2.1 Variety of Modal Discourses

Modal discourse is ubiquitous and it is very much entrenched in our daily lives. We have considered a couple of examples in the Introduction, and it is not difficult to come up with a much longer list of scenarios where modal propositions (or modal beliefs) are at the core of our reasoning or decision-making processes. As crudely characterised in the Introduction, a modal proposition involves some modal notion – central among them are possibility and necessity. In the following, it is the absence of modal notions in (1) and their presence in (2) that makes only the second proposition a modal one:Footnote ¹

1. (1) Iris’ knee is bleeding.

2. (2) The fall must have been worse than it looked.

As with any other type of proposition, modal propositions can be true or false. Regardless of their truth-value, all the propositions below are modal in virtue of each involving a modal notion:

1. (3) Iris could be more careful.

2. (4) Two plus five must be seven.

3. (5) One can’t always be a Good Samaritan.

4. (6) Being a philosopher is accidental to Socrates.

5. (7) A rocket can travel faster than light.

6. (8) Necessarily, if Ernest isn’t married, he is a bachelor.

7. (9) You can drive without a safety belt when you’re heavily pregnant.

8. (10) If Ernest isn’t married, he’s necessarily a bachelor.

9. (11) Umar can’t be at the hospital.

10. (12) You can jump this stream.

11. (13) You must respect people’s turns (e.g., in a queue).

12. (14) It must have been raining.

13. (15) You can’t torture people.

These propositions, and some contrasts among them, will first serve us to illustrate the ubiquity of modal discourse, and they will then help us draw distinctions between different types of modalities (Sections 2.2, 2.3, and 2.4). Following this, we will tackle the much-contested issue of unification (Sections 2.5 and 2.6) and use this discussion to reflect on the contemporary role of possible worlds (Section 2.7) and the prospects of precisifying, within modality, the de re/de dicto distinction (Section 2.8).

Of the propositions above, some might seem artificial (they have been chosen with a purpose) but others are ordinary modal propositions and it’s not difficult to conceive of scenarios where one might easily apply them. For example, someone tells you that your neighbour, Umar, was admitted into hospital yesterday night with severe Covid-19; this surprises you as you’ve just spoken to him on the phone this morning. You reply with (11) – Umar can’t be at the hospital. In a second example, your daughter is playing in the park, which is divided by a stream. She’s on one side, but wants to join a group of children who are playing on the other side. She’s impatient, and wonders whether to walk down to the bridge, cross it, and walk up again, or whether she should dare jumping across the stream. After assessing the circumstances, you encourage her with (12) – You can jump this stream. And a third example: your nephew enters a busy candy shop and goes straight to the counter demanding a lollipop. You intervene with (13) – You must respect people’s turns.

These are just a couple of examples. They may be trivial, but they are illustrative of how quotidian modal thought and modal reasoning is. Beyond quotidian life, preventive medicine is a health specialisation whose goal is to prevent people from contracting illnesses they can (relatively easily) contract. At a more abstract level, modal reasoning is central in scientific methodology. The process of acquiring information about how the world is can be seen as the process of ruling out that the world is some other possible way. Let us suppose that there are two hypotheses, H₁ and H₂, that seem to equally explain our body of evidence, E. For all we know, the world could be like H₁ says, but it also could be like H₂ says. If we want to know how the world is, and given that evidence E is neutral between H₁ and H₂, we need disambiguating evidence. This extra evidence can be achieved by designing and carrying out experiments; this is common scientific practice. And yet, designing and carrying out experiments can be very costly (financially and otherwise). Could we justify this practice if we had sufficient reasons to believe that either H₁ or H₂ are impossible? Or if we had sufficient reasons to rule one out? When a hypothesis is taken seriously, we are assuming, at least implicitly, that the world could be the way the hypothesis describes it.

The reader who is already familiar with the distinction between alethic, epistemic, and deontic modalities might be wondering why I’m not being more rigorous. Is it epistemic or alethic possibilities that are being assumed in scientific practice, for instance? Is it in an epistemic sense or in a physical sense that Umar can’t be at the hospital? However, this lack of rigour, at this stage, is intended. It illustrates that there are indeed different senses associated with our modal vocabulary, and which one is involved easily varies from context to context (including a speaker’s intentions). Consider again proposition (11) – Umar can’t be at the hospital. Is this true or false? This question cannot be answered once and for all; it depends on the sense (and context) in which it is uttered. For instance, above, I pictured a context intended to be one where an utterance of (11) is very likely to be true. If you know that you’ve heard Umar at home this morning, talking on the phone, then (it is likely that) he couldn’t have been admitted into hospital with severe Covid-19 the evening prior. There must have been a misunderstanding somewhere: maybe he was checked but not kept in? The sense of modality in which these conclusions are true is, as we shall see shortly, an epistemic one: it is dependent on what we know.

But (11) could be uttered in other contexts where we don’t mean an epistemic sense of ‘can’. Imagine a group of friends and one of them, Shyla, asks where Umar is. Joel replies: ‘Well, he’s quite healthy, so he can’t be in the hospital’, to which Kiran protests that his being quite healthy doesn’t mean that he cannot fall ill or have an accident. In this context, (11), as uttered by Joel, is likely to be false, and what makes it false is not dependent on what the group of friends know or believe about Umar, but rather on what’s modally true of him: regardless of his degree of health, Umar, as an organism, is not immune to illnesses or accidents. As we will also see shortly, this dependence on truth makes this sense of modality an alethic one. In addition to the epistemic and the alethic, there’s yet another kind of modality that we will also focus on in this section: the deontic one, which has to do with norms. To get a taste of it, consider (15) – You can’t torture people. If this strikes you as true, you’re most likely reading it in the deontic sense, and, if so, the message you’re taking from it is that it’s not morally permissible to torture people. Notice that, in an alethic sense, (15) is false: as too often witnessed, there aren’t many physical impediments to people torturing others.

It is the aim of the next three sections (Sections 2.2, 2.3, and 2.4) to unfold these brief remarks by focusing on three main families of modalities: epistemic, deontic, and alethic. I shall first introduce them separately. After this, in Sections 2.5 and 2.6, I will be most interested in exploring the relations between them, paying special attention to debates in recent literature having to do with the prospects of finding a unifying treatment. Before all this, let me introduce the notions of possibility and necessity as duals of one another. Roughly, by ‘duality’ in this context we mean that we can define possibility in terms of necessity, and vice versa.Footnote ² Specifically, p is possible – in symbols, ◊p – means that it is not necessary that not p – in symbols, ¬□¬p. We have just defined possibility in terms of necessity. And we can correspondingly define necessity in terms of possibility: p is necessary (□p) means that it is not possible that not p (¬◊¬p). With duality in place, let us turn to the different types of modalities.

2.2 Epistemic Modalities

Assuming the duality between possibility and necessity, it is open to us to directly characterise the epistemic sense of only one of the two modal notions – necessity or possibility – and to arrive at the other by means of the conceptual path that their duality affords. I shall illustrate this as we move along, starting with the notion of epistemic possibility. As a first approximation, epistemic possibility can be characterised in the following way:

It is this dependence on knowledge that gives epistemic modality its name, from the ancient Greek episteme, meaning knowledge or science. The first thing to note is that (EP) characterises epistemic possibility as relative to a subject. This cannot be otherwise due, precisely, to its dependence on a given subject’s body of knowledge. Note also that, since different subjects will clearly know different things, which propositions are (or are not) epistemically possible will vary accordingly across subjects. To illustrate: if I have no idea what is the highest speed a spur-thighed tortoise can reach, it’s epistemically possible for me that Clark (my friend’s spur-thighed tortoise) walked at three kilometres per hour yesterday; such speed is certainly compatible with all I know – virtually nothing – about tortoises. However, a herpetologist will have relevant information about tortoises that puts her in a position to rule out that Clark ever reached that speed. Thus, it is not epistemically possible for the herpetologist that Clark walked at three kilometres per hour yesterday.

(EP) is a good first approximation. It captures a kind of epistemic modality often made salient in ordinary contexts, as the Umar example above and the tortoise case just described, serve to illustrate. Given that we’re assuming the duality of the notions of necessity and possibility, we now have two options to characterise the corresponding epistemic necessity: we either characterise it directly, or else we do it from (EP), exploiting the duality. The two ways will (and should, if the duality is such) be extensionally equivalent:

(EP) and (EN) jointly characterise what is perhaps the most paradigmatic type of epistemic modality. To be rigorous, however, they characterise potentially as many different epistemic modalities as there are individuals (or, more rigorously, as there are pairs of individuals and times). For what we’ve got is a schema, rather than a modality, and we can replace ‘S’ by any individual, each of these moves resulting in an epistemic modality.

But even leaving this schematicity to one side, this schema (of epistemic modalities relativised to one single individual) is not the only one within the family of epistemic modalities, not even the one that will always be salient. Sometimes, the context might make salient instead an epistemic modality relativised to a group of individuals. To capture these other types of epistemic modalities, we would need to mention explicitly a group of individuals in the schema. In addition, we would need to accompany this by an unambiguous notion of collective knowledge. This gives rise to alternative, non-equivalent (schemas of) epistemic modalities, as the following illustrates without being exhaustive:

As above, these are schemas. In order to get an epistemic modality from them, we would need to plug in a given group of people in each case. Technically, for any group of people we can think of, we could plug it in, and we would obtain a specific epistemic modality as a result. Admittedly, some of these modalities are of greater interest than others. For instance, in the middle of a pandemic, plugging in a worldwide group of epidemiologists would generate a much more interesting epistemic modality (in either the union or the intersection sense) than the group of members in my household, especially with respect to possibilities concerning, for instance, how stressed hospitals will be in a year’s time, or how risky it is to book a flight for two months’ time.

We have focused so far on epistemic modalities in a strict sense: that is, modalities that are dependent on knowledge. One might wonder what the result would be if we considered alternative notions in the vicinity, such as belief, or even justified belief. The answer, simply put, is that we would get different types of modalities which, with a suitably relaxed understanding of the label ‘epistemic modality’, might still be taken to be such, and for which, with a more stringent insistence on labels, ‘doxastic modalities’ would be more apt. Regardless of our terminological choices, all these modalities have in common their relativisation to an individual or group of individuals, and that what is possible or necessary for them depends on the body of information that the individuals are committed to, at least at the level of belief. This makes all the elements in this (relaxed) group of modalities quite close to one another as phenomena.

And yet, one interesting difference between epistemic modalities and doxastic ones (in stringent senses of these labels), stems from the facticity of knowledge and the lack of facticity of belief (even of justified belief). We know that what is known is indeed the case – knowledge is factive – but that beliefs, even justified ones, can be false – belief is not factive. This difference has a sharp impact on the modal logics that can be used to model epistemic and doxastic modalities. Think of the principle according to which what’s necessary is (also) the case, which is known as principle (M) in modal logic (in symbols, □p→p). With a stringent-epistemic sense of ‘necessary’ this principle comes out as valid (cannot fail to be true), but this is not the case with the doxastic sense of the term. We will take the cases in turn. If p is epistemically necessary (if □p, in the epistemic sense), then p follows from a body of knowledge (be that knowledge of a single individual or of a group of individuals). Since knowledge is factive, p is the case. As a result, if □p then p. And since the choice of p was arbitrary, this concludes the reasoning for the epistemic sense. By contrast, if p is doxastically necessary (if □p, in the doxastic sense), then certainly p follows from a body of beliefs, but this is insufficient to guarantee the truth of p; indeed, p could be falsely believed (that is, the body of information from where p follows could be false). As a result, in the doxastic case, we cannot safely transition from □p to p: some of these transitions could lead us from truth to falsehood. Things being so, if one is to model epistemic modality with modal logic, it will need to be with a modal logic that includes principle (M), whereas one would need to exclude it if one is modelling doxastic modalities.Footnote ³ We will return to (M) when considering deontic modalities, to which we now turn.

2.3 Deontic Modalities

Deontic modalities, you will recall from Section 2.1, have to do with permission and obligation. Recall proposition (15): You can’t torture people.

