Semantics & Pragmatics Vol 3 (2010)

Semantics & Pragmatics Volume 3, Article 1: 1–72, 2010 doi: 10.3765/sp.3.1 Quantifiers in than-clauses∗ Sigrid Beck Uni...

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Semantics & Pragmatics Volume 3, Article 1: 1–72, 2010 doi: 10.3765/sp.3.1

Quantifiers in than-clauses∗ Sigrid Beck University of Tübingen

Received 2009-01-13 / First Decision 2009-03-17 / Revised 2009-06-17 / Second Decision 2009-07-06 / Revised 2009-07-27 / Accepted 2009-07-27 / Published 201001-25

Abstract The paper reexamines the interpretations that quantifiers in than-clauses give rise to. It develops an analysis that combines an interval semantics for the than-clause with a standard semantics for the comparative operator. In order to mediate between the two, interpretive mechanisms like maximality and maximal informativity determine selection of a point from an interval. The interval semantics allows local interpretation of the quantifier. Selection predicts which interpretation this leads to. Cases in which the prediction appears not to be met are explained via recourse to independently attested external factors (e.g. the interpretive possibilities of indefinites). The goal of the paper is to achieve coverage of the relevant data while maintaining a simple semantics for the comparative. A secondary objective is to reexamine, restructure and extend the set of data considered in connection with the problem of quantifiers in than-clauses.

Keywords: comparatives, degrees, intervals, quantifiers, indefinites, plurals, scope ∗ Versions of this paper were presented at the workshop on covert variables in Tübingen 2006, at two Semantic Network meetings (in Barcelona 2006 and Oslo 2007), at the 2009 Topics in Semantics seminar at MIT, and at the Universität Frankfurt 2009. I would like to thank the organizers Frank Richter and Uli Sauerland and the audiences at these presentations for important feedback. Robert van Rooij and Jon Gajewski have exchanged ideas with me. The B17 project of the SFB 441 has accompanied the work presented here — Remus Gergel, Stefan Hofstetter, Sveta Krasikova, John Vanderelst — as have Arnim von Stechow and Irene Heim. Several anonymous reviewers and Danny Fox have given feedback on earlier versions, and David Beaver and Kai von Fintel have commented on the prefinal version. I am very grateful to them all.

©2010 Sigrid Beck This is an open-access article distributed under the terms of a Creative Commons NonCommercial License (creativecommons.org/licenses/by-nc/3.0).

Sigrid Beck

1 Introduction The problem of quantifiers in than-clauses has been puzzling linguists for a long time, beginning with von Stechow 1984, via Schwarzschild & Wilkinson 2002, Schwarzschild 2004, and Heim 2006b, to very recent approaches in Gajewski 2008, van Rooij 2008 and Schwarzschild 2008. It can be illustrated with the examples below. (1)

John ran faster than every girl did.

(10 )

a. For all x, x is a girl: John ran faster than x. b. #The degree of speed that John reached exceeds the degree of speed that every girl reached. i.e. “John’s speed exceeds the speed of the slowest girl.”

(2)

John ran faster than he had to.

(20 )

a. #For all w, w is a permissible world: John ran faster in @ than he ran in w. b. The degree of speed that John reached in @ exceeds the degree of speed that he has in every permissible world w. i.e. “John’s actual speed exceeds the slowest permissible speed.” (@ stands for the real world)

Example (1) intuitively only has a reading that appears to give the universal NP scope over the comparison, namely (10 a): all the girls were slower than John. The reading in which the universal NP takes narrow scope relative to the comparison is paraphrased in (10 b). Here we must look at degrees of speed reached by all girls; depending on the precise semantics of the thanclause (see below), this could mean the maximal speed that they all reached, i.e. the speed of the slowest girl. Example (1) has no reading that compares John’s speed to the speed of the slowest girl. Sentence (2), on the other hand, only has a reading that gives the modal universal quantifier narrow scope relative to the comparison, (20 b). That is, we consider the degrees of speed that John reaches in all worlds compatible with the rules imposed by the modal base of have to. This will yield the slowest permissible speed, and (2) intuitively says that John’s actual speed exceeded this minimum requirement. The sentence is not1 understood to mean that John did something that was 1 Heim (2006b) and Krasikova (2008) include a discussion of when readings like (20 a) are available. The reading can be made more plausible with a suitable context, depending on the modal chosen. For the moment I will stick to the simpler picture presented in the text. See

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Quantifiers in than-clauses

against the rules — that is, reading (20 a), in which the modal takes scope over the comparison, is not available. We must ask ourselves how a quantifier contained in the than-clause can have wide scope at all, why it cannot get narrow scope in (1), and why (2) is the opposite. Since — as we will see in more detail below — these questions look unanswerable under the standard analysis of comparatives, the researchers cited above have been led to a revision of the semantic analysis of comparison. Schwarzschild & Wilkinson (2002) employ an interval semantics for the thanclause and give the comparative itself an interval semantics. Heim (2006b) adopts intervals, but ultimately reduces the semantics of the comparison back to a degree semantics through semantic reconstruction. This allows her to retain a simple meaning of the comparative operator. A than-clause internal operator derives the different readings that quantifiers in thanclauses give rise to. The line of research in Gajewski 2008, van Rooij 2008 and Schwarzschild 2008 in turn adopts the idea of a than-clause internal operator but not the intervals. In this paper, I pursue a strategy that can be seen as an attempt to simplify Schwarzschild & Wilkinson’s proposal. Like them, I derive a meaning for the than-clause without a than-clause internal operator, and that meaning is based on an interval semantics. But I combine this with a standard semantics of the comparative in the spirit of von Stechow 1984. This means that the end result of interpreting the than-clause must be a degree. Everything will hinge on selecting the right degree, so that each of the relevant examples receives the right interpretation. In Section 2, I present the current state of our knowledge in this domain. The analysis of than-clauses is presented in Section 3. Section 4 ends the paper with a summary and some discussion of consequences of the proposed analysis. 2

State of affairs

I first present a sample of data that I take to be representative of the interpretational possibilities that arise with quantifiers in than-clauses. Then I sketch Schwarzschild & Wilkinson’s (2002) and Heim’s (2006b) analyses in Section 2.2, and in Section 2.3 a summary of the proposals in Gajewski 2008, van Rooij 2008 and Schwarzschild 2008. Section 3 for more discussion.

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2.1 The empirical picture 2.1.1 A classical analysis of the comparative The basis of our present perception of the problem presented by (1) and (2) is the analysis of the comparative construction, because the data are understood in terms of whether the quantfier appears to take wide scope over the comparison according to a classical analysis of the comparative, or whether it would have to be seen as taking narrow scope relative to the comparison. My presentation assumes a general theoretical framework like Heim & Kratzer 1998 and begins with specifically Heim’s (2001) version of the theory of comparison promoted in von Stechow 1984 (see also Klein 1991 and Beck 2009 for an exposition and Cresswell 1977; Hellan 1981; Hoeksema 1983; Seuren 1978 for theoretical predecessors). This theory is what I will refer to as a classical analysis of the comparative. For illustration, I discuss the simple example (3a) below. In (3b) I provide the Logical Form and in (3c) the truth conditions derived by compositional interpretation of that Logical Form, plus paraphrase. Interpretation relies on the lexical entries of the comparative morpheme and gradable adjectives as given in (4). (3)

a. b. c.

(4)

a. b. c.

