deontic conditionals: weak and strong

7/27/2019 Deontic Conditionals: Weak and Strong

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Deontic Conditionals:

Weak and Strong*

Alex Silk

[email protected]

Dra of July

Abstract

Recent discussions of the Miners Puzzle have prompted renewed interest

in how deontic modal claims can be sensitive to relevant information. But

these discussions have focused on a limited range of data. I argue that what

makes the Miners Puzzle a puzzle are features unique to the semantics of weak

necessity modals like ‘ought’. In light of an independently motivated seman-

tics for ‘ought’, as compared with ‘must’ and ‘may’, we can explain the data

concerning information-sensitivity without introducing any novel complexi-

ties into our semantics for modals and conditionals more generally. By con-

sidering examples with possibility modals and strong necessity modals, andexamining the import of subtle shis in context, we can illuminate how con-

text and content mutually interact to guide how we coordinate our actions and

expectations in conversation, deliberation, and planning.

Recent discussions of the Miners Puzzle have prompted renewed interest in how

deontic modal claims can be sensitive to relevant information. e following is adescription of the Miners Case and a standard account of the data that it provides.

Ten miners are trapped either in sha A or in sha B, but we do notknow which. Flood waters threaten to ood the shas. We have enoughsandbags to block one sha, but not both. If we block one sha, all the

*anks to Bob Stalnaker, Eric Swanson, and Steve Yablo for helpful discussion.

mailto:[email protected]



water will go into the other sha, killing any miners inside it. If we

block neither sha, both shas will ll halfway with water, and just oneminer, the lowest in the sha, will be killed.

Since we do not know which sha the miners are in, and the consequences will be

disastrous if we choose the wrong sha, () seems true.

() We ought to block neither sha.

e conditionals in ()–() are also natural to accept. Aer all, given that the miners

are in Sha A (/Sha B), blocking Sha A (/Sha B) will save all the miners.

() If the miners are in Sha A, we ought to block Sha A.

() If the miners are in Sha B, we ought to block Sha B.

()–(), along with (), which we know, seem to entail ().

() Either the miners are in Sha A or the miners are in Sha B.

() Either we ought to block Sha A or we ought to block Sha B.

But () contradicts (). Hence the miners’ puzzle.

In light of the apparent joint satisability of ()–(), K & MF argues that modus ponens for the indicative conditional is invalid. Others have

also argued that cases like the Miners Case pose a serious challenge to the classic se-

mantics for modals and conditionals. ese reactions have been premature. Dis-cussions of information-sensitivity in deontic modals and conditionals have focusednearly exclusively on sentences with weak necessity modals like ‘ought’ and ‘should’.

But there are important differences between deontic conditionals with weak neces-sity modals, on the one hand, and deontic conditionals with strong necessity modals

like ‘must’ and possibility modals like ‘may’, on the other. I will argue that whatmakes the Miners Puzzle a puzzle has nothing to do with deontic modals and condi-

tionals as such, but has everything to do with ‘ought’. By attending to independently attested differences in the meaning of ‘ought’, as compared with ‘must’ and ‘may’,we can explain the data concerning information-sensitivity without introducing any

novel complexities into our semantics for modals and conditionals more generally.

K & MF : –. e case was originally discussed in P ,credited to Donald Regan. See also J for similar cases.

C . , C , L , S a. For a dissenting view, see F .

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Such complexities might be warranted on other grounds. But if the arguments in

this paper are right, they are not required by cases like the Miners Case.e main contributions of my account are, rst, to introduce a broader range

of data concerning information-sensitivity in deontic modals and conditionals; sec-ond, to highlight previously underappreciated contrasts and sensitivities to context

in deontic ‘ought’ and ‘must’ claims, simple and complex; and, third, to capture in-tuitions driving previous responses to the Miners Puzzle in a manner that improves

in empirical coverage and independent motivation.Roadmap: § presents new data concerning the Miners Case. § argues that

these data raise trouble for existing accounts of information-sensitivity in deonticmodals and conditionals. § offers an independently motivated semantics for weak necessity modals like ‘ought’. § shows how this semantics can help make the correct

predictions about the broader range of data concerning the Miners Case.

Information-sensitivity with ‘must’ and ‘may’

We need more data on information-sensitivity in deontic modals and condition-

als. In this section I will present new data that highlight contrasts in information-sensitivity with ‘ought’, on the one hand, and ‘must’ and ‘may’, on the other. (Addi-

tional data will be provided in later sections as well.) I want to ag that judgmentsconcerning some of the examples can be admittedly subtle, and they can vary givensubtle changes in context. Indeed, this will be part of what needs to be explained.

e positive account in §§– will, I hope, crystalize the informal reactions de-scribed in this section.

Intuitively, the ‘ought’ conditionals in ()–() say what is best on a condition:Given that the miners are in Sha A (Sha B), our blocking Sha A (Sha B) is the

expectably best action. ()–() do not impose an obligation on us conditional onhow the world happens to be, unbeknownst to us. By contrast, ()–() do seem to

impose such an obligation.

() ?If the miners are in Sha A, we must block Sha A.

() ?If the miners are in Sha B, we must block Sha B.

is is part of why using ‘must’ in the conditionals is dispreferred in many contexts.Informally, using ‘must’ in the conditionals seems to be more emphatic than is war-

I use‘?’ to indicate that using the marked item is dispreferred. us‘?’ marks a weakerinfelicity than ‘’.

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ranted. However, the relative felicity of ‘ought’ and ‘must’ can vary depending on

the context. Consider a context in which it is particularly urgent that no miners belost. Suppose we are members of a rescue team called upon to save the miners. We

have a longstanding record of never losing anyone on the job, and we intend to keepthat record intact. Aer all, people’s lives are at stake! Someone might die! May it

never be! Getting into this frame of mind can improve the felicity of ()–(). Buteven if there are contexts in which ()–() are acceptable, it is important that in these

contexts (), and even (), no longer seems true. Alice’s response in () is marked.

