply as an account of how we come to think about (and consequently to know about) metaphysical possibility. I am not saying that p's being metaphysically possible consists in the truth of ‘it can be that p’ in some (actual? or possible?) context. The proposal is merely that this kind of relaxation of actual contextual restrictions is what leads us to thinking about metaphysical possibility, and ultimately also about metaphysical necessity. (And as the examples illustrate, we need not have a notion of linguistic context in order to perform this kind of relaxation of contextual restrictions.) An analogous claim, I have suggested, is plausible for the metaphysical notion of existence.

We need careful attention to individual cases and contexts to see just how far such an extension can go. But that too is unsurprising: figuring out the extension of the metaphysically possible is hard; every metaphysician can attest to that. Note, however, that even absent a demarcation of the limits of metaphysical possibility, we know a great deal about metaphysical possibility on this approach. Can statements entail statements of metaphysical possibility, and given an understanding of metaphysical possibility along the lines I have sketched, this entailment is now something that we are in a position to know.

It is important here to keep in mind the distinction between the two questions that I have distinguished in Section 1: how we get to think about metaphysical modality, and how we manage to extend our knowledge about it. I am suggesting that the two extensions I have outlined – relaxing context, abstracting from times – are enough to get us thinking about metaphysical modality proper (as opposed to some more restricted form of modality): metaphysical possibility is, as Williamson has said, the ‘maximal’ or most general form of objective possibility, that is, of the kind of possibility that we express in ordinary talk with can statements. I emphatically do not say that the two extensions I have outlined are enough to get us all the knowledge we need about metaphysical modality. It is just a start. (Again, the comparison with existence claims holds: relaxing context and abstracting from times is not enough to know what the right ontology is.) But I take it that what we need to make further progress is not all that different from what we do when theorizing in metaphysics about other phenomena: we need to carefully reflect on features of the everyday phenomenon with which we started (here: our understanding of can statements) and apply systematic metaphysical theorizing to them. For instance, reflection on certain temporal asymmetries in can statements, explicit or implicit, may give rise to the idea that an object could not have originated otherwise than it did. We can use all the resources of philosophical (and scientific) theorizing: considerations of simplicity and elegance, parsimony, the internal coherence or instability of a theory, formal representations and models, and so forth.

What is distinctive about knowledge of metaphysical modality is not so much how we get on once we have started the inquiry; it is rather how we get into an inquiry of this phenomenon, it is the entry point from which we generalize. It is this claim about the entry point – can statements, rather than counterfactual conditionals – that I will defend in the remainder of this paper.

Williamson discusses, albeit very briefly, a possibility-based alternative to his own modal epistemology (Williamson Reference Williamson2007, 177f.) which differs from my proposal in this section by taking ‘could have’ statements, rather than can statements, as its starting point. He takes the two approaches as ‘not mutually exclusive but rather as different cases in which the cognitive mechanisms of the one already provide for the other’ (Williamson Reference Williamson2007, 178). My discussion in this paper should go some way towards showing that there are indeed substantial differences between the two approaches. Williamson then goes on to raise two worries about the envisaged possibility-based approach.

First, it is less clear how the possibility-based approach, starting as it does from more ordinary cases of circumstantial possibility, ever reaches the ‘limiting case’ of metaphysical possibility. Williamson's own epistemology, of course, does so smoothly: by incorporating contradictions (or a quantifier), it takes us immediately to the limiting case. My favoured approach, proceeding by gradual extension, gives no guarantee of ever reaching the limiting case. I take this to be part of what is otherwise an attractive feature of the approach: it provides a degree of continuity between ordinary and metaphysical modal thought that seems truer to the spirit of anti-exceptionalism than Williamson's leap from ordinary counterfactuals to the rather unordinary counterfactuals in his equivalences. Still, I agree that there is a worry here; to point out just one case, I have not even said anything thus far on how we get to de dicto possibility statements. Important as the worry is, I will only address it very briefly in my concluding remarks in Section 7. I want to focus, instead, on Williamson's second challenge to a possibility-based approach.

Here is the second challenge. A possibility-based approach, Williamson says, needs to provide ‘some account of what demarcates the relevant forms of possibility from irrelevant ones, such as epistemic possibility’ (Williamson Reference Williamson2007, 178). The question arises twice over: first with our entry point, and second with the extension to the limiting case.

