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.

Sider's Quasi-Conventionalism About Modality

Starting in his (2003), and in an unpublished draft from around the same time which is not to be cited, Theodore Sider has proposed a theory of necessity de dicto called quasi-conventionalism. The most up to date version can be found in his (2011) and his replies to a symposium on that work. It states necessary and sufficient conditions for a proposition to be necessary, but as we will see, one of the key concepts involved has been left open-ended, so the account is to be regarded as partial. The account is supposed to reduce necessity de dicto to non-modal notions, and to be extendable to de re modality.

What makes Sider’s account so worthy of discussion from my point of view is that it takes what I believe to be an important step forward with respect to the task of giving an account of necessity de dicto. The step forward is that it embodies a certain structure, which my account shares. Abstracting from the details of Sider’s account, the shared structure can be expressed in the form of a schematic analysis as follows:

(Schema) A proposition is necessary iff it is, or is implied by, a proposition which is both true and meets a certain condition C.

(Sider, as we shall see, does not quite use his schema, but his analysis can easily be re-expressed so as to conform to it.)

So, Sider’s view takes, as I will argue, an important step forward. But it also has grave defects. Considering Sider’s view, then - seeing that it instantiates the suggestive and appealing (Schema), and seeing what is wrong with it - offers a nice way of leading up to and motivating my own account, which I will give in the next chapter. (This is not the way I actually arrived at my account, but it could have been.)

Two of SIder’s main starting points seem to be: (i) the desire to find a way of reducing modal concepts to non-modal concepts, and (ii) a hunch that conventionalist theories according to which necessities are true by convention were on to something: roughly, that convention should play some key role in the analysis of necessity. Regarding (i) and the underlying motivation for it, there are two interrelated strands here: one is a relatively theory-neutral feeling that modality is mysterious, or cries out for explanation, but this then plays into the second strand, which is emphasized in his (2011): a desire for an account of the “fundamental nature of reality”, “reality’s fundamental structure” - an account that “carves nature at the joints”.

Sider argues that it was always a mistake to try to account for necessary truth by means of the idea of truth by convention: the idea is of dubious coherence, and in view of necessary a posteriori truths especially, would not seem to line up with the idea of necessary truth anyway. But that doesn’t mean convention can’t play a crucial role in, not truth-making, but necessity-making, or accounting for the necessity of necessary truths. (I make the analogous point, with the meanings or natures of propositions in place of convention, in arguing for my account.) Part of the motivation and attraction of truth by convention theories of necessity, Sider allows, was their promise of shedding light on the epistemology of logic and mathematics. The theory of modality Sider is offering makes no claim to do that. But so what? Who says the place to look for insight into the epistemology of logic and mathematics is in a theory of modality?

In his (2011), Sider labels his account ‘Humean’. Here is his first pass at expressing it there:

To say that a proposition is necessary, according to the Humean, is to say that the proposition is i) true; and ii) of a certain sort. A crude Humean view, for example, would say that a proposition is necessary iff it is either a logical or mathematical truth. What determines the “certain sort” of propositions? Nothing “metaphysically deep”. For the Humean, necessity does not carve at the joints. There are many candidate meanings for ‘necessary’, corresponding to different “certain sorts” our linguistic community might choose. (Sider 2011, p. 269.)

The role of convention in Sider’s account, then, lies in distinguishing this “certain sort” - or “certain sorts” (Sider switches as this point to the plural):

Perhaps the choice of the “certain sorts” is conventional. Convention can do this without purporting to make true the statements of logic or mathematics (or, for that matter, statements to the effect that these truths are necessary), for the choice of the certain sorts is just a choice about what to mean by ‘necessary’. Or perhaps the choice is partly subjective/projective rather than purely conventional. (p. 270.)

As can be seen at the end of this last quote, Sider has some uncertainty about whether the choice of the “certain sorts” is ‘purely conventional’. We will not get deeply into Sider’s ideas of ‘conventional’ and ‘subjective/projective’ here. It is enough for our purposes that the “certain sorts” are, for Sider, ‘not objectively distinguished’ (p. 270). Or again in different words:

The core idea of the Humean account, then, is that necessary truths are truths of certain more or less arbitrarily selected kinds. (p. 271.)

At this point Sider introduces a refinement, and it is this that will allow us to see how Sider’s account embodies (Schema) above:

More carefully: begin with a set of modal axioms and a set of modal rules. Modal axioms are simply certain chosen true sentences; modal rules are certain chosen truth-preserving relations between sets of sentences and sentences. To any chosen modal axioms and rules there corresponds a set of modal theorems: the closure of the set of modal axioms under the rules.[footnote omitted] Any choice of modal axioms and modal rules, and thus of modal theorems, results in a version of Humeanism: to be necessary is to be a modal theorem thus understood.[footnote omitted] (“Modal” axioms, rules, and theorems are so-called because of their role in the Humean theory of modality, but the goal is to characterize them nonmodally; otherwise the theory would fail to be reductive. [...]) (p. 271.)