() We may block neither sha.

() Alice: If they’re in A, we must block A! And ifthey’re inB, we must block B! Aer all, people’s lives are at stake. No one is going to die, not

on my watch!Bert: So what should we do?

Alice: We should (/may) block neither sha.

e ‘must’ conditionals in ()–(), along with (), appear to be jointly inconsistent

with (), and even with ().Surprisingly, similar points appear to hold for ‘may’. Consider the following vari-

ant of the Miners Case — call it ‘Miners*’. As before, ten miners are trapped eitherin Sha A or Sha B, though we do not know which, and we only have enough sand-

bags to block one sha. But now suppose that Sha A is connected to another sha,Sha C, in such a way that blocking Sha A or Sha C will save all the miners if they

are in Sha A but will kill all the miners if they are in ShaB. Sha B is likewise con-nected to another sha, Sha D, in such a way that blocking Sha B or Sha D will

save all the miners if they are in Sha B but will kill all the miners if they are in ShaA. Many nd using ‘may’ in ()–() to be anomalous, where this anomalousnessseems similar in character to that from using ‘must’ in ()–().

() ?If the miners are in Sha A, we may block Sha A.

() ?If the miners are in Sha B, we may block Sha B.

It is not counterintuitive that part of what sounds odd about using ‘may’ in ()–()

is that it grants us a permission to block such-and-such sha conditional on how the

world happens to be, independent of our knowledge, similarly to how using ‘must’in ()–() appears to impose such an obligation. e ‘ought’ conditionals in ()–()are acceptable in a way that the ‘may’ conditionals in ()–() are not. Deontic

‘ought’ does not imply deontic ‘may’.



What is most important for present purposes, however, is that if the ‘may’ con-

ditionals in ()–() are accepted, () no longer seems true. It is hard to hear the‘may’ conditionals as acceptable except in a context in which () is also accepted,

as brought out in ()–().

() We must block one of the shas.

() Alice: If they’re in A, we may block A. And if they’re in B, we may block

B.Bert: So what should I tell the team? Should I ip a coin to decide which

sha to block?

Alice: What are you talking about? We can’t block either sha!

() Alice: If they’re in A, we may block A. And if they’re in B, we may block

B.Bert: But we don’t know which sha they’re in. Why not hedge our bets

and guarantee saving nine of the miners?Alice: Because I won’t settle for a suboptimal outcome. People’s lives are

at stake! We must block one of the shas!

e Miners Puzzle is no puzzle at all when expressed with ‘must’ or ‘may’.

As these data with ‘must’ and ‘may’ provide the primary basis for my positiveaccount in §§– it is worth pausing to reiterate what I take the data and their sta-

tus to be. is may be helpful for readers who nd themselves questioning some of the judgments I have recorded. e rst piece of data concerns intuitions of rela-

tive felicity — namely, that using ‘must’ in the deontic conditionals is dispreferredto using ‘ought’ in the original Miners Case, and that using ‘may’ in the deontic

conditionals is more dispreferred in the variant Miners* than is using ‘ought’ in thedeontic conditionals in the original Miners Case. Importantly, however, these rela-tive felicities are not absolute, but can vary given certain shis in context (more on

which below). e second piece of data concerns intuitions about natural languageentailments — namely, that ()–(), unlike () and ()–() or () and ()–(), are

jointly consistent with (). e intuitions recorded here appear from preliminary polling to be sufficiently robust to warrant our beginning to theorize about them;

they are not idiosyncratic. But it is worth noting that there is a sense in which they

are also expected in light of independent and more well-established data concerningdeontic modals in root clauses. ere is a robust body of evidence, much of whichis garnered from work in descriptive linguistics, that deontic ‘must’ and ‘may’ have

performative aspects to their conventional meaning — specically, that an utteranceof deontic ‘Must ϕ’ issues an imperative and an utterance of deontic ‘May ϕ’ grants



a permission. By contrast, it is oen claimed that deontic ‘Ought ϕ’, even if it can

be used to perform an imperatival speech act in certain contexts, it does not doso as a matter of its conventional meaning. When seen against the backdrop of

these broader data, the data in this section are perhaps less surprising. Indeed they may be understood as an extension to the case of deontic ‘ought’, ‘must’, and ‘may’

in another type of matrix environment or main clause, namely, the consequent of conditional. e question now is how to capture these contrasting semantic and

discourse properties of deontic modals, especially as they bear on recent discussionsof information-sensitivity. It is to this question that I now turn.

Previous treatments

e examples in § suggest that deontic ‘must’ and ‘may’ are not subject to the samesorts of apparent modus ponens violations as deontic ‘ought’, and that contextual

factors can affect the relative felicity of ‘ought’, ‘must’, and ‘may’. Previous treatmentsof information-sensitivity in the literature are ill-suited to capture these points.

First, the accounts in K & MF , C . ,L , F , and S a are silent on the contrast between‘ought’ and ‘must’ and its relevance for discussions of the Miners Puzzle. ese ac-

counts are not simply incomplete, however. Given certain natural assumptions, themechanisms by which they respond to the Miners Puzzle overgenerate and predict

the felicity of the ‘may’ and ‘must’ conditionals and their joint consistency with ().

Start with the semantics in K & MF . On this semanticsdeontic modals are interpreted with respect to a body of information i, representedby a set of possible worlds, and a selection functiond that selects a set of best worlds

from this domain: ‘Ought ϕ’ is true at ⟨w, i⟩ iff ‘ϕ’ is true at all worlds w′∈ d (i).

