Notes on Modality II - "Deserving the name", the grandeur of the idea of metaphysical modality, &c.

I want to explore a 'no clear best deserver' view of the - very inchoate - role that the distinction between (metaphysically) necessary vs. contingent truths is supposed to play.

The idea is that once you drill down in the borderlands, you see that there are different ways of going.

So no clear best deserver. But also: it's not clear that anything is a good enough deserver.

The 'no clear best deserver' hypothesis raises questions: why wouldn't everyone agree? Why would this be news?

One reason might be that there really is a best desever. Or that it seemed like there was a clear best but on further reflection there are competitors and it's not clear that any one has the edge. But I think there's more to say about why this might be news. There is something very natural about thinking that there is some single distinction here. There is a strong inclination to think that there some one major, fundamental distinction between the truths that could have been otherwise and the ones that couldn't. 

So if there is a sense in which this is not so - or if we want to be circumspect about it - we could try to tell a positive story about how this comes about.

Also, it is important to remind ourselves that the strong inclination I am speaking of may not be universal, or even normal. (Think of people who encounter this philosophical discourse, feel vaguely skeptical, maybe kind of interested but not particularly compelled, don't sign up for any view in particular, or flirt with some unusual view (an undergrad fellow student of mine defended the view that all truths are necessary in a course essay), and simply move on with their lives and don't ever really think about the matter, except as something some people are concerned with.)

But, at the same time: it's not just some specific problem in some particular subliterature. Versions of it, or closely related things, come up in philosophy at many times and places. And I have the feeling that it springs from a kind of root that also gives rise to certain philosophical thoughts and frames of mind that all sorts of people have.

So, how might it come about? Perhaps: Some kind of drive towards systematic understanding run rampant. Desire to see world as mechanism with discrete states. And the point isn't that that's naive, or probably not true after all, or something like that. But one issue here may be: why should there be one clear best way of seeing the world that way? 

It is possible to get into a frame of mind where it seems like there must in some sense be a single or primary set of facts about the possible states of the world, if there really is a world at all. It is like Wittgenstein's demand for substance, for eternal objects, in the Tractatus. It can seem like if the thing you're demanding weren't so, there would be no world at all, or nothing would be true.

There's something here I want to say in connection with this 'no clear best deserver' idea, along the lines of: how little is said when the idea of metaphysical modality is introduced! How could there be enough specific information there - in phrases like 'really could have been that way' - to narrow things right down to a particular, clear distinction!  It feels completely "lay", really quite free of theory (but of course you can theorise about 'really' or formulate it in terms of 'some fundamental sense' and then theorise about that).

But on the other hand, isn't that a bit fallacious? Can't specific, detailed things come out of arrangements of ordinary, quite general concepts? And don't, for example, specific seeds produce specific trees, despite being so small?

So this thought needs to be stated carefully. There's not some general rule here that's being appealed to. Still I think there's a point here, a way to see something  - a way to break the grip of something.

The words and associated ideas we're using here are quite flexible things, on reflection. 'Things', 'really', 'could'.

You might say there's a kind of naive level of "buying into" the idea of this one major distinction between contingent and necessary truths. Just not thinking about it too much. But then if you've thought about it and seen it threatened or scoffed at or considered uninteresting, but still want to pursue it - OK, now you're after something. Now you have a dream, I feel like saying.

I think, awkward as it is to talk about, there is really no getting away from the fact that there's something fantastic about the idea, something grand. '"How things really could have been" - what could be more interesting than that?!'

* * *

Consider Kripke's suggestive remark at the end of Naming and Necessity about leaving open the extent to which metaphysical modality will turn out to be closer to physical than suspected.

It's remarkable how little investigation or facing up there has been to the issue of how such a thing might be decided. (Williamson talks about 'detailed theoretical investigation' but I can't help but feeling that this is a kind of mirage, like how Russell and the early Wittgenstein palmed off the question of what the logical atoms will turn out to be.)

Decades later, we seem to just have different viewpoints - some rationalists who are far from thinking it coincides more with physical possibility than you might think, and others who are captured by the idea of empirical insight into hard limits (due to what seems to me a kind of misinterpretation of the necessary a posteriori, but working out where the stand offs there lie would be good).