Paule is older than Knut is. [-er [hd,ti than 2 [Knut is t2 old]] [hd,ti 2 [Paule is t2 old]]] max(λd. Paule is d-old) > max(λd. Knut is d-old) = Age(Paule) > Age(Knut) “The largest degree of age that Paule reaches exceeds the largest degree of age that Knut reaches.” “Paule’s age exceeds Knut’s age.” 0 -er = λDhd,ti . λDhd,ti . max(D 0 ) > max(D) oldhd,he,tii = [λd. λx. x is d-old] = [λd. λx. Age(x) ≥ d] Let S be a set ordered by R. Then maxR (S) = ιs[s ∈ S & ∀s 0 ∈ S[sRs 0 ]]

Importantly, the role of the comparative operator is ultimately to relate the maximal degree provided by the than-clause to some matrix clause degree. The than-clause provides degrees through abstraction over the degree argument slot of the adjective. Different versions of such a classical analysis are available (for instance von Stechow’s (1984) own or Kennedy’s

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(1997)), but the problem of quantifiers in than-clauses presents itself in a parallel fashion in all of them. I will make one small revision to the above version of the classical analysis: I will suppose that what is written into the lexical entry of the comparative morpheme as the maximality operator in (4a) is not actually part of the meaning of the comparative itself. Rather, it is a general mechanism that allows us to go from a description of a set to a particular object, for example also in the case of free relative clauses in (5) (Jacobson 1995); see also Beck 2009. I represent maximality in the Logical Form, as indicated in (40 b). The meaning of the comparative is then simply (40 a), the ‘larger than’ relation. It is basically this meaning of the comparative that I will try to defend below. The resulting interpretation remains of course the same. (5)

a. b.

We bought [what we liked]. max(λx. we liked x)

(40 )

a. b.

-er = λdd .λd0d . d0 > d [-er [d than max 2 [Knut is t2 old]] [d max 2 [Paule is t2 old]]] max(λd. Paule is d-old) > max(λd. Knut is d-old)

c. 2.1.2

Apparent wide scope quantifiers

Universal NPs are a standard example for an apparent wide scope quantifier (see e.g. Heim 2006b). The sentence in (6) below only permits the reading in (60 a), not the one in (60 b). This can be seen from the fact that the sentence would be judged false in the situation depicted below. (6)

John is taller than every girl is.

(60 )

∀x[girl(x) → max(λd. John is d-tall) > max(λd. x is d-tall)] “For every girl x: John’s height exceeds x’s height.” b. #max(λd. John is d-tall) > max(λd. ∀x[girl(x) → x is d-tall]) “John’s height exceeds the largest degree to which every girl is tall.” “John is taller than the shortest girl.” a.

_ _ _ _ _ • _ _ _ _ _ _ _ _ • _ _ _ _ _ _ _ _ • _ _ _ _ _ _ _ _ • _ _ _ _ _/

g1 ’s height

J’s height

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g2 ’s height

g3 ’s height

Sigrid Beck

The classical semantics of comparatives makes this look as if the NP had to take scope over the comparative. The LF given in (600 a) can straightforwardly be interpreted to yield (60 a); analogously for (600 b) and (60 b). Thus, strangely, the sentence appears to permit with (600 a) only an LF which violates constraints on Quantifier Raising (QR): QR is normally confined to a simple finite clause (May 1985 and much subsequent work). The LF in (600 b), which would be unproblematic syntactically, is not possible. (600 )

a.

[[every girl] [1 [[-er

b.

[[-er

[d [d

than

[d [d

than

max 2 [t1 is t2 tall]] max 2 [John is t2 tall]]]]

max 2 [every girl] [ 1 [t1 is t2 tall]]] max 2 [John is t2 tall]]]

The example with the differential in (7) shows the same behaviour (it uses a version of the comparative that accomodates a difference degree, (7c)). (7)

a. b. c.

John is 200 taller than every girl is. ∀x[girl(x) → max(λd. John is d-tall) ≥ max(λd. x is d-tall) + 200 ] = For every girl x: John’s height exceeds x’s height by 200 . -erdiff = λd. λd0 . λd00 . d00 ≥ d + d0

The problem posed by (5) and (7) is exacerbated in (8), as Schwarzschild & Wilkinson (2002) observe. We have once more a universal quantifier, but this time it is one that is taken to be immobile at LF: the intensional verb predict. Still, the interpretation that is intuitively available looks to be one in which the universal outscopes the comparison, (80 a). The interpretation in which comparison takes scope over predict, (80 b), is not possible. This is problematic because the LF we would expect (8) to have is (10), and (10) is straightforwardly interpreted to yield (80 b). (8)

John is taller than I had predicted (that he would be).

(9)

My prediction: John will be between 1.70 m and 1.80 m. Claim made by (8): John is taller than 1.80 m.

(80 )

a.

∀w[wR@ → max(λd. John is d-tall in @) > max(λd. John is d-tall in w)] “For every world compatible with my predictions: John’s actual height exceeds John’s height in that world.” b. # max(λd. John is d-tall in @) > max(λd. ∀w[wR@ → John is d-tall in w])

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“John’s actual height exceeds the degree of tallness which he has in all worlds compatible with my predictions.” “John’s actual height exceeds the shortest prediction, 1.70 m.” (where R is the relevant accessibility relation, compare e.g. Kratzer 1991) (10)

[[-er

[hd,ti [hd,ti

than

max 2 [ I had predicted that [ John be t2 tall]]] max 2 [ John is t2 tall]]]

This is the interpretive behaviour of many quantified NPs, plural NPs like the girls, quantificational adverbs, verbs of propositional attitude and some modals (e.g. should, ought to, might). See Schwarzschild & Wilkinson 2002 and Heim 2006b for a more thorough empirical discussion. 2.1.3 Apparent narrow scope quantifiers Not all quantificational elements show this behaviour. A universal quantifier that does not is the modal have to, along with some others (be required, be necessary, need). This is illustrated below. (11)

Mary is taller than she has to be.

(12)

Mary wants to play basketball. The school rules require all players to be at least 1.70 m. Claim made by (11): Mary is taller than 1.70 m.

(110 )

a. ?#∀w[wR@ → max(λd. Mary is d-tall in @) > max(λd. Mary is d-tall in w)] = For every world compatible with the school rules: Mary’s actual height exceeds Mary’s height in that world; i.e. Mary is too tall. b. max(λd. Mary is d-tall in @) > max(λd. ∀w[wR@ → Mary is d-tall in w]) = Mary’s actual height exceeds the degree of tallness which she has in all worlds compatible with the school rules; i.e. Mary’s actual height exceeds the required minimum, 1.70 m.

These modals permit what appears to be a narrow scope interpretation relative to the comparison. Example (11) does not favour an apparent wide scope interpretation. Krasikova (2008) argues though that some examples with have to–type modals may have both readings, depending on context. (13) is one of her examples favouring a reading analogous to (110 a), an apparent

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wide scope reading of have to (see Section 3 for more discussion). (13)

He was coming through later than he had to if he were going to retain the overall lead. (from Google, cited from Krasikova 2008) = He was coming through too late.

Existential modals like be allowed also appear to take narrow scope: (14)

Mary is taller than she is allowed to be.

(15)

a. #∃w[wR@ & max(λd. Mary is d-tall in @) > max(λd .Mary is d-tall in w)] = It would be allowed for Mary to be shorter than she actually is. b. max(λd. Mary is d-tall in @) > max(λd. ∃w[wR@ & Mary is d-tall in w]) = Mary’s actual height exceeds the largest degree of tallness that she reaches in some permissible world; i.e. Mary’s actual height exceeds the permitted maximum.

And so do some other existential quantifiers and disjunction: (16)

Mary is taller than anyone else is.

(17)

a. #There is someone that Mary is taller than. b. Mary’s height exceeds the largest degree of tallness reached by one of the others.

(18)

Mary is taller than John or Fred are.

(19)

a. ?#For either John or Fred: Mary is taller than that person. b. Mary’s height exceeds the maximum height reached by John or Fred.

This is the interpretive behaviour of some modals (e.g. need, have to, be allowed, be required), some indefinites (especially NPIs) and disjunction (compare once more Heim 2006b). It is also the behaviour of negation and negative quantifiers, with the added observation that the apparent narrow scope reading is one which often gives rise to undefinedness, hence unacceptability (von Stechow 1984; Rullmann 1995). (That this is not invariably the case is shown by (22), illustrating that we are concerned with a constraint on meaning rather than form.) (20)

*John is taller than no girl is.

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(21)

a.

John’s height exceeds the maximum height reached by no girl. The maximum height reached by no girl is undefined, hence: unacceptability of this reading. b. #There is no girl who John is taller than.

