Williamson's Metaphysical Modal Epistemology and Vacuism about Counterpossibles

Timothy Williamson has argued that our capacity for metaphysical modal judgement comes along with our capacity for counterfactual judgement. This passage gives a flavour of his view:

Humans evolved under no pressure to do philosophy. Presumably, survival and reproduction in the Stone Age depended little on philosophical prowess, dialectical skill being no more effective then than now as a seduction technique and in any case dependent on a hearer already equipped to recognize it. Any cognitive capacity we have for philosophy is a more or less accidental byproduct of other developments. Nor are psychological dispositions that are non-cognitive outside philosophy likely suddenly to become cognitive within it. We should expect cognitive capacities used in philosophy to be cases of general cognitive capacities used in ordinary life, perhaps trained, developed, and systematically applied in various special ways, just as the cognitive capacities that we use in mathematics and natural science are rooted in more primitive cognitive capacities to perceive, imagine, correlate, reason, discuss… In particular, a plausible non-skeptical epistemology of metaphysical modality should subsume our capacity to discriminate metaphysical possibilities from metaphysical impossibilities under more general cognitive capacities used in general life. I will argue that the ordinary cognitive capacity to handle counterfactual carries with it the cognitive capacity to handle metaphysical modality. (Williamson, The Philosophy of Philosophy (2007), p. 136. Found in Section 3 of the SEP article 'The Epistemology of Modality'.)

In order to argue for this, Williamson takes a schematic semantic story about counterfactual conditionals:

Where “A>B” express “If it were that A, it would be that B”, (CC) gives the truth conditions for subjunctive conditionals: A subjunctive conditional “A>C” is true at a possible world w just in case either (i) A is true at no possible world or (ii) some possible world at which both A and C are true is more similar to w than any possible world at which both A and ¬C are true.(Formulation from Sec 3 of the SEP article.)

On the basis of this, he proves the following equivalences:

(NEC) □A if and only if (¬A>⊥)
It is necessary that A if and only if were ¬A true, a contradiction would follow.

(POS) ◊A if and only if ¬(A>⊥)
It is possible that A if and only if it is not the case that were A true, a contradiction would follow.

(Renderings and spellings out from the SEP article. The box and diamond are metaphysical modal operators, and the falsum - which looks like an upside-down 'T' - represents a contradiction.)

But this only works because the schematic theory of counterfactuals Williamson adopts is understood as working against a background of a notion possible worlds, where Williamson understands this as the notion of metaphysically possible worlds. This theory deems true all counterfactuals with metaphysically impossible antecedents, and this is crucial to his demonstation of the equivalences on the basis of his assumed schematic theory.

There are lots of reasons not to adopt a theory of counterfactuals which uses the notion of metaphysical possibility in this way. One reason to move away from a theory like this is if you think that there are counterpossibles - counterfactual conditionals with metaphysically impossible antecedents - which have their truth-values non-vacuously. But you might be agnostic about that. For instance, you might be happy with metaphysical modal distinctions but doubt that there are any clear cases where countepossibles have truth-values non-vacuously. In that case you might see no good reason for the backdrop of worlds or scenarios in a theory of counterfactuals to be exactly the metaphysically possible ones. Or, you might be skeptical about the very distinction between metaphysical possibility and impossibility, in which case you won't want to understand the backdrop in a way that involves that distinction. And it seems that you can get most, or even all, of the theoretical benefits of a Stalnaker-Lewis approach to counterfactuals without using that distinction. It doesn't really seem to play a starring role in the theories. 

If a semantic theory for counterfactuals which does not draw on any bright line between metaphysically possible and metaphysically impossible scenarios is as good or better than the theory that Williamson uses to prove his equivalences, that seriously undermines the equivalences, and in turn Williamson's story about how we get metaphysical modal knowledge.

(And note that this turns on Williamson's understanding his chosen theory so that 'possible world' means 'metaphysically possible world' - even accepting an identically worded theory, but where 'possible world' is understood in a way which does not involve the distinction between metaphysical possibility and impossibility, would make Williamson's equivalences unavailable.)

Two Sources of Interest in Metaphysical Modality (and Kripke in Light of Them)

Source 1: We want to know the vocabulary and syntax of being, or as Rosen puts it in 'The Limits of Contingency', 'the combinatorial essence of the world'. What are the basic elements and how may they be combined?