In a physical sense of ‘can’, one certainly can torture people. The sense in which (15) is intended to be true is rather a deontic one: it’s not permitted for you to torture people (or, exploiting the duality from Section 2.1, it is an obligation for you not to do so). As with epistemic modalities, and as the plural indicates, deontic modalities constitute a family, unified by the fact that they all relate to permission and obligation. Any code of conduct – in a school, at work, at home, in relation to a game, in a state, in a community, etc. – amounts to a deontic modality. Among the many members in this family, moral modality and legal modality are most salient. In the moral sense, (15) tells us that torturing people would amount to transgressing a moral principle. In the legal sense, (15) tells us that torturing people is not allowed by a given system of (man-made) laws. Even these types of modalities are, yet again, families: there’s not just one system of (man-made) laws in the world, but many; each state (and not only states) has its own set. And, regardless of whether or not there is an absolute (universal) moral code, in an equally legitimate use of the term ‘morality’, there are various moralities; these are quite often associated with (but not limited to) the variety of religions.

A schema for deontic possibilities can thus be as follows:

This schema allows us to see a structural difference compared with epistemic modalities: deontic modalities are not relativised to individuals in the way epistemic modalities are.

To give a couple of examples, consider Christian morality, according to which you shall not murder, you shall not steal, you shall not commit adultery, etc. We can call ‘ChM’ the code of conduct encoded in the Ten Commandments. Similar to what we did with epistemic modalities, we can now characterise Christian-Morality modality as follows:

It follows from the above characterisation that it is Christian-morally necessary that Cain doesn’t kill Abel. And yet (assuming for the sake of the example that what we have heard about them is true), Cain killed Abel. We can thus identify a proposition – Cain doesn’t kill Abel – that is both necessary, in the current sense of the term, and fails to be true. As such, this proposition alone suffices to compromise the validity of principle (M), □p→p, for the current modality; and it doesn’t take much imagination to identify a whole battery of other propositions with the same effect.

Scottish-Legal modality, to give one further example, behaves similarly. Let us call the Scottish Legal system ‘SLS’. We can then characterise Scottish-Legal possibility as that which is compatible with all the elements in SLS. According to SLS, drink-driving is an offence and, as such, the proposition that Finley drove home while noticeably drunk is Scottish-Legally impossible. Despite such status, in a physical sense of ‘possible’, it’s certainly possible for him – and anyone – to drive home while noticeably drunk. Any instance of drink-driving in Scotland is proof of the invalidity of principle (M) for the case of Scottish-Legal modality.

These reasonings generalise to any deontic modality. Indeed, deontic modalities all have in common with doxastic modalities their invalidation of principle (M): just as there’s no guarantee that people (will) believe truly, there’s also no guarantee that people (will) do what they deontically must. It is characteristic of deontic modalities that their musts can typically (in a physical sense) be transgressed. As we will see in the next section, this feature distinguishes alethic modalities from deontic modalities.

2.4 Alethic Modalities

In comparison to epistemic modalities, which, as seen in Section 2.2, can be characterised as dependent upon a given body of knowledge (or beliefs), alethic modalities can be characterised instead as dependent on a body of truths. And it is this feature which gives alethic modalities their name – from the ancient Greek aletheia, for truth. The schema for them is very similar to that in the case of deontic modalities and, in particular, they share with the deontic family that they are not relativised to individuals:

There are several questions that soon appear when trying to structurally characterise alethic modalities. An important issue, which will shape our discussion here and be relevant in much of Section 2.5, can be informed by the following remarks. Consider the epistemic modalities in the stricter sense; those dependent on knowledge. As will be appreciated, potentially any set of true propositions, so long as they are graspable, can constitute a body of information known by some individual (or group). As a consequence, the family of epistemic modalities is potentially vast. And even if it might not actually be as vast, it is no doubt already very large: there are many people in the world, and any variation – no matter how slight – in the body of knowledge of any two people will determine different epistemic modalities. The question is: can we say something similar about the family of alethic modalities? That is, is there an alethic modality for any (whichever) set of truths? This question is important. It is also a controversial issue that cannot be answered in a theoretically neutral way. For this reason, I shall postpone addressing it until Section 2.5, when we will look into the question whether there is something that unifies the different types of modalities (different answers to this question have different implications about the size of the family of alethic modalities). For the time being, I shall focus on some typical (and some less typical) examples of alethic modalities. These examples raise their own controversies, some of which are deserving of more attention than they have been given so far. (As a note of caution, please bear in mind that, as in Sections 2.2 and 2.3, I’ll be talking about ways of characterising (alethic) modalities, not ways of defining them. More on this in Section 2.5.)

2.5 Unification of Alethic Modalities?

It is now time to go deeper into the related family of issues we’ve been stocking up in Section 2.4. How many alethic modalities are there? This is now our central question. Let me start by noting that I have not been speaking of the characterisations of the different alethic modalities as definitions of them. This is purposeful. For we’re now moving to a discussion about how many different kinds of modality there are, at a fundamental level. And, had I been speaking of the characterisations in Sections 2.2, 2.3, and 2.4 as definitions, I would have easily begged the question (against my intended neutrality) in favour of one side of this debate – the one which we shall call ‘the reductivist relativist side’. Characterisations are, importantly, different from definitions. For instance, I can characterise the property of being a cat as the fundamental kind of my pet. And because I have only cats as pets (and in fact I have only one pet), that characterisation uniquely identifies the property of being a cat. Indeed, something is the property of being a cat if and only if it is the fundamental kind of my pet. With this characterisation, I am committing myself to the extensional equivalence between the two sides of the bi-conditional. But this commitment to the extensional equivalence doesn’t commit me in turn to there being a definitional equivalence between the two. And, at least in this case, that is good, for I would rather deny the definitional equivalence: surely there is more to being a cat than being the fundamental kind of my pet!

Consider now all the characterisations in Section 2.4: the nomic, the metaphysical, the conceptual, etc. And consider the question of whether there is, in each case, a definitional equivalence between their two sides. As a first approximation, we can characterise the reductivist relativists in this debate as those who answer this question in the affirmative. By contrast, for the non-reductivists (whether relativist or not), among whom I count myself, there is more to being a certain type of alethic modality than satisfying the corresponding characterisations.

As we shall briefly see, one of the biggest selling points of the reductivist relativist is what we can refer to as ‘the unification power’. Such a relativist has a readily available answer to the question what makes every kind of modality, precisely, a kind of modality: it is their all being relativised forms of logical modality. But at the same time, there’s a feature of this reductionist stand, which we can label ‘cheap proliferation’, that, for many, myself included, is a ‘not-buying’ point. We will structure the discussion in this section around these two points, and we start with the former one: the unification power.

Jessica Leech is a prominent contemporary reductivist relativist, and she has defended this metaphysical stance in Reference LeechLeech (2016), where she neatly distinguishes it from the non-reductive relativist one. Following this, Reference Hale and LeechHale and Leech (2017) have contributed further to our general understanding of the prospects and strengths (as well as weaknesses) of the different relativist projects. For they each have different metaphysical agendas, and one of the differences consists, precisely, in that it is only Leech who is a reductivist relativist. For Leech (but not for Hale) what they submit as good relativist characterisations of the different modalities exhaust, metaphysically, what these modalities are.

What are these relativist characterisations, on which they both agree despite their metaphysical discrepancy? The literature contains a very thorough, precedent discussion about what a relativist characterisation should look like. With the aim of providing a contemporary focus to the current Element, I shall simply set aside earlier proposals (and the problems they face) and jump directly to the relativist proposal as found in Reference Hale and LeechHale and Leech (2017).Footnote ²⁰ Here is, in maximal generality, their relativist proposal (Reference Hale and LeechHale and Leech 2017, 14):

where □ stands for logical necessity – and thus, ‘□(q →p)’ is to be read as ‘p is a logical (necessary) consequence of q’ – and where the variable ϕ (on the left-hand side) ranges over any potential type of relative necessity.Footnote ²¹ The following examples are all instances of this schema:

where ‘π(q)’, ‘β(q)’, and ‘τ(q)’ abbreviate, respectively, ‘it is a law of physics that q’, ‘it is a law of biology that q’, and ‘it is a law of technology that q’. According to the first instance, then, something (p) is physically necessary if and only if it logically follows from a law of physics.

Let’s not be distracted by the fact that the form of Hale and Leech’s relativist characterisations is very different from the one we’ve become used to so far: they include the existential quantification over certain types of propositions. The reason for this is that, without this change, any relative modality would unavoidably inherit the satisfaction of the S4 axiom (□p → □□p) from the fact that logical modality satisfies it. And yet, it is desirable, they contend, not to impose the satisfaction of this principle.Footnote ²²

Regardless of form, unification, as anticipated above, is one of the biggest selling points of the reductivist relativist project. In the words of Reference Hale and LeechHale and Leech (2017, 19), ‘what drove that project’ was precisely such a unificatory aim. That is, ‘to show that, contrary to appearances, there is no need to recognize a variety of independent kinds of necessity – physical, mathematical, etc. – by showing that each of these ostensibly different kinds of modality may be fully explained using just one single kind of modality, such as logical modality’ (Reference Hale and LeechHale and Leech 2017, 20).

Unification, afforded here by the reductive relativist project, thus brings with it explanatory power. Let us look back at the general schema above: no matter which (relative) type of modality we’re characterising – that is, no matter what we substitute for the variable ϕ – they are all characterised as relative on the basis of one and the same absolute modality: the logical one. When such a vast array of modalities are characterised, even defined (as per the reduction), in this way, an important feature that is shared by all of them is thereby identified and, ultimately, this shared feature can account for our taking them all to be kinds of modality. How successful is, however, this explanation?

To see a threat to it, note that there is a distinctive feature of the relativist characterisations proposed by Hale and Leech that deserves attention: namely, the fact that it rests, in each case, on an antecedent understanding of the type of truth, ϕ, relative to which a given kind of ϕ-necessity is being defined. To stick with the example of physical necessity, the definiens ‘∃q(π(q) ∧ □(q →p))’ above says that p follows as a matter of logical necessity from a law of physics. This feature can be thought to threaten the unifying and explanatory power of the proposal. The reason is that, for such a definiens to work as intended, one needs to appeal to the notion of a physical law. In turn, for such appeal not to threaten the unifying power, this notion had better not involve a sui generis notion, and kind, of modality. But the concern is, precisely, that it might not avoid such sui generis modality. (And note that the reasoning is not specific to physical modality; rather, it generalises.) To uncover where the concern comes from, recall that, in Section 2.4.3, I mentioned that, typically, the kinds of truths relative to which one characterises an alethic modality all seem to enjoy a law-like character. To put the current concern in those terms, the worry is that, in each case, such a law-like character amounts to a type of modal force not to be assimilated to that of logical necessity (that of the ‘□’ in the schema). And, if this is so, logical necessity on its own will not support the sought-after unification.

It is largely around this issue that Hale’s and Leech’s metaphysical agendas come apart. Hale is less concerned about reduction and unification and is happy to settle for the less ambitious aim ‘of achieving an improved understanding of the contrast between merely relative and absolute kinds of necessity. The achievement of that aim is in no way compromised by the irreducibility – if such it is – of the various kinds of putatively relative necessity to a single absolute necessity’ (Reference Hale and LeechHale and Leech 2017, 20).

For current purposes, what we need to stress is that the potential unification power is, by conception, a potential selling point for the reductive relativist, like Leech. As such, it is this type of relativist who needs to provide a response to the threat just identified. As we’re about to see, this response can be tailored in tandem as a response to what we can label ‘the problem of cheap proliferation’.

The source of this label traces back to Fine. In Reference FineFine (2005), he describes the reductive relativist as suffering from an unacceptable proliferation of modalities, and claims that there’s nothing they can appeal to in order to explain the difference between, for instance, Physical modality and the gerrymandered Alaskan modality (Section 2.4.3). According to Fine, the former is non-trivial and the latter is trivial, cheap, and this distinction should not be lost.

This problem brings us back to the overarching question in this section: how many alethic modalities are there? Or, in other words, is there an alethic modality for any (whichever) set of truths? In the spirit of this complaint, one could say that it’s just a by-product of the schema above that we can characterise Alaskan modality, but that there really isn’t anything genuinely modal about it. And yet, when one (like Leech) takes the characterisations as definitions, in a reductive manner, there’s no way of excluding these gerrymandered properties from being modalities.