The picture I have now is this: there's a certain inchoate role, inchoate requirement or job description for this idea of the ways things really could have been (metaphysically), and then it recedes into the background when we look at cases and theories. But this needs to be scrutinised more, and this will shed light on skepticism about the notion, and on different positive views.

I don't mind if you settle on a best deserver and are happy with it, but I will want to be clear that this is what is happening, and be wary of an alternative way of thinking about the matter as something which has been investigated and a view found correct. <-- Inadequate, but there is an important feeling here that I don't want any smoke and mirrors.

A large part of the worry is: that this process of coming to rest upon a choice of best deserver gets misrepresented as investigation into how things could have been. A failure to distinguish between getting to a concept and investigating what it applies to. But there are dangers with this hypothesis too.

'Philosophers framed the question of how things really could have been, and detailed philosophical research has led to a convergence on the view that this turns out to be a matter of ...'

In terms of what we want from the term, what gives it its life and feeling of importance - this is so easy to write off as a trifling, preliminary thing. Almost indecent to talk about. But it is very important. And it's amazing how far it reaches, so to speak. 

A New Account of the Conditions Under Which a Proposition is Necessary

The previous posts were quite raw and had me wrestling with new data. In this post, I try to be clearer and more accessible, and give a first outline of a new account of necessity that has emerged from my research on these topics. 

My old account of necessity was:

A proposition is necessarily true iff it is, or is implied by, a proposition which is both inherently counterfactually invariant (ICI) and true.

A proposition P is ICI iff  P's negation does not appear in any (genuine) counterfactual scenario description for which P is held true.

(I.e. if you hold P true, then you won't produce (genuine) CSDs in that capacity (of holding P to be true) according to which not-P.)

(You might wonder about what exactly a CSD is and what it takes for one to be genuine, but this will not be our focus here.)

This account nicely handles an example like 'Hesperus is Phosphorus or my hat is on the table'. This proposition isn't itself ICI - after all, you can hold it true by holding it true that my hat is on the table but Hesperus is not Phosphorus, and in that case you'd be prepared to produce CSDs in which it's false. But it is implied by a true ICI proposition, namely 'Hesperus is Phosphorus'.

The account also handles more complicated cases where there is no component ICI proposition (as there happens to be in the last example). It is enough that a true ICI proposition implies the necessary truth we are interested in.

But this account recently fell, due initially to an example from Jens Kipper (discussed in recent posts here). The example is 'Air is airy'. The point of this sentence is that it denotes something which isn't a natural kind - i.e. has no particular underlying nature - and predicates of it its superficial properties. Since, as it turns out, air isn't a natural kind, 'Air is airy' is necessarily true; there couldn't have been non-airy air, since, as it turns out, what is is to be air is just to be airy. If on the other hand air had turned out to have an underlying nature, like water does, we would regard 'Air is airy' as contingent, like we do 'Water is watery'; there could have been non-watery water, i.e. H20 in a situation where it isn't watery. 

The problem for my old account is that 'Air is airy' is necessarily true, but it is neither ICI nor is it implied by an ICI true proposition. 

(After the Kipper example, I have also come upon an example due to Strohminger and Yli-Vakkuri: 'Dylan is at least as tall as Zimmerman'. Since Dylan is Zimmerman, this is necessary. But it isn't ICI, since you could hold it true while holding that Dylan and Zimmerman are distinct. With this example, you could try to save my account by maintaining that - in a rich sense of 'implies' - this troublesome example is implied by 'Dylan is Zimmerman' (which is true and ICI), so my account gives the right answer after all, provided we have the rich sense of 'implies' on board. But I see little point in this, as this trick doesn't help with 'Air is airy'.)

What I think all this shows is that, in our analysis of necessity, we need, not the notion of implication, but more specialised relevant relationships between propositions. In particular, we need to consider when the truth of a proposition P would make a proposition Q necessary. Or, for a more penetrating analysis, when P would make Q counterfactually invariant.

Let's say that P is a positive counterfactual invariance decider for Q iff Q does not vary across genuine CSDs for which P is held true.

(A proposition P varies across a bunch of CSDs iff it is true according to some of them but not according to others.)

