Desire

1. Introduction

Our topic concerns two puzzles involving desire reports. They can be illustrated by considering the following case:

Coins: Three fair coins will be flipped, and Bill’s reckless brother has bet the family fortune on the outcome. If the first coin lands heads, and the second or third coin lands tails, the entire fortune will be lost. If all three coins land heads, the fortune will be doubled. If the first coin lands tails, nothing happens, i.e., nothing is lost (or gained).

(1) is easily heard as true in this scenario:

• (1) Bill wants all three coins to land heads.

After all, if all three coins land heads, Bill knows that the fortune will be doubled, and he would certainly like that. But by the same token, (2) is also easily heard as true:

• (2) Bill wants the first coin to land tails.

After all, if the first coin lands heads, Bill knows there’s a good chance that the fortune will be lost, and he certainly would not like that.

However, (1) and (2) cannot be felicitously conjoined (as indicated by the ‘#’ preceding the example):

• (3) # Bill wants all three coins to land heads, and he wants the first coin to land tails.

(3) sounds incoherent. But this is surprising: if both (1) and (2) are true, then why can’t they be put together, as in (3)? Let us call this the three heads and tails puzzle, or the 3H-T puzzle.

The second puzzle begins with the observation that (4) is unacceptable in context:

• (4) # Bill wants the first coin to land heads.

A natural response to (4) would be: “but if the first coin lands heads, Bill knows that the fortune will likely be lost, and he definitely wouldn’t like that”. However, the negation of (4) cannot be felicitously conjoined with (1):

• (5) # Bill wants all three coins to land heads, but he doesn’t want the first coin to land heads.

(5) sounds incoherent. But this is unexpected: if (1) is true and (4) is false, why isn’t the conjunction of the former along with the negation of the latter acceptable? Let us call this the three heads and not-first-heads puzzle, or the 3H-$\overline{H}$ puzzle.¹

In this paper, we try to solve both the 3H-T puzzle and the 3H-$\overline{\text{H}}$ puzzle by developing a novel semantics for desire reports. This account is built around three ideas. First, we propose that desire ascriptions are evaluated relative to a contextually supplied set of propositions, or alternatives. $\text{S}$’s preference ordering over these alternatives determines the semantic value of desire reports.² On our entry, there are no sets of alternatives relative to which the conjunctions (3) and (5) are true, which explains their unacceptability.

Second, we propose that desire reports carry a requirement to the effect that the prejacent of the ascription must be suitably related to the background set of alternatives. That is, we propose a representation condition on the prejacent. As we show, this constraint explains why the natural set of alternatives relative to which (1) is evaluated is one where the report comes out true.

Finally, we propose a dominance condition concerning the subject’s ranking of the alternatives. If there is some top-ranked $p$-entailing alternative by $S$’s lights, then $\text{S}$ must prefer every $p$-entailing alternative to every $\neg p$-entailing alternative, i.e., the $p$-entailing alternatives must dominate the $\neg p$-entailing alternatives. As we show, this explains why (4) is unacceptable. Overall, we argue that our theory provides us with an elegant resolution of our puzzles, and yields a promising approach to desire.

The paper is structured as follows. In §2, we show that existing theories of desire ascriptions fail to provide solutions to our puzzles. Then, in §3, we develop our theory in several stages. Finally, §4 concludes by discussing the relationship between desire verbs and deontic modals.

2. Existing Accounts

In this section, we consider how some existing approaches to desire fare with respect to our puzzles. To this end, we consider two influential accounts: the monotonic analysis of von Fintel (1999) (§2.1) and the decision-theoretic semantics of Levinson (2003) (§2.2). We argue that although these accounts can explain some aspects of our puzzles, neither provides us with satisfying solutions to them.³

2.2 Levinson’s (2003) Account

Now let us consider Levinson’s decision-theoretic account of desire reports. On this proposal, the desirability of a proposition for a subject $S$ is tied to the expected value of this proposition for $S$. The expected value of $p$ for $S$ is the utility of $p$ for $S$ weighted by $S$’s subjective probabilities (Jeffrey, 1965). More precisely, $⌜\text{S}$ wants $\text{p}⌝$ is true just in case the expected value of $p$, for $S$, outweighs the expected value of $\neg p$:¹⁰