First: starting, as I have suggested we do, from can statements, how do we know that some of those can statements do not express epistemic possibility? It is well known that epistemic possibility, unlike circumstantial possibility, does not entail metaphysical possibility: it is epistemically possible that Goldbach's conjecture is true and epistemically possible that it is false, but one of these epistemic possibilities corresponds to a metaphysical impossibility. So if some of the can statements that we start from expressed epistemic possibility, we would have no guarantee that by generalizing from can statements we would not end up including metaphysical impossibilities.

Second: even if it were granted that we start only with properly objective can statements, how can we be sure that in generalizing from them we do not generalize too far, thus again including some epistemic possibilities that are metaphysically impossible? I suggested above that there is a natural limit of our contextual extension; yet how can we be sure that the limit is firmly located between metaphysical and epistemic possibility?

Let me refer to this double challenge as the demarcation challenge. I will argue in the remainder of this paper, first, that my own possibility-based approach easily meets the demarcation challenge (Section 4); and second, that it is in fact the counterfactual-based account that is faced with a serious demarcation challenge regarding its own entry point, counterfactual conditionals (Sections 5 and 6). The considerations on which my argument is based will also bring into sharper focus the second aspect of my entry point that has so far been somewhat in the background – the fact, that is, that we use ‘can’ to ascribe modal properties to objects.

4. The demarcation challenge

What, then, demarcates ‘the relevant forms of possibility from irrelevant ones, such as epistemic possibility’? My answer to this question, in the present section, will appeal to some recent work in linguistics which indicates that we very clearly distinguish circumstantial modality (the relevant form for our purposes) from irrelevant, in particular epistemic, modality at the level of logical form. We have a deeply engrained, if mostly implicit, knowledge of that distinction; and respecting the relevant features of the distinction, as (we will see) my sketch in the previous section did, we run little to no risk of confusing the circumstantial possibility expressed by can statements with epistemic possibility, either at the level of the entry point or in properly extending from there to the limiting case of metaphysical modality.

In the now classic approach to modal expressions (henceforth abbreviated to ‘modals’), shaped especially by Angelika Kratzer (see Kratzer Reference Kratzer2012), all modals are alike at the level of logical form: they are sentence operators that take a whole sentence to form a new sentence. The resulting sentence is true or false depending on whether the embedded sentence is true or false in all or some of the selected worlds. Epistemic modals differ from circumstantial ones merely in their selection of worlds.

More recent work in linguistics, though still very much in the Kratzerian spirit, presents a more nuanced picture. It is now widely recognized that ‘different semantic categories of modals are located in different positions in syntactic structure’, and in particular that ‘epistemic modals reside higher in the tree than non-epistemic ones’ (Portner Reference Portner2009, 143), at any rate higher than circumstantial modals.Footnote ¹² Specifically, it can be seen across languages that epistemic modals take scope over the tense, aspect, and sometimes over quantifiers of the embedded sentence; while circumstantial modals scope below any tense, aspect, and quantifiers, which is to say, their complement does not itself contain any tense, aspect, or quantifiers.

There is a growing linguistic literature on these contrasts and how to interpret them (see, for instance, Brennan Reference Brennan1993; Cinque Reference Cinque1999; Viebahn and Vetter Reference Viebahn and Vetterforthcoming; Hacquard Reference Hacquard2006, Reference Hacquard2009, Reference Hacquard2010, and for an overview Portner Reference Portner2009). In the present context, I will only be able to illustrate them briefly before continuing to discuss their implications for our present purposes. My illustrative examples will all be English, but the phenomenon is well attested across many languages of different families (Cinque Reference Cinque1999).

Circumstantial modals scope below, and epistemic modals above, tense and aspect. A first, though still somewhat superficial observation in this direction is that we can embed verbs with explicit tense and aspect under an epistemic, but not a circumstantial modal, as testified by the following sentences (‘may’ is a standard expression of epistemic, and ‘can’ of circumstantial possibility):

1. (1) (a)He may have travelled to Paris last summer. (epistemic) (b)*He can have travelled to Paris last summer. (circumstantial)

2. (2) (a)He may be travelling to Paris right now. (epistemic) (b)*He can be travelling to Paris right now. (circumstantial)

We can also see how the same form of a modal, when read either epistemically or circumstantially, elicits different readings:

1. (3) (a)Mary had to be home at the time of the crime. (Epistemic: it is now necessary that in the past Mary was home at the time of the crime.) (b)Mary had to sneeze. (Circumstantial: in the past, it was necessary for Mary to sneeze.)