How problematic, however, is this proliferation for the reductive relativist? By their lights, not much at all. Even Reference LeechLeech (2016) speaks of the many relative modalities as cheap when responding to Fine’s challenge. And her doing so should not suggest that she shares with Fine his diagnosis of the proliferation as a problematic feature. On the contrary, she adopts the phrase ‘cheap modality’ but not its negative connotations. At a metaphysical level, Leech can’t explain the difference in kind between a trivial and a non-trivial modality. But this is not deemed problematic because, by her lights, there is none. According to Reference LeechLeech (2016), there need not be – and there isn’t – anything objectively special about the type of truth, ϕ, to which a given ϕ-necessity is relativised. Because of this, the door is open to define as many relative modalities as sets of truths, ϕ, one desires to consider. One can embrace all modalities, gerrymandered or not, because, metaphysically, modalities are indeed cheap and ontologically all on a par. Which relative modalities, among the vast many, we find interesting will depend on which sets of truths we find interesting. As a matter of fact, we find Physical modality, Mathematical modality, Biological modality, and a limited range of other modalities, more interesting than Alaskan modality or, to borrow Reference LeechLeech’s (2016) own example, Argos modality – defined as relative to truths about items listed in the Argos catalogue. But, on her reductive framework, this difference in interest (by us humans) does not reflect any deep, metaphysical contrast between them.

In a nutshell, therefore, Leech’s response to Fine’s proliferation problem rests on denying a presupposition in Fine’s complaint: the presupposition that some modalities are trivial and some are not. A reductivist relativist, like Leech, therefore, would happily bite the bullet of proliferation, and answer our overarching question in this section (about how many modalities there are) with something like ‘as many as non-equivalent sets of truths there are, and no significant metaphysical distinction is to be made among them’.

As anticipated, this response constitutes, in turn, a response to the unification threat above: the vast many relative modalities are still, all of them, just relativised forms of logical modality. No sui generis modality sneaks in. Unification is thus achieved, despite the threat.

For many, however, embracing all these properties as modalities is unsatisfactory and indeed one of the main reasons for moving away from a reductivist relativist approach. What, then, are the alternatives? One alternative is clear from the above: non-reductive relativism. When one, like Hale, does not take reduction and unification as a goal in one’s metaphysical agenda, one can insist (even when partaking in relativism) that any set of truths relative to which a (relative) modality is characterised must be such that its elements should have, precisely, a certain degree of modal force. (And when one is not attempting reduction, this appeal to a sui generis modal force need not be jeopardising.) If this is one’s theoretical choice, the alleged Alaskan modality or Leech’s Argos modality would easily be banned from being considered genuine modalities. Indeed, the intuitive contrast between them and, for instance, Physical modality is now explainable precisely in terms of the elements of LN – the set of laws of nature – having a certain degree of sui generis modal force, something that is absent in the case of the (now banned) gerrymandered modalities.

As far as we know, however, in giving up the reduction, non-reductive relativism also gives up the aim of unification; or, at the very least, it gives up the aim of unifying by relativising. In the remainder of this section, I shall focus on the two questions that are, in view of this, most dialectically relevant. First, what are the non-relativist alternatives? And, second, how do they fare with the prospects of unification?

In addressing these two questions, rather than covering a wide range of alternatives, I shall limit myself to illustrating answers to them by focusing on the contemporary work of Reference KmentKment (2006b, Reference Kment2014) and Reference FineFine (2005). These works are interesting in themselves, but they are also interesting in comparison to one another, as the following will make clear. (In Section 3, when we turn to the metaphysics of metaphysical modality in particular, we will consider other accounts (Thomasson’s, for instance) whose consequences relate back to the issue of unification.)

Reference FineKit Fine (2005) opens up ‘The Varieties of Necessity’ with the question of unification, making it very clear from the outset that he doesn’t think that full unification (even of alethic modalities) is possible:

The diversity he settles for is tripartite, identifying three fundamental types of necessity, irreducible to one another: deontic, natural (i.e., physical, nomic), and metaphysical. In line with the above discussion, we will set aside for the time being the deontic type and focus instead on the two alethic ones: the natural and the metaphysical. In his exploratory remarks, Fine considers two different unification strategies. The first is the by now familiar relativisation (understood reductively) and the second, restriction. To briefly see why Fine considers these two types of alethic necessities as fundamental – and thus neither as definable in terms of the other – it is convenient to note that relativisation would allow us to define a broader type of necessity in terms of a narrower type, whereas restriction would allow us to define a narrower type of necessity in terms of a broader one.

What do we mean by this? Take, for instance, logical necessity in comparison with metaphysical necessity. It is standard to consider all logical necessities as metaphysical necessities, but not the other way around: that Kit Fine is a person would be a metaphysical necessity that fails to be a logical one. Because of this relation of proper inclusion – the logical necessities are properly included in the metaphysical ones – metaphysical necessity is taken to be broader than logical necessity. On this basis, we can either define metaphysical necessity in terms of logical necessity by relativisation (à la Leech), or we can define logical necessity in terms of metaphysical necessity by restriction. We are already familiar with the first strategy, and we know that Fine considers the ‘cheap proliferation’ feature of this strategy a reason (among others) to be unhappy with it. For him, unification by restriction has a better chance of succeeding. The specific way in which he envisions this strategy (in our current example) can be illustrated as follows. For Kit Fine, metaphysical necessity is the necessity that obtains in virtue of the identity (nature, essence) of all things. Because of this universality, there is a good sense in which metaphysical necessity is maximally broad, or absolute: namely, there isn’t a necessity that is broader than it, in the specific sense of including all the metaphysical ones plus others.

Metaphysical necessity is, as a result, a good candidate on the basis of which to define narrower necessities by restriction. How would this go? Rather than considering the nature of all things, we’d consider instead the nature of a restricted type of things. Consider, for instance, only the nature of logical functions, and you get logical necessity; consider, instead, only the natures of mathematical entities, and you get mathematical necessity, etc. These narrower necessities are still, nonetheless, all grounded in the essences of things (that is, in the essences of more or less restricted collections of things). And because of this, ‘each of them can be regarded as a species of metaphysical necessity’ (Reference FineFine 2005, 237), allowing for a certain degree of unification: unification by restriction.

What, however, in the case of two necessities, such that none is broader/narrower than the other? This, to cut Fine’s story short, is what happens with the pair of natural (nomic) and metaphysical necessities and this fact, according to Fine, lies at the heart of their irreducibility to one another.

The following remarks explain why Fine takes metaphysical necessity to be neither broader nor narrower than natural necessity. Metaphysical necessity, obtaining as it does in virtue of the identity of things, is considered to be a de re necessity. At the fundamental level, there are particular identity facts – for instance, that Kit Fine is a person – that ground the necessities about those particulars – continuing with the example, that Kit Fine is necessarily a person. By contrast, natural necessity is, according to Fine, de dicto: the natural laws, from where natural necessity emerges, are instead generalisations. The following (largely overlooked) passage is worth quoting in full:

What this means is that we can find certain generalisations – the natural laws – that (assuming their metaphysical contingency) would be natural but not metaphysical necessities, and we can in turn find certain particular facts – e.g., Kit Fine is a person – that would be metaphysical but not natural necessities, a result very much in line with our findings in Section 2.4.

None of them being strictly broader than the other, therefore, the natural and the metaphysical necessities generate a halting point when implementing the strategy of unifying by restriction. (And recall: this comes at a point where unifying by relativisation has already been ruled out, on grounds of the cheap proliferation with which Fine is unhappy.)

It is on this point that I find it very interesting to compare the work of Kit Fine with that of Boris Kment. Reference KmentKment (2006b, Reference Kment2021), like many modal metaphysicians, shares with Fine a hesitancy about the relativisation strategy: cheap proliferation is to be avoided as this would result in non-genuine modalities, in turn obscuring what genuine modalities have in common. This is how Kment phrases the concern (which, let it be recalled, would not worry a reductive relativist like Leech):Footnote ²³

Unlike Fine, Kment is hoping for a larger unification. He praises accounts that, like Fine’s, step away from reductive relativism and nonetheless manage to reduce – to three, in Fine’s case – the number of fundamental modalities. But that would still be unsatisfactory according to Kment:

Dialectically, it is important to note that if Kment were to succeed in answering these questions, then unification – one of the biggest selling points of the (reductivist) relativist – would not be a theoretical virtue exclusive to the relativist, making them lose abductive persuasion (on top of the problem, for many at least, that stems from cheap proliferation). As we shall see next, however, Kment’s unification has some unexplained features, and there are reasons, congenial to Fine’s considerations above, to doubt the naturalness of the unification he achieves. In presenting Kment’s views, I avail myself (as he does) of the heuristic use of worlds. (More on worlds, briefly, in Section 2.7.)

Consider the set (or class) of logically consistent worlds, among which there is the actual world. This set is considered to form a sphere around the actual world. As is standard, a sphere is taken to be a subset of worlds that includes all worlds that are not further away than a certain distance from a given world, w, at the centre of the total space of worlds; and, for current purposes, the actual world, @, will always be the world at the centre.Footnote ²⁴ As such, the claim that the logically consistent worlds form a sphere around the actual world means that any logically inconsistent world would be further away than all logically consistent ones (see Reference KmentKment 2014, Ch. 2.). According to Kment, the worlds in this sphere can be ordered by their degree of possibility, which relates to the inexorability of facts. Without needing to get too deep into this, we can take this inexorability to track the modal force of facts: the less easily a fact could have failed to obtain, the more secure, inexorable, it is: i.e., the greater its necessity. When we order the worlds in this sphere by their degree of inexorability, we realise – Kment contends – that the nomically possible worlds, too, form a sphere around the actual world, and so do the metaphysically possible worlds. Not only this: we also realise that, of the three spheres so far, the nomic sphere is the smallest one, and the logical one is the largest. What this means is that there is a point in the inexorability scale, v_n, below which all worlds are nomically possible and above which all worlds are nomically impossible; and there is also a further away point in that same scale, v_m, below which all worlds are metaphysically possible and above which all worlds are metaphysically impossible. Lastly, we would also find in the same scale the point of the logical sphere.

Now, in his book Modality and Explanatory Reasoning, Reference KmentKment (2014) considers the outer sphere to be populated by the logically consistent worlds, just as we have done. This is a slight change from his paper, ‘Counterfactuals and the Analysis of Necessity’ (Reference KmentKment 2006b), where he considered instead the set of conceptually coherent worlds. We don’t need to worry about this change. As mentioned in Section 2.4.3, we’re resting in this Element on a working notion of logical necessity broad enough to include conceptual (analytical) necessities, and it will not harm this presentation if we do not distinguish them. If we don’t, we can graphically illustrate the above, by means of Figure 1.

Figure 1 Kment’s inexorability scale and system of spheres.

Source: Reference KmentKment (2006b, 259)

In terms of necessities, this image represents that, among the nomic, the metaphysical, and the conceptual ones, the nomic is the least inexorable, followed by the metaphysical one, with the conceptual being the most secure of the three types: you could more easily violate a natural law than a metaphysical one, but you can more easily violate a metaphysical law than a logical one.

It is the existence of these points, v_n, v_m, and v_c, on the same scale that, according to Kment, makes logical, metaphysical, and nomic modality all species of the same genus. With it, Kment achieves a salient unification, one that Fine had aborted: namely, subsuming nomic and metaphysical modality under one same genus. What makes these two modalities types of modalities is that they both identify points in the inexorability scale. In turn, it is the non-existence of corresponding points for the notions of biological, technological, epistemic, mathematical, or practical necessities (among others) which makes Kment not count them as further species of the same genus.Footnote ²⁵ Instead, for this other battery of modal notions, Kment considers, much like Fine does, the option of defining them by restriction or relativisation. And in so doing, Kment considerably widens the unification power of his account.

Should we, however, be happy with the unification that Kment achieves? In particular, should we be happy that nomic necessity is a species of the same genus as metaphysical necessity? It would not have escaped the reader that, on Kment’s account, and contrary to Fine’s, nomic necessity is strictly broader than metaphysical necessity. And conversely for the possibilities: the nomically possible worlds are properly included in the metaphysically possible worlds. Crucially, it is only because of this that Kment is able to identify point v_n in the inexorability scale, allowing him to declare nomic modality as a species of the same genus as that of metaphysical modality. But the ultimate reason why he achieves this result is, I contend, because he has stipulatively embedded metaphysical necessity into nomic necessity:

The italics on the right-hand side of (DN) correspond to Kment’s definition of metaphysical necessity. It follows from Kment’s definition of nomic necessity that nomically necessary propositions are those metaphysically necessary propositions that meet an additional condition: namely, not violating any natural law. This, as seen above, opens up a theoretical possibility that Fine considers unavailable: namely, construing one necessity in terms of the other, by restriction or relativisation.

