Reply to Barbara Vetter

Barbara Vetter raises the very interesting, though neglected, question of ‘how the essentialist view [of metaphysical necessity] fits with an understanding of ordinary modality’ (p. 3). There is the related question of how the special modalities—such as metaphysical or natural or logical necessity—fit with an understanding of ordinary modality and the question, in particular, of how metaphysical modality fits with an understanding of ordinary modality, which question can, of course, be detached from the question of whether we should adopt an essentialist view of metaphysical necessity.

Vetter is of the view that certain sentences of ordinary language can be used to express ‘ordinary necessities’ such as ‘the fact that it is necessary for the journey from Berlin to Portland to take at least 10 hours’. Let us call a sentence of this sort an ‘ordinary modal sentence’, or an ‘OMS’ for short. She goes some way towards explaining what these sentences are and when they may be used to express an ordinary modality. Thus, they will characteristically involve certain modal idioms—such as ‘possible’, ‘can’, and ‘must’—where these idioms are used in a circumstantial, rather than a deontic or epistemic, sense (p. 3). It would be desirable to have a fuller characterization, but I think Vetter has given us a pretty good idea of the kind of sentences and their uses that she has in mind.

A caveat is in order. Sentences making use of the special modalities are usually expressed in the form □A, for □ a sentential operator and A a sentence.¹ But OMS’s are rarely of this form. ‘Mary had to sneeze’ (example (1)b, from p.4) is not of this form; and nor, for that matter, is ‘it is necessary for the journey from Berlin to Portland to take at least 10 hours’, since the operator ‘it is necessary (for)’ does not govern a sentence. Some OMS’s not of this form may be equivalent, for all intents and purposes, to OMS’s that are of this form. The previous sentence concerning the journey from Berlin to Portland, for example, is presumably equivalent to the sentence ‘it is necessary that the journey from Berlin to Portland takes at least 10 hours’. But for other OMS’s, such as ‘I can ride a bicycle’, it is not so clear that they can put in the required form.²

However, when an OMS is not of the required form, it is not so clear how the link between the OMS and the special modalities is to be achieved, since the OMS provides no clear guidance as to which sentence the special modal operator is to be attached.³ For this reason, we shall follow Vetter’s practice (p.5 et seq) and confine our attention to OMS’s that are of, or can be put into, the required form. Thus, an OMS will be of the form OA, where O is an ordinary modal operator, such as ‘it is necessary that’ and A is an ordinary sentence. It is worth noting, though, that if we allowed special indexed operators, such as the essentialist operator, then the scope of our enquiry might be extended to OMS’s that invoke a division between the subject and the predicate of the OMS, as with ‘it is impossible for Mary to like Bill’, in which the subject is ‘Mary’ and the predicate is ‘to like Bill’.

Let us now consider the connection between ordinary modality and the special modalities. In the special case of necessity, Vetter proposes what she regards as a definition of the one in terms of the other (p. 5):

where R is ‘the conditions to which necessity is being relativized’. We should, of course, here think of R as expressing the conjunction of the relevant conditions. Moreover, it should be assumed that R is an actual condition, and so since, from a formal point of view, R is merely a proposition, the right-hand side of the definition should be taken to have the form ‘R and it is metaphysically necessary that if R then p’.

She later dismisses the proposed definition on the grounds that it is either extensionally inadequate or explanatorily redundant. However, as I hope later to make clear, it seems to me that the definition contains the germs of a viable account and that, once it is suitably modified, the kind of objections that Vetter makes against it can be avoided.

The phrase ‘it is ordinarily necessary’ is not, of course, itself an ordinary modal operator. I take it that what she has in mind is something schematic, under which the phrase is to be replaced by something, such as ‘it is necessary that’, which is an ordinary modal operator.

But we now face a certain awkwardness. For the clause ‘it is necessary that p’ on the left is context-sensitive in a way in which the clause ‘it is metaphysically necessary that if R then p’ is not. The relevant condition or conditions R will presumably depend on the context, but there is no indication of how this is so. So, in order to make this explicit, we might state the definition in the form:

But there is now a scope ambiguity. R_c may be designated as ‘the conditions determined by c’. But in the definition, does this definite description take narrow scope or intermediate scope over the metaphysical necessity operator or wide scope over the whole definition (though in that case we would not have what is strictly speaking a definition)? The narrow scope reading is not plausible. After all, the necessity in question is not about the context. This then leaves the readings under which, for any suitable context c, either:

If only extensional adequacy were in question then the difference between the two formulations would not matter. But Vetter is after a definition, or, at least, something akin to a definition; and the wide scope reading is then highly implausible. For, in saying that it is (ordinarily) necessary that p in a given context, I am not saying anything about the specific conditions determined by the context: the sneezer’s particular physical make-up, say, or the particular time-tables for air traffic between Portland and Berlin. All I am saying is that the relevant conditions, whatever they may be, are such as to necessitate the proposition in question.

