Toward an Account of De Re Modal Ascriptions

This is the third post in a series on de re modality and quantification into modal contexts. This one is quite exploratory and anything but final. The first two posts are here and here.

Let us begin by considering a simple proposal and two problems with it:

a is necessarily F iff 'a is F' is necessary.

The first problem may best be called a potential problem. It affects this approach if the question 'Can propositions which ascribe the same property (or relation) to the same object (or n-tuple of objects) differ in modal status?' is correctly answered in the affirmative.

If propositions can be ascriptionally identical and yet differ in modal status, then while my proposition 'a is F' may be necessary, someone else may have a proposition in another system, let us say using the sign 'b is G' (but of course it may also be the same sign as I use), which is ascriptionally identical but contingent. In such a case, we might not want to say that a, that object, is necessarily F, since some propositions which ascribe the property F'ness to the object a are not necessary – we might want to say, generally that an object fails to be necessarily F if there is any proposition which ascribes F to it and isn't necessary.

This gives rise to various terminological opportunities and options – e.g. we might want to distinguish 'weak' and 'strong' necessity, and may go different ways on questions like 'If something is F, but is not strongly necessarily F, is it contingently F?'. We will come back to this. For now, we will go along with saying that a thing fails to be necessarily F if some proposition says of it that it is F, and that proposition fails to be necessary.

Furthermore, we will go along with the idea, while actually remaining agnostic, that ascriptionally identical propositions can differ in (ICI, and in turn) modal status – that is, we will try to solve this potential problem, without actually deciding for sure that it is a problem.

The second problem, unlike the first (potential) problem, does not threaten the truth or validity of the account, but rather its power. Recall the simple proposal we began with:

a is necessarily F iff 'a is F' is necessary.

The second problem lies with generalizing this: the above, if it is not read as being about some specific proposition, is a schema. And getting a general statement, a universal quantification, about when an object x, say, is necessarily F (or necessarily has some property y), is still a non-trivial task given the above, since the schematic letters occur on the right hand side in a quotational context.

I will now pursue the first problem for a long and tortuous stretch (this will hopefully be instructive). In the end, it will emerge that by solving the second problem in a certain way, we can modify the result so that it solves the first problem (using, for this modification, what we will have learned by that point about the first problem). This solution is, in essentials, the solution we will offer in the next post to the problem of quantifying into modal contexts, although the success conditions there may be a bit different. Therefore in this section, at the end of the long and tortuous stretch, I will just briefly state the solution, and explain how it solves the second problem as well.

Again: the first problem is, roughly, that instances of the simple schema might come out false if, while my proposition 'a is F' is necessary, there are other propositions ascribing F'ness to a which are not.

This naturally suggests the following:

a is necessarily F iff all propositions ascribing F'ness to a are necessary.

One problem with this which is, I think, not hard to surmount, lies with the possibility of non-rigidly designating an object and ascribing a property to it, in the sense of: ascribing that property to whatever falls under the description. I mean, for example, propositions such as:

The number I have written on this piece of paper is odd.

This can certainly be read as a contingently true proposition. Suppose I have '3' written on a piece of paper. Now, we will want to say that the number three, that very object, is necessarily odd. But since I might have written a different number, the above proposition, on the reading I have in mind, is contingent. And yet we might say that this proposition, so construed, satisfies the condition 'is a proposition ascribing F'ness to a'. The solution is to add the condition that the proposition rigidly designates a.

So really, what we want to consider is:

a is necessarily F iff all propositions rigidly designating a and ascribing F'ness to it are necessary.

Another problem is that a proposition may rigidly designate a and ascribe F'ness to it, but also do a bunch of other things, such as designating b and ascribing G'ness to it. And this extra stuff may make them contingent. For example: '3 is odd and this piece of paper has a 3 on it'.

The solution to that problem is to add a “that's all” clause – e.g. to talk about propositions which just rigidly designate a and ascribe F'ness to it, and do nothing else.

These problems, then, are easily solved. In the discussion of more serious difficulties which follows, I will not incorporate these solutions in order to keep things simple.

So, what (besides the two problems we saw how to fix) is wrong with:

a is necessarily F iff all propositions ascribing F'ness to a are necessary?

The problem is: what if there just aren't enough relevant propositions around in the actual world? (Whether this is a problem depends on the view of propositions one takes.)

And that leads to the thought:

a is necessarily F iff all possible propositions ascribing F'ness to a are necessary.

Disambiguation of 'Possible Propositions'

There is an unfortunate ambiguity here in talking about 'possible propositions'. I will not try to fix the terminology, but only explain the ambiguity: this means 'a proposition which can exist'. By contrast, when I speak of a proposition being necessary, I mean being subjunctively necessary, necessarily true in the Kripkean sense. I don't mean a proposition which must exist. A subjunctively possible proposition, then, is one which is true and not necessary – but the talk here of 'possible propositions' does not mean this. Fortunately this ambiguity is, for me, largely confined to these modes of construction, rather than particular constructions, since I hardly ever speak of the property of being subjunctively possible, and I never – except in this note – speak of propositions which must exist: so 'possible proposition' always means 'proposition which can exist', and 'necessary proposition' means 'proposition which is necessarily true'.

The 'All Possible Propositions' Strategy

We were considering the thought: a is necessarily F iff all possible propositions ascribing F'ness to a are necessary

This raises two worries: (i) is there a circularity problem here?, and (ii) what about impossible propositions, or perhaps better: what about objects and properties such that no possible proposition can say of the object that it has the property?