What makes the semantics “information sensitive” in an interesting sense is that the

selection function is sensitive to which worlds are eligible. Even if a world is selectedas “best” relative to some domain, it might not be selected relative to a subset of thatset of which it is a member. is property of the selection function helps capture

how a deontic modal in the consequent of a conditional can be interpreted with

See esp. W : – and ; N ; P : , –; S

c. See also, among many others, L , L , , W , H- , L , W , C , P , , M , V- , H & P , S .

For related discussion in the case of conditional imperatives see S , K &

S ; cf . the treatment of conditional questions in I & R .See C and S a for further discussion.

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respect to the information carried by the antecedent: ‘If ψ, ought ϕ’ is true at ⟨w, i⟩

iff ‘ϕ’ is true at all worlds w′∈

d (i ∩ ψ). is semantics predicts that ()–() are jointly consistent. ough the best worlds relative to our information state, which is

unsettled as to the location of the miners, are worlds in which we block neither sha,the best worlds relative to our information state strengthened with the information

that the miners are in, say, Sha A are worlds in which we block Sha A.is semantics overgenerates. Let ‘blX ’ denote the proposition that we block

Sha X or Neither sha, and let ‘inX ’ denote the proposition that the miners arein Sha X. First, if we treat ‘may’ as expressing existential quantication over the

set of deontically best worlds, as would be expected, then the ‘may’ conditionalsin ()–() are predicted to be unambiguously true and consistent with (). If allworlds in d (i ∩ inA) are blA-worlds, then some worlds in d (i ∩ inA) are blA-worlds.

Second, insofar as ‘ought’ is already given a semantics of necessity, expressing uni- versal quantication over the set of best worlds, the semantics, at least as it stands,

has no mechanism for predicting the contrasting discourse properties of ‘ought’ and‘must’. But however the semantics might be rened to make ‘must’ logically stronger

than ‘ought’, it is unclear why the ‘must’ conditionals in ()–() would not also beacceptable or consistent with () insofar as the deontic selection function for a de-

ontic modal embedded in the consequent of a conditional is given as argument thestrengthened information state — i.e., the initial information state updated with the

information carried by the antecedent.Kolodny and Macfarlane might respond by interpreting ‘must’ and ‘may’ with

respectto a different deontic selection function, one that is notinformation-sensitive.But this seems ad hoc. In our examples, the values and norms that bear on what weought to do are, intuitively, the same as those that bear on what we may and must

do. Other things equal, I think we should prefer an account that captures this point.(Similar remarks hold for the semantics in S a, which, among other

things, integrates Kolodny and Macfarlane’s discussions of information-sensitivity into a standard ordering semantics framework.)

Roughly, on this account deontic modals are interpreted with respect to a “preorder selector”

λi . ≲i, or a function from an information state i to a preorder ≲i on the worlds in that informationstate. Preorder selectors can be understood as representing expected values of actions given differentbodies of information. e preorder selector for a deontic modal in the consequent of a conditional

is given as argument the strengthened information state; this is to capture how just as () can beunderstood as expressing a judgment about what is expectably best, conditionals like ()–() can beunderstood as expressing judgments about what is expectably best on a condition, i.e., judgments of

conditional expected value. Even if the≲i best worlds are worlds in which we block neither sha, the≲i∩ inA best worlds, e.g., may be worlds in which we block Sha A. us, ()–() are jointly satisable.

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e semantics in L faces analogous problems. Lassiter develops

a scalar semantics for modals and treats deontic modals as making claims aboutexpected values. Roughly, ‘Must ϕ’ is true iff the expected value of ϕ exceeds some

high threshold value; ‘May ϕ’ is true iff the expected value of ϕ exceeds some low threshold value; and ‘Ought ϕ’ is true iff the expected value of ϕ is greater than the

expected value of any contextually relevant alternative ψ. Deontic conditionals aretreated as claims about conditional expected values. is semantics predicts that the

‘must’ and ‘may’ conditionals in ()–() and ()–() are true and consistent with(). It also makes no provisions for how shis in context affect the relative felicity of

‘ought’ and ‘must’.C . builds information-sensitivity into the semantics by adding

a “decision problem” parameter δ to a standard ordering semantics framework. e

decision problem partitions the set of contextually live worlds i, where each cell inthe partition represents an action that is available, or choosable, to the agent. In

effect, actions in the decision problem get ranked in terms of their worst possibleoutcome as determined by a preorder≲ that ranks worlds in terms of their realization

of certain basic values or ends (e.g., the number of miners’ lives saved). ‘Ought’universally quanties over the worlds in the best cell — or, we might say, over the ≲i

δ

best worlds. In the Miners Case, the decision problem partitions the informationstate i into three cells: worlds in which we block neither sha, worlds in which we

block Sha A, and worlds in which we block Sha B. We save nine miners in allworlds in i in which we block neither sha. But since we do not know which sha

the miners are in, we save no miners in some worlds in which we block Sha A andin some worlds in which we block Sha B. Since saving no miners is ≲ worse thansaving nine miners, the cell in which we block neither sha is ranked highest. us,

() is true. Treating conditional antecedents as restricting the given informationstate, ()–() are also predicted to be true. In the case of (), i is restricted to worlds

in which the miners are in Sha A. Relative to this restricted information state, wesave all ten miners in each world in the cell in which we block Sha A, but save only

nine miners in each world in the cell in which we block neither sha and save nominers in each world in the cell in which we block Sha B. us, the cell in which

we block Sha A is ranked highest relative to the strengthened information state,and () is predicted to be true. ( Mutatis mutandis for ().)

is semantics also overgenerates. If we treat ‘may’ as expressing existentialquantication over the worlds in the best cell, the ‘may’ conditionals in ()–()are predicted to be true and consistent with (). In the case of (), if all the ≲i∩ inA

δ

best worlds are blA-worlds, then some of the ≲i∩ inAδ

best worlds are blA-worlds. Andgiven that the decision problem partitions the strengthened information state in the



interpretation of conditionals, it is not obvious how this semantics would predict

the contrasts between the ‘ought’ and ‘must’ conditionals.Unlike the above accounts, F proposes no revisions to the stan-

dard semantics in responding to the Miners Puzzle. In his attempt to save the stan-dard semantics, von Fintel denies that the ‘ought’ conditionals in ()–() are literally

true. He treats them, instead, as elliptical for conditionals like ()–().