But why this definition? Why include the metaphysical laws (or axioms) as constraints upon nomic modality? We know the terms in which Fine would disagree with Kment: nomic modality has to do with certain generalisations, the natural laws. In requiring, by definition, that nomically possible worlds also be metaphysically possible, what is being defined – a Finean could complain – is rather the conjunctive property of being both metaphysically and nomically necessary. Should we fight over labels? Let’s not, as we didn’t in Section 2.4 either. Even if we allow the label ‘nomic necessity’ to be invested in this way, the following concern remains. There is a legitimate notion of alethic necessity, let’s call it ‘nomic* necessity’, that is not conjunctive in that way (thus simpler? more fundamental?), that has to do with the laws of nature, and such that the nomically* possible worlds do not form a sphere around the actual world. Instead of forming a sphere, the set of nomically* possible worlds is the union of the sphere of (Kment’s) nomic worlds plus a shell hovering over the sphere of metaphysically possible worlds. (A shell, in contrast to a sphere, is to be understood as a subset of worlds that includes all worlds that are neither closer than a certain distance nor further away than a certain other, longer distance from the centred world, in our case, @. A shell, but not a sphere, therefore, has a spheric empty cavity.)

All the worlds in that shell satisfy the laws of nature but in metaphysically impossible ways: in some of them, for instance, Socrates is a dog; in others, my desk is made of cast iron instead of wood, etc. Apart from these metaphysical oddities, these worlds are physically far from extraordinary: Socrates barks in all such worlds where he is a dog. Now, nomic* necessity cannot, by Kment’s lights, be taken as a species of the same genus as metaphysical modality: for the distribution of its worlds means that there is no point in the inexorability scale below which all worlds are nomically* possible and above which all worlds are nomically* impossible. As a result, this property, regardless of labels, threatens the unification attempt. Furthermore – and now I am fighting for the label – nomic* necessity is not just a robust kind of necessity. It is also, I contend, the kind of necessity that our folk notion of natural necessity is tracking: it doesn’t matter to the physical order which individuals fall under which categories. The alternative (arguably Finean) graphic is thus as in Figure 2.

Figure 2 Roca-Royes’ system of spheres and shells.

Source: Reference Roca-RoyesRoca-Royes (2012, 153)

Nothing in the above is conclusive, but it does alert us to the point that we should be cautious about the prospects of achieving a unified, non-relativist account of alethic modalities. (This issue will emerge again in Section 3.5.)

2.6 Broader Unification?

The previous section focused exclusively on alethic modalities and, even when so restricted, the discussion has already proved complex and far from conclusive. To complicate things further, let’s not lose sight of the other families of modalities – the epistemic ones and the deontic ones. For what we say about them might have an impact on the discussion we’ve just had in Section 2.5, in one of at least two ways. First, Fine, for instance, thinks that normative necessity is a fundamental kind of necessity, and one that can subsume neither the nomic nor the metaphysical type. One might want to scrutinise the reasons for this. If one agrees with them, the fact that metaphysical and nomic necessities cannot be unified either could easily be seen as having less relevance: once we accept that there is in any case no one fundamental necessity, how concerned should we be if there are three rather than two of them?

In the other direction, we know that the friends of (reduced) relativised modalities have unification as one of their biggest selling points. In Section 2.5 we explored the relativist strategy but, again, only focusing on alethic modalities. But turning our attention to the epistemic and normative modalities might reveal the achieved unification – within the alethic modalities – to be less of a big selling point than initially thought. For, if it turned out that the epistemic and the deontic families cannot be subsumed under the relativisation strategy, how much unification does this strategy really achieve? This (potentially) decreased value of the relativist approach would come on top of the cheap proliferation feature of alethic modalities, considered by many (as we have seen) to be a problematic one, even if dialectically inert.

A lot, then, is still left to be scrutinised about the unification agenda. For now, it suffices, as we have just done, to identify the dialectical relevance of these remaining issues. To date, Reference LeechLeech (2020) has walked some distance into exploring the prospects of extending reductive relativism to other families of modality, such as the epistemic and the normative, thus providing some reasons for optimism (even if moderate by her very own lights) that a wider unification might be workable.

The unification aspirations of some theorists will become salient again later on (in Section 3), when we focus on the metaphysics of metaphysical modality. Indeed, unification (or non-unification) agendas are not neutral on the metaphysics of the different types of modalities. Far from it, they can be seen as attempts to homogenise (or else leave heterogeneous) the metaphysics of the seemingly different families of modalities. As hinted at here, Leech’s unification agenda goes hand in hand with a reductive relativist approach. And, as we shall see in Section 3.5, Amie Thomasson’s modal normativism is, in the first instance, the project of understanding metaphysical modality as a type of normative (deontic) modality. But Thomasson’s wide-scope project is much more ambitious than this: she aims to unify all alethic modalities by understanding them all as normative (Reference ThomassonThomasson 2007, 136–7). Before turning to the metaphysics of metaphysical modality, however, there are two further issues to consider (Sections 2.7 and 2.8), still under the general phenomenon of modality.

2.7 Analyses of Modalities in Terms of Worlds

There is a widespread practice in philosophy of providing truth-conditions for modal claims (or propositions) in terms of possible worlds. Some authors who endorse an analysis of modality in terms of possible worlds hold that the analysis is reductive, Reference LewisDavid Lewis (1986) being the chief example. Others may be happy with the analysis as an extensional one, but not as a definitional one. And others think that no notion of possible world is suitable to mount even an extensionally adequate analysis of modality upon it, and yet they might nonetheless recognise the heuristic value of speaking of modality in terms of possible worlds; witness the widespread practice of doing this. In this section, we will consider the main rubric of the analysis and how it behaves in relation to the various types of modalities distinguished in the sections above.

In maximally general terms, the analysis is as follows:

According to the analysis – which is in fact a schema – ‘necessarily’ behaves like a universal quantifier over possible worlds and ‘possibly’ as an existential one. Consequently, to the extent that we’re committed to at least the extensional adequacy of such analysis, and to the extent that we in turn believe that, for instance, the sun could shine in Stirling today, we’re committed to there being a possible world where it is sunny today in Stirling. Endorsing the analysis (as more than a heuristic), therefore, incurs an ontological commitment: namely, to possible worlds.

This ontological commitment has generated a lot of literature over many years. Among the questions raised, there is the issue of the nature of possible worlds: what kind of entities would they be (or are they)? There is also the question whether they would be fit to reduce modality (or certain kinds at least) to them. If they were, our overall theory of the world would be able to dispense with primitive modal notions (of those kinds, at least), as we would be able to analyse them in non-modal terms. And there is also the question whether the set (or class) of possible worlds that one accepts into one’s ontology is large enough for one’s theoretical purposes.Footnote ²⁷

When it comes to analysing modality reductively, Reference LewisDavid Lewis (1986) uses possible worlds to analyse, in the first instance, what I shall call ‘combinatorial modality’, and he then analyses other modalities derivatively. Combinatorial modality is to be understood as that modality that tracks ways in which matter and fundamental properties can occupy (be distributed over) a space–time system. This is importantly silent on de re matters (more on this in Section 3.1) and, as such, it will be convenient to understand combinatorial modality, for now, as defined for purely general propositions only.Footnote ²⁸ For any purely general p:

For Lewis, possible worlds are concrete in the same sense in which our world (the actual world) is concrete. They are spatio-temporally unified, and also spatio-temporally isolated from one another.Footnote ²⁹ And there’s a plenitude of them: there are at least as many of them as (qualitative) ways our world (and any other concrete world) could be. This plenitude is a necessary condition for the at least extensional adequacy of the account: if not all possibilities for our world were witnessed by some world, the left-to-right direction of the ◊-analysis above would fail. (For instance, if there could be talking donkeys but no world contained talking donkeys.) Lewis also takes it to be the case that every (qualitative) way some world is is a possible way for our world to be, with which he also secures the right-to-left direction of the account. Once the extensional adequacy is guaranteed, Lewis argues that his concretism is the only way in which one can hope the possible worlds analysis of (combinatorial) modality to be reductive.Footnote ³⁰

Are these (Lewisian) worlds, however, enough for our theoretical goals? Do we not need impossible worlds in addition? The answer depends on what exactly our theoretical goals are, and how much theoretical unity we’re hoping for. Lewis can go a long way with his concrete worlds. He certainly can’t afford any combinatorially impossible worlds (the extensional adequacy of the account, or else its reductiveness, would be jeopardised if there were some). And yet, some of his worlds will be impossible in other senses of the term. For instance, the nomic one: if, as many think, the natural laws of our world are (combinatorially) contingent, then there are Lewisian worlds where they are false. Any such world would be (relative to us) nomically impossible. As such, an analysis of nomic modality (in terms of worlds) is available to Lewis by restriction:

Generalising, Lewis could use his concrete worlds to straightforwardly analyse, by restriction, those modalities, i, such that the set of i-possible worlds is included (properly or not) into the set of his possible worlds.Footnote ³¹

With the help of counterpart theory (as we will see more extensively in Section 3.1), Lewis can also, albeit less straightforwardly, provide an analysis of what he calls de re modality (a modality intimately linked to essentialism and, as such, much closer to what we referred in Section 2.4.2 as ‘metaphysical modality’).

Complications arise when it comes to analysing modalities, j, whose set of possible worlds outruns, or would outrun, the set of Lewisian worlds. For in that case, the most straightforward analysis that Lewis could afford with his concrete worlds would fail. The analysis would be something like this:

And because the concrete worlds that the analysis can avail itself of are all combinatorially possible (the ontological commitments of Lewis’ theory don’t go beyond them), there will be cases of p’s such that p is (intuitively) j-possible and yet there isn’t any world where it is true. Thus, the analysis would fail left-to-right for possibility-j. Conversely, there will be cases of p’s such that not-p is true in all concrete worlds and yet not-p fails to be (intuitively) j-necessary. Thus, the analysis would fail right-to-left for necessity-j.

Given that Lewis’ combinatorial modality is already very liberal (after all, it covers all ways in which a possible space–time system might be filled in), it is not easy to find natural j-examples among alethic modalities. Doxastic modalities, on the other hand, are a source of such examples. They have been found problematic for Lewis given that a single subject might (perhaps inadvertently) believe both that p and that not-p. These doxastic cases are problematic because all combinatorially possible worlds are logically possible: logic puts a limit on how space–time can be filled in. To deal with these cases, less simple manoeuvres would need to be engineered to adequately analyse such modalities with the ontology available. For instance, as has been suggested, one could use classes of worlds instead of worlds, or a mixture between concrete and abstract worlds.Footnote ³² The literature, however, contains doubts that extensional adequacy can be achieved.Footnote ³³

Despite the theoretical benefits of Lewisian Concretism (see Reference LewisLewis (1986, Ch. 1)), his concretism has been a severe no-no for most contemporary metaphysicians of modality.Footnote ³⁴ Other, related, reasons can be summed up with the phrase ‘combinatorial modality should not be the target modality.Footnote ³⁵

Moving away from Lewis’ concretism, the most salient alternative concerning the nature of possible worlds is abstractism – the family of views that Lewis labelled, less sympathetically, ‘ersatzism’. This family is unified, as the name reveals, by their taking possible worlds to be abstract entities. And while this agreed abstractness still allows for disagreement about their specific nature, linguistic abstractism is arguably the prevalent option. When it comes to analysing metaphysical modality (understood as introduced in Section 2.4.2), a linguistic possible world, w, would be a set of sentences or propositions such that: (i) it is consistent; (ii) for any sentence or proposition, p, either p or its negation, but not both, belongs to w; and (iii) all the elements that belong to LM – the metaphysical axioms – belong to w.Footnote ³⁶ Reference LewisLewis (1986) makes a very strong case that any abstractist account would need to sacrifice reductive aspirations: with any such account, primitive modality will sneak into the theory somewhere. For instance, the indispensable notion of consistency in (i) above is modal, and such modality is not definitionally analysable (without circularity) by means of (i)–(iii).