So, for example, 'Hesperus is Phosphorus' is its own positive CI decider; if you hold it true, then, in that capacity of holding it true, you won't produce any genuine CSDs according to which Hesperus is not Phosphorus. ('Hesperus is not Phosphorus' is also a positive CI decider for 'Hesperus is Phosphorus', although it happens to not be true.) But really, these are vacuous cases; since 'Hesperus is Phosphorus' and 'Hesperus is not Phosphorus' are inherently counterfactually invariant, any proposition you like counts (on the above definitions, which may not be optimal) as a positive CI decider for these.

(UPDATE 26/10/2017: This last claim is false. Some random proposition like 'Snow is white' actually doesn't count as a positive CI decider for 'Hesperus is Phosphorus', since you might hold it true but not hold 'Hesperus is Phosphorus' true. If CI deciderhood had been defined by referring to the genuine CSDs in which P (the potential decider) and Q (the potentially decided) are held true, rather than just P. )

The notion comes into its own with non-ICI propositions:

'Hesperus is Phosphorus' a positive CI decider for 'Hesperus is Phosphorus or my hat is on the table'; if you hold the former true, you won't let the latter vary across CSDs.

'Hesperus is not Phosphorus' is a negative CI decider for 'Hesperus is Phosphorus or my hat is on the table'; if you hold the former true, you will let the latter vary across CSDs (depending on whether my hat is on the table or not in the scenarios being described).

'Hesperus is Phosphorus' is a negative CI decider for 'Hesperus is not Phosphorus or my hat is on the table', and 'Hesperus is not Phosphorus' is a positive CI decider for 'Hesperus is not Phosphorus or my hat is on the table'.

Furthermore, this apparatus gives us good things to say about Kipper's counterexample to my old account:

'Air is not a natural kind' is a positive CI decider for 'Air is airy'; if you hold the former true, then the latter won't vary across CSDs.

(UPDATE 26/10/17: This last claim may be faulty, because you could perhaps hold 'Air is not a natural kind' true and also hold 'Air is not airy' true. This depends on how 'airy' is defined - is it part of its meaning that to be airy is to have the actual properties that air has, whatever those are? Then maybe you couldn't really coherently hold it false. But if it's defined in terms of a list of properties that we think air has, then you could get all skeptical the way Kripke does with cats and hold it true that air actually doesn't have these properties and it's some elaborate ruse which makes us think it does. This could be gotten around by narrowing our attention in the definition of positive CI deciderhood to genuine CSDs where, not just P (the potential decider) is held true, but also Q (the potentially decided). However, I don't think that this is required to save the analysis as formulated in this post, since we can just give up on 'Air is not a natural kind' itself being a CI decider (at least all by itself) of 'Air is airy' and instead appeal to 'All there is to being air is to be airy' or even just 'Air is airy and is not a natural kind'.)

(Likewise for the Strohminger/Yli-Vakkuri example: 'Dylan is Zimmerman' is a positive CI decider for 'Dylan is at least as tall as Zimmerman'.)

I think a good account of necessity can now be given as follows:

A proposition is necessary (i.e. necessarily true or necessarily false) iff it has a true positive CI decider.

Note: it seems plausible that CI deciderhood is an a priori tractable matter; whether some P is a CI decider for some Q, and if so whether it is a positive or a negative decider, seem to be the sort of thing we can work out a priori. What we might not be able to know a priori is the truth-values of P and Q.

I will keep working on the best way to present this sort of approach, but I think the essentials are now in place.

Caught in the Act of Confusing Subjunctive Necessity and Apriority: The Importance of the Sprigge Quote in Naming and Necessity

One of the big questions surrounding Kripke's innovations in Naming and Necessity is the extent to which, with his doctrines about necessity and the necessary a posteriori, Kripke corrected false views about necessity, as opposed to just emphasizing a neglected notion of necessity on which 'necessary a posteriori' is a non-empty category. Also unclear is the extent to which pre-Kripkean thinkers were confusing the Kripkean notion of subjunctive necessity with other notions, or just not giving that notion much attention. It's not clear, for instance, that Putnam in 'It Ain't Necessarily So' ever invoked subjunctive necessity.