(22)

I haven’t been to the hairdresser longer than I haven’t been to the dentist.

Here is how the empirical picture presents itself from the point of view of a classical analysis of comparatives. It appears that there are two different scope readings possible for quantifiers embedded inside the than-clause, wide or narrow scope relative to the comparison. But there is usually no ambiguity. Each individual quantifier favours at most one reading (negation frequently permits none). Apparent narrow scope readings are straightforwardly captured by the classical analysis. It is unclear how apparent wide scope readings are to be derived at all. As Schwarzschild & Wilkinson argue, they are beyond the reach of an LF analysis. It is also unclear what creates the pattern in the readings that we have observed. Before we examine modern approaches to this problem, a final comment on the data. I have presented them the way they are presented in the literature on the subject, as if they were all impeccable and their interpretations clear. But I would like to use this opportunity to point out that I find some of them fairly difficult and perhaps not even entirely acceptable. This concerns example (6), for which I would much prefer a version with a definite plural (the girls instead of every girl). The NP the girls is, if anything, more problematic under the classical analysis, as Schwarzschild & Wilkinson (2002) point out (having less of an inclination towards wide scope); but see Section 4 for a comment on how this issue may be relevant for the analysis developed in this paper. (6000 )

a. ?John is taller than every girl is. b. John is taller than the girls are. ∀x[x ∈ the girls → John is taller than x]

Another instance are examples with intensional verbs like predict or expect; when a genuine range is predicted or expected, intuitions regarding when sentences with differentials like (800 ) would be true vs. false are not very firm. This seems to me an area in which a proper empirical study might be helpful. The issue is taken up in Section 3.4.

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Sigrid Beck

(800 )

a. b.

John is two inches taller than I had predicted (that he would be). John arrived at most 10 minutes later than I had expected.

2.2 New analyses I Since it is very hard to see how the data can be derived under the classical theory, the two theories summarized below (Schwarzschild & Wilkinson 2002 and Heim 2006b) both change the semantics of the comparative construction in ways that reanalyse scope. The quantificational element inside the thanclause can take scope there even under the apparent wide scope reading. The two theories differ with respect to the semantics they attribute to the comparison itself. They also differ in their empirical coverage. 2.2.1

Schwarzschild & Wilkinson 2002

Schwarzschild & Wilkinson (2002) are inspired by the scope puzzle to a complete revision of the semantics of comparison. The feature of the classical analysis that they perceive as the crux of our problem is that the than-clause provides a degree via abstraction over degrees. According to them, the quantifier data show that the than-clause instead must provide us with an interval on the degree scale — in (23) below an interval into which the height of everyone other than Caroline falls. (23)

Caroline is taller than everyone else is. ‘Everyone else is shorter than Caroline.’ interval that covers everyone else’s height _ _ _ _ _ _ _• _ _ _ _•_ _ _ _ •_ _ _ _ _ _ _ _• _ _ _/

x1

x2

x3

C

(the interval is related to Caroline’s height by the comparative) (24)

than everyone else is = λD. everyone else’s height falls within D (where D is of type hd, ti)2

To simplify, I will suppose that it is somehow ensured that we pick the right matrix clause interval (Caroline’s height in (23), Joe’s height in the example 2 I present the discussion here in terms of the classical theory’s ontology, where degrees (type d, elements of Dd ) are points on the degree scale and what I call an interval is a set of points, type hd, ti.

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below). (25)

Joe is taller than exactly 5 people are.

Here is a rough sketch of Schwarzschild & Wilkinson’s analysis of this example. (26)

Subord: Matrix + Comp: Whole clause:

[λD. exactly 5 people’s height falls within D] max D 0 : [Joe’s height − D 0 ] 6= 0 the largest interval some distance below Joe’s height the largest interval some distance below Joe’s height is an interval into which exactly 5 people’s height falls.

Note that the quantifier is not given wide scope over the comparison at all under this analysis. The interval idea allows us to interpret it within the than-clause. While solving the puzzle of apparent wide scope operators, the analysis makes wrong predictions for apparent narrow scope quantifiers (cf. example (27)). The available reading cannot be accounted for ((28a) is the semantics predicted by the classical analysis, corresponding to the intuitively available reading; (28b) is the semantics that the Schwarzschild & Wilkinson analysis predicts). (27)

John is taller than anyone else is.

(28)

a. John’s height > max(λd. ∃x[x 6= John & x is d-tall]) b. #The largest interval some distance below John’s height is an interval into which someone else’s height falls = Someone is shorter than John.

The breakthrough achieved by this analysis is that we can assign to the thanclause a useful semantics while interpreting the quantifier inside that clause. For this reason, the interval idea is to my mind a very important innovation. The analysis still has a crucial problem in that it does not extend to the apparent narrow scope quantifiers. That is, it fails in precisely those cases that were unproblematic for the classical analysis. I will also mention that the semantics of comparison becomes rather complex under this analysis, since the comparative itself compares intervals. This is not in line with the plot I outlined above of maintaining as the semantics of the comparative operator the plain ‘larger than’-relation.

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2.2.2

Heim 2006b

Heim (2006b) adopts the interval analysis, but combines it with a scope mechanism that derives ultimately a wide and a narrow scope reading of a quantifier relative to a comparison. Her analysis extends proposals by Larson (1988). Larson’s own analysis is only applicable to than-clauses with an adjective phrase gap denoting a property of individuals — a limitation remedied by Heim. Let us consider her analysis of apparent wide scope of quantifier data, like (29), first. Heim’s LF for the sentence is given in (30). She employs an operator Pi (Point to Interval, credited to Schwarzschild (2004)), whose semantics is specified in (31). Compositional interpretation (once more somewhat simplified for the matrix clause, for convenience) is given in (32). (29)

John is taller than every girl is.

(30)

[ IP [ CP than [1 [every girl [2 [ AP [Pi t1 ] [3 [ AP t2 is t3 tall]]]]]]] [ IP 4 [[-er t4 ] [5 [John is t5 tall]]]]

(31)

Pi = λD.λP . max(P ) ∈ D

(32)

a. b.

c.

main clause: [[[4 [[-er t4 ] [5 [John is t5 tall]]]]] = λd. John is taller than d than-clause: [than [1 [every girl [2 [ AP [Pi t1 ] [3 [ AP t2 is t3 tall]]]]]]] = D 0 /1 λD 0 . [every girl [2 [ AP [Pi t1 ] [3 [ AP t2 is t3 tall]]]]]]]g = 0 x/2 0 g D /1 λD . ∀x[girl(x) → [ AP [Pi t1 ] [3 [ AP t2 is t3 tall]]] ]= x/2 0 0 λD . ∀x[girl(x) → [λD.λP . max(P ) ∈ D](D )([3 [t2 is t3 tall]]g )] = λD 0 . ∀x[girl(x) → [λD.λP . max(P ) ∈ D](D 0 )(λd. Height(x) ≥ d)] = λD 0 . ∀x[girl(x) → max(λd. Height(x) ≥ d) ∈ D 0 ] = λD 0 . ∀x[girl(x) → Height(x) ∈ D 0 ] intervals into which the height of every girl falls main clause + than-clause: (29) = [λD 0 . ∀x[girl(x) → Height(x) ∈ D 0 ]](λd. John is taller than d) = ∀x[girl(x) → Height(x) ∈ (λd. John is taller than d)] = for every girl x: John is taller than x

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The than-clause provides intervals into which the height of every girl falls. The whole sentence says that the degrees exceeded by John’s height is such an interval. Semantic reconstruction (i.e. lambda conversion) simplifies the whole to the claim intuitively made, that every girl is shorter than John. The analysis assumes that the denotation domain Dd is a set of degree ‘points’, and that intervals are of type Dhd,ti . The analysis is a way of interpreting the quantifier inside the than-clause, and deriving the apparent wide scope reading over the comparison through giving the quantifier scope over the shift from degrees to intervals (the Pi operator). It is applicable to other kinds of quantificational elements like intensional verbs in the same way. Our example with predict is analysed below; the intuitively plausible reading can now be derived straightforwardly from the LF in (34). (33)

a. b.