Concerning this, Reference FineFine’s (1994) ontological divorce between the essential and the modal has been understsood by some as giving the linguistic abstractist enough reductive power; an excellent example here is Reference PeacockePeacocke (1999).Footnote ³⁷ But even if one were to agree with Lewis about the poor prospects of reductive abstractism, modal metaphysicians would often be ready to sacrifice reductiveness – if need be – for the sake of other virtues such as believability (in its adequacy).Footnote ³⁸

In this context, the following remarks are relevant. Reference NolanDaniel Nolan (1997, Reference Nolan2013) is salient as a source of theoretical reasons why one might want to endorse an ontology of (metaphysically or combinatorially) impossible worlds. Many of these reasons refer to theoretical benefits that are unavailable when admitting only (combinatorially) possible worlds.Footnote ³⁹ Now, if we – for these or other reasons – are realist about (combinatorially) impossible worlds, then abstractism about them is arguably the most natural approach. (What kind of entity would a concrete, yet combinatorially impossible world be?Footnote ⁴⁰) And once we are abstractist about (combinatorially) impossible worlds, then, presumably, for parity reasons, abstractism too about possible worlds is the most natural approach.Footnote ⁴¹ This reason for ‘abstractism across the board’ would come on top of the independent reasons one might already have to stay away from Lewisian Concretism.

Those leaning towards abstractism irrespective of the above reasoning might still wish to accommodate Nolan’s recommendation about accepting an ontology of impossible worlds. It should be good news for them that they can do so in a far from extravagant manner. For instance, if abstract (metaphysically) possible worlds are understood as being regulated by (i)–(iii) above, then any set of sentences (or propositions) that doesn’t satisfy some of these three conditions can be taken as a metaphysically impossible world. Ontologically, a possible and an impossible world would be on a par: they both would be sets of sentences or propositions. Not only does the extension not need to involve ontological extravagance, it wouldn’t involve ontological inflation either. Regardless of whether we decide to put them to theoretical use or not, there already are sets of sentences (or propositions) which fail to satisfy some of (i)–(iii); or, at any rate, there are by the lights of anyone who already accepts an ontology of possible worlds understood in that way, and thus the extension to impossible worlds doesn’t involve inflation.

Such a plenitude of worlds allows for a straightforward possible worlds analysis of any alethic or deontic modality, i. The schema is the familiar one:

In the case of epistemic (and doxastic) modalities, the analyses would be analogous, but with explicit mention of the subject(s) to whom they are relativised.

Going back to something we discussed in Section 2.5, I shall wrap up this section with a remark on the prospects of reductively analysing the target modalities in terms of abstract possible worlds: it is precisely the use of the notion i on the right-hand-side of the analysis (i.e., on the analysans) that would threaten, unless such mention is eliminable, the reductiveness of these analyses.

2.8 Modality De Dicto and Modality De Re

To end this first part of the Element, I turn now to a distinction that I’ve merely used so far (mostly in Section 2.5) but that deserves more prominent attention. This is the distinction between modality de dicto and modality de re.Footnote ⁴² Let me start by requoting a passage from Reference FineFine (2005, 243): ‘All forms of de re necessity (and of essence) will be fundamentally metaphysical, even though some forms of de dicto necessity may not be.’

A guiding aim of this section is to come to understand – better than we did in Section 2.5 – the reasons to hold this claim, and to bring out, to some extent, its truth.

The task is not straightforward. A prior difficulty is that of characterising the difference between modality de re and modality de dicto, so that we are clear about what the claim says in the first place. This is difficult because the literature contains several ways of understanding the distinction which are not always equivalent.Footnote ⁴³ We are thus facing two different tasks that nonetheless have to be carried out in tandem: we want (i) to find agreement with Fine’s claim, but on (ii) an understanding of the distinction between modality de re and modality de dicto that is not too removed from our intuitive grasp of it. What we don’t want is the claim’s truth to rest on an artificial sense of the distinction.

The etymological is perhaps the standard way of informally characterising the distinction, and it’s the one that I will use to measure my success in relation to task (ii). On this characterisation, modality de dicto refers to the phenomenon of propositions or sentences being necessarily, possibly, or contingently true or false. The bearers of de dicto modality are thus truth-apt entities, and this feature gives modality de dicto its name, which comes from the Latin dictum, for sentences or propositions (or, more generally, truth-apt entities). An example of de dicto modality thus results from applying the notion of necessity (or possibility, or contingency) to, for instance, the proposition that lions don’t fly, the result being the proposition that necessarily, lions don’t fly. By contrast, on the same characterisation, modality de re refers to the phenomenon of entities bearing properties in different modes: necessarily, possibly or contingently. We know for instance that Socrates bears (i.e., instantiates, exemplifies) the property of being human. The thought that Socrates has this property as a matter of necessity – i.e., that Socrates is necessarily human – would therefore be a de re modal thought, which refers to the fact that being human is necessary of Socrates.Footnote ⁴⁴

There is something of this intuitive grasp of the distinction, though, that creates noise and needs clarification. Consider the proposition that Socrates is human. This is as much a truth-apt entity as the proposition that lions don’t fly. If we now apply necessarily to it, we get Necessarily, Socrates is human, and we would be inclined, as per the above, to count this modality as de dicto. But is it? The claim ‘Necessarily, Socrates is human’ doesn’t seem to differ in truth-conditions, and hardly in meaning, from ‘Socrates is necessarily human’, and yet the latter is taken (as per the above too) to involve modality de re. How can they (or should I say ‘it’) involve different types of modalities?

To clarify this, let me note that this intuitive characterisation is often captured in syntactic terms. Roy’s way of doing this is particularly helpful here to pre-empt the noise just identified:

There are two things to note from this: first, the intuitive distinction between modality de re and modality de dicto is an exclusive one and, consequently, we don’t want ‘Necessarily, Socrates is human’ to be taken as both de dicto and de re.Footnote ⁴⁵ Second, this proposition is taken to be de re (only) and this is how it should be when precisifying the intuitive grasp of the distinction. Indeed, much in line with the suspicion that ‘Necessarily, Socrates is human’ doesn’t differ in meaning from ‘Socrates is necessarily human’, the two claims are symbolised in exactly the same way; namely, □Hs (where ‘H’ stands for being human and ‘s’ is a constant for Socrates).

We can now see that, as a result, modality de dicto applies to dictums of a purely general type; that is, to sentences or propositions with no reference to particular individuals.Footnote ⁴⁶ What this means is that de dicto modality tracks necessary (or contingent, or impossible) relations among the distribution of properties and relations, whereas de re modality tracks modes in which entities have properties (or stand in relation to other entities).

With this, I take myself to have achieved task (ii) above; namely, to have reached an understanding of the distinction between modality de re and modality de dicto that is not removed from our intuitive understanding. This is indeed, I believe, the prevalent understanding. As we shall see in Section 3, this is also the understanding that guides Wang’s classification of the different accounts of metaphysical modality as de dicto first or de re first. (More on this very soon.)

But before coming to this, what about task (i)? Is this understanding of the distinction one with which to understand better the reasons behind Fine’s opening quote, as well as to bring out its truth? I believe so. The quote can be divided into three sub-claims. First, within metaphysical modality one finds both fundamental de re and fundamental de dicto necessities. Second, one may find fundamental de dicto necessities outside metaphysical modality. And third, one will not find fundamental de re necessities outside metaphysical modality.

We know from Section 2.5 that Fine settles for a three-tier account of fundamental modalities: normative, natural (nomic), and metaphysical. As we did there, I shall leave aside the normative one (for now) and focus on the alethic modalities: the nomic and the metaphysical. I take the three sub-claims in turn.

First, we know that metaphysical modality originates for Fine (and as per our working conception since Section 2.4.2) in the essences of things. Some of these things are particular individuals, and thus their essences will generate de re necessities which, in flowing directly from the things’ essential properties, will be fundamentally metaphysical. Socrates being essentially human, for instance, results in the fundamental de re necessity of him being necessarily human. Similarly, all humans being essentially humans generates the de re (and also fundamental) modal principle that all humans are necessarily human (in symbols, so that one can check this claim against Roy’s quotation above, ∀x(Hx ⊃ □Hx)). But equally, some of these things are properties, and (NKE) – Natural Kind Essentialism, to recall Section 2.4.2 – is a rich source of examples here: for instance, necessarily, all cats are mammals (which differs from all cats are necessarily mammals); in symbols, □∀x(Cx ⊃ Mx), where ‘C’ and ‘M’ stand, respectively, for being a cat and being a mammal. The examples afforded by (NKE), let me remark, will be de dicto necessities irrespective of their (epistemic) status as analytic or synthetic. Explicit definitions are another rich source of examples (see Reference HaleHale (2013, Sect. 11.2)): for instance, necessarily, all squares have four straight sides. In this case, the resulting de dicto necessities will be analytic. Whether analytic or synthetic, these de dicto modalities are also (much like the de re ones) fundamentally metaphysical: they follow directly (and solely) from essential properties. This concludes the reasons for the first sub-claim.

Second, the fact that the natural laws are all generalisations with no mention of particular individuals makes their necessity de dicto. Of Fine’s quote, we can now understand what is meant by ‘some forms of de dicto necessity may not be [fundamentally metaphysical]’. Indeed, there may be some fundamental nomic de dicto necessities; there will be some so long as some natural laws are metaphysically contingent. For, if there are, their nomic necessity does not, by the nature of the case, originate in essences.Footnote ⁴⁷

Lastly, the case for the third sub-claim is basically the point made in Section 2.5 against it being nomically necessary that Socrates is human. The laws of nature don’t prescribe Socrates’ humanity, as they don’t prescribe any property of any object. Roy makes essentially the same point here:

The context of Roy’s quote is metaphysical modality, but the point is exactly the same: one does not get de re necessities (or impossibilities) from only de dicto necessities. (The reader will recall that, back in Section 2.4.2, this point made us include particular propositions in the set of metaphysical axioms; because, in the metaphysical case, embracing the possibility that Socrates (or any other entity, for that matter) could be anything was an option to rule out.) Indeed, a modality that is constrained exclusively by de dicto necessities will be very liberal when it comes to de re possibilities.

We now have a better understanding of the opening quote in this section (as well as of the full passage quoted in Section 2.5). Also, I intend the above as sufficient reasons for the claim that, as far as alethic modalities are concerned, fundamental, de re necessities are to be found only within the metaphysical.

I did leave aside the normative modality, though. To wrap up this section, let me say in relation to this that, if normative modality is also, like the nomic one, constrained by generalisations, the same results apply to it, too. Moral particularists, however, might complain here, and this would need to be scrutinised (something I leave to the reader). For current purposes, that the case holds at least with the (limited) generality I have achieved – concerning alethic modalities – is sufficient.

3.1 Lewisian Concretism

Lewisian Concretism is arguably the reductive view of modality par excellence.Footnote ⁵⁰ As seen in Section 2.7, Lewis analyses his target modality (which we called combinatorial) in terms of possible worlds. To recall, for all purely general propositions, p:

This analysis is not merely intended as an extensional one but also as a definitional one: what it means for one such p to be possible is that there is a world where p; and what it means for one such p to be necessary is that p is true at all the worlds there are. For instance, what it means for the (purely general) proposition that there are talking donkeys to be possible is for there to be a possible world where there are talking donkeys.

Reference WangJennifer Wang (2015) has conveniently introduced a distinction that will help us classify the different accounts of modality to be seen in this section. This is the distinction between de re first and de dicto first accounts: ‘the former ground all modal facts in de re modality, the latter in de dicto modality’ (Reference WangWang 2020, 189). And we can agree with Wang that Lewis’ account is a de dicto first account:

For many contemporary modal metaphysicians, it would be combinatorial modality, once supplemented with counterpart theory, that has a serious claim to be identified as metaphysical modality. Thus supplemented, the analysis turns into the following: for any proposition p, purely general or otherwise:

where the counterpart relation increases the representational power of the plurality of worlds: the world where Wang’s counterpart has a sister is one according to which Wang (herself) has a sister.

This being so, metaphysical modality so understood still reduces to truth at/according-to worlds, and this reducibility renders metaphysical modality non-fundamental: the source of metaphysical modality is plain truth, namely, truth at (or according to) worlds. To the extent that such reduction is not seen as a deflation (and it arguably should not be seen as such), Lewisian Concretism is a realist approach and, quite straightforwardly, therefore, a mind-independent one: what worlds there are is a mind-independent matter and, consequently, so is what is possible and what is necessary.