Then, getting more specific with a preliminary proposal:

A simple version of Humeanism to begin with: the sole modal rule is first‐order logical consequence, and the modal axioms are the mathematical truths. (Logical truths are logical consequences of any propositions whatsoever, and so do not need to be included as modal axioms.) (pp. 271 - 272.)

At this point, we can see how Sider’s account, or type of account, will embody (Schema); his notion of ‘modal axiom’ combines the requirements of truth and being of a “certain sort” (or one of “certain sorts”), and the main point of the ‘modal rules’ seems clearly to be to draw out implications of the axioms. So, separating the truth and “certain sort” requirements again, we can with little or no distortion put Sider’s preferred type of account into (Schema):

(SiderSchema) A proposition is necessary iff it is, or is implied by, a proposition which is both true and is of a more or less arbitrarily selected “certain sort”.

The presence in the account of implication (or something like it) is in my view an important and laudable feature. It is perhaps not sufficiently emphasized by Sider, and has been glossed over in subsequent discussion of his view. For instance, Merricks (2013) glosses Sider’s account as saying that ‘Sider reduces a proposition p’s being necessarily true to: p is true-and-mathematical or true-and-logical or true-and-metaphysical or…’. The importance of implication (or something like it) in (Schema) and views embodying it is made clear in my recent post on my account.

After giving his preliminary version of Humeanism, Sider goes on to consider a series of worries, responding with ‘a combination of refinement and argument’ (p. 272.) He never arrives at a definitive proposal, but aims to develop his strategy sufficiently to justify his general approach.

I think we have already gotten a pretty good sense of Sider’s approach, but I want more or less to complete the exposition of Sider’s approach before, in my next post, moving on to objections, none of which are among the worries Sider considers. So before moving on to objections, I will now briefly convey six further points which emerge in Sider’s responses to the worries.

1. Logical consequence must be non-modal: Sider wants his account to avoid modal notions, so modal characterizations of logical consequence are out. Remaining options include primitivism about logical consequence, something Sider calls the “best system” account of logical truth (which he describes in section 10.3 of his (2011)) extended to an account of logical consequence, and model theoretic approaches.
2. Analytic truths added as axioms: Sider holds that analytic truths should come out necessary, and proposes to that end that each analytic truth be added as a modal axiom (p. 274). This move is unapologetically ad hoc. (You might worry, as I do, that some examples of the contingent a priori should count as analytic, in which case not all analyticities are necessities. But perhaps there are different notions of analyticity which may give different results here. In any case let’s set this aside.)
3. “Metaphysical” statements added as axioms: again, modulo some fuzziness about what it takes for a statement to count as metaphysical - the gloss Sider uses is ‘truths about fundamental and abstract matters’ (p. 275) - true metaphysical statements are to be added as axioms. Again this is unapologetically ad hoc, or treated as a brute fact: ‘What justifies their status as modal axioms? This is just how the concept of necessity works. Such propositions have no further feature that explains their inclusion as modal axioms.’ (p. 275)
4. A new class of ‘natural kind axioms’: another unapologetically ad hoc addition, this time to accommodate the necessity of natural kind type examples of the necessary a posteriori, e.g. ‘Water is H20’. I refer the reader to (pp. 282 - 283) for details.
5. Contextual variation of the “outer modality”: it is conventional wisdom that modal talk in the wild should be understood as being about a contextually variable space of possibilities. This is often combined with a picture of an outer, unrestricted space of possibilities which does not vary. Sider suggests, as ‘more attractive’ (p. 281), that even the outer space is contextually variable - that ‘there can be contextual variation both in the modal axioms and the modal rules’ (p. 281).
6. Family resemblances (maybe): on (p. 288) Sider rehearses his (by now familiar) attitude to necessity thus: ‘Why are logical (or mathematical, or analytic, or …) truths necessary? The Humean’s answer is that this is just how our concept of necessity works.’ But then he turns around and suggests (pp. 288-289) that ‘a Humean need not be quite so flatfooted. [...] [The Humean] resists the idea that there is a single necessary and sufficient condition for being a modal axiom. Nevertheless, she 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. Doing this would help to show that the Humean concept of necessity is not utterly arbitrary or heterogeneous.’ This no doubt helps the plausibility of Sider’s account in a way, but may also play into the hands of an objector, as we shall soon see.

This completes our exposition of Sider’s theory. In the next post we will consider some objections.

References

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

Sider, Theodore (2011). Writing the Book of the World. Oxford University Press.

(eds.), The Oxford Handbook of Metaphysics. Oxford University Press 180-208.

Sider, Theodore (2013). Symposium on Writing the Book of the World. Analysis 73 (4):751-770.

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.