Scope of degree operators and association with focus: To account for the ambiguity of

superlatives between absolute and relative readings, cf. (5), and the role focus plays in the latter, Heim (1999) proposes that (i) the superlative operator -est is restricted by a covert variable C providing a comparison class, which is resolved contextually factoring in the effect of focus; and (ii) -est can take local (i.e. DP-internal) or non-local scope, where the material in the scope of -est determines the relation relative to which the members of C are compared. The absolute reading obtains from LF (6a) where -est takes DP-internal scope. In this configuration, the comparison class C consists of contextually relevant mountains, e.g. (6b), which are compared in terms of height. The relative reading obtains from LF (7a) where -est takes non-local scope and focus on the subject restricts the comparison class C to consist of contextually relevant individuals, which are compared in terms of mountain climbing achievement.

(5) John climbed the highest mountain.

‘ John climbed a mountain higher than any other (relevant) mountain’ ABSULTE ‘John climbed a higher mountain than any other (relevant) individual’ RELATIVE (6) a. LF: John climbed the [DP [-est C] [1 [ t1-high mountain]]]

b. C = { Ben Nevis, Ben Macdhui, Braeriach...}

(7) a. LF: JohnF [-est C] [1 [climbed [DP A t1-high mountain]]] b. C = { John, Mary, Bill,...}

properties (i) and (ii) above do not only hold for the superlative operator, but also for the (phonologically null) positive operator POS. POS requires the degree relation D serving as its first argument to hold of its second argument to a degree exceeding a contextual standard θ, cf. (8). The standard θ is determined relative to the comparison class C, taking into account the dispersion of values onto which D maps the different members of C (Solt 2011).

(8) [[ POS C]] = λD.λx. ∃d [D(d)(x) & d > θC ]

PROPOSAL With these ingredients, the different readings of many result from different

scope of the positive morpheme POS and (free in Beaver & Clark’s (2008) terms) association with focus.We propose that the proportional reading arises if POS takes DP-internal scope, cf. (9). Following Hackl’s (2009) analysis of the proportional reading of most, we assume that in this configuration the comparison class C consists of

the pluralities in the NP denotation, e.g. in (2a) the sets of books that can be assembled out of the books on the reading list, which are compared in terms of cardinality. Note that the number of sets in C with a certain cardinality corresponds to a binominal distribution yielding a bell- shaped curve, as shown in Fig. 1. Given this distribution, the standard for ‘many’ness relative to C is likely to be located somewhere in the rightmost third of the curve. In

effect, the truth conditions in (9c) express that John read a plurality of books whose cardinality is high relative to the cardinalities of the members of the power set of the set of books on the reading list. This mirrors the meaning (2c) assigned to proportional many by the GQT analysis, but crucially without making reference to actual proportions.

(9) a. LF: John read [DP ∅∃ [POS C] [1 [t1-many books on the reading list]]]

b. C = {{b1},{b2},{b3},…,{b1,b2},{b1,b3},{b2,b3},…, {b1,b2,b3},...} c. ∃x[ ∃d [|x| ≥ d & books_ otrl (x) & d > θC] & read(j,x)]

Cardinal readings are derived if POS takes non-local scope, cf. (10). In this configuration, the value of C is fixed contextually (possibly restricted by focus). In (1), for instance, C is likely to consist of other kids, which are compared relative to the number of toys they own. (10) a. LF: Tom [POS C] [1 [ has [DP ∅∃ [t1-many toys]]]]

b. C = { Tom, Nick, Max, ...}

c. ∃d [ ∃x[toys(x) & |x| ≥ d & has(t,x)] & d > θC]

Cashing in the observation that the reverse proportional reading requires focus on the NP sister of many (Herburger 1997) and following Romero (2015), we argue that it is the role that focus plays in determining the comparison class C that gives the impression of a ‘reverse’ reading in (3), and conservativity can be maintained. In contrast to Romero, who bases the reverse reading on the proportional determiner in (2c), we argue that the reverse proportional reading arises as a special case of a cardinal reading. As shown in (11), focus on Scandina-vians restricts C to consist of inhabitants of different world regions, which – because of non-local scope of POS – are compared with respect to the number of NP winners they have produced. With this the truth conditions in (11c) are fulfilled just in case the number of NP winners from Scandinavia is large compared to the number of NP winners from other parts of the world. This holds iff Scandinavians make up a significant proportion of all the NP winners, corresponding to the truth conditions assigned by the GQT analysis in (3d).