I have so far followed Vetter in taking the special modality on the right to be metaphysical necessity. But one might think that, depending on the context, it could be some other special modality, such as logical or nomological necessity. We therefore arrive at the following more general version of (2b):

where ‘necessarily_c’ (or □_c) is the special modality determined by the context c. There is now, in principle, a further ambiguity in the scope of ‘necessarily_c’. But, in this case, there would appear to be no harm in giving it a wide scope. Thus, the context will determine the sense of the special modality in terms of which the conditions for the ordinary modal claim are then to be given.⁴

There are a couple of other ways of formulating the connection between ordinary modality and the special modalities. They are somewhat more general, but come at a slight cost. In a suitable context (though not necessarily in all contexts), an OMS will express an objective modal proposition. Let us call such a proposition an ‘ordinary modality’ or ‘OM’ for short.⁵ The present route to an OM proposition is through a sentence, the OMS, by means of which it may be expressed; and it is perhaps through the use of such sentences that we can best get a grip on what the OM propositions are.

We might now think that our task is not to state when an OMS obtains in a given context but to state what OM proposition it expresses in that context. Accordingly, (3) now takes the form:

From this point of view, we do not have a definition in the usual sense of the term. Indeed, it is not even clear that we can properly make sense of the locution ‘it is necessary that p in context c’ just as we cannot properly make sense of the locution ‘I am cold in the context c’, given that the context may be one in which someone other than myself is the speaker. Thus, we might think of the present formulation as stating in the formal mode what was previously improperly expressed in the material mode. It enables us, in addition, to avoid unwarranted reference to the context. For the proposition expressed by φ is not only non-specific but, in contrast to the right hand side of (3), it makes no reference to the context but simply appeals to the contextually determined standards by which the relevant conditions are to be determined.

We might also provide a formulation in the vicinity of (3a) in terms of ground. According to (3a), the proposition expressed by φ in the context c is an existential proposition: it says that there are relevant conditions R for which R and necessarily if R then p. So, it is natural to think that if it is true it will be fully grounded by a particular instance of the existential proposition, one to the effect that the particular proposition R₀ is a relevant condition for which R₀ is the case and necessarily if R₀ then p. But this instance will be partially grounded in the proposition necessarily if R₀ then p. Thus, we have:

Thus, each ordinary modal truth will be true partly in virtue of a special modal truth; and, of course, (3b) may obtain even if it does not receive support in this way from something like (3a).

We see that, if we are willing to adopt an ontology of propositions or the ideology of ground, we may provide a more general and perhaps somewhat more accurate account of the link between ordinary modality and the special modalities.

It should also be noted that if both the conditions R_c and the special modality □_c are subject to contextual determination, there is some question as to what pertains to the conditions and what to the modality. Suppose, for example, that, in a given case, □_c is nomological necessity. Then we might alternatively take □_c to be logical necessity and expand R_c to include the nomological necessities. The two different propositions obtained in this way might even be taken to be the same under a sufficiently relaxed criterion of propositional identity.⁶

My own inclination is to suppose that we may operate under a more fine-grained criterion of propositional identity under which there is a genuine question as to what goes into the conditions and what goes into the modality and that, under such a fine-grained criterion, we should expect there to be a non-modal characterization of the relevant conditions.⁷ There is, in this way, a division of labor, with the conditions prescribing a non-modal basis for the application of the modality. We can thereby make sense of the claim that each OMS in a given context will have a distinctive modal force, as given by the particular modality □_c that is to be determined from the context.

Let us now turn to Vetter’s objections to the original proposal ((1) above), in which the special necessity is taken to be metaphysical necessity. She thinks the proposal is subject to a dilemma: either the conditions R are non-modal, in which case it will be extensionally inadequate, or they are modal, in which case it will be explanatorily redundant (p. 7). In the case of the OMS ‘it must be that I sneeze’, for example, her point is that the speaker’s physical make-up will not metaphysically necessitate that the speaker sneezes and that it is only if the underlying conditions R include modal facts (such as the speaker’s dispositions or the laws of nature), that we can get them to metaphysically necessitate that the speaker sneezes. But in that case the ‘source of the necessities … is not exclusively the essences that give rise to the necessity’ (p.7).

To be strictly accurate, the difficulties with achieving extensional adequacy arise, not from the conditions themselves being non-modal, but from their determination being non-modal. Suppose it is a law of nature that anyone with the speaker’s physical make-up will sneeze. Then we only need to include the non-modal generalization that anyone with this physical make-up will sneeze to get the desired entailment. But, of course, in this case the truth of the ordinary modal claim will still turn upon there being such a law. What puts the generalization into the conditions is its nomological status.

