## Sunday, 15 February 2015

### De Re Modality and Quantifying In

This is the first in a series of posts about these issues, the plan for which is given below.

Followup posts

### On Kripke's Intuitive Anti-Quinean Defence of De Re Modality

Toward an Account of De Re Modal Ascriptions

My account of subjunctive necessity treats subjunctive necessity, in the first instance, as an attribute of propositions. That is, it is in the first instance an account of de dicto subjunctive necessity, in the sense that it applies to attributions of necessity and other definable modal properties to propositions (dicta).

As it stands, this account does not apply to propositions which say, of some object, that it necessarily has some property. For example, 'John is necessarily not a number'. That is, the account does not deal with de re subjunctive necessity (assuming such a thing is to be recognized at all).

Now, 'John is necessarily not a number' may look like just another way of saying '“John is not a number” is necessary'. Of course, nothing is stopping us stipulating that it is to be read that way. But furthermore, it might seem to already, naturally, say something equivalent to that. Or it might not. This issue will be seen below to turn on the issue of whether extensionally identical atomic propositions can differ in counterfactual invariance, and in turn modal, status – or more strictly speaking, it will be seen to turn on that given a certain natural approach to the interpretation of de re modal ascriptions.

Unlike '”John is not a number” is necessary', which refers to a proposition and predicates necessity of it, 'John is necessarily not a number' refers to John, and seems to be open to quantification in a way that the de dicto attribution is not: we can seemingly infer from it that something is necessarily not a number, whereas existential generalization on the de dicto attribution yields only 'Something is necessary'. This suggests that de re modal attributions like 'John is necessarily not a number', at least on one natural reading, do not have corresponding de dicto attributions which say exactly the same thing (even if they are equivalent in some sense). It also raises the issue of the interpretation of quantification into modal contexts.

I will begin in this post with some further consideration of what the problems of de re modality and quantifying in amount to.

In the next post in the series, I will discuss Kripke's criticism in Naming and Necessity of Quine's attempts to make genuine de re modal attributions look bizarre or unintelligible, including the discussion of Nixon, where Kripke argues that de re modal attributions make good intuitive sense.

In the next post after that, I will go in search of an account of de re modal attribution given in terms of de dicto modality, eventually lighting on one, but leaving certain complications undiscussed for the time being.

In the next post after that, I will address the problem of quantification into modal contexts by giving an interpretation of the formulae of quantified modal logic (in the form of a method of translation into natural language).

The Nature of the Problem of De Re Modality

Here is Kripke introducing the problem of de re modality in Naming and Necessity (first lecture):
There is one more question I want to go into in a preliminary way. Some philosophers have distinguished between essentialism, the belief in modality de re, and a mere advocacy of necessity, the belief in modality de dicto. Now, some people say: Let's give you the concept of necessity. A much worse thing, something creating great additional problems, is whether we can say of any particular that it has necessary or contingent properties, even make the distinction between necessary and contingent properties. Look, it's only a statement or a state of affairs that can be either necessary or contingent! Whether a particular necessarily or contingently has a certain property depends on the way it's described. This is perhaps closely related to the view that the way we refer to particular things is by a description.

It is important to separate three parts of what Kripke says 'some people say' here:
1. Given an understanding of de dicto necessity, the issue of de re modal attribution remains, and creates additional problems.
2. It's only a statement or state of affairs that can be necessary or contingent.
3. Whether a particular necessarily or contingently has a certain property depends on the way it is described.
I fully endorse (1), as the existence of this section would suggest. But that does not mean I endorse (2) or (3), both of which are curious and not altogether clear. I do not want to be overly pedantic about something which was said, in a fairly preliminary way, in a lecture delivered without notes, but separating these things and considering what (2) and (3) might mean will help us get clearer about the issue of de re modality. It will also help when we consider, in the next post, Kripke's intuitive defence of de re modality (which he gives right after the above quoted passage).

(2) needs finessing if it is not to be a trivial point of language. Someone – say, an Aristotelian essentialist, or Kit Fine – can hold that de re modal attribution makes perfect sense, and fully reject any (3)-like suggestions that the truth of these attributions is somehow description-dependent, and still agree with (2) as stated. They are not saying that an object (one which isn't a statement) can 'be necessary or contingent', but that it can have properties and stand in relations necessarily or contingently.

The real suggestion behind (2), I suggest, is that the notions of necessity and contingency – the notions of subjunctive or metaphysical modality clearly isolated by Kripke – only apply to statements (propositions) or states of affairs. And 'apply' here is understood in such a way that these notions are not automatically precluded from appearing in some other way than in predications of the form 'x is necessary', for example adverbially ('x is necessarily F').

(2), so understood, is not something I want to endorse. While I accept that de re modal attribution poses difficulties over and above de dicto, I think it may be possible to meet these difficulties. However, the meeting of these difficulties will be attempted here by accounting for de re modal attributions (and quantification into modal contexts) in terms of de dicto attributions. (But that doesn't mean there is no other way – I am giving an account, not the account.)