() If we learn that the miners are in Sha A, we ought to block Sha A.

() If we learn that the miners are in Sha B, we ought to block Sha B.

ere are a number of concerns with this sort of response (see C for furtherdiscussion). What I want to emphasize here is simply that it overgenerates. ere

is a clear contrast in acceptability between ‘must’ and ‘may’ conditionals with ‘if ψ’and ‘if we learn that ψ’ as their antecedents. Even in a context in which ()–() and()–() are anomalous, the following conditionals are perfectly felicitous.

() If we learn that the miners are in Sha A, we must block Sha A.

() If we learn that the miners are in Sha B, we must block Sha B.

() If we learn that the miners are in Sha A, we may block Sha A.

() If we learn that the miners are in Sha B, we may block Sha B.

It would odd, to put it mildly, if the antecedents of deontic ‘ought’ conditionals were

reinterpreted in the proposed way but the antecedents of deontic ‘must’ and ‘may’conditionals were not.

e lesson that I want to highlight is this: An explanation of the Miners Puzzlewill not lie simply in a denial of modus ponens or in general considerations about

the semantics of deontic modals and conditionals. ‘Ought’ holds the key.C recognizes that ‘ought’ and ‘must’ differ with respect to their

information-sensitivity. On Charlow’s semantics, ‘must’ quanties over the bestworlds in a preorder that ranks worlds in terms of their realization of certain basic

values. Like Cariani et al., Charlow captures information-sensitivity with ‘ought’,in part, by coarsening this preorder. In the coarsened ordering that gures in theinterpretation of ‘ought’, worlds cannot be ranked differently unless they differ with

respect to the realization of our actionable values, i.e., those we know how to realize.First, Charlow’s account makes no provisions for how the relative felicity of

‘ought’ and ‘must’ can depend on standing contextual assumptions, and incorrectly predicts that the truth of a ‘must’ claim never depends on relevant information or

what we know. Even if we are quite sure that we will not learn which sha the miners



are in, if this is not denitively settled in the conversation, using ‘ought’ to express

our obligation to block neither sha, as in (), is preferred. But if we settle that wewill not learn the miners’ location, using ‘must’ becomes acceptable, even preferred.

() Alice: Well, it looks like we’re never going to be able to nd out which

sha the miners are in.Bert: So what should I tell the team?Alice: at we must block neither sha.

But Charlow’s semantics incorrectly predicts that ()

() We must block neither sha.

is false since it treats ‘must’ as only being interpreted with respect to the relevantbasic values — here, the number of lives saved.

Second, Charlow’s semantics predicts that the ‘must’ and ‘may’ conditionals in

()–() and ()–() are all true (assuming, as is plausible, that ‘may’ gets treatedas the dual of ‘must’). Even if there are contexts in which these conditionals are ac-

ceptable, they are not acceptable in all contexts. Drawing on his remarks about asimilar issue (: –), Charlow might reply that the ‘must’ and ‘may’ condi-

tionals are unassertable even if true. He might say that in light of the conventional,but non-semantic, performative properties of ‘must’ and ‘may’, utterances of these

conditionals impose an obligation or grant a permission, respectively, on us condi-tional on how the world happens to be; but since blocking either sha is inadvisable,

given our limited information, performance of such speech acts would be generally infelicitous. Such considerations about the conventional force of ‘must’ and ‘may’

are right as far as they go, but they are incomplete. We still need an account of pre-cisely what features of context affect the relative felicity of ‘ought’, ‘must’, and ‘may’.Also, other things equal, we should prefer an account that treats the truth conditions

and performative properties of ‘must’ and ‘may’ as integrated — e.g., by deriving thelatter from the former — rather than as thoroughly dissociated, as on Charlow’s ac-

count. It is hard to know precisely what is predicted by an account that so radically divorces truth conditions from felicity conditions.

Semantics for ‘ought’, ‘must’, and ‘may’

In this section I will offer an independently motivated account of the contrast be-

tween ‘ought’, on the one hand, and ‘must’ and ‘may’, on the other, an account which



I develop in greater detail elsewhere (S , c). In the next section I will

argue that this semantics for deontic modals makes the correct predictions aboutour data.

It is well established that ‘ought’ and ‘should’ (“weak necessity modals”) areweaker than modals like ‘must’ and ‘have to’ (“strong necessity modals”). For in-

stance, ‘Ought ϕ’ can be followed by ‘Must ϕ’, as in (a), but not vice versa, as in(b). Similarly, (a) is consistent in a way that (b) is not.

() a. I ought to help the poor. In fact, I must.b. I must help the poor. In fact, I ought to.

() a. I ought to help the poor, but I don’t have to.b. I must help the poor, but it’s not as if I should.

Further, as we saw in §§–, the relative felicity of ‘ought’ and ‘must’ depends onstanding assumptions in the context. Suppose you are considering whether to ght

in the Resistance or take care of your ailing mother. You mention that the value of family, which supports your helping your mother over your ghting, is important,

and I agree. But the issue is acknowledged to be complex, and it is not settled in thecontext whether there might be other more important competing values. Sensitive

to this, I may nd it more appropriate to express my advice thatyou helpyourmotherby using ‘ought’ than by using ‘must’.