(34)

[ IP [ CP than [1 [I had predicted [ CP [Pi t1 ] [2 [ AP John t2 tall]]]]]]] [ IP 3 [John is taller than t3 ]]]

(35)

a. b.

c.

John is taller than I had predicted (that he would be). ∀w[wR@ → max(λd. John is d-tall in @) > max(λd. John is d-tall in w)] = For every world compatible with my predictions: John’s actual height exceeds John’s height in that world.

main clause: [3 [John is taller than t3 ]] = (λd. John is taller than d in @) than-clause: [than [1 [I had predicted [ CP [Pi t1 ] [2 [ AP John t2 tall]]]]]]] = 0 [λD 0 . ∀w[wR@ → [ CP [Pi t1 ] [2 [ AP John t2 tall]]]g[D /1] ] = [λD 0 . ∀w[wR@ → max(λd. Height(John)(w) ≥ d) ∈ D 0 ]] = [λD 0 . ∀w[wR@ → Height(John)(w) ∈ D 0 ]] intervals into which John’s height falls in all my predictions main clause + than-clause: (34) = [λD 0 . ∀w[wR@ → Height(John)(w) ∈ D 0 ]] (λd. J is taller than d in @) = for every w compatible with my predictions: John’s actual height exceeds John’s height in w.

The effect of the Pi operator on the predicate of degrees it combines with is sketched below for the AP tall. As long as a than-clause quantifier takes

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scope over the Pi operator, the resulting meaning of the whole sentence will be one that lets the quantifier take scope over the comparison, even though it is interpreted syntactically below the comparative operator and inside the than-clause. (36)

Pi shifts from degrees to intervals: [λd. Height(x) ≥ d] =⇒ [λD. Height(x) ∈ D]

In contrast to Schwarzschild & Wilkinson’s original interval analysis, Heim is able to derive apparently narrow scope readings of an operator relative to the comparison as well. The sentence in (37a) is associated with the LF in (38). Note that here, the shifter takes scope over the operator have to. This makes have to combine with the degree semantics in the original, desired way, giving us the minimum compliance height (just like it did before, without the intervals). The shift is essentially harmless. (37)

a. b.

(38)

[ IP [ CP than [1 [[[Pi t1 ] [2 [has-to [Mary t2 tall]]]]]]] [ IP 3 [Mary is taller than t3 ]]]

(39)

a. b.

c.

Mary is taller than she has to be. max(λd. Mary is d-tall in @) > max(λd. ∀w[wR@ → Mary is d-tall in w]) Mary’s actual height exceeds the degree of tallness which she has in all worlds compatible with the school rules; i.e. Mary’s actual height exceeds the required minimum, 1.70 m.

main clause: [3 [Mary is taller than t3 ]]] = (λd. Mary is taller than d in @) than-clause: [than [1 [[[Pi t1 ] [2 [has-to [Mary t2 tall]]]]]] = 0 λD 0 . [[Pi t1 ] [2 [has-to [Mary t2 tall]]]]]]g[D /1] = λD 0 . max(λd. has-to [Mary t2 tall]]]]]]g[d/2] ) ∈ D 0 λD 0 . max(λd. ∀w[wR@ → Mary is d-tall in w]) ∈ D 0 intervals into which the required minimum falls main clause + than-clause: (38) = [λD 0 . max(λd. ∀w[wR@ → Mary is d-tall in w]) ∈ D 0 ] (λd. Mary is taller than d in @) = Mary is taller than the required minimum.

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Other apparent narrow scope operators receive a parallel analysis. The crucial ingredient to this analysis is that the Pi operator is a scope bearing element, able to take local or non-local scope. Pi-phrase scope interaction is summarized below: (40)

Pi takes narrow scope relative to quantifier =⇒ apparent wide scope reading of quantifier over comparison Pi takes wide scope relative to quantifier =⇒ apparent narrow scope reading of quantifier relative to comparison

Thus than-clauses include a shift from degrees to intervals, which allows us to assign a denotation to the than-clause with the quantifier. The shift amounts to a form of type raising. Through semantic reconstruction, the matrix clause is interpreted in the scope of a than-clause operator when that operator has scope over the shifter. In contrast to Schwarzschild & Wilkinson, comparison is ultimately between degrees, not intervals. Heim’s analysis is able to derive both wide and narrow scope readings of operators in than-clauses. It does so without violating syntactic constraints. There is, however, an unresolved question: when do we get which reading? How could one constrain Pi-phrase/operator interaction in the desired way? One place where this problem surfaces is once more negation, where we expect an LF that would generate an acceptable wide scope of negation reading. That is, the LF in (41b) should be grammatical and hence (41a) should be acceptable on the reading derived from this LF in (42). (41)

a. *John is taller than no girl is. b. [ IP [ CP than [1 [no girl [2 [[Pi t1 ] [3 [ t2 is t3 tall]]]]]]] [ IP 4 [[-er t4 ] [5 [John is t5 tall]]]]

(42)

a. b.

c.

main clause: [4 [[-er t4 ] [5 [John is t5 tall]]] = λd. John is taller than d than-clause: [than [1 [no girl [2 [[Pi t1 ] [3 [ t2 is t3 tall]]]]]]] = λD 0 . for no girl x : max(λd. x is d-tall) ∈ D 0 intervals into which the height of no girl falls main clause + than-clause: (41b) = [λD 0 . for no girl x : max(λd. x is d-tall) ∈ D 0 ](λd. J is taller than d) = for no girl x: John is taller than x

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Sigrid Beck

Adopting the interval analysis, but combining it with a scope mechanism and semantic reconstruction, allows Heim to derive both types of readings (apparent narrow and apparent wide scope), and to reduce the comparison ultimately back to a comparison between degrees. Thus her empirical coverage is greater and the semantics of comparison simpler than Schwarzschild & Wilkinson’s analysis. The problem that this analysis faces is overgeneration. We do not have an obvious way of predicting when we get which reading. The fact that in general, only one scope possibility is available makes one doubt that this is really a case of systematic scope ambiguity. 2.3 Alternative new analyses: Gajewski, van Rooij, Schwarzschild There is a group of new proposals — Gajewski 2008, van Rooij 2008 and Schwarzschild 2008 — for how to deal with quantifiers in than-clauses whose approach seems to be inspired by Heim’s (2006b) analysis. I present below a simplified version of this family of approaches that is not entirely faithful to any of them. I call this the NOT-theory. It can be summarized in relation to the previous subsection as ‘keep the than-clause internal operator, but not the intervals’. It adopts the idea that there is an operator — like Heim’s Pi — that can take wide or narrow scope relative to a than-clause quantifier, dictating what kind of reading the comparative sentence receives. It does not adopt an interval analysis, and thus the operator is not Pi and the semantics of the comparative is not the classical one. Instead, the operator is negation and the proposed semantics is basically Seuren’s (1978). 2.3.1 Seuren’s semantics for the comparative (operator: NOT) Seuren (1978) suggests (43b) as the interpretation of (43a). The than-clause provides the set of degrees of tallness that Bill does not reach. It does so by virtue of containing a negation, as illustrated in the LF in (44). This meaning could be combined intersectively with the main clause and the degree existentially bound, as represented in (45). (43)

a. b. c.

John is taller than Bill is. ∃d[Height(J) ≥ d & ¬ Height(B) ≥ d] There is a degree of tallness that John reaches and Bill doesn’t reach.

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than λd[NOT Bill is d-tall] λd[¬ Height(B) ≥ d] = λd[Height(B) < d]

(44)

a. b.

(45)

[∃ [λd [John is d-tall] [than λd [NOT Bill is d-tall]]]

The authors mentioned above note that this semantics gives us an easy way to derive the intuitively correct interpretation for apparent wide scope quantifiers. This is illustrated below for the universal NP. In (46) I show that the desired meaning is easily described in this analysis and in (47) I provide the LF for the than-clause that derives it. (48) illustrates that some, another apparent wide scope quantifier, is equally unproblematic. (46)

a. b. c.