Regarding the first worry, it is not obvious that there is a circularity. Recall that we are not trying to analyze all modal notions in terms of other notions (indeed, the very idea of doing that may, for all that is said in this book, be chimerical) – inherent counterfactual invariance, for instance, is characterized in terms of all counterfactual scenarios a system can produce. Furthermore, the use of 'possible' here doesn't on the face of it seem to be the sort of de re modal attribution we are concerned to analyze. It's not about properties or relations possibly holding of actual things, but about possible things (in this case propositions), things which might exist, and that is very different. Secondly, the modal space in question may best be regarded as broader and more inclusive in certain respects than subjunctive modal space.

Furthermore, even if there is a circularity here (which may be quite indirect and subtle – i.e. may be present even if the 'possible' here is not itself to be regarded as directly invoking subjunctive modality), perhaps it's not a vicious circularity – for instance, we could say that we have still reduced the mysteries of necessary property possession (de re modality) to the mysteries of logical space.

Regarding the second worry, about the possibility of things and states of affairs which no possible proposition can refer to or represent: perhaps this can be overcome by taking 'possible' in a very wide sense.

Accordingly, I think this analysis may not be without value, but these worries create difficulty enough that a somewhat different approach seems desirable.

I think something like the following: intuitively, part of what the truth of a proposition of the form 'a is necessarily F' reflects is an internal connection between a proposition's ascribing F'ness to a and its modal status. One strategy we might try for capturing this is two-pronged: semantically ascend and invoke a priority. As a first pass:

a is necessarily F iff 'All propositions ascribing F'ness to a are necessary' is a priori.

Or equivalently:

a is necessarily F iff 'If a proposition ascribes F'ness to a, it is necessary' is a priori.

But this cannot be quite right, for necessity implies truth, and some necessary propositions are a posteriori. If 'a is F', for example, is just such a necessary a posteriori proposition, then it can't be a priori that if a proposition ascribes F'ness to a, it is necessary. Just like with our main analysis of necessity, i.e. as a category of propositions, we have to separate truthmaking from necessity-making.

This suggests employing, as we did in the main analysis of necessity, the notion of inherent counterfactual invariance:

a is necessarily F iff (a is F and 'All propositions ascribing F'ness to a are inherently counterfactually invariant' is a priori).

This is a definite improvement, but now out analysis falls victim to the same type problem which motivated our holding that necessity is closed under implication. Recall that we can't say:

A proposition is necessary iff it is inherently counterfactually invariant and true.

Since a disjunction of a necessary a posteriori proposition and a contingent proposition, where the necessary disjunct makes it true, is not inherently counterfactually invariant (since if it is held true on the basis of the second disjunct only, it will be allowed to vary across counterfactual scenario descriptions), but this disjunction will be necessary in the case that its necessary disjunct makes it true, so that the above analysis undergenerates: it says that, e.g., 'All cats are animals or I had lunch today' is not necessary, when it is. And recall that this problem is avoided by the account advocated:

A proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant and true.

We get a similar problem with the above analysis of de re modal attribution, but involving disjunctive properties rather than truth-functional, propositional-level disjunction. Consider for example:

'Hesperus is either identical to Phosphorus or a common object of philosophical examples'

Or, to remove any possibility of a truth-functional construal:

'Hesperus has the property of either being identical to Phosphorus or being a common object of philosophical examples'.

(Instead of 'being identical to' I will just say 'being'. I will also abbreviate 'being a common object of philosophical examples' as 'being a comex'.)

Now, according to the rough, dimly seen intuitive meaning of de re modal attributions which we are trying to analyse, it would seem we should say, since Hesperus is Phosphorus and in view of Kripkean considerations:

'Hesperus necessarily has the property of either being Phosphorus or being a comex'.

But this doesn't come out true on the analysis we are now considering. Plugging it in, we get:

Hesperus necessarily has the property of either being Phosphorus or being a comex iff:

- Hesperus has the property of either being Phosphorus of being a comex, and

- 'All propositions ascribing being either Phosphorus or being a comex [or, more strictly uniformly, having the property of being either etc.] to Hesperus are inherently counterfactually invariant' is a priori.

And the second clause fails to be true – far from being true a priori, the proposition mentioned is not true at all, since it is possible to hold it true while disbelieving that Hesperus is Phosphorus but believing that Hesperus is a comex, in which case it would be allowed to vary across counterfactual scenario descriptions (since things could have been such that quite other objects were comexes). Indeed, the mentioned proposition is false a priori.

But if we close under implication, as in our main analysis of necessity:

- 'For all propositions ascribing either being Phosphorus or being a comex to Hesperus, there is some inherently counterfactually invariant proposition which implies that proposition' is a priori.

we get something true, as required. We are making progress, but while both clauses come out true in this case, the analysis will still not give intuitively right results. Now it will overgenerate in some cases. Consider, for example:

Hesperus necessarily has the property of either being Saturn or being a comex.

This is intuitively false, since Hesperus is, intuitively, necessarily not Saturn, and only contingently a comex.

But the following both hold:

- Hesperus has the property of either being Saturn or being a comex, and

- 'For all propositions ascribing the property etc., there is some inherently counterfactually invariant proposition which implies that proposition' is a priori.

The second clause comes out true, because 'Hesperus is Saturn', while false, is inherently counterfactually invariant and does imply 'Hesperus has the property of either being Saturn or a comex'. And presumably, for any other proposition which might also ascribe the property in question to Hesperus, there would be some proposition identifying it with Saturn which implies it.

This would be solved by somehow requiring the (possibly hypothetical) implying propositions to be true as well as ICI, without jeapoardizing a priority. But it is not clear to me how this could be done.