() You ought to (/?must) take care of your mother.

But if we settle on the status of the value of family vis-à-vis other values, the judg-ment with ‘must’ improves.

() You: Family is most important — more important than country or any-thing else.

Me: I agree. You must take care of your mother.

e deontic necessity of your helping your mother depends on the value of family

being more important in your situation than any other potentially competing value.

See, e.g., S ; H , ; W ; H , ; L

; W ; C ; MN ; P , ; H & P- ; F & I .See W : ch. and MN : ch. for prescient discussion and

related cases. See R , for recent emphasis of how the relative felicity of ‘ought’and ‘must’ depends on standing assumptions in the context. I critically discuss her view in my .See also S . : –, F & I : –.

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Using ‘must’ is preferred if this condition is common ground. What is illuminating

is that even if it isn’t — i.e., even if it isn’t common ground that this precondition foryour having a genuine obligation to help your mother is satised — I can felicitously

express my advice that you help your mother using ‘ought’, advice which you may accept.

We can make progress in capturing these points with a more nuanced under-standing of the premises that gure in the interpretation of modals. Norms — and

values, goals, desires, etc. more generally — typically do not come in the form of blunt categorical imperatives or commands. ey are not usually of the form No

matter what, ϕ! . Rather they oen come with what I will call “applicability condi-tions” (“ACs”), or conditions under which they apply. If I want to go for a run, thecontent of my desire need not be that I go for a run, come what may. More plausi-

bly, it is that I go for a run given that it’s sunny, that I do not prefer to do anythingelse more, and so on. Our preferences are oen conditional, preferences for certain

circumstances. Similarly with moral norms. Suppose you promised Alice that youwould help her move. A norm against breaking your promise might be something to

the effect that you help Alice unless you made a more important conicting promiseto Bert, or keeping your promise would lead to some serious harm, or… Norms can

thus be understood on the model of conditional imperatives, imperatives that enjoinan action or state of affairs given that certain circumstances obtain. is captures

the intuitive idea that depending on the circumstances, only certain norms may be“in force” (see my b for further discussion and motivation). (Categorical norms

can be treated as having the tautology as their applicability condition.)ese points can be integrated into a standard premise semantic framework formodals. Modalsaretreated as receiving their interpretation from a contextually sup-

is phenomenon is not unique to deontic readings of ‘ought’ and ‘must’. Similar points holdin the epistemic domain. Suppose we are working on a class art project together. I ask you wherethe colored pencils are. Normally you put them in the drawer with the crayons, but sometimes youaccidentally put them on the shelf. In this scenario it is more appropriate for you to use ‘ought’ andreply with ‘ey ought to be in the drawer’. Suppose, alternatively, that we are looking for the colored

pencils together, and you indicate that you have just seen something that leads you to conclude thatthe colored pencils are in fact in the drawer. Perhaps you noticed that they weren’t on the shelf, andthat is the only other place you think they could be. Here it is more natural for you to use ‘must’and reply with ‘ey must be in the drawer’. e epistemic necessity of the colored pencils’ being in

the drawer depends on the fact that this isn’t one of the atypical days when you accidentally put thecolored pencils on the shelf. Using the strong necessity modal ‘must’ is preferred if, and only if, youknow that conditions are normal in this way. Parallel to the deontic case, you can use ‘ought’ evenif you aren’t in a position to judge whether this precondition for the truth of the epistemic necessity claim is satised.

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plied set of premises. Since modals can themselves occur in intensional contexts,

it is standard to index premise sets to a world of evaluation (written ‘Gw’). Whichpremise sets are relevant for the evaluation of a given modal sentence can depend on

how things happen to be in the actual world, or on how things could be but aren’t orcould have been but weren’t. What Little Timmy’s parents command might change

from one world to the next; thus the meaning of a phrase like ‘what Little Timmy’sparents command’ that determines the intended reading for ‘must’ in ()

() In light of what Little Timmy’s parents command, Little Timmy must be inbed by eight.

can be treated as a function that assigns to every possible world the set of propo-

sitions describing Little Timmy’s parents’ rules in that world. Similar remarks holdfor the meanings of phrases like ‘in view of the relevant circumstances’, ‘according toU.S. law’, ‘in light of your goals’, and so on. It is these functions that context is said to

supply for the interpretation of modals. Call these functions unsaturated premise sets

(written ‘P ’). Call the value of an unsaturated premise set given a world of evaluation

a saturated premise set — or simply a premise set (written ‘P w’).We can capture the role of applicability conditions in terms of variability in the

values of unsaturated premise sets at different worlds. Suppose we have a norm thatenjoins ϕ given that conditions C obtain. e content of this norm can be repre-

sented, intuitively, with an unsaturated premise set P that assigns to every relevantC -world a premise set that includes ϕ. e premises in a saturated premise set thus

reect what is enjoined by a body of conditional norms — or what is preferred inlight of a body of conditional preferences, what is the case in light of a body of evi-dential relations, etc. — given the circumstances that obtain in the evaluation world.

ese conceptual points about the premises relative to which modal claims areinterpreted can inform our semantics for deontic modals. I give ‘must’ and ‘may’

their usual semantics of necessity and possibility. Roughly, ‘Must ϕ’ says that theprejacent proposition ϕ follows from P w — where P w is the premise set that is the

value of the given unsaturated premise set P at the evaluation world w. Slightly lessroughly, given an unsaturated premise set F (a “modal base”) that describes some

set of relevant background facts, and given some further unsaturated premise setG (an “ordering source”) that represents the content of some ideal — morality, your

goals, etc. — ‘Must ϕ’ says that ϕ follows from every maximally consistent subset of F w ∪ Gw that includes F w — or, introducing some notation in Denition , that ϕ

Equivalently, a preorder (L ). See especially K , , ; also F , L , V .