Levinson’s semantics for want

$⌜\text{S}$ wants $\text{p}⌝$ is true in $w$ iff $E{V}_{w,S}(p)>E{V}_{w,S}(\neg p)$

Since we think that this account has few plausible responses available to our puzzles, we will be relatively brief here. First, let us suppose that Bill’s credences/utilities in the Coins scenario are as follows ($3H$ denotes the proposition that all three coins land heads, and $T$ denotes the proposition that the first coin lands tails):

To repeat, the 3H-T puzzle concerns the fact that both (1) and (2) are acceptable in the Coins scenario, but (3) is not:

• (1) Bill wants all three coins to land heads.

• (2) Bill wants the first coin to land tails.

• (3) # Bill wants all three coins to land heads, and he wants the first coin to land tails.

A routine calculation confirms that $EV(theresultisthreeheads)>EV(\neg theresultisthreehea$, and that $EV(thefirstcoinlandstails)>EV(\neg thefirstcoinlandstails)$. Thus, this semantics predicts that both (1) and (2) should be true. So given a standard meaning for natural language conjunction, the account predicts that (3) should be true as well. But then it is unclear why this sentence should be unacceptable.

As for the 3H-$\overline{\text{H}}$ puzzle, it involves the fact that both (4) and (5) are infelicitous:

• (4) # Bill wants the first coin to land heads.

• (5) # Bill wants all three coins to land heads, but he doesn’t want the first coin to land heads.

It is easy to show that $EV(theresultisthreeheads)>EV(\neg theresultisthreeheads)$. So Levinson’s account predicts that (4) should be false. Since (1) is predicted to be true, (5) is then predicted to be true as well. So we would expect this conjunction to be acceptable, contrary to observation.^11,12

It is worth noting that conjunctions that have the form of (5) have been used by proponents of von Fintel’s semantics to argue against accounts that invalidate Monotonicity, e.g., Levinson’s theory.¹³ The idea is that if p entails q, then conjunctions of the form $⌜\text{S}$ wants p, but S doesn’t want $\text{q}⌝$ are always unacceptable. However, such conjunctions can be true on views that reject Monotonicity. So, if Monotonicity-rejecting views are correct, it is unclear why these sentences should be infelicitous. By contrast, accounts that validate Monotonicity can offer a straightforward explanation: such conjunctions are simply false (von Fintel 1999; Crnič 2011). As should be clear, we think the picture is more complicated than this argument suggests. The real challenge from conjunctions of the form $⌜\text{S}$ wants p, but S doesn’t want $\text{q}⌝$ (where $p$ entails $q$) arises from the 3H-$\overline{\text{H}}$ puzzle: it involves cases where both $⌜\text{S}$ wants $\text{q}⌝$ and $⌜\text{S}$ wants p, but S doesn’t want $\text{q}⌝$ are unacceptable. As we’ve shown, this puzzle poses a problem for Monotonicity-accepters and Monotonicity-deniers alike.

In this section, we considered how existing accounts fare with respect to our puzzles. Although our survey hasn’t been exhaustive, we hope to have provided at least some motivation for thinking that these puzzles are genuine, and are not easily solved by existing theories. In the next section, we will try to explain these phenomena by developing a novel approach to desire reports.

3. The Meaning of want

In this section, we present our positive proposal in several stages. First, we provide a basic entry that captures some of the central features of our account (§3.1). Then we propose a constraint that governs the relationship between the prejacent of want reports and the set of possibilities relevant for the evaluation of these reports (§3.2). Finally, we posit a dominance condition on desire ascriptions (§3.3).

3.2 Representation

In §2.1, we saw that even if von Fintel’s account could somehow allow (2) (‘Bill wants the first coin to land tails’) to be true, it would then predict that the clearly unacceptable (8) should be true:

• (8) # Bill wants the first coin to land tails, so he wants a result other than three heads.