Lewisian Concretism has been highly discussed and, as anticipated in Section 2.7, it isn’t a popular view among modal metaphysicians.Footnote ⁵² However, I urge the reader to familiarise themselves with Wilson’s quantum modal realism for a Lewisian account that (pending scrutiny) is admirably well placed, at least in principle, to allay some of the strongest reasons to be reluctant about Lewis’ account. Notwithstanding this, in contemporary literature the prevalent trend of thought, on which I have relied (in Section 2.4.2) in order to introduce the notion of metaphysical modality, is to analyse (and define) it in terms of essence.

3.2 Essentialist Theories

Essentialist Views of metaphysical modality constitute a vast family and space doesn’t allow me to present them individually. And even when presenting them jointly, I shall do so in broad strokes, unavoidably not doing adequate justice to them. With this cautionary remark in place, the most salient common trait of these accounts is, in Hale’s words, the idea that ‘metaphysical necessities have their source in the natures [essences] of things, and [that] metaphysical possibilities are those left open by the natures of things’ (Reference HaleHale 2013, 253). In Wang’s terms, again, Essentialist Views of metaphysical modality are undoubtedly de re first, quite in line with Fine’s conception (as seen in Sections 2.5 and 2.8) that metaphysical modality is the only one to be fundamentally de re. It is precisely Reference FineFine’s (1994) ‘Essence and Modality’ that inaugurated this contemporary – broadly neo-Aristotelian – family of views. Here, Fine argues for a definitional account of essence: essences are real definitions, that is, definitions of things (as opposed to definitions of the nominal type, which are of words).

This real-definition account of essence stands in opposition to the up-to-then traditional modal account of essence, which analyses them, reductively, in modal terms. Crudely, according to the modal account of essence, for a property to be essential to a given object is for it to be a necessary property of that object. If one reduces essence to modality, one cannot in turn (on pain of vicious circularity) identify essences as the source of modality. Thus, it is precisely because of its departure from the modal account, that Finean Essentialism, as we might call it, opens the door to accounts that ground modality in essence. And this is a theoretical opportunity that has been taken up, as indicated above, by a vast family of philosophers, which include Reference Correia and SkilesCorreia and Skiles (2019, Reference Correia and Skiles2021), Reference HaleHale (2002, Reference Hale2013, Reference Hale and Leech2018), Reference KmentKment (2006b, Reference Kment2014), Lowe (Reference Lowe2008, Reference Lowe2012), Reference PeacockePeacocke (1999, Reference Peacocke2002), and Reference Tahko, Fischer and LeonTahko (2017, Reference Tahko, Carruth, Gibb and Heil2018), and others.Footnote ⁵³

Because they ground modality in essences, structurally, the mind-independence (or else mind-dependence) of modality will, on these accounts, be inherited by their proponents’ views on the mind-independence (or else mind-dependence) of essence, and there is theoretical room to go either way. Typically, however, such theorists share a broadly neo-Aristotelian framework, and thus they tend to agree in viewing the phenomena as mind-independent. More disagreement is to be found, however, about the extent of the reduction of modality to essence. On this, Vaidya and Wallner ask the following:

There has been a tendency to take Finean Essentialism to provide a reductive account of modality, whereby modality is reduced to essence, and essence becomes a primitive. But Penelope Mackie, for instance, has argued against ‘the viability of an account of essence in terms of real definition that is both non-modal and yet yields the result that essential properties are also necessary properties’ (Reference Mackie and DumitruMackie 2020, 262). In this spirit, some authors conscientiously distance themselves from reductivism. Reference HaleHale (2013, 150 fn. 12), for instance, thinks that ‘a major difference between my theory and Fine’s [is that while] Fine sees himself as giving a reductive explanation of modality in terms of essence or nature, I do not. This means that the two theories incur quite different explanatory obligations.’

Hale puts forward a non-reductive essentialist theory of modality, whereby essences are themselves modal. On his account, we can explain metaphysical modality in general by appeal to essences, thus succeeding in identifying the source of modality. This is so because, despite the fact that essences are modal – they are themselves necessary and thus have unexplained modal import – the explanations of modality in terms of essence are non-transmissive, which, in the current context, is to be understood as explanations ‘of the form ‘□p because q’ in which the explanans, q, is indeed necessary … but in which what explains the necessity of the explanandum is not q’s necessity, but its truth simpliciter’ (Reference HaleHale 2013, 131).

To appreciate Hale’s point, note that such non-transmissive explanations would be equally available (at least in principle) to someone who held essential facts to be contingent.Footnote ⁵⁴ It would still be available to such a philosopher to explain □p in terms of essence (simpliciter), compatibly with holding essences to be contingent (resulting in some of those necessities being themselves contingent: ¬□□p). More recently, and in a similar way to Hale, Reference WilschWilsch (2017) has put forward Sophisticated Modal Primitivism, a view that, in the terms of the current discussion, is also to be received as a form of non-reductive essentialism. The key move of Wilsch’s view is to characterise essences as essentially modal, thereby making them good candidates as the sources of metaphysical modality: their being essentially modal amounts to them encoding principles to the effect that the essential feature they are about is necessary of the object.

Despite the substantial differences among them, we can bring Essentialist Views of metaphysical modality together under the slogan ‘essence is the mother of metaphysical necessity’. This slogan carries a commitment to a specific type of explanatory and ontological priority: essence is prior to metaphysical modality. But this feature has generated a lot of hostile literature. Some authors accuse these views of explanatory incompleteness. According to this line of objection, essence cannot be the sole mother of metaphysical necessity because it is incapable of explaining all the necessities that there (intuitively) are, thus leaving theoretically open more possibilities than, intuitively, the view should do, resulting in extensional inadequacy. What, for instance, is the source of the necessity of essences (for the non-reductive essentialist)? To the extent that these intuitive necessities are left unexplained, should the proponents of the view renounce them?

Others attack the explanatory adequacy of the theories. Quite often, this complaint traces back to a dissatisfaction with Fine’s departure from the modal account of essence, which, in turn, results in closing down the theoretical option that Finean Essentialism opened: namely, that of grounding modality in essence at all.Footnote ⁵⁵ A related but different challenge for essentialist theories of modality is that of accounting for the modal facts of mere possibilia; that is, entities that could but do not exist. Reference PeacockePeacocke (2002) has taken up this challenge very seriously, in a way that makes it manifest that it might be a requirement for any essentialist view of modality that aspires to extensional and explanatory adequacy to work not just with essences (and essential properties) but also with individual essences (and sufficiency properties). On this particular challenge, the necessitists among the essentialists are an exception:Footnote ⁵⁶ their specific way of denying the existence of mere possibilia allows them to accommodate intuitions about ‘them’ while securing extensional adequacy. The problem for them, on the other side of the coin, is one of ontological commitment and believability: for them, a possible child of Wittgenstein exists, and is non-concrete yet essentially human.Footnote ⁵⁷

3.3 Dispositionalism

In this context, it is most pertinent to turn to Barbara Vetter’s Potentialism, a type of Dispositionalism in modality which is undoubtedly also a de re first account of metaphysical modality. There are other thorough dispositionalist theories of modality,Footnote ⁵⁸ but what makes Vetter’s especially salient for our purposes is not just the positive view per se, developed in Reference VetterVetter (2015) and refined in Reference VetterVetter (2021), but also the comparative criticism against the Essentialist Views contained in the latter piece.

Given that a core difference between Essentialism and Dispositionalism is a structural one, we can start by identifying it from the outset to then flesh out, albeit briefly, Vetter’s Dispositionalism. The main difference is one of explanatory priority, and this difference is better appreciated having identified some shared standpoints. First, as noted in Section 3.2, a typical Finean essentialist will be realist, and mind-independentist, about modality, and so will a dispositionalist. Also, both types of views account for modality in a de re first manner or, as Vetter aptly calls it, in a ‘localized manner’: the essentialist localises the source of modality in the essences of things, and, the potentialist, in their potentialities.Footnote ⁵⁹ Against this background of similarities, the differences are, sharply, as follows:

With the key difference identified, let us see how Vetter’s potentialist story gets fleshed out. For Vetter, modality is grounded in potentialities. The conception of a potentiality is a theoretical generalisation from that of a disposition. Reference VetterVetter (2015, Ch. 3) offers the core of her positive account of dispositions, which, as she tells us, is a possibility conception of dispositions, thus distancing herself from the standard, conditional conception. On her account, a disposition (e.g., fragility) is a potentiality (e.g., the potentiality to break); but it is not always the case that a potentiality is a disposition (e.g., things don’t need to be fragile for them to have the potentiality to break). For potentialities come in degrees and, whenever a given object, x, has the potentiality to ϕ – understood as x can ϕ – we speak of x having (also) the disposition to ϕ only if it can easily ϕ – that is, only if the degree of its potentiality is above a certain threshold, usually determined by context. Thus, starting out from the notion of a disposition, Vetter reaches that of a potentiality, where ‘[p]otentiality can now be recognized as the common genus of dispositions and such related properties as abilities’ (Reference VetterVetter 2015, 102). Because of the modal nature of potentialities, it’s not an item in Vetter’s agenda to reduce the modal to the non-modal: ‘The account of possibility that I am offering is reductive in that it provides a straightforward definition of the possibility operator. It is not reductive in the sense of “reducing the modal to the non-modal”. The notion of potentiality is a modal one if anything is’ (Reference VetterVetter 2015, 198).

Now, in line with the view’s localised account of modality, potentialities reside in the things. A potentiality is always a potentiality for some object to do something, or to undergo something, etc. As a result, Vetter tells us, this doesn’t fit the grammar of possibilities, which aren’t so localised. To get a potentiality-based definition of possibility, we need to abstract the object away, and this is what Vetter does, thus putting forward this definition:

In connection with Section 2.8 (on the de dicto/de re distinction), note that p here can in principle be either purely general or else involve particular individuals. If the former (e.g., pigs can run faster than humans), however, the general possibility will be so because there are individuals that host the relevant potentialities (e.g., actual pigs hosting the potentiality to run faster than actual humans).

We must understand what the occurrence of ‘iterated’ means in this definition (as well as in the first quote above). To answer this, we should note that a preliminary question arises about the extensional adequacy of the account: are our worldly potentialities rich enough to deliver all the possibilities we intuitively think there are? What about the possibility that a granddaughter of mine lands on Mars? What about the possibility that the solar system disappears? Which object is the bearer of the corresponding potentialities? We won’t be going into detail here, but extensional adequacy is certainly something that Vetter takes conscientious care of (like Finean essentialists). To do so, the theory incorporates a battery of different types of potentialities (extrinsic, joint, and iterated) that, together and in interaction with one another, allow Vetter to make at least a prima facie case for the extensional adequacy of her account (see especially Reference VetterVetter (2015, Ch. 7)). And it is in this context that the notion of an iterated potentiality is vital. An iterated potentiality is, roughly, the potentiality for something to have further potentialities, of whichever type: simple, extrinsic, joint, or (already) iterated. By availing herself of iterated potentialities, Vetter greatly diminishes the risk of running out of potentialities before having accounted for all (intuitive) possibilities, something which would jeopardise the account’s extensional adequacy.

Despite this prima facie case, Reference LeechLeech (2017) has put forward an insightful concern that strikingly mimics that of mere possibilia for the essentialists (flagged in Section 3.2). According to Leech, Vetter’s account will, by design, struggle to account for many de re possibilities. She starts her complaint by calling attention to the (intuitive) possibility that a given object, x, might never have existed, and argues that, on Vetter’s account, the corresponding potentiality should be hosted in x’s past by some other individual. Leech then further argues that there’s nowhere in x’s past where that potentiality is to be found. After making her case about the possible non-existence of actual individuals, Leech explains why

Another criticism is offered by Reference WangWang (2020). She argues that Vetter’s Potentialism cannot adequately account for de dicto modality. For instance, for any given negatively charged entity, x, Potentialism is well equipped to account for x’s impossibility of being positively charged. Vetter can do so by means of the notion of a maximal potentiality: a potentiality that must manifest. Taking x’s potentiality to be negatively charged to be a maximal disposition, we get that x must be negatively charged, thus yielding that it cannot be positively charged. Generalising from here (x is arbitrary after all), we get that no negatively charged object can be positively charged. Wang rightly notes, however, that this generalisation is still a de re modal claim, one that attributes to all existing negatively charged objects the impossibility of being positively charged. As such, it falls short of the target de dicto claim, ‘Necessarily, no negatively charged objects are positively charged.’ If this is on the right track, there is more to be developed to accommodate such de dicto claims – if they must be – under Vetter’s Potentialism.