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follows from every set in (F w,Gw). Treating ‘may’ as the dual of ‘must’, ‘May ϕ’

says that ϕ is compatible with some set in (F w,Gw).

Denition . (Q,Q′) ∶= {P ⊆ (Q ∪ Q′) ∶ Q ⊆ P ∧ cons(P ) ∧ ∀P ′∶ P ⊂ P ′ ⊆

(Q ∪ Q′)→ ¬cons(P ′)}, where, for a set of propositions S, cons(S) iff ⋂S ≠ ∅

Denition . ‘Must ϕ’ is true at w iff ∀P w ∈ (F w,Gw) ∶⋂P w ⊆ ϕ

Denition . ‘May ϕ’ is true at w iff ∃P w ∈ (F w,Gw) ∶⋂(P w ∪ ϕ) ≠ ∅

e truth of ‘Must ϕ’ and ‘May ϕ’ depend on the values of the unsaturated premisesets F and G at the world of evaluation. In order for deontic ‘Must ϕ’ or ‘May ϕ’ to

be accepted in a context, and thus true at all live possibilities in the context, the con-

text set must be restricted to worlds w in which the relevant applicability conditionsobtain; for all worlds w in the context set, the circumstances in w must be such thatthe premise set Gw (along with F w) veries the deontic necessity or possibility of ϕ.

(e context set is the set of worlds compatible with what is mutually presupposedfor the purposes of the conversation. For expository purposes, I will suppress the

references to F unless otherwise noted.)e same doesn’t hold for ‘ought’. On my view, what makes weak necessity

modals “weak” is that they express a kind of conditional necessity, necessity on the

supposition that certain conditions, the applicability conditions of certain relevantpremises, are satised (see S , c for further motivations and rene-

ments). Roughly, ‘Ought ϕ’ is true iff ‘Must ϕ’ is true at all relevant worlds in which

the considerations that bear on the necessity of ϕ apply and are not defeated. Moreformally, where s is a selection function that selects a set of closest relevantχ-worldsto the world of evaluation, for some contextually supplied condition χ (more on χ

below):

Denition . ‘Ought ϕ’ is true at w iff ‘Must ϕ’ is true at all worlds w′∈ s(w, χ) iff

∀w′∈ s(w, χ)∶ ∀P w′ ∈ (F w′,Gw′) ∶⋂P w′ ⊆ ϕ

Treating ‘ought’ as conditional in this way carves out a crucial role for expressionsof weak necessity in conversation, thought, and planning. In uttering ‘Must ϕ’ we

For simplicity I make the limit assumption (L : –) and assume that the givenpremise sets have maximally consistent subsets — i.e., that ordering the consistent subsets of F ∪ G

(that include F as a subset) by set inclusion ⊆ yields a set ofsubsets that are ⊆-maximal. For semanticswithout the limit assumption, see L ; K , ; S .

In my c I defend a pragmatic constraint on this selection function that the set of selectedworlds not be included in the context set c, i.e., that s(w, χ) ⊈ c.

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assume a body of relevant circumstances and norms, and assert that ϕ is necessary

relative to what the norms enjoin given those circumstances. By using ‘ought’ wecan coordinate on the necessity of ϕ without having to restrict the future develop-

ment of the conversation in such a way that decisively settles on the truth of certainapplicability conditions. Since ‘Ought ϕ’ can be true at w even if Gw does not sup-

port the necessity of ϕ, by accepting ‘Ought ϕ’ we can proceed as if ϕ is necessary while remaining open to new evidence about whether the relevant ACs are satised,

or even neutral on what the relevant ACs are.Returning to ()–(), the deontic necessity of your helping your mother de-

pends on the value of family being more important in your situation than otherpotentially competing values. In (), since this condition that the value of fam-ily is to take precedence is common ground, my ‘must’ claim is felicitous and true

throughout the context set. But in (), where this AC is not common ground, wereI to use ‘must’ I would imply that I am foreclosing certain possibilities that you have

le open. Unless I have the authority to do so, my using the weak necessity ‘ought’ ispreferred. By using ‘ought’ I can propose that you help your mother while remain-

ing neutral on whether the AC for your helping your mother might not be satised.If you accept my proposal, we can plan accordingly without committing ourselves

hereaer to an assumption about the status of the value of family vis-à-vis other values we accept or may come to accept.

Finally, I will treat indicative deontic conditionals as updating contexts by re-moving worlds in the context set in which the antecedent is true that do not verify

the modalized consequent clause.

Given our analyses for ‘must’, ‘may’, and ‘ought’above, this yields the following:

Denition . ‘If ψ, mustϕ’ is accepted in a context c iff for every ψ-world w ∈ c, andevery set P w ∈ (F w,Gw) ,⋂P w ⊆ ϕ

Denition . ‘If ψ, may ϕ’ is accepted in a context c iff for every ψ-world w ∈ c, and

some set P w ∈ (F w,Gw) ,⋂(P w ∪ ϕ) ≠ ∅

Denition . ‘If ψ, ought ϕ’ is accepted in a context c iff for every ψ-world w ∈ c,

‘Must ϕ’ is true at all worlds w′∈ s(w, χ)

(I give acceptance conditions rather than truth conditions here so as to remain neu-tral on certain independent issues concerning truth conditions for conditionals.)

See L , , ; K , .For recent discussion, see, e.g., S , W , R ,

Y , .