Unfortunately, the same problem arises for Account 1. (2) is true relative to ${\mathcal{A}}_{\text{coarse}}$, so ‘Bill wants a result other than three heads’ should also be true relative to ${\mathcal{A}}_{\text{coarse}}$, since t entails that the coins land in a pattern other than three heads.

Intuitively, what goes wrong with (8) is that the proposition the result is other than three heads makes salient certain distinctions that are not in play when we are evaluating the first conjunct, i.e., (2). Put another way, when we hear (2) as true, we are “backgrounding” the outcome where all the coins land heads. We can make this more precise through the following definition. Given a set of alternatives $\mathcal{A}$ and proposition $p$, let us say that $p$ is represented by $\mathcal{A}$ just in case every alternative in $\mathcal{A}$ either entails $p$ or entails $\neg p$.²² For instance, the proposition that the first coin lands tails is represented by ${\mathcal{A}}_{\text{coarse}}=\left\{\text{T},\text{H}\right\}$, but the proposition that the outcome is other than three heads is not, since h neither entails this proposition nor its negation.

We propose adding a representation requirement to the semantics of desire reports. More precisely, we will include this as a definedness condition on desire ascriptions.²³ The account then looks as follows:

Account 2

$⌜\text{S}$ wants $p⌝$ is defined relative to $〈w,\mathcal{A},\mathcal{O}〉$ only if $p$ is represented by $\mathcal{A}$ If defined, $⌜\text{S}$ wants $p⌝$ is true relative to $〈w,\mathcal{A},\mathcal{O}〉$ iff for every $q\in \text{BEST}\left({\mathcal{O}}^{\mathcal{A},w}\left(S\right)\right)$: $q\subseteq p$

Account 2 explains why (1) is evaluated relative to ${\mathcal{A}}_{\text{fine}}$ so long as we take on board the following widely accepted principle: hearers tend to interpret sentences so as to avoid presupposition failure. That is, within reasonable limits, hearers will make the assumptions necessary to avoid undefinedness.²⁴ For instance, even if I suspect that you have no siblings, I will come to assume that you have a sister once I’ve heard you utter (17):

• (17) I have to fetch my sister from the airport tomorrow.

That is, the presupposition triggered by the possessive ‘my sister’, namely that I have a sister, is taken to hold when evaluating (17).

To repeat, we are supposing that there are two relevant sets of alternatives in the Coins scenario, namely ${\mathcal{A}}_{\text{coarse}}$ and ${\mathcal{A}}_{\text{fine}}$. (1) fails to be defined relative to ${\mathcal{A}}_{\text{coarse}}$, since the proposition All three coins land heads isn’t represented by this set of alternatives. But (1) is defined relative to ${\mathcal{A}}_{\text{fine}}$. Assuming that hearers will try to avoid interpretations that result in presupposition failure, they will then be moved to evaluate (1) relative to ${\mathcal{A}}_{\text{fine}}$ rather than ${\mathcal{A}}_{\text{coarse}}$. This is exactly the result that we wanted.

We can also explain why (2) should sound true. Even though the proposition The first coin lands tails is represented by both ${\mathcal{A}}_{\text{coarse}}$ and ${\mathcal{A}}_{\text{fine}}$, there is an important difference between these two sets of alternatives. (2) is true relative to ${\mathcal{A}}_{\text{coarse}}$, but false relative to ${\mathcal{A}}_{\text{fine}}$. So, assuming that hearers generally tend to interpret speakers in a way that makes their utterances come out true—the so-called “principle of charity”—we would expect there to be a tendency to evaluate context-sensitive expressions relative to parameters which make the speaker’s assertions true.²⁵ In particular, then, by default we should expect (2) to be evaluated relative to ${\mathcal{A}}_{\text{coarse}}$ rather than ${\mathcal{A}}_{\text{fine}}$.