For if we just tack on 'and true' to 'some inherently counterfactually invariant' above, yielding this as a second clause:

- 'For all propositions ascribing the property etc., there is some inherently counterfactually invariant and true proposition which implies that proposition' is a priori.

We are back to our problem of the second clause failing to be true as required for the case of Hesperus necessarily either being Phosphorus or a comex: its not a priori that the implying proposition, 'Hesperus is Phosphorus', is true, even though it is true.

We want our second clause, in general, to say something like: for all propositions P ascribing F'ness to a, there is some true proposition Q such that it is a priori that Q implies P.

But if we say that we have forgone the semantic ascent part of our two-pronged strategy, taking us back to our problems of non-existent and impossible propositions (or things for which there are no possible propositions of the relevant kind).

I find it surprising that it is apparently impossible to solve all these problems at once. I am far from sure that I haven't overlooked a possibility (i.e. an analysis quite close to the last few above, involving the strategy of semantic ascent together with the invocation of a priority, or a similar strategy, but which doesn't face such blatant material adequacy problems).

Be that as it may, there is still a further issue with any account along these lines. And it happens that, by considering this further issue which would still arise and describing that issue in a natural way, a quite different strategy comes into view.

Would Semantically Ascending Achieve Anything, or Just Mask Something?

It may seem that our move from talking about, say, 'all possible propositions' (with all its attendant difficulties) to talking about whether a priority is possessed by a proposition which says that all propositions of a certain kind are a certain way (namely a priori) – even if it could surmount the difficulties found above – would be a silly move, merely complicating things and getting us nowhere.

It might seem that this is so, because the right hand side of the analysis involves mentioning a proposition about the object in question, and so we can only state it when dealing with an object which we can talk about. But note that this doesn't stop it from being the case that all instances of:

a is necessarily F iff <one of our last analyses' RHSs>

are true (although other things were seen to). What this does get us is a way of dealing with any 'a is necessarily F'-form proposition, as it comes a long. We cannot apply it to an object which we cannot speak about – or rather, 'applying it to an object which we cannot speak about' makes no sense here. But given that we have such a proposition, what the analyses were designed to do was avoid any problems pertaining to nonexistent (and perhaps in a sense impossible) propositions: if some of those ascribe (or would ascribe if they existed) F'ness to a and aren't (wouldn't be) necessary, we do not want to say that a is necessarily F.

This shows that the strategy was not totally idiotic. Better than that, the last sentence (especially the clauses in brackets) suggests another approach to the first problem: solve it by first solving the second problem along conditional lines, where the antecedent condition (which very arguably doesn't have to be possible) covers all the cases which might have caused the first problem. (This should become clearer along with the proposal.)

So, we will go back to our original simple schema, and propose a conditional approach to our second problem – the problem of generalizing it. The simple schema was:

a is F iff 'a is F' is necessary.

Now as we saw, if we go along with the first problem, not all instances of this will be true. Let us ignore this for the moment, and consider how we might generalize it along conditional lines. We might say the underlying point of this (faulty) schema is something like:

An object x possesses a property y necessarily iff: if you were to say of x that it possesses the property y, you would say something necessary.

Now, if we interpret this conditional on the right hand side in one way, we get the first problem again, just as we did with the simple, faulty schema. (And that is fitting, for a generalization of the schema.) But if we interpret it in another way (in broadly Lewisian terms, by widening the class of relevant A-worlds), it is no longer a generalization of the schema, and is no longer vulnerable to the first (potential) problem.

I will briefly explain this here, but leave discussion of certain further difficulties of interpretation to the discussion of quantification into modal contexts in the next post, where the approach taken to quantification is very much along the lines of this approach to de re modal attributions. I will first state two basic assumptions about counterfactual conditionals. (Not that they're absolutely required – see below.)

Two Basic Assumptions About Counterfactual Conditionals

I will take as a basic assumption about how counterfactuals work that they can be understood as requiring a set of A-scenarios (scenarios at which the antecedent is true) to all be C-scenarios (scenarios at which the consequent is true). This is not to commit to any particular story (for example, David Lewis's) about how the relevant A-scenarios are determined. It also doesn't commit us to only dealing with possible scenarios, as for example Lewis does. It also doesn't commit us to any particular story about the nature of scenarios.

The second basic assumption is that (and here I agree with Lewis) the relevant set of A-scenarios will not always be the same. And it isn't just that different forms of words induce different relevant sets – the counterfactual conditional in the analysis above, for example, can be intended and interpreted different ways, making different A-scenarios relevant. And in the present philosophical context, we need to explicitly specify and discuss different interpretations (that is, I know of no other way of inducing contexts in which they get the readings I am interested in, and have no reason to think there should be a way).

These assumptions can in principle be jettisoned, by trading in the counterfactual conditional form in the proposed analysis above (and in our special treatment of quantification below) for explicit talk about what 'all relevant scenarios' are like, and then specifying which they are (but this time not as a way of fixing a reading of some conditional). But making the assumptions serves a heuristic purpose, since they are very plausible and the counterfactual conditional form is highly familiar to us.

Two Interpretations of the Words of the Account

Now, recall that the account I propose, in its simplest (but in a sense ambiguous) form, runs:

An object x possesses a property y necessarily iff: if you were to say of x that it possesses the property y, you would say something necessary.

Now, we must ask, about the counterfactual on the right hand side: which A-scenarios (scenarios in which you say of x that it is y) are required to be C-scenarios (scenarios in which you say something necessary) here? Which facts about the actual world are to be held fixed, and which allowed to vary? Or briefly, what is the relevant set of A-scenarios?