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Information-sensitivity in context

. ‘Must’ and ‘may’

Let’s apply these analyses to the Miners Case. Consider the following worlds, AK,

AK, BK, BK, characterized with respect to which sha the miners are in and whetherwe know it. Simplifying quite a bit, we cancapture the dependence of our obligations

on our epistemic state with an unsaturated premise set like G, which assigns premisesets that include blN to worlds in which we do not know which sha the miners are

in, and premise sets that include blX to worlds where we learn that the miners arein Sha X.

() GAK = {blA}GAK = {blN }GBK = {blB}GBK = {blN }

Start with the ‘must’ conditionals in ()–(), reproduced below.

() If the miners are in Sha A, we must block Sha A.

() If the miners are in Sha B, we must block Sha B.

Given that we do not know which sha the miners are in, and that it is not settledthat we will learn which sha the miners are in, the context set includes AK and

BK. is correctly predicts that ()–() are not acceptable in our original context:blA does not follow from GAK, and blB does not follow from GBK. However, suppose

now that, as in the context in (), we have an unconditional obligation to block thesha that the miners are actually in, as reected in G′.

() G′

AK = {blA}G′

AK= {blA}

G′

BK = {blB}G′

BK= {blB}

()–() are accepted relative to G′. But if () is also accepted, then () is false at all

worlds in the context set and is thus rejected.

() Either the miners are in Sha A or the miners are in Sha B.

() We may block neither sha.



Similar considerations hold concerning the ‘may’ conditionals in ()–().

() If the miners are in Sha A, we may block Sha A.

() If the miners are in Sha B, we may block Sha B.

Reconsider the variant of the Miners Case described in §. ere are two additional

shas, Sha C and Sha D. Blocking Sha A or Sha C will save all the miners if they are in Sha A but will kill all the miners if they are in Sha B; and blocking

Sha B or Sha D will save all the miners if they are in Sha B but will kill all theminers if they are in Sha A. is version of the case might call for an unsaturated

premise set like G′′.

() G′′

AK

= {blA ∨ blC }G′′

AK= {blN }

G′′

BK = {blB ∨ blD}G′′

BK= {blN }

()–() are not acceptable relative to G′′: blA is notcompatible with G′′

AK, and blB is

not compatible with G′′

BK. But if the ‘may’ conditionals are accepted — e.g., if context

supplies the unsaturated premise set G′′′ in () — then () is false throughout the

context set.

() G′′′

AK = {blA ∨ blC }G′′′

AK= {blA ∨ blC }

G′′′BK = {blB ∨ blD}

G′′′

BK= {blB ∨ blD}

() We mustn’t block any sha.

ere is no Miners Puzzle with ‘must’ or ‘may’.

. ‘Ought’

Now turn to the ‘ought’ examples in ()–(), reproduced below.

() We ought to block neither sha.

() If the miners are in Sha A, we ought to block Sha A.

() If the miners are in Sha B, we ought to block Sha B.



Start with (). Recall that according to the semantics for ‘ought’ in Denition ,

‘Ought ϕ’makesaclaimaboutthenecessityof ϕ at certain closestχ-worlds, for somecontextually supplied condition χ. Given the role for ‘ought’ described in §, and

given plausible conversational maxims — especially, that given a set of alternativepropositions a speaker asserts the proposition she thinks is most likely to remain

accepted throughout the evolution of the conversation —χ will be some conditionsuch that there is no alternative condition that is (presumed to be) at least as likely

as χ with respect to which ‘Oughtψ’ would be true, for contraries ‘ϕ’ and ‘ψ’. issuggests that in our original context for the Miners Case, χ will be the proposition

that we do not learn which sha the miners are in. is correctly predicts that () istrue: blN follows from GAK and GBK.

Our treatment of weak necessity as conditional necessity illuminates the role of

using ‘ought’ in (). Accepting (), as opposed to its variant with ‘must’ in (), al-lows us to plan under the supposition that we will remain ignorant of which sha

the miners are in while remaining open to the possibility that we will get new ev-idence about their location. But if we settle that we will not learn which sha the

miners are in, so that the context set is restricted to worlds that verify the necessity of blN , then using ‘must’ becomes acceptable and preferred:

() Alice: Well, it looks like we’re never going to be able to nd out which shathe miners are in.

Bert: So what should I tell the team?Alice: at we must block neither sha.

We can capture how the relative felicity of unembedded ‘ought’ and‘must’ judgmentsdepends on context.

Now turn to the ‘ought’ conditionals in ()–(). I suggest that when we accept()–(), we treat χ as the proposition that we learn which sha the miners are in.

is correctly predicts that the ‘ought’ conditionals are acceptable: blA follows fromGAK, and blB follows from GBK. Treating χ in the conditionals in this way is also mo-

tivated by independent principles of interpretation. Uttering a conditional with the

is sensitivity to probabilistic information can be derived pragmatically. Upon hearing anutterance of ‘Ought ϕ’ a hearer might reason as follows: “S said ‘Ought ϕ’. So S must think there

is some live condition p given which ‘Must ϕ’ would be true. If S thought there was another livecondition q given which ‘Must ψ’ would be true (for contraries ‘ϕ’ and ‘ψ’) such that she assigns ahigher probability to q than to p, she would think ‘Must ψ’ was more likely to be true and acceptedthan ‘Mustϕ’. So S would have said ‘Oughtψ’, assuming that sheis being cooperative and obeying themaxims. But S didn’t say ‘Oughtψ’. So she must think p is not less likely than any relevant alternativecondition with respect to which ‘Ought ψ’ would be true.”