(11) a. LF: ScandinaviansF [POS C] [2 [1 [DP ∅∃ [t2-many t1]] have won the NP]]

b. C = { Scandinavians, Mediterraneans, Eastern Europeans, South Americans, … } c. ∃d [ ∃x[Scandinavians(x) & |x| ≥ d & won(x,the_NP)] & d > θC]

SUMMARY We show that the various readings of many can be derived under a single

uniform analysis, where many is decomposed into a gradable cardinality predicate and the positive morpheme POS. The proportional reading is generated from an LF where POS takes DP-internal scope. When POS takes non-local scope, cardinal readings are derived, with reverse proportional readings being a special case arising if the host NP is focused.

SELECTED REFERENCES Hackl, M. 2009. On the grammar and processing of proportional

quantifiers, NLS 17 •Herburger, E. 1997. Focus and weak noun phrases, NLS 5 •Heim, I. 1999. Notes on Superlatives, ms. •Solt, S. 2009. The Semantics of Adjectives of Quantity. PhD thesis •Solt, S. 2011. Notes on the comparision class, ViC2009 •Romero, M. 2015. The conservativity of many, AC 20.

I want to, but…

Milo Phillips-Brown / milopb@mit.edu

I want to pass the exam, but I don’t want to study; I want to go to the concert, but I don’t want to take the bus. When we constrain the metasemantics in standard ways, the prominent extant semantics for ‘want’ badly mishandle such sentences.1_{Suppose that I believe that I} can only get to the concert by bus. Then these views wrongly predict that ‘I want to go to the concert’ and ‘I don’t want to take the bus’ can’t both be true. We need to thread a needle between getting these core cases right without overgenerating elsewhere. My goal here is largely negative: I present novel cases, showing that neither of two promising proposals threads this needle.2_{I then suggest a way forward.}

Case study

Consider a “best-worlds” semantics with ordering sourceg and modal basef. Both take a worldwand return a set of propositions. Given a preorder⪯g(w),BEST(g, f , w)is the subset

of∩f (w)minimal according to⪯g(w).3

(1) Best-worlds semantics.⟦A wantsφ⟧c,w,g,h= 1iff∀u ∈BEST(g, f , w) :⟦φ⟧c,u= 1.

On this semantics, the two metasemantic constraints standard in the literature are

(2) Unique ordering source. There is a unique ordering sourceg available for evaluating⌜A wantsφ⌝:g(w)represents A’s total preferences atw.

(3) Unique modal base. There is a unique modal basef available for evaluating⌜A wantsφ⌝:

∩f (w)is A’s belief set atw.

Here’s a case where (1)–(3) jointly go wrong. Jo’s favorite pianist is performing in Miami tonight. She believes, truly, that she can only get to Miami by bus. Jo hates the bus.

(4) Jo wants to go to the concert.

(5) But she doesn’t want to take the bus [= she wants to not take the bus]. Intuitively, (4) and (5) are both true, but (1)–(3) together can’t predict this. Bw

Jois Jo’s belief set andg_Jowrepresents her total preferences. If (4) is true, then theg_Jow-best worlds in Bw

Joare concert worlds. If (5) is true too, then these worlds are also no-bus worlds. But Jo believes that she can only get to the concert by bus: i.e. there aren’t any concert-no-bus worlds in Bw_Jo. It follows that (4) and (5) can’t both be true.4

In other words, (1)–(3) together entail that among the possibilities Jo thinks might come about, she most prefers those possibilities where she both goes to the concert and avoids the bus. But Jo believes that she can only get to the concert by bus: i.e. going to the concert while avoiding the bus is a possibility that Jo thinks can’t come about.

The problem is not unique to (1); given analogs of (2) and (3), the other prominent semantics get the core cases wrong. To get the core cases right, we must drop (2) or (3).

1_{Along with the Kratzer (1991)-von Fintel (1999) view I’m discussing, these views include Heim’s (1992), Levin-} son’s (2003) and van Rooij’s (2006, §6) decision-theoretic accounts, Villalta’s (2008) contrastive account.

2_{Another proposal, van Rooij’s, predicts ⌜¬(A wants φ)⌝ and ⌜¬(A wants ¬φ)⌝ are incompatible.} 3_u⪯

g(w)viff {χ ∈ g(w) : v ∈ χ} ⊆ {χ ∈ g(w) : u ∈ χ}; BEST(g, f , w) ={u ∈ ∩f (w) : ¬∃v ∈ ∩f (w),v ≺g(w)u}; I make the limit

assumption.