I leave it to the reader to decide whether one should be persuaded by Wang’s concern. In connection with things that have been developed in earlier sections of this Element (for instance Section 2.8), however, I shall wrap this concern up with a note and a suggestion. The note is that the Essentialist Views, in taking it that properties (and not just particulars) have essences, would easily be able to explain the de dicto necessities that Wang raises concerns about. The target de dicto necessity above, for instance, would have its source in the ‘incompatibility relation between the property of being negatively charged and the property of being positively charged’ (Reference WangWang 2020, 193). In view of this, the potentialist might want to take up Reference WangWang’s (2020, 196) suggestion and explore the idea that both particulars and properties host potentialities.

A related concern (and the last to be sketched here) that one could voice against Vetter’s (or any other) Dispositionalism is about the kind of modality it delivers. Given that the view starts by focusing on ordinary dispositions and abilities, is Dispositionalism theorising about metaphysical modality, or is it theorising about a more mundane type of modality, for instance, a sort of practical or circumstantial modality? Maybe the account theorises about a family of them (and Vetter’s use of the plural in speaking about circumstantial modalities suggests so), but is metaphysical modality ever among the type of modalities her potentialism delivers? The concern is that those modalities tend to be broader necessities than the metaphysical: maybe I can’t jump across a given stream in most of the practical senses that will ever be relevant to me, but I can still jump it in the metaphysical sense.

This issue is dialectically relevant in that it might be thought to give the essentialist a distinctive advantage: we saw in Section 2.4.2 how essence is taken to imply metaphysical modality and, as such, there isn’t scope for the analogous concern in the case of essentialists. The following remarks, however, should make it clear that the dispositionalist has all the ingredients needed to put this concern to rest. The main ingredient is the locality of modality inherent, as we saw above, to Dispositionalism (as well as to Essentialism). Whether in their essences or in their potentialities, the target modality, for the essentialists and the dispositionalists alike, is born in things. In Wang’s terms, again, the accounts are of the de re first type. As such, the modality on Vetter’s plate is primarily de re, and the necessities she gets (recall her notion of a maximal potentiality) will thus be fundamentally de re. At this point, one only needs to agree with Fine’s claim that only metaphysical necessities (among the fundamental ones) are fundamentally de re in order to be content that the modality delivered by the dispositionalist is the intended, metaphysical one. (And we have seen reasons in Section 2.8 to agree with this claim.)

But haven’t I just said that the various necessities Vetter starts theorising from are broader than the metaphysical one? At this point, recall also (from Section 2.5), that Fine suggests that, from metaphysical necessity, we can get narrower necessities by restriction, and that ‘each of them can be regarded as a species of metaphysical necessity’ (Reference FineFine 2005, 237). In a similar vein, one can get broader necessities by (non-reductive?) relativisation from metaphysical modality. With this in mind, one might say that Vetter’s Dispositionalism gives explanatory priority to (some of) these broader necessities (this is something in need of scrutiny, but not for this occasion). This (the analogy goes) would not make them any less metaphysical than the metaphysical modality that Vetter encounters with maximal potentialities, not even (as should be clear) by the lights of a Finean essentialist.

3.4 Mind-Dependent Accounts

The accounts of metaphysical modality seen so far, whether reductivist or not, all share, broadly, the idea that modality is mind-independent in a very robust manner: according to these accounts, modal truth is not up to us, as thinkers, in any way. Coming to know a metaphysical modal truth (thus understood) is, on these accounts, a remarkable cognitive success: a sign that we are adequately cognitively equipped to discover mind-independent modal truths. For several authors, however, to class such cognitive successes as ‘remarkable’ is to understate the puzzle they give rise to: it would be a plain mystery if we were able to know at all metaphysical modality, construed mind-independently. Since our perceptual system is confined to being affected by what is actual, a posteriori modal knowledge would be puzzling. But a priori modal knowledge is puzzling too: how could human mental activity be so well aligned with extra-mental truth, which is not up to us?

This puzzlement has traditionally fostered a family of views on the metaphysics of modality which, to some extent, reconceive modal truth, and in a way that would make modal knowledge somewhat less mysterious. Despite being very different, these views are referred to in the literature by means of labels such as ‘mind-dependent’, ‘non-cognitivist’, ‘lightweight realist’, ‘thinker-dependent’, ‘anti-realist’, etc. None of these labels are however univocal, and we should be cautious when using them.

With this warning, I shall focus in this section on three types of views which, I believe, all have a claim to be seen as mind-dependent accounts of modal truth. As we shall see, they are all, at least in principle, at an advantage when it comes to explaining our knowledge of (metaphysical) modal facts.

Our first type of view is Modal Fictionalism, especially of a non-timid type as characterised by Rosen. Non-timid Fictionalism

A modal fictionalist achieves this by providing a theory of modal truth which is parasitic on a chosen theory of possible worlds, in Rosen’s case, Lewis’. Rather than endorsing the chosen possible-worlds analysis of modality, however, they consider it a fiction and provide instead the following, alternative analysis: For any modal proposition, □p or ◊p,

whereby the prefix ‘according to …’ cancels any ontological commitment to possible worlds. It is this dependence on a created fiction which renders Fictionalism (of this full blooded, or non-timid, type) a thinker-dependent account, as the truth-conditions now depend on the existence of a theory, created by a theorist. Rosen’s account also borrows Lewis’ (brief) epistemological remarks on modal knowledge to the effect, roughly, that we know about modal facts by the use of imagination (Reference LewisLewis 1986, Sect. 2.4). But whereas those remarks hardly put the epistemological puzzlement to rest in the case of Lewisian Realism – on the contrary, how would human imagination and mind-independent modal truth be so (conveniently) aligned? – they do pre-empt it in the case of Rosen’s Fictionalism:

While these epistemological remarks are spot on, Rosen’s Fictionalism suffers on the metaphysical side: that metaphysical modal truth consists in truth at a fiction is not plausible, and the merits of the account are not enough to outweigh its implausibility (see Reference Nolan and ZaltaNolan 2020, Sects. 3–4).

I turn now to the second and third types of view: Conventionalism and Quasi-Realism. We can group them together as a family of otherwise different views that nonetheless converge in taking the unimaginability of not-p to play (to varying degrees) a constitutive role in p’s necessity. Consider for instance a view according to which what it means to say that a proposition p is impossible just is that we’re unable to imagine p to be true. On this view, unimaginability plays a maximal constitutive role in metaphysical necessity (and impossibility). The relation however, while still constitutive, can be less close than that, as the following broad-strokes presentation of a classical triad helps to illustrate.

Classical thinker-dependent accounts that were developed in the 1980s include the non-radical conventionalisms of Reference Craig and HackingCraig (1985) and Reference WrightWright (1980), and Blackburn’s non-conventionalist Quasi-Realism (1986). According to the former, it is a matter of convention to regard certain claims as necessary (or possible or contingent). We won’t go too much into this, but, briefly, the non-radicality of their views rests on the fact that, while the radical conventionalist would deny any possible axiomatisation of the class of necessary claims, according to the non-radical type there is a class of conventional necessities, C – whose negations we’re unable to imagine – such that any other (conventionally) necessary claim can be said to be a consequence of some claim in C.Footnote ⁶⁰ Blackburn’s Quasi-Realism differs from them in that his account is emphatically not a conventionalist one. Blackburn would agree that judging that something is necessary consists in realising that one fails to be able to imagine its negation. On Wright’s and Craig’s views, however, realising that one cannot imagine ¬p is not enough for the judgement (hence truth) that necessarily p. It will be sufficient only under the appropriate kind of convention of doing so; hence the conventionalism of these accounts. In contrast, for Blackburn, there’s no additional step to be taken: the modal is simply the vocabulary in which we express the imaginability states. For Blackburn, therefore, the constitutive role that imagination plays in modality is more intimate than in Craig’s or Wright’s views.

Within Conventionalism, Reference SidelleAlan Sidelle’s (1989) modal conventionalism offers an influential contemporary example.Footnote ⁶¹ The pre-Kripkean scene was largely conventionalist, with analyticity understood, by default, as the source of necessity and, aprioricity, its epistemic default.Footnote ⁶² Reference KripkeKripke’s (1972/1980) a posteriori necessities, however, shook those defaults, generating a still-lasting wave of neo-Aristotelian essentialism (and de re modality) which brought with it a new mind-independence default for modality.Footnote ⁶³ However, as indicated above, this carries with it the (presumed) disadvantage of epistemological puzzlement.

Sidelle’s conventionalism developed as an explicit reaction to Kripkean a posteriori necessities. By conception, the theory thereby places a lot of emphasis on distinctively metaphysical necessities (and the essentialist thesis in their vicinity). Sidelle distinguishes between real necessity (roughly, what we’re understanding here as mind-independent necessity) and conventional necessity, adding that ‘[r]eal necessity is something we would need to be forced into accepting’ (Reference SidelleSiddle 1989, 83). Against the received view, he then argues that the Kripkean a posteriori necessities don’t have the required force to make us believe in real necessities. A paradigm example of such necessities is necessarily, water is H₂O. Kripke made a case that this necessity is synthetic and a posteriori. For Sidelle, however, there’s a way of accommodating it back into conventionalism without neglecting it. Roughly, the strategy is to factor out this necessity into an a posteriori yet non-modal claim (namely, water is H₂O) and an analytic modal principle to the effect that if water is H₂O then it is necessarily H₂O: ‘[we] violate a convention by denying that it is necessary that water is H₂O while affirming that water is H₂O’ (Reference SidelleSidelle 1989, 99).Footnote ⁶⁴ The case generalises to other principles with traditional essentialist flavour, like the Necessity of Origins or the Necessity of Kind. In each case, Sidelle calls the corresponding analytic principle a principle of individuation; and they are, for him, the only source of alleged (de re) modality to be admitted. In sum, ‘Modality does not find its home in the mind-independent world, but rather in us, in our ways of speaking and thinking, and thus the necessity is nothing beyond analyticity’ (Reference SidelleSidelle 1989, 2).

While acknowledging that analyticity is a problematic phenomenon, Sidelle thinks that there are two major problems with real necessity which add up to a more serious problem than analyticity. One is the epistemological problem already cited – how could we possibly know of mind-independent modal facts?; the other, is metaphysical – what would mind-independent modal facts be, in the first place? (see, especially, Reference SidelleSidelle 1989, Ch. 4.) All in all, Sidelle thinks, we’re far from being forced into real modality.

This sort of ontological and epistemological considerations that worry Sidelle and Rosen have long been identified as concerns that fuel mind-dependent accounts of modality, and we have witnessed this here with Fictionalism, Conventionalism, and Quasi-Realism. The next section is devoted to a view (the last to be seen in this Element) which, while sharing the ontological and epistemological motivations with those seen here, nonetheless resists being classed as mind-dependent.

3.5 Modal Normativism

In the words of Amie Thomasson, ‘The ontological and epistemological difficulties encountered by both heavy-weight and Lewisian realist views of modality are enough to motivate developing a different understanding of modal discourse’ (Reference ThomassonThomasson 2007, 136).

Thomasson addresses these difficulties by denying that modal discourse has a descriptive function.Footnote ⁶⁵ As we shall see in this section, modal truth comes out as mind-independent in her account, but not of a kind waiting to be discovered. Early expressions of non-descriptivism about modal discourse (especially Reference AyerAyer’s (1936/1952) and Reference WittgensteinWittgenstein’s (1922/1933)) already had the ingredients to avoid those difficulties but, to Thomasson’s puzzlement, they have been misunderstood and prematurely rejected, largely as a result of this misunderstanding. Her modal normativism is Thomasson’s meticulous, contemporary contribution that aims to repair this historical oddity.