Source 2: We want to know, as it were in advance, whether various kinds of statements that are not put in terms of the basic elements count as high-level descriptions of any possible world. 

Many of Kripke's arguments that certain kinds of statements are necessary furnish considerations which purport to show that whatever the possibilities are exactly, none of them is correctly described as one in which '...'. 

This mode of argumentation on Kripke's part can make it look like his modal notions can ultimately be explicated along conceptual or semantic lines. But, as Putnam came to appreciate in between 'The Meaning of "Meaning"' and 'Is Water Necessarily H2O?', this is not so.

In this connection it is notable that all of Kripke's distinctive modal theses are negative as regards possibility. (His claims, in the course of arguing against descriptivism about names, that well-known facts about Aristotle etc. could have been different, are an exception, admittedly - but for those arguments, I don't see that he needs these alternative possibilities to be real, metaphysical possibilities. The modality used in those arguments could be deflated to conceptual or semantic without affecting the arguments, which are after all for a semantic conclusion - that names aren't synonymous with descriptions.) As far as I know, Kripke never seriously argues that such and such really is possible, really is a way the world could have been. Rather, he just works on the assumption that there are many quite various ways things could have been, but then seeks to draw some limits in high-level vocabulary.

But these Kripkean results, if that's what they are, only satisfy interest in metaphysical modality that derives from the second source. How we might satisfy our interest that derives from the second source is largely left untackled, and this is one reason why many have found Kripke's work frustrating. He elicits epistemic hopes, someone might complain, without giving us even so much as a roadmap for how so satisfy them.

His suggestion that metaphysical possibility may coincide more closely with physical possibility than has often been supposed may however be suggestive. On the other hand, he is against physicalism, so this couldn't be the whole story from his point of view.

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.

Strohminger & Yli-Vakkuri Improve (in Some Respects) Upon Kipper's Bombshell (and My Account of Necessity May Be False)

This post is quite compressed and relies on things explained in the previous posts on the task of linking necessity to apriority, as well as alluding to my account of necessity as expressed in my PhD thesis. In a future post, I intend to explain and explore what these developments mean for my account of necessity.

There has recently appeared an unpublished manuscript on PhilPapers (PDF available here at time of writing) which contains even stronger counterexamples to both Casullo's and my proposed link between necessity and apriority. It is by Margot Strohminger and Yuhani Yli-Vakkuri.

Strohminger & Yli-Vakkuri argue that Kipper's examples are contentious, relying on dubitable assumptions about natural kind terms and perhaps even embracing what they call 'Chalmersian two-dimensionalist ideology'. They provide even simpler examples of propositions whose general modal status cannot be known a priori (and, relevantly for me, these examples also don't seem to be implied by propositions whose general modal status can be known a priori). For example:

Bob Dylan is at least as tall as Robert Zimmerman.

This is necessary, since Bob Dylan is Robert Zimmerman. But for all we can know a priori, Dylan and Zimmerman are distinct, in which case this proposition would not be necessary, but contingent.

But hold on a minute! My link appeals to implication, and I said that the example above isn't implied by a proposition whose general modal status is knowable a priori. But can't we say that it is implied by 'Bob Dylan is Robert Zimmerman', which we can know a priori to be necessary? Yes, we can - although here we need a notion of implication which takes into account the meaning of 'is at least as tall as' - or at least the fact that it's a certain kind of comparative expression - rather than just the meanings of subject-neutral particles like 'or', 'all' and 'some'. So, from the point of view of disproving Casullo's proposed link, this example may be the best available so, but from the point of view of disproving my proposed implication-involving link, Kipper's natural kind examples may still have an edge.

It seems to be a very exciting time to be thinking about these issues! So far, in this post and the last, I've been talking about how these examples affect my proposed link between necessity and apriority. But the situation is more serious than that for me. The centrepiece of my PhD thesis was an account of the conditions under which a proposition is necessarily true (I've blogged about this account quite a bit here). And these developments, as far as I can tell, may well show that account to be false. This is very momentous for me, as I worked on that account for several years and considered it to be maybe my best bit of work.

I can't believe I didn't think of the example above in connection with my account! I even considered a very similar example when making a side point about using my notion of a genuine counterfactual scenario description (used in my account of necessity) to arrive at a definition of rigid designation which is in some ways more fundamental than the Kripkean one.

Stay tuned for more on whether and how these developments affect my account of necessity, and what can be done about it if they do.