However, the representation requirement and the principle of charity still don’t explain why (4) should be evaluated relative to ${\mathcal{A}}_{\text{coarse}}$ rather than ${\mathcal{A}}_{\text{fine}}$. After all, The first coin lands heads is represented by ${\mathcal{A}}_{\text{fine}}$. Moreover, (4) actually comes out true relative to this set of alternatives. So, a different sort of explanation is needed to explain why the report sounds bad. We turn to this next.

3.3 Dominance

What is crucial to providing a complete solution to our puzzles, we suggest, is recognizing that desire reports carry a dominance requirement. We introduce this idea in two stages. We begin by discussing a fairly simple condition but raise some problems for it. Then we present a more sophisticated notion of dominance.

On the semantics from §3.2, if $⌜\text{S}$ wants $p⌝$ is defined, then all that matters for its semantic value is whether or not all of the top-ranked alternatives entail $p$. But we could require something stronger. We could require not just that every top-ranked alternative entails $p$, but that every p-entailing alternative outranks every $\neg p$-entailing alternative. When this happens, let us say that $p$dominates (with respect to the background parameters):

Dominance

Given a set of alternatives $\mathcal{A}$, ordering $\succ$ over $\mathcal{A}$, and proposition $p$, $p$ dominates iff for every $q\in \mathcal{A}$ such that $q$ ⊆ $p$, and every $r\in \mathcal{A}$ such that $r\subseteq \neg p$: $q\succ r$.

One could add a dominance requirement to our semantics from §3.2. More specifically, it could be imposed as an additional presupposition or definedness condition triggered by desire reports. This yields the following entry:

Account 3

$⌜\text{S}$ wants $p⌝$ is defined relative to $〈w,\mathcal{A},\mathcal{O}〉$ only if

1. $p$ is represented by $\mathcal{A}$; and

2. $p$ dominates

If defined, $⌜\text{S}$ wants $p⌝$ is true relative to $〈w,\mathcal{A},\mathcal{O}〉$ iff for every $q\in \text{BEST}\left({\mathcal{O}}^{\mathcal{A},w}\left(S\right)\right)$: $q\subseteq p$

This semantics explains why (4) should be unacceptable. Recall that Bill’s preference ordering over ${\mathcal{A}}_{\text{coarse}}$ looks as follows:

While Bill’s preferences over ${\mathcal{A}}_{\text{fine}}$ are:

It is easy to see that the proposition The first coin lands heads dominates on neither ${\mathcal{A}}_{\text{coarse}}$ nor ${\mathcal{A}}_{\text{fine}}$.²⁶ In particular, other entails that the first coin lands heads, but this alternative is ranked below t in ${\mathcal{A}}_{\text{fine}}$. Thus, Account 3 predicts that (4) should suffer from presupposition failure when evaluated relative to either ${\mathcal{A}}_{\text{coarse}}$ or ${\mathcal{A}}_{\text{fine}}$.

Although Account 3 captures the infelicity of (4), this entry isn’t quite right. One problem is that it generates problematic truth-conditions for negated desire reports. To bring this out, consider the following scenario:

Dinner: I’m meeting my friend for dinner. There are three items on the menu: spaghetti bolognese, lasagna, and chicken. I’m going to be late, so my friend—who has no idea about my preferences—is going to order for me. Given my past experience, I like the spaghetti most, I find the chicken to be average, and I hate the lasagna.

• (18) I don’t want my friend to order chicken for me.

18 is perfectly acceptable. However, Account 3 predicts that the report should suffer from presupposition failure on the most natural set of alternatives. The relevant set of alternatives is $\mathcal{A}=\left\{\text{SPAGHETTI},\text{LASAGNA},\text{CHICKEN}\right\}$, where SPAGHETTI is the proposition that my friend orders spaghetti for me, LASAGNA is the proposition that my friend orders lasagna for me, etc. My preferences look as follows:

Note that CHICKEN fails to dominate on this set of alternatives. Now, one feature of presuppositions is that they project from certain embedded environments, namely negation.²⁷ Thus, on Account 3 the negated report (18) also presupposes that CHICKEN dominates. So, given that this presupposition is not satisfied, and cannot be accommodated, (18) is predicted to be unacceptable.²⁸

Some might be tempted to respond by making the dominance condition a regular entailment of desire reports rather than a presupposition. But this would make it too easy for these ascriptions to be false. For instance, consider (19) in the Dinner scenario:

• (19) I don’t want my friend to order pasta for me.