This makes the following quote from Sprigge, which Kripke uses in N&N (p. 111), particularly interesting. It seems to provide a clear case of a philosopher confusing subjunctive necessity, on the one hand, with either indicative necessity or apriority on the other hand:

The anti-essentialist says that there would be no contradiction in a news bulletin asserting that it had been established that the Queen was not in fact the child of her supposed parents, but had been secretly adopted by them, and therefore the proposition that she is of Royal Blood is synthetic. In this way the anti-internalist parries the argument of the internalist by suggesting with regard to each proposed internal property of the particular in question, that we can quite well imagine that very same particular without the property in question. For a time he is winning. Yet there comes a time when his claims appear a trifle too far fetched. The internalist suggests that we cannot imagine that particular we call the Queen having the property of at no stage in her existence being human. If the anti-internalist admits this, admits that it is logically inconceivable that the Queen should have had the property of, say, always being a swan, then he admits that she has at least one internal property. If on the other hand he says that it is only a contingent fact that the Queen has ever been human, he says what it is hard to accept. Can we really consider it as conceivable that she should never have been human? (Sprigge (1962), p. 203.)

It seems pretty clear that here Sprigge takes the possibility of the bulletin - the possibility of finding out that Elizabeth II is not actually born of royal blood - as tantamount to it being the case that things could have gone such that she was not born of royal blood.

So, this quote makes it seem almost certain to me that someone - namely Sprigge - was actually confusing subjunctive necessity with either apriority or indicative necessity. Further questions are how widespread the confusion was around the time Sprigge wrote, and whether this was a relatively new thing at the time. Is it the case that, by the time Sprigge wrote the above but not for long before that, the notion of subjunctive or counterfactual necessity was "in the air", was salient, and so this sort of confusion is a relatively short term phenomenon occurring only in the lead-up to N&N (and shortly after, while people had yet to digest Kripke)? Or is the confusion something we can find much earlier evidence of?

References

Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.

Putnam, Hilary (1962). It ain't necessarily so. Journal of Philosophy 59 (22):658-671.

Sprigge, Timothy (1962). Internal and external properties. Mind 71 (282):197-212.

Does Kripke Really Have Obstinate Rigidity in Mind at All in Naming and Necessity?

Philosophers, in the wake of Naming and Necessity, have distinguished the main Kripkean notion of rigid designation, which applies to an expression when it designates the same object in all possible worlds (or counterfactual situations) in which that object exists, from a putative notion called 'obstinate rigidity', which applies to an expression when it designated the same object in every possible world whatever, including worlds where that object doesn't exist. (The term 'obstinate rigidity' was introduced by Nathan Salmon on page 34 of his 1981 book, Reference and Essence.)

I'm not even sure I can make sense of the notion of obstinate rigidity. My main purpose here is not to discredit it, however, but to do something more modest: I want to suggest that a line of interpretation of Kripke, which has him sometimes working with a notion of obstinate rigidity instead of his normal official notion of rigidity, is mistaken.

From the Stanford Encyclopedia of Philosophy article 'Rigid Designators':

In other places, Kripke seems to have in mind another account of rigidity: one according to which a rigid designator designates its object in every possible world, whether or not the designatum exists in that world. Hence, he says, “If you say, ‘suppose Hitler had never been born’ then ‘Hitler’ refers here, still rigidly, to something that would not exist in the counterfactual situation described” (Kripke 1980, p. 78).

The interpretative suggestion before the quote seems wrong to me. I find it more natural to think that Kripke is saying that 'Hitler' actually refers, rigidly, to something that would not exist in another counterfactual situation - not that it refers to that thing in that situation.

Here we have to be careful to distinguish:

What does expression X refer to in counterfactual situation Y? (Which in turn must be carefully disambiguated, in a familiar Kripkean way, so that it does not get interpreted as asking about how language would be used in counterfactual situation Y.)

from

What does expression X actually refer to when it appears in this description of counterfactual situation Y?

You can answer 'Nothing' to the first and 'Hitler' to the second.

(Things may get even subtler when you consider definite descriptions. Suppose John is the tallest man in the world, but Paul might have been. Then if we say 'Paul might have been the tallest man in the world', should we still say that the actual referent of 'the tallest man in the world' in that sentence is John? To this, one wants to object that John isn't really involved. (But does that matter, when the question was about what the actual referent is?) Perhaps someone could find principled grounds for denying 'The actual referent of "the tallest man in the world" in that sentence is John' while accepting the 'Nothing'/'Hitler' pair of answers above. Perhaps Donnellan's distinction between referential and attributive uses of definite descriptions, or something like that distinction, should come into play here. Still, this complication - and it really is enough to do your head in - shouldn't impinge on the plausibility of what was said above.)