Notes on Counterfactual Scenario Descriptions, Sources of Modal Error (or Uncertainty), and Deep Puzzles of Modality

One interesting thing about my account of subjunctive necessity is the way it separates two kinds of things that we could be wrong or confused about in our judgements of subjunctive modality: the truth of what we're holding true for the purposes of a counterfactual scenario description (CSD) and the genuineness of that CSD.

For example, I might think 'Hesperus is not Phosphorus' is subjunctively possible because I falsely believe that Hesperus is Phosphorus. Or I might be acquainted with some strange animals I call Toves and then not feel sure whether 'Toves are animals' is necessary simply because I am not sure whether the things I am acquainted with are animals.

By contrast, there are modal questions which do not centre - at least not in any definite way - on the truth or otherwise of what is being held true. For example, granting that I am human, could I have been an animal? Or how about a Neanderthal? Or a bank account?

And cosmic questions about whether there could have been less matter or energy, or perhaps just one atom in a void? And here the question arises: how do you know what you have to know in order to know whether something is necessarily the way it is or not? (In some cases, that seems clear. E.g. you have to know whether Hesperus is in fact Phosphorus in order to know whether it necessarily is. But in others it really doesn't.)

Another puzzling thing stems from the way, in my account, you can have CSDs which aren't possible, since the things held true for them aren't true. For instance, if I think wrongly that Hesperus isn't Phosphorus (or even just grant that for the sake of argument), I will be prepared to produce CSDs involving Hesperus not being Phosphorus, and these may be perfectly genuine. This strikes me as an important virtue of my account - i.e., that it is some sort of advance, giving us a fruitful way of talking and thinking philosophically about modality. It is hard to say exactly why. One thing is that it enables us to bracket off distracting sources of modal uncertainty and error, perhaps allowing us to focus better on the stuff which really bothers us philosophically about modality. 

In any case, this thing - about there being genuine CSDs which, despite being genuine, aren't possible because false things are held true for them - gives rise to some puzzlement in its own right. When we can go different ways on the question of whether Hesperus is Phosphorus or Clark Kent is Superman - questions of the identity or distinctness of things - it seems like our underlying way of thinking about things, our conceptual apparatus, is basically the same. And to a fair, but perhaps lesser extent, going different ways on the question of the underlying nature of cats, or Toves, or water also seems to leave our conceptual apparatus largely the same. (There may be something wrong or lacking in this description.) We get the sense that we can flip the switch either way on these things quite readily, and continue in much the same way in either case when it comes to grasping a range of genuine CSDs which arise on the assumption that things are the one way or the other. On the other hand, what of things which are - in a conceptual sense, I want to say - far from true? 

Things get puzzling very quickly once such questions come into view. If I somehow hold it true that humans are cats, can I then produce genuine CSDs according to which that is true? It is hard to know what to say. One thing is that there might be an issue about whether we can really hold such things true, or perhaps better, whether it makes sense to talk of holding such things true. But to that it may always be replied - OK, but we can sometimes do something here, in these cases where you might worry about whether we can really hold the things in question true or not.

Are there two ways, then, of getting out of the sphere of genuine CSD-hood? One by holding things true which are either true, or not a big deal or problematic to hold true, and then going further and further away from actuality, so to speak, until you say things we might hesitate to call CSDs (e.g. holding it true that I am human, but then talking about a scenario where I'm a cat), and another by holding far-out things true?

Another worry concerns what might be called modal encroachment. The idea that, if we learn more about some things, we might realise that some things aren't possible that we thought were. And there is a question here about whether that could affect what we think about genuineness of a CSD, or whether what we formerly thought were not only genuine CSDs but possibilities (i.e. that the things being held true for those CSDs are the case) can always be retained as genuine CSDs by holding the right false things true.

I feel that with these issues my account, which could seem merely logic-choppy and perhaps trivial in a way, begins to make contact with some of the deeper puzzles surrounding modality. 

In a future post I want to try to explore how our ideas might be prone to shifting and slipping without our realising it when we philosophize about modality. For instance, the obscure way the stakes can seemingly be raised in some way by the question of 'But could that really have happened?'. I also hope to make some progress on puzzles concerning 'whether the ground of modality is in us or the world', by trying to better uncover the thought processes underlying that unsatisfactory question. Perhaps then we will see better what the real issues are in this thicket of philosophy.