John is taller than every girl is. ∃d[Height(J) ≥ d & ∀x[girl(x) → Height(x) < d]] every girl is shorter than John.

(47)

a. b. c.

than every girl is than λd [every girl [1 [NOT [t1 is d tall]]]] than λd.∀x[girl(x) → Height(x) < d]]

_ _ _ _• _ _ _ _ _ _ _•_ _ _ _ •_ _ _ _ _ _ _ • _ _ _ _ _ _ _ _ _ _ _/

g1 (48)

a. b. c.

g2

g3

g4

...

John is taller than some girl is. ∃d[Height(J) ≥ d & ∃x[girl(x) & Height(x) < d]] there is a girl who is shorter than John.

An interesting application is negation, here illustrated with the negative quantifier no. Proceeding in the now familiar way, we derive (49b). Rephrasing this in terms of (49c) makes it clear that the resulting semantics is very weak. Whenever the girls have any measurable height at all — that is, whenever the than-clause can be appropriately used — there will be a height degree that John reaches and that all the girls reach as well. The smallest degree on the scale will be such a degree. The NOT-theory proposes that the sentence is unacceptable because it is necessarily uninformative. (49)

a. *John is taller than no girl is. b. ∃d[Height(J) ≥ d & for no girl x : Height(x) < d] c. ∃d[Height(J) ≥ d & for every girl x : Height(x) ≥ d] uninformative! (The lowest degree on the height scale makes this true.) 1:17

Sigrid Beck

2.3.2

NOT has to take varying scope

The NOT-theory needs another important ingredient: Just like the Pi-operator above, other than-clause internal operators have to take flexible scope relative to NOT in order to create the different readings we observe. This is illustrated below with the familiar have to example, and with allowed. (50)

a. Mary is taller than she has to be. b. #∃d[Height(M)(@) ≥ d & ∀w[wR@ → NOT Height(M)(w) ≥ d]] Mary should have been shorter than she is. c. ∃d[Height(M)(@) ≥ d & NOT∀w[wR@ → Height(M)(w) ≥ d]] Mary is taller than the minimally required height.

(51)

a. John is taller than he is allowed to be. b. #∃d[Height(J)(@) ≥ d & ∃w[wR@ & NOT Height(J)(w) ≥ d]] ∃d[Height(J)(@) ≥ d & ∃w[wR@ & Height(J)(w) < d]] John would have been allowed to be shorter than he is. c. ∃d[Height(J)(@) ≥ d & NOT∃w[wR@ & Height(J)(w) ≥ d]] John is taller than the tallest permissible height.

(52)

a. #than λd [allowed [λw [NOT [John is d tall in w]]]] b. than λd [NOT [allowed [λw [John is d tall in w]]]]

Just like the Pi-theory, then, the NOT-theory is able to generate the range of readings we observe for operators in than-clauses. It seems somewhat simpler than the Pi-theory in that it does not take recourse to intervals in addition to a scopally flexible than-clause internal operator. But as in the case of the Pi-theory, we must next ask ourselves what prevents the unavailable readings, e.g. what excludes the LF in (52a). 2.3.3

Which reading?

The NOT-theory would have an empirical advantage over the Pi-theory if constraints on scope could be found to deal with the overgeneration problem we noted above. A first successful application are polarity items. Example (53a) can only have the LF in (54b), not the one in (54a), according to constraints on the distribution of NPIs. Thus we only derive the approproate interpretation. Note though that the Pi-theory has the same success since the scope of Pi is a downward entailing environment, but the rest of the than-clause isn’t (compare Heim 2006b). (55) is the mirror image.

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(53)

a. John is taller than any girl is. b. #∃d[Height(J) ≥ d & ∃x[girl(x) & Height(x) < d]] there is a girl who is shorter than John. c. ∃d[Height(J) ≥ d & NOT ∃x[girl(x) & Height(x) ≥ d]] John reaches a height degree that no girl reaches. = John is taller than every girl.

(54)

a. *than λd [any girl [1 [NOT [t1 is d tall]]]] b. than λd [NOT [any girl [1 [t1 is d tall]]]]

(55)

John is taller than some girl is.

Let us next reexamine negation. Two interpretations need to be considered. The one in (56b) was already rejected above as uninformative. It turns out that the alternative interpretation is equally uninformative. The ungrammaticality of negation in than-clauses is thus captured elegantly by this theory. Here it has an advantage over the Pi-theory. (56)

a. *John is taller than no girl is. b. ∃d[Height(J) ≥ d & for no girl x : Height(x) < d] uninformative c. ∃d[Height(J) ≥ d & NOT for no girl x : Height(x) ≥ d] uninformative = ∃d[Height(J) ≥ d & some girl x : Height(x) ≥ d]

Among the proponents of the NOT-theory, Schwarzschild (2008) examines modals. He argues that the NOT-theory predicts that modals in than-clauses should give rise to the same reading that they have with ordinary clause-mate negation. This prediction is borne out, as the examples below illustrate. (57)

a. b.

John is not allowed to be that tall. than he is allowed to be.

NOT allowed

(58)

a. b.

John might not be that tall. than he might be.

(59)

a. b.

John is not supposed to be that tall. than he is supposed to be.

supposed NOT

(60)

a. b.

John is not required to be that tall. than he is required to be.

NOT required

might NOT

While this is helpful with modals, it stops short of explaining the interpretation associated with intensional full verbs like predict.

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Sigrid Beck

(61)

a. b.

John was not predicted to be that tall. than he was predicted to be.

NOT predict — #

Two further possible constraints are discussed. Van Rooij (2008) examines universal DPs and Gajewski (2008) investigates numeral DPs. Let us consider both in turn. Note first that a universal DP is ambiguous relative to clause mate negation. In particular it allows a reading in which the universal takes narrow scope relative to negation. Thus there are no inherent scope constraints that would help us to exclude (630 b) as an LF of (63a). But exclude it we must, since it gives rise to the unavailable reading (63c). (62)

a. b.

Every girl isn’t that tall. than every girl is.

ambiguous

(63)

a. b.

John is taller than every girl is. ∃d[Height(J) ≥ d & ∀x[girl(x) → Height(x) < d]] ‘Every girl is shorter than John.’ c. #∃d[Height(J) ≥ d & NOT ∀x[girl(x) → Height(x) ≥ d]] ‘John reaches a height that some girl doesn’t.’ = John is taller than the shortest girl.

(630 )

a. than λd [every girl [1 [NOT [t1 is d tall]]]] b. *than λd [NOT [every girl [1 [t1 is d tall]]]]

Van Rooij observes that (630 a) yields stronger truth conditions than (630 b). He proposes that if no independent constraint excludes one of the LFs, you have to pick the one that results in the stronger truth conditions. This amounts to the suggestion that than-clauses fall within the realm of application of the Strongest Meaning Hypothesis (SMH; Dalrymple, Kanazawa, Kim, Mchombo & Peters 1998). If they do, the NOT-theory can make the desired predictions about every DPs (and some other relevant examples). So could the Pi-theory, though, so this does not distinguish between the two scope based theories of quantifiers in than-clauses. While I am sympathetic to the idea of extending application of the SMH, I see some open questions for doing so in the case of than-clauses. Dalrymple et al. originally proposed the SMH to deal with the interpretation of reciprocals. (64a) receives a stronger interpretation than (64b), for example, because the predicate to stare at makes it factually impossible for the reading of (64a) to ever be true. Similarly for (64c) vs. (64a,b). But (64a) only has one inter-

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pretation, the strongest one, and (64b) also cannot have a reading parallel to (64c). The SMH says, very roughly, that out of the set of theoretically possible interpretations you choose the strongest one that has a chance of resulting in a true statement, i.e. that is conceptually possible.3 (64)

a. b. c.

These three people know each other. = everyone knows everyone else. These three people were staring at each other. = everyone was staring at someone else. These three people followed each other into the elevator. = everyone followed, or was followed by, someone else.