4_{Assuming that B}w

Jo, ∅ (if ∩f (w) , ∅,BEST’s definition ensures the best subset of ∩f (w) is non-empty). 1

Dropping (2): multiple ordering sources

To get the core cases right, Levinson (2003) drops (2):5

(6) Levinson’s metasemantics. There may be multiple ordering sourcesg available for evalu- ating⌜A wantsφ⌝: eachg(w)must represent part of A’s preferences atw.

Let Jo’s preference for music be represented by ordering sourceg1. Againstg1, (4) is true because Jo attends the concert in theg1-best (i.e. music) worlds in BwJo. On this view,g1 is available for (4), so (4) has a true reading; similarly, (5) has a true reading because there is some available ordering sourceg2that represents Jo’s preference for avoiding discomfort. So, Levinson’s view gets the core cases right.

But consider a new case: the setup is as before, yet now Jo learns that the bus will be overcrowded. She decides to stay home. Consider:

(7) Jo wants to go to the concert, but the bus will be overcrowded, so she’s staying home. (8) Jo wants to take the bus.

Intuitively, (7) has a true reading here, but (8) does not. Because (7) has a true reading, there is someg3available for (7), such that concert worlds areg3-best in BwJo.6Every concert world in Bw

Jois a bus world, so bus worlds areg3-best in BwJo—i.e. (8) is true relative tog3. So, ifg3 is available for (8), then Levinson wrongly predicts that (8) has a true reading—i.e. ifg3 is

available for (8), Levinson’s view overgenerates. But given thatg₃is available for (7), why would

it not be available for (8)? We need principled constraints on ordering source availability. Levinson doesn’t attempt to give any, and here are selected reasons to doubt that any can be given: Jo’s beliefs are constant in the case, Jo’s preferences are constant too, and (8)’s prejacent alone can’t makeg3 unavailable—if Jo’s only preference were for music, then on Levinson’s view,g3would be the onlyg available for any sentence⌜Jo wantsφ⌝, and sog3 would be available for (8).

Levinson’s way of dropping (2) does get the core cases right. But, I argue, no principled constraints on ordering source availability are forthcoming: Levinson overgenerates.

Dropping (3): multiple modal bases

In a contrastive framework, Villalta (2008) drops (3) to get the core cases right:

(9) Villalta’s metasemantics. There may be multiple modal basesf available for evaluating

⌜A wantsφ⌝: a given∩f (w)may contain worlds outside of A’s belief set atw.

Here’s a natural way to get the core cases right. Let∩f1(w)be BwJoplus some worlds where Jo attends the concert but doesn’t take the bus. Jo’s most preferred worlds in ∩f1(w) are these concert-no-bus worlds: (4) and (5) are both true againstf1. Iff1 is available for both, we predict the correct true readings in the core cases.

But consider a new case. Lu is ill. She doesn’t take antibiotics because she believes she can’t be cured.

(10) Lu wants to take antibiotics.

Here, (10) has no true reading. Yet (10) is true againstf₂, where∩f2(w)is Lu’s belief set, plus some worlds where she takes antibiotics and is cured. On this view, what would makef2

5_{Both van Fraasen (1973) and von Fintel (2012) give similar proposals for deontic modals.}

6_{More carefully: because Jo believes she won’t take the bus, (7) must be evaluated against a certain superset of} Bw

Jo(Heim 1992). Every concert world in that set is a bus world, so my argument goes through.

2

unavailable for (10), given thatf₁is available for (4) and (5)? To prevent overgeneration, we need principled constraints on modal base availability.

Villalta indeed gives constraints, but they don’t get the core cases right. Roughly trans- posing her semantics into our framework: (4) is evaluated againstf₃, where∩f3(w)contains

every concert world, every world where Jo stays home, and no others. It’s completely im-

plausible, though, that every best world in that set is a concert world. Surely there are some stay-home world that Jo likes just as much as any concert world (in some stay-home worlds, there is a concert in her home!). So, Villalta’s constraints wrongly predict that (4) doesn’t have a true reading.

Worlds where there is a concert in Jo’s home are irrelevant to Lu’s desire to stay home. This is because they’re possibilities which Jo believes can’t come about. But Villalta’s way of dropping (3) gets the core cases right with worlds outside of the belief set. I argue that so long as we go beyond the agent’s beliefs, we can’t expect to find principled constraints on ordering source availability that properly treat desire ascriptions, in the core cases or elsewhere.

Prospects

Here is a brief sketch of my coarse worlds semantics. Coarse worlds (i.e. propositions; Yalcin 2011) needn’t settle every issue—e.g. some coarse worlds settle whether Jo attends the con- cert, but not whether she takes the bus. A coarse worldwsettles whether a proposition p

obtains iffwentails eitherpor¬p;wis compatible with an agent A’s beliefs iff every propo- sitionw entails is compatible with A’s beliefs. A modal baseF takes a world and returns a set of coarse worlds.