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antecedent ‘if the miners are in Sha A’ makes salient the possibility that the miners

are in Sha A. In a context in which we are planning for various contingencies, ut-tering ‘if the miners are in Sha A’ can also make locally salient the live possibility

that we learn that the miners are in Sha A. Aer all, contingency planning is plan-ning about what to do for the situation of recognizing that we are in such-and-such

circumstances. If our obligations about how to respond to the miners’ plight dependon our evidence or knowledge, a hearer can interpret utterances of ()–() as felic-

itous and acceptable by treating χ as the proposition that we learn which sha theminers are in. Principles of interpretive charity then motivate her to do so. Even if

in the global discourse context it is regarded as highly unlikely that we will discoverthe miners’ location, if it is not settled in the conversation that we won’t, then the‘ought’ conditionals can still be accepted.

Treating χ in the conditionals in this way has several further desirable features.First, it correctly predicts that if we settle that we won’t learn which sha the miners

are in, it becomes harder to hear the ‘ought’ conditionals as felicitous.

() Alice: Well, it looks like we’re never going to be able to nd out which shathe miners are in.

Bert: So what should I tell the team?

Alice: We should block neither sha. ?But if they’re in A, we ought toblock A, and if they’re in B, we ought to block B.

Alice’s response to Bert is marked.

Second, it makes sense of an otherwise puzzling suggestion in the literature men-tioned in §, namely, that the antecedents of the conditionals are elliptical for ‘if theminers are in Sha A (/Sha B) and we learn it’ ( F ). Our account

has the advantage of capturing the intuitions driving this move without having toclaim that the antecedents of certain ‘ought’ conditionals, but not those of various

other conditionals, are reinterpreted.ird, we correctly predict that there should be a reading of a deontic conditional

with ‘we ought to block neither sha’ as its consequent clause, namely, if χ is heldxed as the proposition that we do not learn which sha the miners are in. On the

readings of ()–() on which they are acceptable, these conditionals allow us to planfor the contingency in which we learn that the miners are in such-and-such sha.

But if the primary question in the conversation is how we should plan given the mostlikely scenario, the relevant worlds at which the necessity of the prejacent of ‘ought’is evaluated will be worlds in which we do not learn which sha the miners are in.

In such a context, it is the ‘ought’ conditional in () that is preferred.



() Even if the miners are in Sha A, we ought to block neither sha.

(Note, however, that a construction like ‘even if ’, ‘whether or not’, or the like must

be prexed to the antecedent condition; this is to block the implicature or presup-position of a hypothetical conditional ‘If ψ, ϕ’ that ‘If ¬ψ, ¬ϕ’ is also true (see, e.g.,

G & Z , I , A , H ).)Fourth, our treatment of the ‘ought’ conditionals elucidates a previously unno-

ticed feature of the Miners Case: Aer uttering (), it is much less natural, perhaps

even infelicitous, to begin an utterance of the conditionals with ‘and’ as opposed to‘but’.

() We ought to block neither sha. But (/And) if the miners are in Sha A,

we ought to block Sha A; and if the miners are in Sha B, we ought toblock Sha B.

e need for ‘but’ is also evident in the reverse sequences involving an utterance of the conditionals followed by an utterance of ().

() If the miners are in Sha A, we ought to block Sha A; and if the minersare in Sha B, we ought to block Sha B. But (/And) we ought to block

neither sha.

Adversative conjunctions like ‘but’, in contrast to ‘and’, are required when the sec-

ond conjunct contradicts an expectation raised by the rst conjunct. But if ()–()

are jointly consistent, as the literature has largely assumed, it is puzzling why ‘but’should be required here. e above account provides a natural explanation. ‘But’is required in ()–() to mark that there is a shi in which live possibilities we

are considering in our planning and contingency planning. In (), uttering ()makes salient live possibilities in which we do not learn the miners’ location, and

thus leads us to expect that such possibilities will be the main topic of our delibera-tion and planning. Using ‘but’ before uttering the conditionals is required in order

to mark that this expectation is canceled. (Analogous remarks hold for ().)ough I have said that the ‘ought’s in (), on the one hand, and ()–(), on the

other, are interpreted with respect to different values of χ, this need not imply thatthere is an equivocation in a sense that would render ()–() jointly unsatisable. If

we say, familiarly, that the consequent of a conditional is interpreted with respectto the local context set up by the antecedent — i.e., the global context incrementedwith the antecedent (K , S , H ) — then ()–

() can all be true with respect to a constant global context: e shi in the value



of χ in the conditionals results from a local, or sentence-internal, update. Since it

is standard in assessing entailment relations to interpret all the sentences with re-spect to a constant global context (see, e.g., K & L , F

), we could maintain that ()–() are jointly satisable. Regardless, what is of primary importance for present purposes is the phenomena: e ‘ought’s in ()–()

are interpreted relative to a constant deontic unsaturated premise set but differentcontextually supplied values of χ; this has the result that the necessity claims in

question are evaluated at different relevant worlds.In sum, we correctly predict that ()–() can be simultaneously accepted in our

original context. By accepting the unembedded ‘ought’ claim in () along with the‘ought’ conditionals in ()–(), we can, on the one hand, coordinate on a plan toblock neither sha, while, on the other hand, remain open to the possibility that we

will learn which sha the miners are in and plan for this contingency. It is the weak necessity modal ‘ought’, in contrast to ‘must’ or ‘may’, that plays this complex role in

conversation, deliberation, and planning.

Conclusion

Discussions of the Miners Puzzle have focused on a limited range of examples in-

volving ‘ought’ within a single type of conversational context. Some have used theseexamples as the basis for making sweeping generalizations about deontic modalsand conditionals. is is problematic. What makes the Miners Puzzle a puzzle are

features unique to the semantics of weak necessity modals like ‘ought’. Broaden-ing our data set sheds new light on information-sensitivity in deontic modals and

conditionals. By considering examples with possibility modals and strong necessity modals, and examining the import of subtle shis in context, we can illuminate how

context and content mutually interact to guide how we coordinate our actions andexpectations in conversation, deliberation, and planning.

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