The account we are considering predicts that regardless of the relative expected value of pasta and chicken, (19) should have a true reading. In particular, it incorrectly predicts that (19) should have a true reading in contexts where the expected value of pasta is greater than the expected value of chicken.²⁹ For if the dominance requirement was a regular entailment, then ‘I want my friend to order pasta for me’ would simply be false on the natural set of alternatives, since both SPAGHETTI and LASAGNA entail that my friend orders pasta for me, and CHICKEN entails that my friend does not order pasta for me. But then would be true on the natural set of alternatives.

Instead, we suggest responding by weakening the dominance condition. Intuitively, we want dominance to take effect in a report such as (4), but not in a report such as (18). One way of achieving this is by appealing to a conditional version of dominance which only requires that $p$ dominates if there is some top-ranked $p$-entailing alternative. More precisely ($‘\Rightarrow ’$ denotes the material conditional):

Conditional dominance

Given a set of alternatives $\mathcal{A}$, ordering ≻ over $\mathcal{A}$, and proposition $p$, $p$ conditionally dominates iff there is some $q$ ∈ BEST(≻) such that $q$ $q\subseteq p\Rightarrow p$ dominates.

Our final entry is the following:³⁰

Meaning of want

⌜S wants p⌝ is defined relative to $〈w,\mathcal{A},\mathcal{O}〉$ only if

1. p is represented by $\mathcal{A}$; and

2. p conditionally dominates

If defined, ⌜S wants p⌝ is true relative to $〈w,\mathcal{A},\mathcal{O}〉$ iff for every $q\in \text{BEST}\left({\mathcal{O}}^{\mathcal{A},w}\left(S\right)\right)$: q ⊆ p

This semantics also explains why (4) (‘Bill wants the first coin to land heads’) is unacceptable in the Coins scenario. The proposition The first coin lands heads (trivially) conditionally dominates on ${\mathcal{A}}_{\text{coarse}}$, since $t$ is top-ranked. But this means that the report is straightforwardly false on this set of alternatives. By contrast, the proposition The first coin lands heads does not conditionally dominate on ${\mathcal{A}}_{\text{fine}}$, since $3\text{H}$ is top-ranked and entails that the first coin lands heads. Thus, (4) is predicted to be infelicitous on either set of alternatives. Overall, this entry explains all of the key data points undergirding our central puzzles. Moreover, it correctly predicts that (18) should be true in the Dinner scenario, on the natural set of alternatives. For the proposition My friend orders chicken for me (trivially) conditionally dominates given that $\text{SPAGHETTI}$ is top-ranked.

Some might worry that imposing a conditional dominance constraint still yields a semantics that is too strict. For instance, consider (20) in the Dinner scenario:

• (20) I want my friend to order a pasta dish for me.

(20) sounds true, but our view seems to predict that it should be unacceptable. The worry is that the proposition My friend orders a pasta dish for me doesn’t conditionally dominate on $\mathcal{A}=\left\{\text{SPAGHETTI},\text{LASAGNA},\text{CHICKEN}\right\}$. Moreover, maintaining that the report is evaluated relative to the coarse-grained set of alternatives $\mathcal{B}=\left\{\text{PASTA},\text{CHICKEN}\right\}$ doesn’t help. For we can suppose that the expected value of PASTA is less than or equal to the expected value of $\text{CHICKEN}$. In this case, we would predict that (20) should be false on $\mathcal{B}$.

In response, we maintain that the felicity of (20) can be traced to an ambiguity in the interpretation of indefinite descriptions. Sometimes these expressions can be read “specifically”, and concern particular objects or individuals.³¹ We think that this is exactly what’s happening with ‘a pasta dish’ in (20). One simple way to capture this is to assume that the indefinite in (20) takes wide-scope at the level of logical form:

• (21) There is a particular pasta dish $x$ such that I want my friend to order $x$ for me.