The thing to see is that, if we take a “closest worlds” approach, or at least if we take such an approach in a natural and simple way, we will run into the (potential) problem which would stem from ascriptionally identical propositions being able to differ in modal status. If, on the other hand, we take an approach on which a wider set of A-scenarios must be C-scenarios, we may avoid it. (The propriety of doing this without departing from the natural meaning of counterfactuals can I think be defended, but again this is not absolutely essential, since regarding it as a technically modified sort of counterfactual, or going straight for talk about a relevant set of A-scenarios and abandoning the counterfactual form, are both options.)

Suppose, for example, that your proposition 'a is F' is necessary, but that some other proposition, in some other system, which ascribes the same property to the same object, is contingent. In that case, we will (according to the kind of usage I want to go with here) not want to say that a is necessarily F.

Nevertheless, the relevant counterfactual comes out true, if the relevant A-scenarios are to be kept close to the actual world: on this approach, we can say that, indeed, if you were to say of a that it possesses the property F, you would say something necessary – because if you were to do that, you would do it using your proposition 'a is F'!

This is a perfectly legitimate interpretation of that counterfactual, but it is not the one we want. We want to hold less things fixed, and allow more things to vary (which sounds like it amounts to the same thing, but it may not, since we may have to explicitly widen the overall space of scenarios in question, i.e. explicitly allowing impossible scenarios). In this way, for any (actual, possible, or maybe even impossible) proposition which might make trouble for a being necessarily F, by ascribing F to a and not being necessary, will be covered – it will be what you said in some relevant A-scenario – so that the conditional will be falsified as required.

We will return to the question of how to get a better grip on what our relevant sets of A-scenarios for instances of our proposed analysis must be like in the next post in this series, once we have our special interpretation of quantification on the table, since that will raise a similar question.

For now, our account may be regarded as partially but not wholly specified.

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

This is the second post in a series on de re modality and quantification into modal contexts. The first is here.

Immediately after the passage quoted at the beginning of the last post where Kripke introduces the problem of de re modality, he goes on to argue that de re subjunctive modal ascriptions, and the notion of necessary and contingent properties, have intuitive content. I will quote this influential passage in full, and make a criticism of it. I will then suggest a weaker argument from analogy which could be given in its stead, and finally indicate my own view on the matter.

Here is the passage:

It is even suggested in the literature, that though a notion of necessity may have some sort of intuition behind it (we do think some things could have been otherwise; other things we don't think could have been otherwise), this notion [of a distinction between necessary and contingent properties] is just a doctrine made up by some bad philosopher, who (I guess) didn't realize that there are several ways of referring to the same thing. I don't know if some philosophers have not realized this; but at any rate it is very far from being true that this idea [that a property can meaningfully be held to be essential or accidental to an object independently of its description] is a notion which has no intuitive content, which means nothing to the ordinary man. Suppose that someone said, pointing to Nixon, 'That's the guy who might have lost'. Someone else says 'Oh no, if you describe him as "Nixon", then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost'. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. The first man would say, and with great conviction 'Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaign been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds. On the other hand, the term "Nixon" is just a name of this man.' [Presumably the quote from the imagined "first" man should have ended one sentence ago, but this is how it is in the text. -TH] When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. If someone thinks that the notion of a necessary or contingent property (forget whether there are any nontrivial necessary properties [and consider] just the meaningfulness of the notion) is a philosopher's notion with no intuitive content, he is wrong.

I do not want to be dogmatic about this, but I suspect that there may be a bit of a bait-and-switch going on here. Certainly, it seems everyday and intuitive for someone to point at Nixon and say 'That's the guy who might have lost'. But then what this 'first man' says in response to the 'unintuitive man' (the philosopher), is beginning to sound pretty philosophical itself, albeit sounder. It is true that what he says, especially if you're trained in philosophy, seems intuitively compelling. But I think it's quite arguably out of character for the first man.

One way of making good on this suspicion is to reflect that forms like 'could have' and 'might have' do not just signal talk about counterfactual scenarios and counterfactual possibility. They also commonly find a retrospective epistemic modal use. And it seems to me that this is the most natural way to interpret the everyday, non-philosophical remark of the 'first man' above, 'That's the guy who might have lost'. To say that Nixon might have lost, on this suggestion, means something like: at some former stage, things could have gone either way – it would have been unreasonable then to be convinced that he would win.

This seems to me like a fairly everyday thing to say. The meaning Kripke intends – where what is asserted means something like (ignoring the later Finean distinction between essential and necessary properties): it's not part of Nixon's essence that he won the election – seems less so.

We can also argue along Gricean lines that the first interpretation yields something which it might actually be good to say in the sort of conversation about contemporary events Kripke has in mind. But saying this thing about – speaking loosely – Nixon's essence seems pragmatically odd; if you know that, then presumably you know something stronger from which it follows (such as that winning some election can't be an essential property of anyone), rather than making it sound as if there's something special about Nixon here. (Consider an obscure bystander around Nixon's age: it seems, from an unabashedly philosophical point of view now, implausible that it is part of this bystander's essence that he didn't go into politics, get to run for Presidential office in the election in question, and lose. So it seems you could say of that guy too that he might have lost the election, in the sense in which Kripke has in mind.)

So, I find Kripke's story about the first man and the unintuitive, philosophical man unconvincing: if the first man were really not a philosopher, I'm inclined to think that his intuitive-sounding utterance of 'That's the guy who might have lost' is far more plausibly interpreted along epistemic lines. This is somewhat ironic, given Kripke's seminal insistence on carefully distinguishing epistemic modality and a priority on the one hand from subjunctive modality on the other.