We get both readings also with the past-tense/subjunctive ‘could’:

1. (4) (a)Mary could have committed the murder; we certainly have no evidence to rule it out. (Epistemic: it is now possible that in the past Mary committed the murder.) (b)Mary could have committed the murder; she had a weapon at her disposal and plenty of opportunity – but I’m sure she didn’t do it. (Circumstantial: in the past, Mary had the means and the opportunity to commit the murder.)

The availability of epistemic readings as witnessed by (4-a) is one reason why I used the indicative ‘can’, rather than ‘could (have)’, in my positive proposal in Section 3.

There is some debate concerning whether or not epistemic modals can be in the scope of another tense operator: a well-known counterexample is

1. (5) A:Why did you look in the drawer? B:My keys might have been in there. (=It was possible that my keys were in there)

(The example is from Hacquard (Reference Hacquard2006, 121), who adapts the example from von Fintel and Gillies Reference von Fintel and Gillies2008. For discussion, see Hacquard (Reference Hacquard2006, 120–123) and von Fintel (Reference von Fintel, Fara and Russel2012, 476–477)). In fact, we might even get a tense-over-modal reading of our earlier examples: imagine, for instance, (3-a) uttered by a detective who is asked why she ceased to investigate Mary as a possible suspect and uses (3-a) to explain her past state of evidence. But what is uncontroversial in the linguistic literature is that circumstantial modals always scope below, and never above, any temporal operator, while epistemic modals always scope above a temporal operator (whether or not they may also scope below another). Hacquard goes so far as to say that ‘[o]ne way to unambiguously distinguish an epistemic from a root [including a circumstantial] interpretation is to look at the modal's interaction with tense’ (Hacquard Reference Hacquard2009, 289).

As for quantifiers, Brennan (Reference Brennan1993, 93) notes that the following two sentences differ in the availability of a de dicto reading:

• Every radio may get Chicago stations and no radio may get Chicago stations.

• Every radio can get Chicago stations and no radio can get Chicago stations.

(6), featuring the epistemic modal ‘may’, exhibits both a de re reading that (on the obvious background assumption that there are radios) sounds contradictory and a de dicto reading that is consistent; while (7), featuring the circumstantial modal ‘can’, cannot be heard as consistent (on the same background assumption), showing that it has only the contradictory de re reading.

On the basis of this and other evidence, Brennan generalizes to the claim that circumstantial modals allow only for de re reading, taking scope below any quantifiers (unless they are part of the verb phrase), while epistemic modals can scope either above or below any quantifier. (Both epistemic and circumstantial modals can scope above quantifiers that are part of the verb phrase, e.g. as part of the object of a transitive verb: cp. ‘She can keep every ball in the air simultaneously’.Footnote ¹³) Some even argue that quantifiers can never take scope over epistemic modals (see, for instance, von Fintel and Iatridou (Reference von Fintel and Iatridou2003); Swanson (Reference Swanson2010) disputes the view but notes that is it a ‘common view’, Swanson (Reference Swanson2010, 529)). For our purposes, again, it is enough that circumstantial modals always scope below, and never above, quantifiers that are not part of the verb phrase, while epistemic modals may uncontroversially scope above such a quantifier (whether or not they can also scope below one).

How is this claim to be accommodated in a semantic theory? Generally speaking, the idea is this: circumstantial modals ascribe modal properties such as abilities, dispositions, and capacities to objects, typically to the subject of the sentence; such properties may be gained and lost, hence their ascription is tensed. Typically, therefore, they function by relating a sentence's subject to an (untensed) predicate. Epistemic modals express the epistemic standing (typically, at the time of the utterance) of an entire proposition, hence they apply to a sentence that expresses a full-blown proposition complete with tense, aspect and possibly quantifiers.