Assuming that the particular dish here is spaghetti, the prejacent is verified by the proposition My friend orders spaghetti for me. And this proposition does conditionally dominate on $\mathcal{A}$. So in this case (20) is predicted to be true. That this account of (20) is on the right track is suggested by the fact that minimal variants which do not feature indefinites are easily heard as unacceptable:³²

• (22) I want my friend to order pasta for me.

A natural response to (22) would be ‘But what if your friend orders lasagna for you, which you hate?!’. This contrast is quite striking, and further confirms the general shape of our account.³³

It is worth drawing out several further features of our entry. First, our semantics makes some interesting predictions in cases where two or more alternatives are tied best. For example, suppose that Paris and Rome are your two favorite holiday destinations. You’d be thrilled to go to either, but don’t prefer one over the other. In this context, both (23a) and (23b) are unacceptable:

Let us suppose that the relevant set of alternatives is $\mathcal{A}=\left\{\text{PARIS},\text{ROME}\right\}$, where $\text{PARIS}$ is the proposition that I holiday in Paris, and $\text{ROME}$ is the proposition that I holiday in Rome. Then neither alternative conditionally dominates on $\mathcal{A}$, and we predict that both reports will be undefined.³⁴

Second, our account goes some way to explaining an observation by Crnič (2011, 166) to the effect that disjunctions in the scope of desire reports give rise to an “acceptability inference” regarding both disjuncts. For instance, neither (24a) nor (24b) are felicitous:

We can explain this so long as we assume that these reports are being evaluated relative to something like ${\mathcal{A}}_1=\left\{\text{ANN},\text{MARY},\text{PETE},\text{SUE}\right\}$, where $\text{ANN}$ is the proposition that Ann wins, $\text{MARY}$ is the proposition that Mary wins, etc.³⁵ Then, if the first conjunct in (24a) is true, the conditional dominance condition will require (i) that both $\text{ANN}$ and $\text{MARY}$ are the best alternatives, or (ii) that the relative ranking of the alternatives is $\text{MARY}$ ≻ $\text{ANN}$ ≻ $\text{PETE}$, or (iii) that the relative ranking of the alternatives is $\text{ANN }\succ \text{MARY }\succ \text{PETE}$. If (i) or (ii) hold, then the second conjunct in (24a) will be undefined, since the proposition Ann loses will fail to conditionally dominate. And if (iii) holds, then the second conjunct in (24a) will be false. A similar explanation can be given of the unacceptability of (24b).

Finally, it is helpful to compare our conditional dominance condition with a feature proposed by Gajewski (2007) and Križ (2015). These authors aim to explain why ‘want’ is a so-called “neg-raiser”. This is the phenomenon whereby negated want reports are interpreted with negation taking narrow scope with respect to ‘want’, i.e., $⌜$(S wants p)$⌝$ is interpreted as $⌜\text{S}$ wants $\neg p⌝$ (Collins and Postal, 2014). For instance, an utterance of (25a) is felt to be equivalent to (26b):

To explain this, Gajewski and Križ propose a definedness condition on desire reports which, in our framework, can be stated as follows:³⁶

Gajewski and Križ’s definedness condition for S wants p

⌜S wants p⌝ is defined relative to $〈w,\mathcal{A},\mathcal{O}〉$ only if (i) every top-ranked alternative in $S$’s preference ordering entails $p$, or (ii) every top-ranked alternative in $S$’s preference ordering entails ¬$p$.

To see how this works, suppose that (25a) is evaluated relative to $\mathcal{A}=\left\{\text{WIN},\text{LOSE}\right\}$, where $\text{WIN}$ is the proposition that Pete wins, and $\text{LOSE}$ is the proposition that Pete loses. Then if (25a) is true, it can’t be that Bill ranks $\text{WIN}$ above $\text{LOSE}$. Moreover, given Gajewski and Križ’s condition, it can’t be that Bill is indifferent between these two outcomes, i.e., that both $\text{WIN}$ and $\text{LOSE}$ are equally top-ranked. Thus, it must be that $\text{LOSE}$ is ranked above $\text{WIN}$, and so (26b) is true.