We can get a better idea of how it might have happened by recalling the grammatical devices Kripke uses to isolate subjunctive modality: what could be the case for all we know a priori is to be distinguished from what could have been the case (given various things we know, and not always a priori). This may lead to an overconfidence in the subjunctive mood (or whatever you want to call it) as a signal of subjunctive modality proper, a signal of the thing Kripke isolated.

Still, this criticism doesn't imply that there is nothing in what Kripke says in this influential passage. Two things can be gleaned from the passage which do militate in favour of his main conclusion, which is that the notion of necessary and contingent properties makes sense.

One is a kind of argument from analogy: even when you interpret the first man's initial, everyday-sounding utterance along more appropriate, epistemic lines, it is clear that what is under discussion is not a statement: that is, de re epistemic modality makes sense. (For a recent study of that topic cf. Seth Yalcin's work.) And so, putting this consideration together with Kripke's compelling isolation of a concept of necessity applying to propositions which is distinct (intensionally and extensionally) from those of a priority and analyticity, we might naturally expect de re modal constructions where the modality is of this broad sort, having to do with alternative ways the world could have been in some non-epistemic sense, to be possible too.

Another is a direct philosophical appeal to our intelligence: forget guys on the street, forget questions about what they may or may not say without thereby becoming philosophers, and just think about it. What the first man is made to say in response to the unintuitive man, even though it just sounds like Kripke doing philosophy, seems awfully compelling. To quote it again: 'the actual winner, had the course of the campaign been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds'.

The situation, as I see it, is something like this: Kripke has clarified and isolated notions of necessity, contingency etc., which in the first instance apply to propositions and perhaps states of affairs. Now, by analogy with other expressions in our language, we are led to consider forms like 'a is necessarily F' and 'There is an x which is necessarily F' (or 'There is an x such that it is necessary that x is F'), where we have a vague idea that the terms 'necessarily' and 'necessary' here are, in some way, to express this same notion, which we know in the first instance in application to specific propositions. Consider the syntax of quantified modal logic, where modal operators are combined with first-order logic, in advance of any definite understanding of what these formulas are to mean.

Philosophers often behave like little children who scribble some marks on a piece of paper at random and then ask the grown-up "What's that?" — It happened like this: the grown-up had drawn pictures for the child several times and said "this is a man," "this is a house," etc. And then the child makes some marks too and asks: what's this then? C&V 17e

Our problem is, in a way, similar to that of making a game which is like an existing game, but different in some respects – but where the required similarities and differences are not completely spelt out (and how could they be, without thereby completing the task already?). For example, chess for three players, or with no queens.

In the present case, the task draws us in, since we feel we can already make some dim sense of these constructions. The question of whether this can be spelt out clearly, and the spelling out of it should this be possible, is of logico-philosophical interest. Furthermore, the issue is connected in many people's minds with difficult philosophical topics – with Aristotelian essentialism, with metaphysics, and with confused issues to do with whether modality is 'located' or 'grounded' in language and thought, or in other things.

Accordingly, in the next post in this series I will take up the challenge of de re modality, trying to adapt my account of necessity as an attribute of propositions so that it can be applied to de re modality. My main assumption in taking up this challenge is: there must be a connection here, and a tight one (e.g. not something you would have to describe using words like 'sometimes' or 'usually'), and we now have to make this clear. This will also take heat off the idea that de re modality makes no sense, but perhaps in a way which might look strange from the point of view of certain ways of thinking about analysis: the right hand sides of my analyses will in many ways be less simple, more problematic and more difficult than the left hand sides, the things to be analysed. But the problems are not the same ones as affect the left hand sides, and that is important. Roughly, I want to show that de re modal talk is not left hanging by itself, when we have a notion of necessity which applies to propositions. It may in a sense be more intelligible left as it is than when analysed along the lines I propose. But we must distinguish between the first-order intelligibility of a linguistic form on the one hand, and our philosophical conception of how that form works and what it does on the other. Connecting de re modal talk to de dicto can, I think, help a lot with the latter.

(Contrast, for example, Kit Fine's approach of taking essence as something basic – I get the sense of a wall having been erected to keep out trouble, but which also leaves us hapless and isolated. It is similar with his metametaphysical ideas: we must distinguish how things really or metaphysically are from how they are simpliciter, or something like that – and if you don't understand that, too bad: we're up against a wall. The difference, I think, is that in the first case the talk (essence talk) does make some sense, but has been walled off from things which may shed light on it in a way that can make this hard to believe, and hard to grasp, whereas in the second case, you have at most a degenerate, affect-charged sense, and the walls are merely there in a vain attempt to stop this from becoming glaringly apparent.)

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

An Interpretation of Quantified Modal Logic Formulae

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.

Toward an Understanding of De Dicto Subjunctive Necessity (draft paper)

Here. UPDATE March 2013: This document has been completely superseded by An Account of Subjunctive Necessity.

UPDATE March 2014: This latter document will in turn be superseded soon by a forthcoming blog post which will fit together with other posts.

Essence, Belief and Epistemic Modality (Part 2 of Sketch)

This is part 2 of a Sketch of a Way of Thinking about Modality. In this part we shall consider:

- Essences and the de re/de dicto distinction,
- The indefiniteness of necessity,
- Intentional contexts ("propositional attitudes"), and
- Epistemic modality.

The first topic is really the main one. What I say about the remaining topics will be very scant - a rough indication of how these issues are to be approached according to the way of thinking being sketched out here, rather than an attempt to really deal with them. (I hope to really deal with them in my book.) They fit quite naturally here, since intentional contexts come into the more substantial discussion of the first topic. If nothing else, the brief discussion here should prevent readers from thinking that I have given no consideration to such issues, or that my account of modality is straightforwardly unable to deal with them.