Exactly how this general idea is implemented, is somewhat controversial. Brennan (Reference Brennan1993) argues that while epistemic modals are sentence operators just as Kratzer's semantics has it, circumstantial modals are predicate modifiers, taking a verb phrase to form another verb phrase expressing a modal property, which is then attributed to the sentence's subject. Potential counterexamples to this claim include such apparently circumstantial sentences as ‘there can be rain in California’, which lack a semantic subject. Brennan (Reference Brennan1993) and Portner (Reference Portner2009) respond by introducing an additional category of ‘quantificational modals’. Others modify the original proposal, while upholding the general idea. Hacquard, in particular, holds that circumstantial modals apply to a tense- and aspectless ‘proto-sentence’, which expresses an event, and are ‘anchored to’ some object participating in the event – typically, but not always, the object referred to by the sentence's grammatical subject – to which a modal property is ascribed. Epistemic modals, on the other hand, apply to a full-blown sentence and are anchored to the ‘local knowledge bearer’ – typically, but not always, the speaker of the sentence. (Hacquard Reference Hacquard2010, 92)

For our purposes, these differences do not matter. What matters is the general diagnosis: circumstantial modals such as ‘can’ and epistemic modals differ significantly in their syntactic behaviour. Circumstantial modals are restricted to a certain place in the sentence structure: below tense, aspect, and any quantifiers (outside the verb phrase). Epistemic modals appear freer in their syntactic position, but they must have tense and aspect in their scope, and they certainly can scope above any quantifier. Moreover, these differences are best explained by the semantic fact that we implicitly recognize a significant semantic distinction: circumstantial modals ascribe modal properties to the objects that the sentence is about; epistemic modals express, in some way or another, the epistemic standing of a proposition relative to a subject that the sentence need not in any sense be about.

We are now in a position to answer the demarcation challenge, both as it applies to the entry point itself and as it applies to the process of generalizing from it.

How do we manage to start with a non-epistemic modal concept as our entry point? The answer is, first, that we start with an understanding of expressions of circumstantial modality, the modal ‘can’ and its cognates in other languages, and that we have a firm if usually implicit grasp of the distinction between such circumstantial modality and epistemic modality, as evidenced by our mastery of the subtle syntactic differences between them. Secondly, we can now see that this syntactic implementation of circumstantial and epistemic modality is no accident. We use circumstantial modals such as ‘can’ to ascribe modal properties to objects; apart from some special cases, Footnote ¹⁴ we do not generally use epistemic modals to ascribe properties to objects (or only, perhaps, to a special kind of object: propositions). This is not an arbitrary distinction: we tend to think about objective, mind-independent reality as a matter of objects having properties. It is no wonder that we use that same way of thinking for objective, as opposed to epistemic, modality.

Further, given this entry point, how do we avoid generalizing too far and ending up with mere epistemic possibilities after all? The answer should now be clear. The meanings of circumstantial modals are sufficiently different from each other that we should expect there to be a natural boundary between them when we generalize beyond the restrictions of ordinary circumstantial modals. In fact, they are so different from each other that there is little reason to expect a natural passing from one to the other; so the question of a boundary between them may not even arise.

To be sure, we have modals that express both circumstantial and epistemic modalityFootnote ¹⁵); but as we have seen in this section, there are important disanalogies with respect to both syntax and semantics, suggesting that such modals in fact exhibit a kind of ambiguity, or more precisely, polysemy.Footnote ¹⁶

This is emphatically not to say that philosophers never do, in fact, mistake mere epistemic possibilities for metaphysical possibilities; I think they often do, in particular when they simply examine intuitions about sentence-operators such as ‘it is possible that ’, which are epistemic in all ordinary contexts (see Kratzer Reference Kratzer, Eikmeyer and Rieser1981; DeRose Reference DeRose1991). It is to say, rather, that there is a good way of not making that mistake: by linking metaphysically modal thought, however implicitly and however indirectly, to thought about the modal properties of objects.

So far, I have argued that the possibility-based approach has the resources to meet Williamson's demarcation challenge. Williamson's phrasing of the challenge suggests that he believes no analogous problem to apply to his own, counterfactual-based account. In the next two sections, I will argue that this is not so. The counterfactual-based account begins with our understanding of linguistic constructions like the English ‘if it were the case then it would be ’. I will argue for two claims. First, counterfactual conditionals have epistemic as well as circumstantial readings. And second, it is much less clear that we can implicitly demarcate these readings for counterfactuals, making counterfactuals a less suitable entry point into metaphysical, non-epistemic, modal thought and knowledge than can statements. This is my own demarcation challenge to Williamson's modal epistemology, more specifically, to its entry point. Section 5 will defend the first claim, Section 6 the second.