Skepticism About Metaphysical Modality and Unclear Cases

Some philosophers are skeptical of the notion of metaphysical or subjunctive modality isolated by Kripke. They may think for instance that the notion of necessity de dicto is coherent but nothing falls under it, or they may think that isn't even a coherent or legitimate notion. This post is more about the latter.

One cause of such skepticism, I suspect, is that some of the canonical cases Kripke adduces in Naming and Necessity are not particularly clear cases. That is, they are borderline or disputable cases. In addition, the attitude Kripke seems to take to these cases may not be completely appropriate. With these cases, he sometimes gives the impression that the way to know how it is with them is to use intuition - and here the intuiting has a different character than in clear cases. It seems like a kind of hearkening or special receptivity is supposed to be needed. All this may seem, so to speak, occult. And if this doesn't put us off the notion altogether, it may yet mislead us about what sort of account we should look to give of it.

The sorts of cases I have in mind are those of the table - could it have been made of ice? (Kripke intuits that it couldn't.) And the Queen: could she have been born of different parents? (Kripke intuits that she couldn't.) 

(One thing about the Queen case which has troubled me for years is what I call the fish argument. This argument works by iterating the supposed necessity of origin; if the Queen is necessarily the child of her actual parents, and they are necessarily the children of their parents, then we seem to be forced to conclude that the Queen is necessarily the descendant of some fish which she is in fact descended from - call him Colin. That is, there is no possible world involving the Queen where Colin isn't also around. This seems dubious.)

To all this, my suggestion is that we shouldn't get hung up on such cases when it comes to the question of whether the notions of metaphysical or subjunctive modality are legitimate, and when it comes to understanding those notions. Just as, when trying to give someone a grasp of the notion of tallness, it is better to work with examples of people who are definitely tall, or definitely not tall. To start insisting on certain judgements about more borderline cases is not to the point, and may make the whole business seem dubious. I think that following my suggestion may help us both explain and legitimate the notions in question, and may help us account for them in the proper way.

What is Necessity De Dicto?

I recently posted an account of necessity de dicto. The purpose of this post is to pin down exactly what this topic is. The notion in question of course looms large in contemporary analytic philosophy, but it will serve us well and keep us grounded to furnish in as clear a way as possible a basic characterization of it. In a future post, I will turn to specifying the problem or task which my account is addressed to with respect to the topic. In another future post, I will state some of my assumptions and guiding ideas.

The key source for the notion of necessity de dicto is of course Kripke's Naming and Necessity. It was there that our topic was (to the best of my knowledge) first clearly isolated and characterized. Priority aside, Kripke's characterization is not easily improved upon and has been very influential. (Regarding the notion itself, not its characterization: it is a very interesting historical question to what extent this notion was present in earlier thinking. Or to what extent similar notions were, and how they may relate to the present notion. I will make no attempt here to answer this.)

Kripke's starting-point in characterizing the notion of necessity de dicto is to remark that, while many (at the time he was speaking) seem not to differentiate between a priority and necessity, he certainly will not use 'a priori' and 'necessary' in the same way (p. 34). He then, after emphasizing that the notion of a priority is an epistemological one and mentioning some issues which might arise with that notion, gives the following characterisation of necessity:

The second concept which is in question is that of necessity. Sometimes this is used in an epistemological way and might then just mean a priori. And of course, sometimes it is used in a physical way when people distinguish between physical and logical necessity. But what I am concerned with here is a notion which is not a notion of epistemology but of metaphysics in some (I hope) nonpejorative sense. We ask whether something might have been true, or might have been false. Well, if something is false, it's obviously not necessarily true. If it is true, might it have been otherwise? Is it possible that, in this respect, the world should have been different from the way it is? If the answer is 'no', then this fact about the world is a necessary one. If the answer is 'yes', then this fact about the world is a contingent one. (pp. 35 – 36.)

This should go a long way to giving us an acceptable grasp of the notion of necessity de dicto. Kripke also says some things about the extension of the notion which may be of further help to this end. Before proceeding to that, however, I want to tighten up Kripke's characterization in a couple of ways, as well as emphasizing and de-emphasizing certain parts of it.