There is a theoretical question as to when the SMH applies. We would not wish it to apply in (62) for instance because it would predict that there is no ambiguity. When there is ambiguity, the data in question must not be subject to the SMH. Are than-clauses in the domain of application of the SMH? Prima facie, this seems very plausible, because — just like reciprocals — they are (almost always) unambiguous, while semantic theory provides several potential interpretations. What strikes me as problematic is that there is no way to make the weaker reading emerge, even if the stronger reading is conceptually impossible. The following sentences are necessarily false, rather than having the interpretations indicated. (640 )

a.

(about a 100 m race:) The next to last finalist was faster than every other finalist. ≠ the next to last finalist was faster than the slowest other finalist.

3 Below I provide the formulation of the SMH given in Beck 2001. If we extend the domain of application of the SMH to than-clauses, we need to strike out those phrases that make explicit reference to reciprocals, as indicated. The relevant point is that the SMH makes reference to interpretations compatible with non-linguistic information I, which in the examples in (640 ) below would be knowledge about the order of finalists, elevator buttons and weekdays, parallel to knowledge about processions of people and possibilities for staring in (64). (i)

Strongest Meaning Hypothesis (SMH) Let Sr be the set of theoretically possible reciprocal interpretations for a sentence S. Then, S can be uttered felicitously in a context c, which supplies non-linguistic information I relevant to the reciprocal’s interpretation, provided that the set Sc has a member that entails every other one. Sc = {p: p is consistent with I and p ∈ Sr } In that case, the use of S in c expresses the logically strongest proposition in Sc .

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Sigrid Beck

b.

c.

(in an elevator:) The second button from the bottom is higher than every other button. ≠ the second button from the bottom is higher than the lowest other button. Friday is earlier than every other day of the week. ≠ Friday is earlier than the latest other day of the week.

Thus than-clauses do not seem parallel to reciprocals. It would be better if an LF that gives rise to the ‘the least . . . other’ reading for universal DPs simply did not exist. Turning now to numeral DPs, note first that it is not immediately obvious how the NOT-theory predicts a plausible meaning for them at all. Gajewski (2008) points out that the following analysis of exactly-DPs gives rise to truth conditions that are too weak. (650 ) would be true in a situation in which more than three girls stay below John’s height. (65)

John is taller than exactly three girls are.

(650 )

∃d[Height(J) ≥ d & for exactly 3 girls x : Height(x) < d] At least three girls are below John’s height _ _ _ • _ _ _ _ • _ _ _ _ • _ _ _ _ _ _ _ • _ _ _ _ • _ _ _ _ • _ _ _ _/

g1

g2

g3

g4

g5

d

H(J)

Reversing the scope of NOT and the exactly-DP doesn’t help: (6500 )

∃d[Height(J) ≥ d & NOT for exactly 3 girls x : Height(x) ≥ d] there is a degree of height that John reaches that is not reached by exactly 3 girls, i.e. fewer or more girls reach that degree true e.g. if John is taller than every one of five girls

Gajewski develops an analysis that relies on Krifka’s (1999) work on exactly, at least and at most, according to which these elements take effect at the level of the utterance, far away from their surface position. I present this analysis in simplified terms below, using (66) to illustrate. The semantic effect of exactly is due to an operator I call EXACT, which applies at the utterance level and operates on the basis of the ordinary as well as the focus semantic

1:22


value of its argument. The operator’s semantics is given in (67). The truth conditions derived for the example are the right ones, as shown in (68) ((68) uses Link’s (1983) operator ∗ for pluralization of the noun). (66)

a. b.

Exactly three girls weigh 50 lb. [EXACT [XP (exactly) threeF girls weigh 50 lb.]]

(660 )

threeF girls weigh 50 lb.o = ∃X[∗ girl(X) & card(X) = 3 & ∗weigh.50.lb(X)] threeF girls weigh 50 lb.f = {∃X[∗ girl(X) & card(X) = n & ∗weigh.50.lb(X)] : n ∈ N}

(67)

EXACT(XPf )(XPo ) = 1 iff XPo = 1 & ∀q ∈ XPf : ¬(XPo → q) → ¬q ’Out of all the alternatives of XP, the most informative true one is the ordinary semantics of XP.’

(68)

(66b) = 1 iff ∃X[∗ girl(X)&card(X) = 3 & ∗weigh.50.lb(X)] & ∀n[n > 3 → ¬∃X[∗ girl(X) & card(X) = n & ∗weigh.50.lb(X)]] iff max(λn.∃X[∗ girl(X) & card(X) = n & ∗weigh.50.lb(X)]) = 3

Krifka’s analysis of exactly allows us to assign the problematic example (65) the LF in (69), which captures the right meaning, namely the interpretation in (690 ). (69)

EXACT [∃ [λd [John is d-tall] [than λd [threeF girls [λx [NOT x is d-tall]]]]

(690 )

max(λn. ∃d[Height(J) ≥ d & for n girls x : Height(x) < d]) the largest number n such that John reaches a height that n girls don’t is 3. = exactly three girls are shorter than John.

Thus independently motivated assumptions about numerals allow the NOTtheory to derive the desired interpretation. However, there is still the question of the other LF, (70), in which NOT takes scope over the DP. This gives rise to interpretation (700 ). (70)

EXACT [∃ [λd [John is d-tall] [than λd [NOT threeF girls [λx [x is d-tall]]]]

(700 )

max(λn. ∃d[Height(J) ≥ d & NOT for n girls x : Height(x) ≥ d]) the largest number n such that there is a height John reaches and it’s

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Sigrid Beck

not the case that n girls do is 3. = exactly two girls are shorter than John. The reasoning in (71) makes it clear that this reading leads to truth conditions that do not correspond to an available reading; they would make the sentence true in the situation depicted, where there are two girls shorter than John. (71)

a. b.

∃d[Height(J) ≥ d & NOT for n girls x : Height(x) ≥ d] = ∃d[Height(J) ≥ d & fewer than n girls reach d] ∃d[Height(J) ≥ d & fewer than 3 girls reach d]

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _/ • • • • • •

g1

g2

g3

g4

g5

H(J) The NOT-theory would have to come up with an explanation for why this reading is unavailable. I am not aware that there is at present such an explanation. Note that even if we didn’t have the reservations about the SMH pointed out above, it would not apply here, as the two interpretations don’t stand in an entailment relation. To summarize: just like the Pi-theory, the NOT-theory faces an overgeneration problem. Both the Pi-theory and the NOT-theory solve this easily regarding NPIs. The NOT-theory also has a simple story about modals and negative quantifiers. It does not have an explanation for intensional full verbs and numeral DPs, and I argue it does not have a story about universal DPs (or other prospective applications of the SMH) either. Thus I see some progress compared to the Pi-theory, but not a complete analysis. A conceptual advantage seems to be the NOT-theory’s simplicity. But we will need to reexamine that in the next subsection. 2.3.4 Reference to degrees — differentials One of the strengths of the classical analysis of comparatives is the way in which it deals with explicit reference to degrees. For example differentials in comparatives, illustrated in (72) and (73), receive an easy and natural analysis. (72)

a. b. c.

Bill is 1.70 m tall. John is 200 taller than that. Height(J) ≥ 200 + 1.70 m

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(73)

a. b.

John is 200 taller than Bill is. Height(J) ≥ 200 + max(λd. Height(B) ≥ d) = Height(J) ≥ 200 + Height(B)

It is not obvious how to incorporate differentials into the NOT-theory, whose semantics of a simple example is repeated in (74). That is because the than-clause does not refer to a degree. (74)

a. b.

John is taller than Bill is. ∃d[Height(J) ≥ d & NOT Height(B) ≥ d]

Among the proponents of the NOT-theory, Schwarzschild (2008) discusses this problem. He proposes to understand (75a) in terms of (75b); I simplify this to (75c) for the purposes of discussion. (75)

a. b. c.