To get the core cases right, I drop (3):

(11) My metasemantics.7 _{There may be multiple modal bases F available for evaluating ⌜A} wantsφ⌝: the members of any availableF(w)must be compatible with A’s beliefs. On my account, ‘want’ quantifies directly overF(w), not over∩F(w). An agent prefers one coarse worldwto another,v, iff she prefers howw settles issues to howvdoes. So, within

F1, which settles whether Jo attends the concert, but not whether she takes the bus, coarse concert worlds are best: (4) is true. And, withinF2, which settles whether Jo takes the bus, but not whether she attends the concert, coarse no-bus worlds are best: (5) is true. Intuitively, a coarse world ignores certain issues while focusing on others. Focusing on whether Jo attends the concert, but ignoring whether she takes the bus, Jo prefers attending the concert to not. Focusing on whether she takes the bus, but ignoring whether she attends the concert, Jo prefers not taking the bus to taking it.

Villalta failed because she went beyond the agent’s beliefs. I stay within them: (11) is a principled, belief-based constraint on ordering source availability. Levinson’s undoing was the fact that if concert worlds are best and Jo believes that concert worlds are bus worlds, then bus worlds are best. Yet, even if Jo believes that she can’t get to the concert but by bus, and coarse concert worlds are best within an availableF(w), it doesn’t follow that coarse bus worlds are best inF(w). This is because there can be coarse concert worlds inF(w)that are neither coarse bus worlds nor coarse no-bus worlds; such coarse concert worlds don’t settle whether Jo takes the bus.8

7_{This is the core piece of my metasemantics, but there’s more to be said.}

8References. von Fintel, K., ‘NPI-licensing, Strawson-entailment, and context-dependency’ (1999); von Fintel, K., The best we can (expect) to get? (2012); van Fraasen, B., ‘Values and the heart’s command’ (1973); Heim, I., ‘Presupposition projection and the semantics of attitude verbs’ (1992); Kratzer, A., ‘Modality’ (1991); Levinson, D., ‘Probabilistic model-theoretic semantics for want’ (2003); van Rooij, R., Attitudes and changing contexts (2006); Villalta., ‘Mood and gradability: an investigation of the subjunctive mood in Spanish’ (2008); Yalcin, S., ‘Non-factualism about epistemic modals’ (2011).

Ranked ordering sources and embedded modality Drew Reisinger · Johns Hopkins University

Summary. I propose an extension to Kratzer [1991]’s ordering semantics to allow for ordering sources with ranked priorities. My account generalizes Katz et al. [2012]’s binary operator that combines two ordering sources g1 and g2 into a new ordering source that prioritizes the possible

world ordering induced by g1 over that of g2. My proposal retains this intuition, that the contri-

butions of ordering source propositions can have different priorities, but rather than achieving this through a pragmatic operator on contextual parameters, it reanalyzes the ordering source as a func- tion from worlds to partially ordered sets of propositions. This explicitly models how priorities vary with the world of evaluation, and I show that this move better accounts for priority-sensitive modal expressions when they are embedded under attitude verbs. I also introduce the priority join as a step toward a calculus of partially ordered ordering sources.

Motivating example. As in Katz et al. [2012], I motivate introducing priorities with Goble [1996]’s Medicine Problem in (1-a). I then introduce the Embedded Medicine Problem in (1-b), which requires priority to depend on the world of evaluation. In the following scenario, which is a simplification of the Medicine Problem introduced by Lassiter [2011], (1-a) can be judged true.

Scenario: A doctor can administer one of two medicines to a critically ill patient. Medicine A will kill the patient with high probability, but there is a small chance that it will cure the patient completely. Medicine B will definitely save the patient but leave them somewhat debilitated. Doing nothing will kill the patient.

(1) a. The doctor should administer medicine B.

b. The doctor should administer B, but Kat thinks the doctor should administer A. However, a na¨ıve application of Kratzer [1991]’s ordering semantics with ordering propositions {w : Patient survives in w} and {w : Patient is totally healthy in w} predicts that (1-a) must be false, as the optimal worlds under the ordering source are those in which the patient takes medicine A and survives. In order to make the truth conditions of (1-a) sensitive to both the utility and likelihood of outcomes, Katz et al. [2012] introduces a second ordering source that encodes the likelihood that the patient will survive after taking A. If this likelihood ordering is prioritized over the utility ordering using their * operator, (1-a) is predicted to be true.