For one thing, note that Kripke moves freely here between talking of 'facts about the world' as well as things which can be called true or false, as the bearers of necessity. Later, he speaks also of 'states of affairs' and 'statements'. This is fine, but I want to make it clear that the topic I am addressing in my account is the notion of necessity as it applies to things which can be called true or false: statements – or as I say, propositions. This is what I mean by 'de dicto' in 'necessity de dicto'. To be still more precise about what propositions are – for a start, whether they are or involve sentences themselves, or just their meanings – is not necessary, but see this post for an approach I favour.

(At this point I should emphasize that that is all I mean by 'de dicto' in 'necessity de dicto'. The term 'de dicto', and the contrasting term 'de re', are used in various ways in philosophy. It it especially important to realize that I count all attributions of necessity to propositions as attributions of necessity de dicto, even when those propositions are “singular propositions” about individuals – i.e., propositions attributions of necessity to which David Lewis would deploy counterpart theory to understand.)

Something I want to emphasize in Kripke's characterization is the way it cashes out necessity in terms of counterfactual scenarios – to use the language of some two-dimensional semanticists, scenarios considered as counterfactual, rather than scenarios considered as actual. This could be emphasized by calling our topic 'counterfactual necessity de dicto' or 'subjunctive necessity dicto', but I avoid this for the sake of brevity.

(You may think that this is the same as the point that necessity is not to be understood epistemologically, but I'm not so sure. For one thing, I suspect there are notions of 'could actually be the case' and 'must actually be the case' which, even if 'a priori possible' and 'a priori true' may be good expressions for them, can be cashed out non-epistemologically. (Cf. this post.) For another thing, 'Could have been' talk can also be given an epistemological reading, along the lines of 'Was epistemically possible'. In any case, emphasizing that with the notion of necessity de dicto we are dealing with scenarios considered as counterfactual, can only help to avoid misunderstanding here.)

Something I want de-emphasize in Kripke's characterization, on the other hand, is the way he classifies the notion of necessity he wants to talk about as a notion belonging to metaphysics. I do not think this is essential to grasping the notion in question: that can be done without any recourse to a notion of metaphysics. Kripke's use of a category of metaphysics here may be slightly helpful in emphasizing that necessity de dicto is not an epistemological notion, but that point can be emphasized without a notion of metaphysics. Since we can easily get by here without invoking a notion of metaphysics, I think we ought to avoid doing so. I am not going to argue the point at length here, but I suspect that invoking a notion of metaphysics may lead to some unhelpful prejudice about how the notion is best to be understood and analyzed (if it is to be analyzed) – or more to the point, how it is not to be analyzed. In particular, I worry that it may cause prejudice against accounts which crucially involve semantic considerations, by promoting a vague idea that necessity de dicto is “all about” how things are in the world, as opposed to having anything to do with language and thought.

Finally, Kripke's characterization should be supplemented with something about the sense of 'necessary' being unrestricted or very broad. To see this, consider an utterance like 'It is true that I stayed home yesterday. This couldn't have been otherwise, as I had to be there to let the electrician in.' This utterance may be true, but in that case the 'couldn't have been otherwise' part is not about necessity de dicto in the sense I am interested in – we are dealing with a contextually restricted range of ways things could have been. For instance, we are probably ignoring ways things could have been in which I stop caring about having electricity, or in which I never made the appointment with the electrician, or in which the appointment was on a different day. This supplementation of the Kripkean characterization has become customary. Witness Timothy Williamson in an interview:

Something is metaphysically necessary if it couldn’t have been otherwise, in the most unrestricted sense. (Williamson & Antonsen 2010, p. 18.)

Or Daniel Stoljar, referring to:

(…) the completely unrestricted sense of possibility that philosophers sometimes call “logical” or “metaphysical” possibility (…) (Stoljar 2006, p. 34.)

Or this terminological stipulation made by van Invagen:

Modal terms will be used in their “metaphysical” or “unrestricted” sense (…). (van Invagen 2015, p. 35.)