John is 200 taller than Bill is. ∃d[Height(J) ≥ d & 200 (λd0 . d0 ≤ d & Height(B) < d0 )] 200 (λd0 . d0 ≤ Height(J) & Height(B) < d0 )]) “the degrees between Bill’s height and John’s are a 200 interval”

_ _ _ _ • _ _ _ _ _ _ _ _ _ _ _ _ _ _ • _ _ _ _/ 200 interval

H(B)

H(J)

The question is how to derive this interpretation. Schwarzschild proposes to replace NOT in the than-clause with an operator FALL-SHORT. The resulting LF of our example is given in (750 a) and the semantics of FALL-SHORT in (750 b). Diff is a variable that is the first argument of FALL-SHORT, to be bound outside the than-clause and identified with the differential in the matrix clause (as if the differential was raised out of the embedded clause to its main clause position). (750 )

a. b. c.

than [[FALL-SHORT Diff] λd [Bill is d-tall]] FALL-SHORT = λDiff.λDh d, ti.λd. Diff(λd0 . d0 ≤ d & D(d0 ) = 0) Diff(λd0 . d0 ≤ d& Height(B) < d0 ) Bill’s Height is a Diff-large distance below d

We combine with the differential next, as shown in (76). Then, the degree d is bound and the usual semantic mechanisms combine this with the rest of the main clause in (77). This derives (75).

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Sigrid Beck

[200 er] [λDiff [than Bill is tall]] λd. 200 (λd0 . d0 ≤ d& Height(B) < d0 )] Bill’s Height is a 200 distance below d

(76)

a. b.

(77)

[∃ [λd [John is d-tall] [200 er] [λDiff [than Bill is tall]]]

It seems to me that this is a rather substantial modification of the original NOT-theory. The basic points about than-clause scope interaction remain the same (as the reader may verify), but some of the explanation is less obvious. In particular, I don’t see that scopal behaviour of a modal with same clause negation necessarily predicts scopal behaviour relative to FALL-SHORT, any more than it predicts scopal behaviour relative to Pi. I also believe that we lose the explanation of the unacceptability of negative quantifiers. Neither of the readings associated with the two possible LFs below is necessarily uninformative. Finally, I no longer see that the FALL-SHORT-theory is simpler than the Pi-theory. (78)

a. b. c.

John is 200 taller than no girl is. [∃ [λd [J. is d-tall] [200 er] [λDiff [than [[FALL-SHORT Diff] λd [no girl is d-tall]]] [∃ [λd [J. is d-tall] [200 er] [λDiff [than [no girl λx [FALL-SHORT Diff] λd [x is d-tall]]]]]

(780 )

∃d[Height(J) ≥ d&200 (λd0 . d0 ≤ d & [λd. no girl is d-tall](d0 ) = 0)]] = ∃d[Height(J) ≥ d & 200 (λd0 . d0 ≤ d & some girl is d0 -tall])] = John and some girl are at least two inches tall.

(7800 )

∃d[Height(J) ≥ d & no girl x : 200 (λd0 . d0 ≤ d& Height(x) < d0 )] = no girl is 200 shorter than John.

I conclude that while the type of analysis discussed in this section — what one might call scopal theories of quantifiers in than-clauses — has brought forth some very interesting ideas, there are also unanswered questions. It may be worthwhile to pursue a scopeless alternative, which is what I will do in the next section. 3

Analysis: Selection

The strategy I propose in this section is inspired by both Schwarzschild & Wilkinson and Heim. Schwarzschild & Wilkinson’s use of intervals is retained in order to be able to interpret a quantifier inside a than-clause. But like Heim,

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I attempt to make this move compatible with a simple, standard semantics of the comparative. The novel aspect of the analysis below concerns how this is done. I do not adopt a than-clause internal operator Pi and I do not rely on semantic reconstruction. I propose instead that there is a mechanism that derives a particular degree from an interval provided by the than-clause. This degree is compared in the normal way with a matrix clause degree. The trick will be to ensure that the degree chosen is the right one, i.e. that the comparison ultimately made reflects the intuitively accessible reading of the comparative sentence in question. The same selection mechanism will account for both apparent wide scope and apparent narrow scope readings. The analysis will not employ a scoping mechanism that is specific to comparatives. Its relation to the earlier work discussed above can be simply stated as ‘keep the intervals, but not the operator’. Two rationales guide me in pursuing this approach. The first is that a scoping mechanism inside the than-clause overgenerates in ways that we have yet to find the means of constraining. Therefore it would be an advantage to make do without such an extra scopal element. The second is that it remains a strength of the classical analysis that degree operators combine directly with expressions referring to degrees, and that differentials in particular can be accounted for in a direct and straightforward way. Therefore I want to come out of the calculation of the semantics of the than-clause holding in my hand the degree we will be comparing things to. The combination of these two lines of reasoning persuades me to attempt a simplification of Schwarzschild & Wilkinson, which should of course also cover the apparent narrow scope data that were problematic for them. Section 3.1 presents the idea behind the selection analysis and applies it to straightforward cases. Apparent narrow scope universals are not straightforward and addressed in Section 3.2. Apparent wide scope existentials similarly seem problematic and are the issue of Section 3.3. In Section 3.4 I reexamine comparatives that combine a differential with a quantifier in the than-clause and propose a refinement of the analysis of the comparative to capture the data. 3.1

Basic idea and simple cases

I illustrate the idea behind the selection analysis with example (79), which would not in fact require intervals at all of course. But, suppose that we in general compositionally derive as the meaning of the than-clause a set of

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Sigrid Beck

intervals, as suggested in the Schwarzschild & Wilkinson and Heim theories. Suppose furthermore that this comes from the basic lexical entry of the adjective, as indicated in (80). This is what I will assume in this section, for the sake of uniformity (see Section 4 for more discussion). It amounts to (790 ) in the present case. How do I propose to derive the truth conditions of (79a), (79b), from that? (79)

a. b.

(790 )

a. b.

John is taller than Bill is. Height(John) > Height(Bill) [than Bill is tall] = λD 0 . Height(Bill) ∈ D 0 _ _ _ _ _ _ _ _ _ _ _ _ _ • _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _/

H(B)

.. . (80)

_ Intervals containing Bill’s height

_

tall = λD. λx. Height(x) ∈ D

I suggest that general mechanisms available in such situations enable us — in fact, force us — to pick from the set of intervals something that is suitable as the input to the comparative operator repeated in (81). I represent this selection mechanism as the in (7900 ) for the moment. This subsection asks what the appropriate meaning for the is. (Note that the term ‘selection’ is not intended to imply that there is a genuine choice; I intend to provide one semantics for the.) (81) (7900 )

-er = λdd . λd0d . d0 > d John is taller than the than-clause

In the present case, the could be an operator selecting the shortest interval from the set, i.e. Bill’s height, cf. (82). This seems a natural choice, given that all other intervals contain extraneous material and that the point that really ‘counts’ is just Bill’s height. (82)

min(phhd,ti,ti ) = ιD. p(D) & ¬∃D 0 . D 0 ⊂ D & p(D 0 ) (shortest p interval)

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Irene Heim and Danny Fox (p.c.) point out to me that the sense in which choosing the minimal interval is ‘natural’ is informativity. (83) below states what the maximally informative propositions out of a set of true propositions (say, a question meaning) are. (83)

a. b.

m_inf(w)(Q & h hs,hhs,ti,tii ) = λq. Q(w)(q) i 0 0 0 ¬∃q Q(w)(q ) & q 6= q & Q(w)(q0 ) → Q(w)(q) the maximally informative answers to a question Q(w) (Q(w) the set of true answers to Q in w) is the set of propositions q in Q(w) such that there is no other proposition q0 in Q(w) such that Q(w)(q0 ) entails Q(w)(q) (i.e. if q0 is in Q(w) then so is q).

Informativity allows us to capture the fact that an appropriate answer to (84a) is the true answer that entails all the other true answers, i.e. John’s maximal speed (for example the proposition that he drove 50 mph), and in a parallel way the minimum amount of flour that suffices in (84b)(see Heim 1994; Beck & Rullmann 1999). (84)

a.