Postscript (or seedling for next time):

Dim hypothesis re. Kripkean showing of necessity of identity: it shows that things couldn't have been otherwise in a deep way by showing that they couldn't have been otherwise in a shallow way. 

I.e. in a certain frame of mind, we might think 'What do we know about how, and the extent to which, things really might have been different?'. A frame of mind with a sense of cosmic mystery, open to underlying system we have little or no inkling of. Then the Kripkean arguments come along and say 'Well, whatever the truth is about that, things certainly couldn't have been such that Hesperus isn't Phosphorus'.

It is notable that Kripke's results are necessities, or denials of possibility. This leaves it open that we have a way of thinking, or a concept of modality, on which all the Kripkean necessities are necessary as required, but where there is leeway which then disappears on some deeper view.

Reflections on My Claim that Inherent Counterfactual Invariance is Broadly Semantic

This post presupposes knowledge of my account of subjunctive necessity de dicto as expressed in my thesis and in a paper derived from it which I have been working on. (I hope my self-criticism here doesn't cause any should-have-been-blind referees to reject the paper. A revise-and-resubmit verdict I could live with.) Here I try to take a next step in getting clear about the status and significance of the account.

In my thesis and derived paper, I propose that a proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant (ICI) and true, and explicate this notion of ICI.

I claim that ICI is broadly semantic, and put this forward as a key motivation and virtue of the account. I don’t provide much argument for this claim - the intention, I suppose, was that this would just seem self-evident. But I have become increasingly aware of the importance of the fact that this could be challenged, and the importance of getting clearer about the underlying primitive notion of a genuine counterfactual scenario description (CSD).

I do provide one reason, near the end of my presentation of my account, for thinking that ICI is broadly semantic given my preferred approach to propositions and meaning. But there are two reasons for wanting more. One is that it may be hoped that my claim that ICI is broadly semantic could be justified independently of my particular approach to propositions and meaning, where I advocate understanding what I distinguish as the ‘internal’ component of meaning as role in language system. A second, perhaps more suggestive, reason for wanting more is that, even given my preferred approach, the argument I give is basically this: ICI is explained in terms of how a proposition - its negation, really - behaves in certain contexts - namely CSDs. But here of course I have to single out genuine CSDs.

And here’s the thing. (At least, the following seems to be right.) For my claim that ICI is broadly semantic to hold water, the notion of genuineness of a CSD had better be broadly semantic. For it is not enough for a notion to be broadly semantic that it can be characterized in terms of appearance in certain sorts of linguistic context C, where C-hood is blatantly extra-semantic. For instance, we may say a proposition has G iff it (or its negation, to make this more like the ICI case) doesn’t appear in any description which has the property of being written in some notebook I have in my room. In that case, it is plain that whether or not a proposition has G is not a matter of its meaning or nature.

So, I now think that the little argument I give at the end of my presentation of my account, about how my particular approach to propositions and meaning ‘fits well’ with the notion of ICI as broadly semantic only goes so far, and that as an argument that given my particular approach the notion of ICI is or should be seen as broadly semantic, it is weak, since it gives no reason to think that the all-important notion of genuineness of CSD is broadly semantic.

Further, I think it is clear that I want to put forward my account, and I think the account has theoretical value, independent of whether a case can be made that genuineness of CSD is broadly semantic. And so my whole presentation of why my account is interesting and of its motivation is somewhat crude. As a story about what caused it, and the specific things I was thinking, it may have some interest. But as a way of situating the theory and giving a sense of what its value (within philosophy) consists in, it is crude and not really to the point. I do of course hint at other sources of interest (e.g. that the account clarifies the relationship between the notion of necessity and those of truth and implication), and don’t rest everything on the ‘semantic hunch’, but I do perhaps give it too prominent a place - or at least, an incompletely justified place.

So, is the notion of a ‘genuine counterfactual scenario description’ broadly semantic? And what does it mean to be broadly semantic? I may follow up with a post addressing these questions more thoroughly, but for now a couple of remarks. Whatever it is to be broadly semantic, it is not to be conventional in any sense. The idea is perhaps better gotten at, in some ways, by saying that genuine CSD-hood is a conceptual matter. But really I need to roll up my sleeves and investigate this more closely - it is not merely a question of hitting on some formulation. Finally, I propose that the following passage from §520 of Wittgenstein’s Investigations seems very to-the-point when it comes to the questions and difficulties I find myself coming up against here, and may help me plumb the depths of the matter:

So does it depend wholly on our grammar what will be called (logically) possible and what not,—i.e. what that grammar permits?”—But surely that is arbitrary!—Is it arbitrary?—It is not every sentence-like formation that we know how to do something with, not every technique has an application in our life [...].