Three Interpretations of Modal Claims about Individuals

As a preliminary, it should be noted that epistemic modal claims are not counted in this taxonomy. Consider, to begin with, sentences of the form 'a is necessarily F'. I distinguish the following three interpretations of such statements:

(1) The contextual interpretation. The locus classicus for this interpretation is Lewis in On the Plurality of Worlds, who expresses it better than I can:

I suggest that those philosophers who preach that origins are essential are absolutely right - in the context of their own preaching. They make themselves right: their preaching constitutes a context in which de re modality is governed by a way of representing (as I think, by a counterpart relation) that requires match of origins. But if I ask how things would be if Saul Kripke had come from no sperm and egg but had been brought by a stork, that makes equally good sense. I create a context that makes my question make sense, and to do so it has to be a context that makes origins not be essential.' (p. 252)

There is one ruffle here: Lewis (who is notorious for playing fast and loose with ordinary modal language) talks of 'how things would be if Saul Kripke had...', rather than how things would have been. This might suggest a kind of epistemic reading, concerning what it would be like if it turned out that Saul Kripke actually had such-and-such an origin. But the range of possibilities in this sense - the things which could turn out to be true of an individual, for all we know (or all we know a priori) - is something quite different from what we are discussing here. In two-dimensional semantics, this corresponds roughly to the difference between A- and C-intensions.

(2) The "unrestricted" interpretation. In contrast to the above, we are now beginning to enter the realm of what could more legitimately be called 'essence'¹, and are looking at proper metaphysical (or subjunctive) modality. On this interpretation, something like the following holds: 'a is necessarily F' is true iff 'a is F' is satisfied by all configurations of the host system of these propositions, and the concepts involved are adequate to their objects with respect to 'a is F'. (This form of account is introduced more generally in part 1.)

Thus, in this case, we might say that the necessity, as opposed to contingent truth, of 'a is F' stems from the nature of the individual concept of a, rather than any contextual restrictions placed on our representations. Why, then, are there scare-quotes around 'unrestricted'? This is because the present way of looking at things may over-dramatize the difference between the contextual restrictions of Lewis's account, and the constitution of concepts in the relevant fine-grained sense. We might think of the nature of these concepts as being at least partly determined by more-or-less invariant restrictions of some more general apparatus. This more general apparatus can be used to understand epistemic modality (and epistemic space).

On this interpretation, to say that a is necessarily F is to say something like: according to the way I think of a - and this way is adequate - it could not have failed to be F. (This isn't meant to be a proper analysis.) But we will probably want to recognize the possibility of slightly different concepts in other systems which have a as their object, and are adequate. Thus while we might think of John in such a way that we may say, intending the present "unrestricted" interpretation, that he is necessarily F, we might recognize that other people might legitimately think of John in such a way that they may say that he is contingently F. (This could be called 'adequacy pluralism about concepts'.)

(3) The generalized "unrestricted" interpretation. Clearly, we will want an interpretation of modal claims about individuals which does not tie their truth to one particular conceptualization (namely, that embodied in the host system of the modal claim). This interpretation gives us that. On this interpretation, something like the following holds: 'a is necessarily F' is true iff all configurations of all systems containing an adequate concept of a represent a as being F. (Another, less natural interpretation would be to substitute 'at least one system' for 'all systems'. This interpretation would be natural for 'a is possibly F'.)

A Simplification

I have simplified the above by concentrating on subject terms and ignoring different construals of the role of the predicate. One might distinguish interpretations analogous to (2) and (3) above, i.e. an evaluation involving a particular F-concept in a system, versus one involving all systems with some concept of the property F. An analogous simplification will be made below in the discussion of ascriptions of intentional content. 

The Indefiniteness of Necessity

The account of necessity given here, based on the notion of all configurations of a conceptual system, may give the impression that I think a sharp boundary can be drawn between necessary and contingent truths. It is important to realize that this is not the case. (I probably should have emphasized this already in part 1.)

One way of responding to this would be to try to modify our picture of modality - instead of picturing a conceptual system as being like a mechanical apparatus which can be put into a definite set of configurations, one might imagine a device with an indefinite set of configurations; one might, for example, imagine growing resistance as one manipulates the apparatus into further out configurations (i.e. further from what we think is actually the case).

This sort of response has its place, but we needn't respond like that. We can also hold on to our simpler, more definite picture, but with due regard to the indefiniteness of its application.

Either way, it is important to note that there are clear cases. Some propositions are clearly necessary, and some are clearly contingent, and the distinction between them is of fundamental importance.

The following analogies from Wittgenstein are very helpful in connection with this theme:

The use of the words 'proposition', 'language', etc. has the haziness of the normal use of concept-words in our language. To think this makes them unusable, or ill-adapted to their purpose, would be like wanting to say 'the warmth this stove gives is no use, because you can't feel where it begins and where it ends'.

from Philosophical Grammar, Part 1. p. 120.

It is essential to logic to draw boundaries, but no such boundaries are drawn in the language we speak. But this doesn’t mean that logic represents language incorrectly, or that it represents an ideal language. Its task is to portray a colourful, blurred reality as a pen-and-ink drawing.

from The Big Typescript, p. 144.