5. Epistemic counterfactuals

Williamson (Reference Williamson2007) does not explicitly state but clearly assumes that the counterfactuals to which he appeals have circumstantial and not epistemic readings (see also Williamson Reference Williamson, Vaidya and Prelevićms, 10). In a more recent paper, he explicitly states that ‘[n]ormally, counterfactuals are on the objective side of this contrast [between objective/circumstantial and epistemic]’ (Williamson Reference Williamson, Armour-Garb and Kroonforthcoming-a, 14); he does not say anything about any abnormal readings.

I begin by arguing that there are counterfactuals, i.e. sentences of the form ‘if it were/had been that then it would be/would have been that ’, which have epistemic readings. A nice array of examples can be found in Edgington (Reference Edgington2008) (numbers and paragraphs are inserted by me):

1. (i) There is a treasure hunt. The organizer tells me ‘I’ll give you a hint: it's either in the attic or the garden.’ Trusting the speaker, I think ‘If it's not in the attic it's in the garden.’ We are competing in pairs: I go to the attic and tip off my partner to search the garden. I discover the treasure. ‘Why did you tell me to go to the garden?’ she asks. ‘Because if it hadn’t been in the attic it would have been in the garden: that's (what I inferred from) what I was told.’ That doesn’t sound wrong in the context.

2. (ii) Or consider: ‘Why did you hold Smith for questioning?’ ‘Because we knew the crime was committed by either Jones or Smith – if it hadn’t been Jones, it would have been Smith.’

3. (iii) There's also a nice example of van Fraassen's (): the conjuror holds up a penny and claims he got it from the boy's pocket. ‘That didn’t come from my pocket’, says the boy. ‘All the coins in my pocket are silver. If that had come from my pocket, it would have been a silver coin.’

In all three cases, it seems clear that the connection between the antecedent and the consequent of the conditional is not ‘worldly’ but rather relative to our state of information: the utterance in (i) is true even if the organizer never had the intention, or even the option, of hiding the treasure in the garden; it is true simply by virtue of the speaker's having had the evidence that she had. The utterance in (ii), likewise, is true even if there was never objectively any significant objective chance of Smith committing the murder; rather, it is related to the evidence that the speaker had in the past. Finally, the boy in (iii) makes no claim to the effect that the coin would have turned into silver had it been in his pocket. Rather, it is relative to his knowledge that all the coins in his pocket are silver that this coin would have to (epistemic have to!) be silver if it had come from his pocket.

Edgington (Reference Edgington, Hoerl, McCormack and Beck2011) and Khoo (Reference Khoo2015) have both pointed out that we can produce epistemic readings along the lines of (ii) for just about every counterfactual, even the paradigmatic example ‘if Oswald hadn’t shot Kennedy, someone else would have’: just imagine a detective explaining why she was investigating other suspects after it has become clear that Oswald was indeed the shooter (see Edgington Reference Edgington, Hoerl, McCormack and Beck2011, 239; Khoo Reference Khoo2015, 25f.). This should not come as much of a surprise: we noted a corresponding reading for non-conditional modals in Section 4.

I would like to add a hypothesis of my own to extend the class of epistemically-read counterfactuals. Williamson has argued in a number of places (Williamson Reference Williamson2007, 171–175; Williamson Reference Williamson, Armour-Garb and Kroonforthcoming-a) that counterpossibles are vacuously true. Imagine that, while walking in the wilderness, we enter a clearing and something runs past us from an unexpected angle. In fact, it is a harmless gazelle; but we both know that there are dangerous tigers about. Shocked, you say to me:

1. (8) If that had been a tiger, we would be dead now.

This seems a reasonable thing to say under the circumstances, and a useful statement reminding us to be more careful in the future (next time it might be a tiger instead of a gazelle). On the contrary,

1. (9) If that had been a tiger, it would have had tea with us.