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.

Five Objections to Sider's Quasi-Conventionalism About Modality

There are a couple of infelicities in the below which have been fixed in the version of this material appearing in chapter 4 of my PhD thesis Necessity and Propositions.

In a recent post I described Sider's quasi-conventionalism about modality, which in my view takes an important step forward with respsect to necessity de dicto but is mistaken in other ways. (My account of necessity de dicto shares a structure with it.) Here I give five objections to Sider's view.

None of these take the form of counterexamples. As Merricks (2013) observes:

[...] Sider’s general approach—as opposed to specific instances of that approach—is immune to counterexample. For suppose that Sider lists the “certain sorts.” You then come up with an absolutely compelling example of a proposition that is necessarily true and not of a sort on the list. Sider need not abandon his overall approach to reducing necessity. Instead, he could just add a new sort to the list to accommodate that example. Or suppose you come up with an absolutely compelling example of a true proposition that is not necessarily true and is of a sort on the list. Sider could just expunge that sort from the list.

1. Necessity does not seem disjunctive or arbitrary (at least, not to this extent).

This is an objection centering on our intuitive grasp of the concept of necessity de dicto. It seems like this is a notion we can grasp, with the help of Kripke’s characterizations as supplemented in this post. Now, when we grasp this idea, it seems we are grasping a single, unified concept: necessary truths could not have been otherwise, no matter how things had turned out. This just doesn’t seem like a disjunctive matter, and nor does it seem like the sort of thing we make one way or the other with any kind of arbitration - although of course there are unclear or borderline cases, which we may perhaps make stipulations about to some extent.

This is not a knock-down objection, of course. Sometimes philosophy can reveal things to be other than they might seem. But I think it is hard to deny, if we are willing and able to grasp the concept of necessity de dicto and careful to hold in abeyance any of our pet theoretical proclivities which may suggest otherwise, that the notion does seem more unitary and less arbitrary than Sider’s theory would have us believe. And I propose that that should count as a mark against Sider’s theory.

Furthermore, insofar as appearance really is different from what Sider says the reality is when it comes to necessity, there is some explanatory work for Sider, or more generally the would-be quasi-conventionalist, to do here: why the discrepancy? As far as I know, no answer has yet been given.

2. The ersatz substitute worry.

A starting point for this worry is the unapologetically ad hoc nature of Sider’s successive extensions of the toy version of his approach that he begins with (where the “certain sort” of propositions he takes as “modal axioms” are just the mathematical truths). This process seems to be one of going back and forth between a growing list of types of propositions, the list at the heart of an increasingly disjunctive account, and our grasp of the real modal notion of necessity. This gives rise to the worry that all we are doing is building an ersatz substitute for the real notion, by looking at the extensional behaviour of the latter and stipulating this behaviour into the account. No matter how far we pursue this strategy, the disjunctive notion we are building will remain fundamentally different in character from the notion whose behaviour we are modelling with it. Supposing that what we want from an ‘if and only if’ style account of necessity de dicto is not some substitute for that notion, but a biconditional which gives us insight into the notion itself, Sider’s approach will never satisfy.

Something of this worry is even suggested by what Sider says about family resemblances, rehearsed in the previous post as point (6). The quasi-conventionalist could simply insist that each of the items on their list of the types of propositions which count as modal axioms is there as a brute fact - that’s just how the notion of necessity works. But, Sider says, the quasi-conventionalist ‘need not be quite so flat-footed’, and is ‘free to exhibit similarities between various modal axioms, just as one might exhibit similarities between things that fall under our concept of a game, to use Wittgenstein’s example’. This move, offered as an optional extra for the quasi-conventionalist, is plausibly in tension with the way Sider’s successively extended accounts are formulated. Just as the concept of a game - allowing for the sake of argument that it is a family resemblance concept - is plausibly not actually captured by any particular disjunction, but is as we might say inherently open-ended, it is also plausible that we should admit that the real “certain sort” or “modal axiom” notion doing the all-important work in Sider’s account - allowing for the sake of argument that it is a family resemblance concept - is not captured by any particular disjunction either.