The De Re/De Dicto Distinction(s)

This is widely acknowledged to be a confusing topic. The pair of terms 'de re' and 'de dicto' appear to get employed in philosophy to mark several important distinctions (or sorts of distinction). Complete clarification of this will have to wait for another time, but for now I want to characterize two basic sorts of distinction for which these terms can be used:

(1) De re: Generalization (universal or existential) over dicta involving a particular object vs. De dicto: specification of a particular dictum. (Dicta here are contents, propositions - something like that.) The distinction above between the "unrestricted" and generalized "unrestricted" interpretations of modal claims about individuals is an instance of this. It echoes, at least in part, Quine's distinction between believes-notional and believes relational.

In intentional contexts (for example, belief-reports), the distinction appears in the following way. The name 'Hesperus' in a belief report like:

(A) Ralph believes that Hesperus is F.

can be read as doing two things at once. (1) specifying the object of Ralph's belief, and (2) specifying the concept (or mode of presentation) via which he has it. On such a reading, (1) could be expanded to:

(B) Ralph believes, of Hesperus, via his Hesperus-concept, that it is F.

(A similar thing could be done for the 'F'.) Some belief reports, on the other hand - purely de re belief-reports - may be read as only specifying the object. (A) read this way could be expanded to:

(C) Ralph believes, of Hesperus, via some concept(s), that it is F.

(Cases such as 'John believes that Santa Claus exists' suggest that there are also readings where the name just functions to indicate an individual concept or intension involved in the propositional attitude, i.e. does not specify any real extension.)

Substitution of co-referring terms salva veritate (i.e. without change in truth-value) will fail in modal and intentional contexts which are de dicto in this sense.

(2) De re: Involvement of a dictum featuring a rigid (or rigidified) designator vs. De dicto: Involvement of a dictum featuring a non-rigid, unrigidified designator. This distinction most clearly makes its appearance with definite descriptions.

To illustrate: as a result of these two distinctions together, a sentence like 'The winner could have been shot' - once we rule out salient epistemic readings and Lewis-style contextually restricted readings - still has three readings left:

De dicto in both senses (1) and (2): true iff the non-rigid dictum 'The winner was shot' is satisfied by at least one configuration of the host system. (In this configuration (so to speak), the winner might be someone else.)

De dicto in sense (1) and de re in sense (2): using 'The winner' to indicate an individual concept - the concept of the actual winner, that very person - i.e. as a rigidified description, and true iff that dictum is satisfied by at least one configuration of its host system.

De re in sense (1) and therefore neither de re nor de dicto in sense (2): using 'The winner' purely to indicate a particular object, and then making a claim about all dicta which are rigidly about that object and which fulfil certain conditions (in this case: saying that the object was shot, or saying that the object was shot using some particular concept of being shot). It is only on this sort of reading, I submit, that substitution of co-referring terms salva veritate will be valid.

Clarifying and separating these distinctions helps to clarify Quine's skepticism about de re modality, and Kripke's famous arguments against Quine's attitude, as well as making it clearer why this debate is so confusing. Below is a lengthy quote of an important passage of Naming and Necessity. The above discussion can help us disambiguate the ensuing talk of particulars having modal properties independently of how they are described: this may be indicating de re-ness of the second kind (involvement of an individual concept rather than a non-rigid, unrigidified designator), or the first (generalizing over concepts of a particular object, rather than fixing on a particular concept).

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. What is Quine's famous example? If we consider the number 9, does it have the property of necessary oddness? Has that number got to be odd in all possible worlds? Certainly it's true in all possible worlds, let's say, it couldn't have been otherwise, that nine is odd. Of course, 9 could also be equally well picked out as the number of planets. It is not necessary, not true in all possible worlds, that the number of planets is odd. For example if there had been eight planets, the number of planets would not have been odd. And so it's thought: Was it necessary or contingent that Nixon won the election? (It might seem contingent, unless one has some view of some inexorable processes....) But this is a contingent property of Nixon only relative to our referring to him as 'Nixon' (assuming 'Nixon' doesn't mean 'the man who won the election at such and such a time'). But if we designate Nixon as 'the man who won the election in 1968', then it will be a necessary truth, of course, that the man who won the election in 1968, won the election in 1968. Similarly, whether an object has the same property in all possible worlds depends not just on the object itself, but on how it is described. So it's argued.

It is even suggested in the literature, that though a notion of necessity may have some sort of intuition behind it (we do think some things could have been otherwise; other things we don't think could have been otherwise), this notion [of a distinction between necessary and contingent properties] is just a doctrine made up by some bad philosopher, who (I guess) didn't realize that there are several ways of referring to the same thing. I don't know if some philosophers have not realized this; but at any rate it is very far from being true that this idea [that a property can meaningfully be held to be essential or accidental to an object independently of its description] is a notion which has no intuitive content, which means nothing to the ordinary man. Suppose that someone said, pointing to Nixon, 'That's the guy who might have lost'. Someone else says 'Oh no, if you describe him as "Nixon", then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost'. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. The first man would say, and with great conviction 'Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaigner been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds. On the other hand, the term "Nixon" is just a name of this man. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. (Kripke, Naming and Necessity, first lecture.)

Epistemic Modality and Ascriptions of Intentional Content

For the purposes of understanding metaphysical or subjunctive modality, I have been talking about conceptual systems in a fine-grained sense such that changing one's mind about an empirical identity statement involving individual concepts, for example, constitutes a change in the system itself. Since we believe that Hesperus is Phosphorus, there is no configuration of our fine-grained system which satisfies 'Hesperus is not Phosphorus'. And yet we can truly say things like 'It could turn out that Hesperus is not Phosphorus after all', and even (despite worries of Kripke's) 'It could have turned out that Hesperus was not Phosphorus'.