Note that Gajewski and Križ’s condition doesn’t help to resolve our puzzles. For example, it doesn’t predict that (4) (‘Bill wants the first coin to land heads’) should be evaluated relative to ${\mathcal{A}}_{\text{coarse}}$. On the other hand, we think that conditional dominance could provide some insight into the phenomenon of neg-raising. For one thing, our account also predicts that (25a) and (26b) should be equivalent relative to $\mathcal{A}=\left\{\text{WIN},\text{LOSE}\right\}$. For if (25a) is true, then the proposition Pete wins must conditionally dominate on $\mathcal{A}$. But this means that Bill can’t be indifferent between $\text{WIN}$ and LOSE. So, $\text{LOSE}$ must be ranked above $\text{WIN}$, and (26b) must be true.

But our theory also predicts that the neg-raising inference should fail to go through in certain contexts, and that in these contexts $⌜\neg$(S wants p)$⌝$ should be distinguishable from $⌜\text{S}$ wants $\neg$p$⌝$. There is evidence that this is a good prediction:

Coins 2: Two fair coins will be flipped, and Bill’s reckless brother has made the following bet on Bill’s behalf: if both coins land heads (HH), Bill will gain $\text{\$100}$; if the first coin lands heads and the second coin lands tails (HT), Bill will lose $\text{\$100}$; and if the first coin lands tails (T), Bill will lose $\text{\$1000}$. In short, the payoffs are HH = $\text{\$100}$, HT = −$$\text{\$100}$, and T = $\text{-\$1000}$.

• (26) a. Bill doesn’t want the coins to land HT.

• b. ?? Bill wants the coins to not land HT.

We detect a difference in felicity between these reports: to our ears (26b) sounds worse than (26a). The former suggests that a tails-first outcome is preferred to the HT outcome, which isn’t the case. This is what we’d expect if we assume that the relevant set of alternatives is something like $\mathcal{A}=\left\{\text{HH},\text{HT},\text{T}\right\}$. Bill’s preferences over these alternatives look as follows:

Then (26a) will be true, but (26b) will be undefined since the proposition The coins do not land HT does not conditionally dominate on $\mathcal{A}$. Needless to say, much more would need to be done in order to turn these remarks into a complete theory of neg-raising, but we will leave the matter there for now. Although our treatment of neg-raising seems prima facie plausible, our central concern has been to illustrate that a fairly natural dominance condition, when coupled with our alternative-sensitive semantics, allows us to explain the puzzles from §1.

To summarize, we have tried to explain our puzzles by developing a theory of desire reports on which these ascriptions are (i) alternative-sensitive, and (ii) carry representation and dominance conditions. We think that our theory provides us with an elegant account of our data, and more generally yields a promising approach to desire.^37,38

4. Wants and Oughts

Several theorists have noted that ‘want’ and ‘ought’ pattern similarly (Crnič, 2011; Lassiter, 2011; Jerzak, 2019). We add that analogues of our puzzles arise with this modal. For instance, consider a famous case adapted from Jackson and Pargetter (1986, 235):

Professor Procrastinate:

Professor Procrastinate receives an invitation to review a book. The best thing that can happen is that he says yes, and then writes the review. However, were Procrastinate to say yes, he would not in fact get around to writing the review. Thus, although the best that can happen is for Procrastinate to say yes and then write, and he can do exactly this, what would in fact happen were he to say yes is that he would not write the review. Moreover, we may suppose, this latter is the worst that can happen.

These similarities make salient the following intriguing possibility: that both desire verbs and deontic modals share an underlying semantics.³⁹ We’ll leave this as a topic for future research. But we’ll end by noting that Cariani (2013) has put forward an account of deontic ‘ought’ that is similar, in some respects, to the semantics for ‘want’ that we have developed here. For instance, on Cariani’s proposal, ought claims are evaluated relative to a set of alternatives, as well as an ordering over those alternatives.⁴⁰ This could suggest a convergence to a common semantic core.⁴¹