This of course suggests a variant of Sider’s approach, where it is held that the “modal axiom” notion is a family resemblance concept, and admitted that any definite, disjunctive list of types of propositions could only yield, when plugged into the overall account, an ersatz substitute for the notion of necessity de dicto. This variant is not, or at any rate less, vulnerable to the the ersatz substitute worry. But it is not clear whether it could really satisfy a philosopher who wants insight into the notion of necessity de dicto, let alone a philosopher with Sider’s motivations. For instance, can it really claim to be modally reductive? It might on the contrary seem that the family resemblance notion in question should be counted as thoroughly modal. Furthermore, it may seem to yield an account which is insufficiently insightful - essentially all we are now getting is (Schema) itself, together with the pronouncement that the condition C is given by a family resemblance concept. Is there nothing more which can be said? Relatedly, the question now arises: is it after all true that the notion in question is a family resemblance concept? What reason have we to believe that? (I will suggest, somewhat ironically given that I am on the whole much more admiring of Wittgenstein’s philosophy than Sider is, that it isn’t true. The notion playing this ‘condition C’ role, i.e. the notion which when combined with the notion of truth yields a notion playing Sider’s “modal axiom” role, can be defined in terms of a single necessary and sufficient condition.)

3. No iteration?

When Sider says early on in the modality chapter of his (2011) that the account he offers will be partial, there is a footnote to this remark which runs as follows:

(16) For example, the account defines a property of propositions that do not themselves concern modality, and thus is insufficient to interpret iterable modal operators.

This raises the question: how come, faced with this failure of coverage, Sider doesn’t simply make the same move with modal statements as he does with analyticities, “metaphysical” statements, and natural kind statements - namely include them expressly in the account?

Perhaps the answer is that this would threaten the account’s claim of reductiveness. For it seems that in order to include modal statements on the list, we need the concept ‘modal’.

The question then becomes: is ‘modal’ modal? If it is, Sider’s account is in serious trouble: it cannot, as a matter of principle, handle iterated modality. For remember, it is supposed to be modally reductive. And if iterated modality is a real, legitimate thing, then what use is a theory which gives us - by design - some extensionally correct answers but cannot handle this whole class of cases? It seems such a theory could give us an ersatz substitute for modality at best (to recall the above objection by that name). Its failure, if it is a failure, to be extendable to a salient class of cases should perhaps suggest to us that it is on the wrong track.

So, is ‘modal’ modal? It is an interesting question, and suggests interesting analogous questions about other kinds of concepts. One reason to think it is, is that we don’t seem to have a general way of saying what ‘modal’ means which doesn’t work by way of example. We seem to need examples of modal notions - necessity, or contingency, or possibility, or impossibility, or some combination of them - to do the job. To be sure, we could be said to be mentioning rather than using these notions in our explanations of ‘modal’, but is that any help? Don’t we need to use them in some broad sense in order to mention them in the appropriate way?

Another way out which may occur to the reader is to somehow delineate the modal statements using notions which are distinct from ‘modal’ and the like, but which fortuitously give the right extension. I am pessimistic about this. For a start, I can’t think of any good candidate notions. Furthermore, even if there were notions around which could do the job, wouldn’t using them for this purpose play further into the ersatz substitute worry described above? In particular, it seems like this strategy, while it may help Sider’s account deliver extensionally correct answers, would take the account (even) further from the real meaning of modal expressions, or the real nature of modal notions.

One possible strategy remains to be considered: accepting that ‘modal’ is modal and simply giving up the claim to full modal reductivity. From one angle, this seems not unreasonable; the way that ‘modal’ introduces modality, assuming it does, into the account, seems quite special and different from the way modality would be introduced if a notion of possibility or necessity were directly used. So perhaps there is room to claim that a broadly Siderian quasi-conventionalist account involving the notion of ‘modal’ as an unreduced modal element could still constitute a theoretical advance. I have no knockdown objection to this, but I do want to suggest that once this concession is made, other objections, such as the first two considered here - (i) that necessity does not seem as disjunctive or arbitrary as quasi-conventionalism would have us believe and (ii) the ersatz substitute worry - become all the more acute; I am not sympathetic with the following sort of move, but you might try to argue that biting those bullets is worth it if we get in return a complete reduction of modality, with its attendant payoff in eliminating puzzlement and vindicating certain sorts of metaphysical visions, but you can’t do that anymore under the present strategy. Indeed, the whole spirit of the quasi-conventionalist approach seems to be in tension with allowing such a modal element into the mix.