There is something potentially misleading about this talk of difficulties which may perhaps be met (rather than just cleared away, for instance) – as though there is some reason for us to hope that they may be. But that is not how I see the matter. This has to do with my doubts about whether there is any pre-existing intuitive understanding of de re modal attribution and quantifying-in, which I will elaborate in the next post.

So much for (2). What about (3): 'Whether a particular necessarily or contingently has a certain property depends on the way it's described'? This is very curious in a way. Far from being part and parcel of some attitude one might have on these questions consonant with (1) and (2), (3) seems incompatible with what we understood (2) to be getting at; if the relevant modal notions only apply to propositions or states of affairs, then, it would seem, we cannot speak of particulars necessarily or contingently having a certain property, and so we cannot say that their doing so depends on anything.

There is perhaps a way of interpreting what some skeptic about de re modality might mean by this, but there are also good reasons for them not to say it (not least of all that it is highly ambiguous and confusing).

There suggests that there is a danger that (3) is playing a straw man role, or a more subtle bait-and-switch role, in Kripke's influential arguments for the intuitive intelligibility of de re subjunctive modal attributions: trading on a charitable interpretation to make it a plausible attribution to philosophers (the bait), and then switching to an interpretation on which it couldn't possibly be right or even coherent (the straw man).

In light of this, I will now go into (3) at some length. I will do my best to make it easy to keep track of the argument, and its place in the bigger picture.

Something someone could say while maintaining (2) (as we have understood it) is this: the only clear, philosophically hygienic thing it could mean to say 'Nine is necessarily odd' is '”Nine is odd” is necessary', and all it could mean to say that 'The number of planets is necessarily odd' is '”The number of planets is odd” is necessary'. (Note however that I will not be advancing this view.)

Now, such a person would then face the issue: where does that leave the question of whether the referent of 'nine' and 'the number of planets', that particular number, possesses the property of oddness necessarily or contingently? What, if anything, does that mean?

It seems to me that the most consistent course for this person would be to say: this question just amounts to whether the proposition:

'The referent of “nine” and “the number of planets”, that particular number, possesses the property of oddness'

is necessary or contingent. Either that, or it has no clear meaning.

But Kripke has this person say that this question somehow depends on how we describe that particular number. But note carefully that this question, interpreted in the way I suggested was most consistent for the hypothetical person we are imagining, concerns a particular proposition. If someone asks something, and what their question really asks is whether some particular proposition is necessary or contingent, you can't respond by saying 'Well, that depends on how you describe …'. The describing has already taken place, in the proposition in question, and it is now time to proceed to actually answering the question.

Another thing this person could say which is similar to (3), but clearer, is this: that the truth of propositions which, superficially, designate an object somehow and say that it has some property necessarily or contingently, depends on how that object gets designated. But in this case, if we say that, surely we should say that these propositions have a misleading form. We should not go along with this form and say, as a kind of explanation of it, that whether some object has a property necessarily or contingently depends on how it is described. (The most deserving meaning for this expression here may still not be deserving enough.)

This can perhaps be seen better by comparing our case with one in which we might genuinely say something like this – i.e. that whether an object is some way or other depends on how you describe it. Consider these propositions: 'The number of planets is, in the subject-term of this proposition, being described as the number of planets', 'Nine is, in the subject-term of this proposition, being described as the number of planets'. The truth of these propositions patently does depend on how the referent of the subject-term is described (or, we might say more neutrally, designated). And we can say that whether that referent, that particular number, has the property of being described in some given proposition as the number of planets depends on how it is described by that proposition. Indeed this seems like a tautology. Or consider an object which naturally, whenever it is described as red, turns red if it is not already red (i.e., irrespective of whether the description was true, it becomes true), but turns another colour if it is described as non-red. Of such an object, we could say: whether it is red or not depends on how it is described.

The modal case is plainly not like this at all. Saying that whether a particular has a property necessarily or contingently depends on how it is described is, at best, a clumsy way of saying that the truth of (what superficially look like) de re modal attributions depends on how the object in question is designated. At worst, it is a tortuously confused piece of nonsense.

Another, perhaps more Quinean, thing someone might say which is along the lines of (3) is: de re modal discourse is confused, incoherent – in part because the truth of its claims of necessary or contingent property possession for an object would have to depend on how that object is described. This isn't really clearer than saying that the truth of such claims actually does depend on how the object is described, but the unclarity is less objectionable, since it is being asserted that de re modal discourse is incoherent, and so the thing about description-dependence can be regarded as an incoherent, absurd consequence – where the whole point of bringing it in is to argue that we are not able to make real sense of it.

So, (3) itself seems in danger of being a bit of a straw man for Kripke – it has little to recommend it, and doesn't obviously belong to anyone.

So, we have separated and examined three things involved in the position of the skeptic of de re modality as characterized by Kripke. The first, that given an understanding of de dicto necessity, the issue of de re modal attribution remains, and creates additional problems, is important and endorsed by me. The second, the idea that it is only a statement of a state of affairs that can be necessary or contingent, is something which I hope to undermine in subsequent posts. The third, the idea that whether something has a property necessarily or contingently depends on how you describe it, I have tentatively suggested to be a straw man.

Stay tuned for the next post, on Kripke's intuitive anti-Quinean defence of de re modality.