Nevertheless, this account incorrectly predicts that (1-b) is contradictory in a context where Kat agrees with the speaker about the likelihood and utility of outcomes but disagrees about the importance of likelihood to the doctor’s decision. That is, Kat disagrees about the priority of the two ordering sources. To account for this reading, we need to allow the priority relations between ordering sources to vary between the world of evaluation of the utterance and Kat’s belief worlds.

Formal analysis. The denotation of should in (2) is nearly the same as in Kratzer [1991]. (2) _JshouldKw, f ,g,≺= λ p_hs,ti. ∀w0∈ pmax_g(w),≺w(T

f(w)) : p(w0)

The evaluation function has a new contextual parameter, ≺, which is a function mapping each possible world w to a partial order ≺won the propositions in g(w). The pmax operator computes the

maximal worlds in ∩ f (w) according to the ordering ≤_g(w),≺w, defined in (3), where Di f fP(u, v) =

{p ∈ P : p(u) ∧ ¬p(v)}.

(3) u≥_g(w),≺w viff ∀p ∈ Di f fg(w)(v, u) : ∃q ∈ Di f fg(w)(u, v) s.t. ¬q w p

1

That is, u is at least a good a world as v if every ordering source proposition on which v is better than u is dominated by a proposition on which u beats v. If ≺wis graded—roughly, if the ordering

of propositions is completely characterized by their heights in the partial order—computing pmax is optimization over worlds in the sense of Prince and Smolensky [2008] using ordering source propositions as constraints.

In (4), I also define a priority join operator t, a generalization of Katz et al. [2012]’s ∗ operator, which takes two ranked ordering sources as input and glues them together using an auxiliary order ≺PRI, which must satisfy the constraint in (5) (R∗is the transitive closure of R).

(4) [(g1, ≺1) t≺PRI(g2, ≺2)](w) = (g1(w) ∪ g2(w), (≺1,w∪ ≺2,w∪ ≺PRI,w)∗)

(5) ∀w : g1(w) PRI,wg2(w) ∨ g2(w) PRI,wg1(w)

The priority join preserves the orderings of the component ordering sources g1and g2and adds a

new ordering, ≺PRI,w, that prioritizes one of the component orderings over the other in a world-

dependent way.

Solution sketch. To show how this ranked ordering source account can accomodate the afore- mentioned reading of (1-b), I will make the following formal assumptions as in Katz et al. [2012]’s analysis. First, two propositions, L1 (Patient produces the normal enzymes) and L2 (Patient is allergic to medicine A), model the biological details that dictate whether medicine A saves the patient. Medicine A saves the patient if and only if L1 and ¬L2 hold. Second, I will assume the following contextual parameters. The modal base contains information about the causal structure of the problem. For example, it contains A ∧ L2 → dead and B → ¬dead ∧ ¬healthy, among others. For all worlds w, g1(w) = {L1, L2} models what is likely, and g2(w) = ¬dead, healthy models what

is desirable (both g1 and g2 are unordered). Crucially, the these conversational backgrounds are

the same in w@as they are in Kat’s doxastically accessible worlds. Finally, let (g, ≺) = g1t≺PRIg2,

where ≺PRIprioritizes g1in w@and g2in Kat’s belief worlds.

Assuming a standard neo-Hintikkan semantics for think, the denotation of (1-b) is (6). (6) " ∀w ∈ pmax g(w@),≺_w@ T f(w@) : w ∈ B # ∧ "

∀w ∈ DoxKat(w@) : ∀w0∈ pmax g(w),≺w

T

f(w) : w0∈ A !#

Since f (w@) = f (w) and g(w@) = g(w) for all w ∈ DoxKat(w@), and A and B are mutually incon-

sistent, (6) would have to be a contradiction if the priority ranking were the same in the evaluation world as in Kat’s belief worlds. Fortunately, since ≺w@ prioritizes g1, the modal domain of the

first conjunct contains precisely the worlds in which the patient receives medicine B and survives, and ≺wprioritizes g2, the modal domain of the second conjunct evaluated in DoxKat(w@) contains

the unlikely worlds in which the patient survives with perfect health after receiving medicine A. More motivation. This formalism also facilitates expanding the research program in Katz et al. [2012] in which the complex ordering sources required by patterns of truth value judgments or entailments are decomposed into primitives—e.g. purely deontic or bouletic ordering sources— and a set of combinatorial operators for building more complex ideals out of simpler ones. With the addition of ranked ordering sources, the program becomes to identify the primitive orderings underlying modality and a calculus for combining them. Candidates for such primitives include

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