In sum, there is reason to suspect that iterated modality, and the failure of any existing version of Sider’s approach to cover it, poses a serious threat to Sider’s approach in general.

4. Reductivity a bug, not a feature.

Essentially this objection is raised against Sider’s theory by Merricks (2013). The objection is simply that, if we have reason to think that a modal notion like that of necessity de dicto cannot be reduced to non-modal notions, or if we just intuitively feel that to be right, then we should on that score alone be suspicious of Sider’s theory, since it purports to give a reduction. In making this objection, Merricks cites an argument he gives elsewhere (namely in Chapter 5 of his (2007)) for the conclusion that such modal notions indeed cannot be reduced to non-modal ones.

5. Questionable motivation.

As we said at the outset, Sider’s account is partly motivated by general puzzlement about modality, and partly by a metaphysical vision. Both these facets of the motivation can be made the focus of criticism. The following is not supposed to constitute a sharp, incisive objection, but rather to cast some doubt on these general features of Sider’s approach.

Regarding general puzzlement: yes, modality is puzzling to philosophers. But perhaps this puzzlement is not to be treated exclusively by means of reduction (or, for that matter, by ‘if and only if’ analysis whether modally reductive or not). Indeed, pursuing reduction can even be seen as pursuing an easy way out - albeit one which may be impossible in principle. Perhaps the only real way forward, with parts of our puzzlement at least, is, rather than trying to reduce modality to non-modal terms, to work on our way of looking at modal concepts themselves, using philosophical methods other than reductive analysis. (One method which comes to mind is the method, due to Wittgenstein, of imagining simplified language games and comparing and contrasting them to ours. In the Brown Book some steps are taken towards doing this with modality, but only cursorily. I mention this to give a particularly concrete and well-known example of a possibly helpful method, but this is just one among many - I do not mean to suggest it could suffice all by itself.) Non-modally-reductive accounts of necessity de dicto such as mine do not face this criticism, since they do not aim to clear up all of our puzzlement about modality, or even just some core of it, by means of an ‘if and only if’ style analysis. Nor do they aim even to point the way to such a clearing up. By being less ambitious on that front, they offer a more realistic hope of genuine theoretical progress on our understanding of de dicto modal notions - how they relate to other notions both modal and non-modal.

Regarding the metaphysical vision: it is beyond the scope of this post to criticize Sider’s Hume-influenced, Lewis-influenced metaphysical vision head-on. But we may note that, insofar as there may be grave problems with this sort of metaphysics for all we know given the present state of philosophical inquiry - nothing of the sort may be tenable, ultimately - there may also be problems with a highly ambitious approach to modality which is in service of this sort of metaphysics. More generally, perhaps there is reason to be dubious of any approach to modality based upon a metaphysical vision. One reason may be that the vision is, so to speak, too antecedent to modal considerations: perhaps one should let modal considerations shape one’s approach to metaphysical questions, rather than trying to explain modality (away, if you like) in terms of an approach to metaphysical questions which had its appeal quite apart from, or even in spite of, modal considerations. Another reason may be that the best way to make theoretical progress on the notion of necessity de dicto is to keep sweeping metaphysical visions out of it. We may do better to instead treat our topic along broadly logical lines. One way this may help is that it might free us up to throw a wider variety of conceptual resources at the problem - for instance, semantic notions or other modal notions which may seem problematic against some special metaphysical backdrop but are actually quite in order.

That concludes our list of objections or worries. For two further objections, see Merricks (2013).

I think the cumulative effect of the objections canvassed above should be for us to regard Sider’s theory as highly problematic. But note that none of these objections threaten (Schema). This raises the question: what if these were a more soberly motivated, more theoretically satisfying (Schema)-embodying account available? Some other candidate for the condition C in (Schema) which avoids these objections?

References
Merricks, Trenton (2007). Truth and Ontology. Oxford University Press.
Merricks, Trenton (2013). Three Comments on Writing the Book of the World. Analysis 73 (4):722-736.
Sider, Theodore (2003). Reductive theories of modality. In Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics. Oxford University Press 180-208.
Sider, Theodore (2011). Writing the Book of the World. Oxford University Press.
Sider, Theodore (2013). Symposium on Writing the Book of the World. Analysis 73 (4):751-770.