Seems, on the face of it, clearly false. Of course, given the necessity of kindhood (or at least the necessity of not belonging to a very different biological kind), both are counterpossibles, and hence both are true, according to Williamson. The difference between them is one of assertability, not of truth (Williamson Reference Williamson2007, 173; Williamson Reference Williamson, Armour-Garb and Kroonforthcoming-a, 9). Arguably, however, if we had a way of making (8) true and (9) false without getting into trouble, that would be the preferable reading. Williamson, of course, has forceful arguments to show that we do run into trouble unless we accept the truth of both (8) and (9). But, as I have pointed out elsewhere (Vetter Reference Vetterforthcoming) and as Williamson readily acknowledges (see Williamson Reference Williamson2007, 175; Williamson Reference Williamson, Armour-Garb and Kroonforthcoming-a, 14), his arguments turn on the idea that the counterfactuals in question are objective, that is, circumstantial. If (8) and (9) are read epistemically, then the metaphysical impossibility of their antecedents has little bearing on their truth-value.

Compare: on a circumstantial (objective) reading of ‘could’, the following are both false in the scenario described for (8) and (9):

1. (10) This could have been a tiger.

2. (11) This could have been a cloud.

On an epistemic reading, this is not so: (10) is true, while (11) is, presumably, false. Epistemic readings allow us to make distinctions among metaphysical impossibilities that are important, and to allow those distinctions to be just what they appear to be: differences in truth-value, not in assertability. I suggest, therefore, that we read (8) and (9), as well as other (metaphysical) counterpossibles, as epistemic.Footnote ¹⁸ (We will meet the two tiger conditionals again later.)

It seems, then, that there are a reasonably wide range of epistemically read counterfactuals. So, in gaining knowledge about metaphysical modality from our knowledge of counterfactuals, we must make sure that the counterfactuals we start with are understood circumstantially, not epistemically.

Khoo (Reference Khoo2015) appears to offer an easy way out arguing that the circumstantial reading is the default reading of a counterfactual. According to Khoo, epistemic counterfactuals all share with circumstantial counterfactuals (but not with indicative conditionals) a syntactic feature that we have seen to be typical of circumstantial modals: they are embedded under a (past) tense. The epistemic counterfactual in Edgington's (ii) is properly read as saying that in the past it was epistemically necessary, under the supposition that it wasn’t Jones, that it would have been Smith. Khoo takes this to explain why circumstantial readings are the default reading for this kind of construction: we rarely ‘care about past possibilities which are no longer open possibilities (having learnt something new which rules them out)’ (Khoo Reference Khoo2015, 27).

However, I take Edgington's example (iii) to constitute a counterexample to this general claim. In (iii), what we have is an epistemic counterfactual that is relativized to the boy's current evidence (in particular, his knowledge about the coins in his pocket all being silver, and having been so when the conjuror did his trick). It is necessary (at the time of utterance: present tense), given his present evidence, that if in the past the coin had come from the boy's pocket, it would then in the past have been silver. The interaction between the epistemic counterfactual and the past tense appears to be more complex than Khoo's hypothesis allows; and therefore his explanation for, and his claim of, a default circumstantial reading does not apply in all cases. (Moreover, as we will see shortly, there may well be reason to care about counterfactuals even when they concern past possibilities that are no longer open: like circumstantial counterfactuals, they help us learn from experience.)

Of course, to close off the easy way out is not yet to show that there is no other way out. However, I will now argue that it is not at all clear that we are as good at distinguishing the relevant forms of counterfactuals from the irrelevant ones, in particular the epistemic ones, as we are with the simpler modal constructions, such as expressions of possibility.

6. Demarcating counterfactuals

How are we to demarcate circumstantial from epistemic counterfactuals, so as to make sure that we do not infect our metaphysically modal thought with epistemic modality? This section will offer no positive answer to the question, but rather point out that an answer is not as easy to come by as in the case of can statements: we are, I suggest, not all that good at drawing the required distinctions, at least not without some theoretical background. This makes counterfactuals less suited as an entry point into metaphysically modal thought, although it may be that with more advanced theorizing about these kinds of modality, we come to understand and apply the distinction competently and successfully. But that understanding has to start elsewhere; my suggestion has been that it starts with can statements.

I offer three kinds of consideration to support my claim. First, the syntactic considerations that I used for the case of can statements do not carry over to counterfactuals. Second, there is evidence that speakers with the relevant linguistic and metalinguistic competence do indeed disagree dramatically about the readings of standard counterfactuals. And third, given the practical and evolutionary role that counterfactuals play, there is no reason to expect that we should be very good at distinguishing between their epistemic and circumstantial readings, for they serve much the same purposes.