I am inclined to agree that some ordinary necessities, such as that it must be that I sneeze, will lack an exclusively essentialist source. Indeed, there is a way in which this was a foregone conclusion. For, as Vetter had already acknowledged, ‘They [the ordinary necessities] plausibly include … nomological necessities: speaking with an ordinary sense of the modals, it is true that … nothing could travel faster than the speed of light’ (p.3). Yet it is far from clear that such nomological necessities will have an exclusively essentialist source.

However, I am not sure that this conclusion has the dialectical significance that Vetter seems to attach to it. She writes at the end of §3, ‘essences do not play an interesting explanatory role for ordinary objective necessities. But then we need another way of connecting the two notions of necessity’. And this then leads her to consider defining metaphysical necessity as a form of ordinary necessity rather than the other way round.

But why do we need another way of connecting the two notions of necessity? The analyses under (3) provide a connection between ordinary modality and the special modalities. Given that not all (or even that relatively few) ordinary modalities are essentialist in character, why should we think that there is a connection between ordinary modality and metaphysical modality that goes beyond what is already allowed by the analyses under (3)?

However, regardless of its motivation, we can consider Vetter’s ‘head turning’ (or foot stomping) proposal on its own merits. Her suggestion is that:

The idea behind the definition (footnote 6) is that ordinary necessity tells us how a metaphysical necessity is a necessity whilst being an essential truth tells us, in what may be an entirely nonmodal manner, how it is a metaphysical necessity.

There is again a difficulty about understanding this as a definition of the usual sort, since the clause on the right is context-sensitive in a way in which the clause on the left is not. There are two strategies for avoiding this mismatch. The first is to use a notion of ordinary necessity that is not context-sensitive. Roughly, the idea is to say that p is an ordinary necessity in this context-insensitive sense if there is some context or other in which it is an ordinary necessity. Speaking a little more exactly, we may say that, given a sentence ‘p’, we take it to be an ordinary necessity that p if there is some suitable context in which the OMS ‘it is necessary that p’ is true.

The trouble with this suggestion is that ordinary necessity will then coincide with truth. For take any true sentence ‘p’. Then I can truthfully assert the conjunction ‘p and 0 = 0’ and can then go on to infer ‘so it must be that p’. But then the conclusion ‘it must be that p’ will be a true OMS. Thus, for any truth p, there will be a context in which it is an ordinary necessity that p. But if ordinary necessity in some context coincides with truth, then taking a metaphysical necessity to be an ordinary necessity will in no way account for its being a necessity.

This is a somewhat artificial example. But even less artificial examples like ‘It is impossible that one gets from Portland to Berlin in under ten hours’ strike me as having no real modal force. They are simply made true, without the aid of any fancy philosophical theory, by the facts concerning the time-tables for the existing means of transport between the two cities.

Another strategy is to appeal to the idea, not of a proposition being an ordinary necessity, but of a propositional concept being an ordinary necessity. Thus, we do not have a definition of the form:

We may then take the ordinary necessities to be given by the OMS’s, since each OMS, when uttered in a suitable context c, will give rise to an associated concept of necessity, □_c; and we may take the ellipsis ‘…’ to indicate that the ordinary concept of necessity □ is to be such that □P, whenever true, should have its source (or ground) in the essential truth of P.

Both are forms of restrictive definition, though of a kind of proposition in the one case and of a kind of propositional concept in the other case. But the present definition, in contrast to the previous one, is impredicative; the concept of metaphysical necessity is defined by reference to a domain of concepts that includes the very concept in question. I have a general misgiving over giving an impredicative definitions of a concept, but they are especially acute in the present case. For it seems to me we should have a prior understanding of the different concepts of necessity with which our statements of ordinary necessity may be associated. This is not to deny that ordinary modal locutions might provide a good genetic route to grasping these concepts. But they are not a good analytic route; they provide no account of what the concepts are or of how they are to be analyzed. One might, of course, appeal to the general concept of a necessity without tying it to ordinary discourse and then provide a similar definition of metaphysical necessity as a necessity that has an essentialist source. This is not something I considered in Fine (2005); and it strikes me as somewhat more promising than an account that takes ordinary modality as its starting point.⁸ But impredicative worries aside, it still remains unclear to me how we might thereby account for the distinctive hardness of metaphysical necessity (and talk of closeness or ‘degrees of necessity’, as in Kment (2014), just seems to presuppose what is at issue). In saying that something is a color, I provide no account of how some colors are darker than others. Likewise, in saying that something is a necessity, I provide no account of how some necessities are harder than others. In each case, this should be something that is somehow intrinsic to the colors or to the necessities themselves.