This is connected with the idea of 'two spaces of possible worlds' in other approaches. (Cf. Chalmers' 'The Nature of Epistemic Space'.) When we say that it could be that Hesperus isn't Phosphorus, we are not considering a configuration of our existing system in the sense we have been talking about, but are rather considering a change in our system. But in another sense, of course, making this change would constitute a reconfiguration of some "wider" system - the system relevant to epistemic modality. Making various abstractions and idealizations, we can imagine a space of possible ways things could be for all we know a priori - epistemic space. Moving from that to the space of ways things could have been involves getting rid of epistemic possibilities which are not metaphysically possible (the lesson of the necessary a posteriori), but also adding epistemic impossibilities which are metaphysically possible (the lesson of the contingent a priori), i.e. things which couldn't be the case, but could have been, such as this room being bigger than it is. (This latter thing will occupy us in part 3.)

So, we can configure our systems in the wide sense to represent ways things might be, and the way we think things are. But, speaking roughly, such a configuration of the wide system yields a system in the fine-grained sense, of ways things could have been. Sometimes, when we change our beliefs, this can be understood as simply moving to another configuration in the fine-grained system (and thus not directly changing any of our metaphysical modal judgements), whereas other times this must be regarded as involving change of the fine-grained system itself (e.g. going from believing that Hesperus is not Phosphorus to believing that it is).

(Note that I am not saying that the ways things really could be all have corresponding configurations in some system of ours, nor that the ways things really could have been all have corresponding configurations in our fine-grained system - not only may we be wrong, there will be possibilities we haven't dreamt of. Clearly much more needs saying here about these notions of 'the ways'. Some speculations can be found here.)

The Metaphysical Possibility of Metaphysically Impossible Thoughts

Hesperus could be distinct from Phosphorus after all, if we're radically deceived, but given that it is Phosphorus, it could not have been distinct from Phosphorus. So 'Hesperus is not Phosphorus' is not satisfied by any configurations of our fine-grained system. And yet 'John believes that Hesperus is not Phosphorus' is metaphysically possible, is satisfied by configurations of our fine-grained system.

This may be quite puzzling given a certain way of visualizing the fine-grained system and its relation to the wider epistemic system which gives rise to it. For a while it seemed like a real problem to me, and I called it 'the containment problem'. The bothersome thing is the way in which epistemic modal space seems to be contained in metaphysical modal space via our machinery for ascribing intentional states and propositional attitudes - our machinery for representing the thoughts and representations of others - despite epistemic modal space outrunning the metaphysical in the well-known Kripkean way.

It is very tempting to try to "fix" this "problem" by going metalinguistic. I.e. saying something like: 'When we say that John believes that Hesperus is not Phosphorus, we aren't really simulating, constructing, or dealing directly with a thought that Hesperus is not Phosphorus. Rather, we are simply employing our concepts of Hesperus, the Hesperus-concept and the Phosphorus-concept, and forming an idea of a proposition in another system which has the relevant properties.' That may be a good view of what we do sometimes (especially with very foreign thoughts), but it seems wrong - gratuitous, even - to suppose that this is always how we do it. After all, we naturally and frequently envisage epistemic possibilities which fall outside our current fine-grained system. We step outside it all the time. So, when we think something like 'John believes that Hesperus is not Phosphorus', we can think of this as employing - in tandem - our fine-grained system together with a configuration of our wider system which falls outside it, but which is "pointed to": to give ourselves the thing John believes, we step outside our fine-grained system and construct the thought directly, so to speak - and all of this in a sense just constitutes a configuration of our fine-grained system, but of a special kind.

Compare Russell's treatment in the Logical Atomism lectures of 'propositions with more than one verb', and his remark about Wittgenstein's 'discovery' that propositions like 'A believes that p' are 'a new beast for our zoo' (p. 226, Logic and Knowledge).

A Desultory Postscript about Water

Contrary to plan, I haven't included a proper section on 'Water is H20' and related examples (or apparent examples) of the necessary a posteriori. I don't have much to say about such examples for now, except that it is very difficult to avoid dogmatism when treating them; specifically, in the move from the fact that water is H20 - something we've all learned - to a particular interpretation and logical explication of 'Water is H20'.

One might regard this sentence as expressing a 'theoretical identity' as in Kripke. Scott Soames critically examines this way of going in detail in his book Beyond Rigidity. Alternatively, one might regard the 'is' here as being "the 'is' of constitution", and this in turn might be construed as a (non-symmetric) relation. Or one might simply interpret 'is H20' as a predicate. On the 'water' side, one may construe this as being tied to a concept of water in the Kripke-Putnam way (i.e. such that 'Water is H20' is necessary), or it may be construed functionally or phenomenologically, such that 'Water is H20' is contingent.

All these contents seem to exist, so to speak, and all seem like natural ways of interpreting 'Water is H20'. So we must be wary not to fall into holding views which might implicitly suggest otherwise; we can and should develop simplified, systematic, abstract views of logic and language, but we hinder and discredit this very development if we neglect the underlying variety of language use. Among other things, this may give the false appearance that the whole logico-philosophical enterprise depends on there not being this variety.

(Part 1, recently edited, is here.) 

(See this paper for a newer presentation of the basic ideas of part 1.)

1. For present purposes, I pass over Kit Fine's contention that not all necessary properties are essential in an intuitive sense (roughly because they are not all intrinsic to the thing in question). The classic example of a necessary property which is arguably not an essential property is Socrates' membership in his singleton set {Socrates}. There may be something important which distinguishes the essential properties from the merely necessary ones, but they will still be necessary properties, and hence will be amenable to my view.