There is a wrinkle here, however. For some things philosophers say may seem to go against the propriety of characterizing our topic in this way. On the way of speaking I have in mind, there are necessities in the sense of our topic which are not necessary in some other sense – 'logically' or 'mathematically' or 'epistemically' for example. See, for instance, this passage in Nathan Salmon (where he is arguing that an objection made to something he has proposed – the details of which don't matter here – does not hold water):

Metaphysical modality is definitely not an unrestricted limiting case. There are more modalities in Plato’s heaven than are dreamt of in my critics’ philosophy, and some of these are even less restrictive than metaphysical modality. One less restrictive type of modality is provided by mathematical necessity and mathematical possibility. […] Another type of modality less restrictive than metaphysical modality is provided by what is sometimes called ‘logical necessity’ and ‘logical possibility,’ to be distinguished from genuinely metaphysical necessity and possibility, or necessity and possibility tout court. A proposition is logically necessary if its truth is required on logical grounds alone […]. Although there is a way things logically could be according to which I am a credit card account, there is no way things metaphysically might have been according to which I am a credit card account. (Salmon 2005, p. 136)

But notice the contrast at the end of this passage between 'could be' and 'might have been'. Salmon is concerned here with what he calls 'the confusion between the generic notion of a way for things to be and the modal notion of a way things might have been'. According to Salmon, this confusion

is very probably the primary source of the idea that metaphysical modality is the limiting case of restricted modalities, that metaphysical necessity and possibility is the unrestricted, and hence the least restricted, type of necessity and possibility. For metaphysical necessity is indeed truth in all ways things might have been (modal, not generic), and metaphysical possibility is indeed truth in at least one way things might have been (modal, not generic). (ibid, p. 136.)

So, since we are explicitly talking about ways things might have been, it seems that Salmon would have no real disagreement after all with Williamson's succinct characterization of our topic, quoted above (except perhaps for some pragmatic disagreement about what to emphasize, or how best to use language to avoid potential confusions).

In any case, one thing that should be clear is that we are not dealing with a notion where certain contextually relevant matters of fact may be held fixed, as in the electrician example above.

So much for the intensional characterization of the notion of necessity de dicto. Another thing which may help us grasp the notion is consideration of its extension – cases, and what types of cases there are. Most instructive in this way are cases lying outside the overlap of necessity and a priority. After giving his intensional characterization of the notion, Kripke goes on to say that he will be arguing that, in addition to being conceptually different, the categories of necessity and a priority are extensionally different: 'I will argue below that in fact they are not even coextensive—that necessary a posteriori truths, and probably contingent a priori truths, both exist.' (Kripke 1980, p.38.)

An aspect of the character of the notion of necessity de dicto is captured vividly in some of Kripke's intuitive appeals regarding the necessary a posteriori, in particular with the use of the phrase 'given that', and similar language. For instance, if I think some object I have encountered empirically, a, is the same object as I have encountered empirically in other situations, b, then – while I might conceivably turn out to be wrong, i.e. while it might turn out to be the case that a is distinct from b – given that a is indeed b, then a couldn't have been distinct from b; 'a = b' is necessary.

Regarding the contingent a priori, perhaps the most straightforward and instructive type of case occurs when a name is stipulated to refer to whatever object satisfies some description, where the description is of a sort where an object satisfying it could have failed to satisfy it. So if I stipulate that 'a' is to refer to the inventor of the zip (if there was an inventor of the zip), then the proposition 'a, if there is an a, invented the zip' is a priori: in virtue of the way I have set 'a' up to work, it just can't turn out empirically that a exists and yet didn't invent the zip after all. Now suppose that there is an inventor of the zip. In that case, the proposition 'a, if there is an a, invented the zip', while a priori, is contingent: someone else could have invented the zip.

We have now characterized our topic, first intensionally, by taking and modifying slightly Kripke's famous characterization, and then extensionally, by pointing to two striking types of cases. The next question we must address is 'What is the problem or task in relation to the topic, to which your account is a response?' I will concentrate on this in a future post.  

References

Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press. (First published 1971.)

Williamson, Timothy & Antonsen, Paal (2010). Modality & Other Matters: An Interview with Timothy Williamson. Perspectives: International Postgraduate Journal of Philosophy 3 (1):16-29.

Salmon, Nathan U. (2005). 'The Logic of What Might Have Been' in Metaphysics, Mathematics, and Meaning. Oxford University Press. Article originally published in 1989.

Stoljar, Daniel (2006). Ignorance and Imagination: The Epistemic Origin of the Problem of Consciousness. Oxford: Oxford University Press.

van Invagen, Peter (2015). 'Nothing is Impossible' in God, Truth, and other Enigmas, Szatkowski, Miroslaw (ed.),. De Gruyter.

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.