According to modal normativism, the function of metaphysical modal discourse is normative, rather than descriptive. That is, instead of being used to refer to (heavyweight) modal properties in the world, which would act as truth-makers for modal claims, modal vocabulary is claimed to be used to mark, within the object language – i.e., the language we use to speak about the world – certain rules. Typically, those rules are expressible in a meta-language – a language used to speak about a given object language. But, even when they are, and for reasons that Thomasson explains, it is useful to also have the resources to mark them in the object language (Reference ThomassonThomasson 2013, Reference Thomasson2020, Ch. 2).

The central tenet of modal normativism is thus that our (metaphysical) modal vocabulary serves those useful purposes, which explains why, according to the modal normativist, metaphysical modal vocabulary is not descriptive. ‘On this view, which I have called “modal normativism”, the basic function of talk about what’s “metaphysically necessary” is not to try to describe modal features of the world, but rather to provide a particularly useful way of expressing constitutive semantic and conceptual rules in the object language’ (Reference ThomassonThomasson 2013, 145).

For a stock example, consider ‘Necessarily, all bachelors are men’. According to Thomasson, the term ‘necessarily’ in this modal statement marks, as that of a rule, the status of the indicative (and analytical) claim ‘all bachelors are men’. In the meta-language, the rule can be expressed as something like ‘do not apply “bachelor” to those to whom “men” doesn’t apply’. That it is useful that we can mark this type of imperative in the object language stems from a variety of reasons. Among them, ‘the indicative form of expression is far easier than the imperative to use in reasoning with rules, determining what follows from rules, and expressing conditional relations among rules’ (Reference ThomassonThomasson 2007, 138).

And, of the two types of indicatives that Thomasson distinguishes which would serve these facilitating purposes – namely, the simple indicative (as in bachelors are men) and the modal indicative (as in necessarily, bachelors are men) – the modal one has the added advantage of not being so easily mistaken for a description, plus that of allowing us to express permissions, too (Reference ThomassonThomasson 2020, Ch. 2).

This normativist treatment can also be extended to claims of ontological dependence, ‘traditionally stated in the form: Necessarily, if A exists, B exists’ (Reference ThomassonThomasson 2007, 143). These claims, as Thomasson acknowledges, are central in metaphysical discussions and it’s thus important, for the salience of modal normativism, that they can also be subsumed under the same strategy: as marking certain rules of our language. ‘These rules may take many different forms and may be much more complex than the simple rule “Apply ‘bachelor’ only where ‘man’ is applied”, but the pattern is nonetheless the same’ (Reference ThomassonThomasson 2007, 144).

Does all this mean that, according to the modal normativist, (metaphysical) modal vocabulary is devoid of meaning? Being in a position to answer this question in the negative is very important for Thomasson. We won’t go into the details here, but she offers, by way of a negative answer, introduction and elimination rules for modal vocabulary that she takes to be meaning-constitutive (Reference ThomassonThomasson 2020, 83–4). These rules thus guarantee that modal statements (and modal discourse in general) are truth-apt, thus pre-empting concerns from this quarter, such as the Frege–Geach problem.Footnote ⁶⁶ But not only this. As a modal normativist and an easy ontologist (Reference ThomassonThomasson 2015), she can agree with the heavyweight modal realist that there are modal properties and modal facts. Their disagreement is not about the truth-value of this existential claim, but rather one of direction of explanation. While for the heavyweight mind-independent theorist these modal facts and properties are, antecedently, the truth-makers of modal claims, and thus what explains modal truth, for the modal normativist modal truth (once guaranteed by the meaningfulness of the modal vocabulary) explains our talk of modal properties and facts: as sheer ‘hypostatizations out of modal truths’ (Reference ThomassonThomasson 2009, 18).

In the remainder of this section, I shall focus on two other potential concerns that soon come to mind about this metaphysics of modality: the first is about Kripkean a posteriori necessities; and the second is about how modal normativism about metaphysical modality interacts with other kinds of alethic modalities.

As mentioned in Section 3.4 when considering modal conventionalism, Kripkean (de re) a posteriori necessities fuelled the idea that metaphysical modality wasn’t to be seen as born of analyticity. In Reference ThomassonThomasson’s (2007, 144) terms, ‘De re modal claims lend the most weight to heavyweight realist views, as they seem to describe objects as possessing genuine modal properties’. The way Thomasson accommodates them into her normativist programme is not distanced from the way we’ve seen Sidelle accommodates them into his conventionalism. For instance, Thomasson explains the necessity of Hilary Clinton’s genetic origins in terms of a rule that allows us to co-apply the term ‘Hilary Clinton’ to x and y only when ‘same person’ applies to them, where, in turn, the rule governing ‘same person’ requires traceability back to the same genetic origins. Similarly, water’s being necessarily H₂O can be accommodated by appealing to the schematic rule: ‘Whatever the actual chemical composition of this stuff turns out to be, apply “water” only where there is stuff of that chemical structure’, plus (empirical) contribution from the world about how to fill in the schematic slots (Reference ThomassonThomasson 2007, 144–5; see also Reference ThomassonThomasson 2020, Sect. 4.1). One might wonder, however, whether these strategies deliver a phenomenon of the appropriate strength (that is, the strength expected of metaphysical modality) as opposed to something weaker, more aptly referred to by ‘always’ than by ‘necessarily’, akin, for instance, to the fact that genetic origins are perennial properties and that water being H₂O is a universal truth. Here, I simply register this concern, without scrutinising it.Footnote ⁶⁷

For current purposes, I am more interested in the second type of concern. This has to do with how Thomasson views the relation between metaphysical modality and other types of alethic modality, including the natural one, as well as the bunch of modalities that, as seen in Section 2.5, the Finean essentialist can construct by restriction on the metaphysical modality. As anticipated at the end of Section 2.6, the concern will now take us back to the prospects of unifying different types of modalities (alethic and beyond).Footnote ⁶⁸

Thomasson is clear from the outset that her large-scope project is that of unifying the treatment of alethic modal vocabulary in terms of deontic modality. Yet, in developing the project, she quickly narrows down the focus to that of metaphysical modality: ‘The hope is instead to provide a way of understanding alethic modality in terms of deontic modality; more specifically, to make sense of claims about metaphysical necessity by way of understanding the normative rules for using our terms’ (Reference ThomassonThomasson 2007, 136–7; my italics).

The opening quote in this section identified Thomasson’s motivations for treating metaphysical modality in normativist terms; these are the same metaphysical and epistemological difficulties that fuelled mind-dependent accounts (Section 3.4). My concern here, crudely put, is that the force of those motivations isn’t enough to allow Thomasson to achieve her wide-reaching ultimate aim.Footnote ⁶⁹ Indeed, the strength of these concerns is at its highest when we assess them, as Thomasson does, against ‘specifically metaphysically modal claims’; claims of necessity and possibility in the vicinity of essentialist claims (Reference ThomassonThomasson 2021, Sect. 2082). It quickly diminishes, however, when one assesses them against ordinary modal claims. Let me explain.

With respect to the metaphysical difficulties – of providing an account of the source of metaphysical modality – Vetter’s Potentialism (as well as other dispositionalist accounts), for instance, offers a metaphysics of possibility that has among its virtues its lack of scientific extravagance. Admittedly, as seen at the end of Section 3.3, her starting focus is ordinary dispositions and abilities, which might be thought to concern more restricted forms of alethic possibilities. But we have seen there too how this does not make these forms of possibility not metaphysical. Rather, the suggestion was that, in her account, these restricted possibilities are (ontologically) continuous with metaphysical possibility, the ultimate focus of Vetter’s theorising. This being so, Dispositionalism offers a contemporary illustration of how to diminish the puzzlement about the metaphysics of metaphysical modality: it shouldn’t exceed the (minor?) puzzlement about abilities or dispositions.

Now, delving much into the epistemology of (metaphysical) modality is not among the aims of this Element, but I shall say enough nonetheless to motivate the current point that Thomasson’s epistemological concerns don’t warrant a unified, normativist treatment of alethic modalities. With respect to these concerns, we should note that, largely simultaneously with the emergence of dispositionalist accounts of modality, the literature in the epistemology of modality is experiencing what we might call ‘a non-rationalist turn’. Thomasson seems to share (with many contributors) the idea that potentialism in the metaphysics of modality goes very well with non-rationalism in the epistemology of modality. And while seemingly granting explanatory merits to both camps, she nonetheless writes that

What is important to note from this quote (for current purposes) is that, in view of the recent developments she mentions, Thomasson herself seems to be neither as metaphysically nor as epistemically puzzled about the non-specifically metaphysical modalities as she is about the specifically metaphysical one. At this point, one would need to do a bit of exegesis about how best to receive the specifically/non-specifically distinction on metaphysical modal claims, but the context of the quote makes it clear that the specifically metaphysical ones include claims central to philosophy, including essentialist claims and, admittedly, many of the ones that (according to Leech’s worries, as seen in Section 3.2) Vetter’s dispositionalism would struggle (metaphysically) to account for.

But even if we granted Leech’s and Thomasson’s points – i.e., that some metaphysical and epistemological difficulties remain – the fact stands that there are restricted (or else relativised) types of modalities that are, in view of current developments, neither metaphysically nor epistemologically (as) puzzling as the specifically metaphysical one. And, for the reasons given in Sections 2.5 and 2.8, these modalities are still to be seen as metaphysical, even if not specifically so (i.e., even if they are not the absolute one).

Now, there is an increasing number of scientifically friendly modal accounts that demystify some metaphysical modalities (both their metaphysics and their epistemology) while retaining heavyweight mind-independence. In view of this, a normativist treatment of them would be under-motivated. And if this is so, the following is an urgent question for Thomasson: shouldn’t we aim for an account of the specifically metaphysical modal claims that treats them as continuous with those more mundane metaphysical modal claims?

At this point, Thomasson might agree that it would be difficult to treat them discontinuously. And she might, in response, remind us that her wide-scope project is to treat all alethic modalities (metaphysical or not; specifically so or not) under the model of modal normativism. Indeed, she at places considers, in a sharply Humean spirit that we should not overlook, the idea of treating natural necessities as normative ones too: ‘While metaphysical modalities are reflections of constitutive semantic or conceptual rules, the natural correlate view would take the physical necessities expressed in scientific laws to reflect norms of reasoning on the basis of empirical evidence, or something along those lines’ (Reference ThomassonThomasson 2020, 121).

But in response, my concern is that the unification that results from this can be diagnosed, in view of recent developments, as an overreaction: unification in the wrong direction. Epistemically, Thomasson is right that some puzzlement remains.Footnote ⁷⁰ And it’s true that more needs to be done on the metaphysical front too. And yet, recent developments should make us treat this remaining puzzlement as what it is (or as I believe it to be): a remainder of the initial one, small enough, it might be claimed, not to call for a metaphysical re-conception of alethic modalities across the board.Footnote ⁷¹

The ‘descriptivist assumption’ that Reference ThomassonThomasson (2020, Ch. 1) rightly claims to be present in much of the literature on modality is, I contend, a default we should be forced out of.Footnote ⁷² And in view of the fact that the metaphysical and epistemological difficulties aren’t particularly forceful for the restricted (non-specifically metaphysical) modalities, we aren’t forced out of this assumption in their case. In this respect, and although Reference WilliamsonWilliamson (2016, 462), might be right that ‘Arguments for scepticism about metaphysical modality tend to generalize to other objective modalities, irrespective of the theorist’s intentions’, the present point is rather that, in Thomasson’s case, the reasons for her normativism don’t generalise, despite her intentions. To the extent that this is so, it would be by brute force that one could achieve wide-scope, unified normativism.

It is pertinent at this point to ask what are the alternative options. One option is to remain in the descriptivist default across the board and to learn to live with the remaining explanatory deficit (perhaps even acknowledging partial scepticism, as a reminder of our limitations). Another option is to endorse modal normativism only for the distinctively metaphysical modal claims, to the detriment of the unified treatment. Of these two, my preference is for the former. Developing this option is something I leave for a future occasion, and I wrap up this section merely stating what I consider to be its important advantage. Heavyweight realism about the metaphysical modalities (all of them) is best placed to explain what seems to me to be a fundamental difference between the metaphysical and the normative necessities, namely, that only the latter can (in a metaphysical sense) be transgressed: you must change the game to do the alethically impossible, but you cheat in the game if you do the normatively impossible. This difference (which, as seen in Section 2, turns on principle (M): □p→p) is lost, one might fear, with a treatment of any metaphysical modality in terms of normative modality.