How fast did John drive? λw. λp. ∃d p(w) & p = λw 0 . John drove d-fast in w 0 {that John drove 50 mph, that John drove 49 mph, that John drove 48 mph, . . . } b. How much flour is sufficient? λw.λp.∃d[p(w)&p = λw 0 .d-much flour is sufficient in w 0 ] {that 500 g is sufficient, that 501 g is sufficient, that 502 g is sufficient, . . . }

The definition can be extended to (intensions of) arbitrary sets in the following way: (85)

m_inf(w)(p & h hs,hα,tii ) = λq. p(w)(q) i 0 0 0 ¬∃q p(w)(q ) & q 6= q → p(w)(q0 ) & p(w)(q)

The instance of this generalization that we will be interested in is (86). (86)

a. b.

m_inf(w)(p & h hs,hhd,ti,tii ) = λD. p(w)(D) i 0 0 0 ¬∃D p(w)(D ) & D 6= D & p(w)(D 0 ) → p(w)(D) the maximally informative intervals out of a set of intervals p(w) is the set of intervals D such that there is no other interval D 0 in p(w) such that p(w)(D 0 ) entails p(w)(D) (i.e. if D is in p(w) then so is D 0 ). 1:29

Sigrid Beck

Fox & Hackl (2006) argue that we want to extend the definition from the question case to others in order to capture the similarity between (84a,b) above and (87a), (88a). (87a) refers to the maximum speed John reached and (88a) refers to the minimum amount that suffices, both maximally informative in the sense of (85). The instance in (86) extends the analogy from (84a,b) and (87a), (88a) to (87b), (88b). (87)

a. b.

the speed that John drove than John drove

(88)

a. b.

the amount of flour that is sufficient than is sufficient

Hence, the in (7900 ) is m_inf, which yields a singleton, combined with taking from a set its only member (here represented with max). We can understand these operators as semantic ‘glue’ (a term introduced by Partee 1984, see also von Stechow 1995): operations that have to enter into composition, in addition to what the syntax strictly speaking provides, in order to make the sentence parts combinable. Their presence is required by the need for interpretability. (79000 )

John is taller than max(m_inf(than-clause))

The simple example allows me to emphasize another aspect of what I call the selection analysis: there is no choice in ‘selecting’ a point from a set of intervals. Only one interpretation is possible for (79). The ‘glue’ we have here is entirely semantic (and not, say, subject to pragmatic variability). Although we will see in a moment that quantifiers in than-clauses require some more elaboration, this will be preserved. Selection means, basically, taking from the minimal interval(s) the maximal element. 3.1.1 Apparent wide scope universals Let’s return to the now familiar example (89). We take the than-clause to have the denotation in (890 ). (89)

a. b.

John is taller than every girl is. For every girl x: John’s height exceeds x’s height.

1:30


(890 )

[than every girl is tall] = λD 0 . ∀x girl(x) → Height(x) ∈ D 0 interval into which the height of every girl falls

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _/ • • • •

x1

x2

x3

J

The intuitive truth conditions of (89) can be described as making a comparison between John’s height and the end point of the interval into which all the girls’ heights fall. If John is taller than the tallest girl, he is taller than all of them. Thus I propose that from the denotation of the than-clause that is given in (890 ), we first choose the shortest = maximally informative interval that fits the description (i.e. that covers all the girls’ heights) and then select the maximal point of that interval.4 (90)

John is taller than Max> m_inf(than-clause) = John is taller than the height of the tallest girl

(91) and (92) below provide the relevant definitions. We extend the notion of the ordering relation underlying our degree scale from degrees to intervals, (91). We can then define the maximal element of a set of intervals, and finally the end point of an interval, (92). (91)

(92)

d > d0 d is larger than d0 I > J iff ∃d d ∈ I & ∀d0 [d0 ∈ J → d > d0 ] I extends beyond J

a.

ordering of degree points:

b.

ordering of intervals:

a. b.

max> := the max relative to the > relation on intervals or degrees Max> (p) := max> (max> (p)) = the end ‘point’ of the interval that extends furthest

We straightforwardly derive the desired meaning. Other universal quantifiers can be treated in the exact same way. This is illustrated below with the 4 Fox & Hackl propose to replace maximality with maximal informativity. I have not been able to develop an analysis that incorporates that proposal. The reason is lack of entailment among the degrees in the minimal than-clause interval: If I know of a degree d that it falls in between the height of the smallest girl and the height of the tallest girl, I cannot infer that a degree d0 larger than d also falls within that interval (d0 might be beyond the height of the tallest girl) and I cannot infer that a smaller degree d00 also falls within that interval (d00 might be below the height of the shortest girl). Therefore I will use both maximal informativity and ordinary maximality.

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familiar example containing predict. If my prediction was that John would be between 1.70 m and 1.80 m tall, then the interval [1.70–1.80] is the unique shortest interval described by the than-clause. The end point of that interval is 1.80 m, and the example is correctly predicted to be true if John is taller than 1.80 m. (93)

a. b.

(930 )

[than I had predicted (that he would be tall)] = λD 0 . ∀w[wR@ → John’s height in w ∈ D 0 ] intervals into which John’s height falls in all my predictions

(9300 )

John is taller than I had predicted (that he would be). For every world compatible with my predictions: John’s actual height exceeds Johns height in that world.

John is taller than Max> (m_inf(than-clause)) = John is taller than the height according to the tallest prediction

What I call selection yields the maximum relative to the ordering relation linguistically given — ‘larger than’ on the size scale in the case of taller. This follows from more general interpretive mechanisms suggested independently (compare Jacobson 1995; Fox & Hackl 2006). Application of these mechanisms is required by the need for the than-clause to serve as input to the comparative operator. 3.1.2 Apparent narrow scope existentials We can apply the same strategy to narrow scope existentials. This is illustrated with (94) below. In contrast to Heim’s analysis and like Schwarzschild & Wilkinson’s, I assume that the than-clause denotes the set of intervals in (940 ) (once more via the shifted lexical entry for the adjective, (80)). Importantly, remember that I assume that the shift to intervals must take place locally, i.e. within the adjective phrase. I do not assume a genuine mobile operator Pi like Heim (2006b) does (whose LF for (94a) would give Pi wide scope relative to anyone). We dispense with the interpretations for than-clauses that were attributed to wide scope of the Pi operator. (94)

a. b.

Mary is taller than anyone else is. Mary’s height exceeds the largest degree of tallness reached by one of the others.

(940 )

[than anyone else is tall] = λD 0 . ∃x[x ≠ Mary & Height(x) ∈ D 0 ] intervals into which the height of someone other than Mary falls 1:32


The shortest = maximally informative than-clause intervals will be the heights of the other relevant people. (Thus we get rid of the intervals immediately.) Out of these, we choose the maximum. This results in the same meaning as under the classical analysis. Thus the same selection strategy that we used above will predict the right truth conditions. The analysis extends to other apparent narrow scope existentials like be allowed etc. (95)

_ _ _ _• _ _ _ _• _ _ _ _ •_ _ _ _ _ _ _ • _ _ _ _ _ _ _/

x1 (9400 )

x2

x3

M

Mary is taller than Max> (m_inf(than-clause)) = Mary is taller than the height of the tallest other person.

The selection strategy predicts the right truth conditions for these ‘apparent narrow scope’ and ‘apparent wide scope’ quantifier data without changing scope. This allows us to predict ungrammaticality of negation straightforwardly, as illustrated below. 3.1.3 Negation Remember that the unacceptability of (96) could be understood in terms of an undefined contribution of the than-clause (von Stechow 1984; Rullmann 1995). The selection analysis presented here can retain this desirable prediction. The meaning of the than-clause is (960 ), in accordance with what is said above. This is the only meaning possible for the than-clause. (96) (960 )

*John is taller than no girl is. than no girl is tall = λD 0 . for no girl x : Height(x) ∈ D 0 intervals into which the height of no girl falls

(960 ) will not yield a well-defined meaning for the comparative. Just as in the original analysis of these data, the than-clause will not provide us with a maximum, since there is no largest interval containing no girl’s height. Max> is undefined; hence negation in the than-clause leads to undefinedness of the comparative as a whole. Since there is no other option, we no longer face the problem of ruling out the apparent wide scope reading of the negative quantifier. The simple data discussed in this subsection highlight the potential attraction of the selection analysis. We keep a simple semantics for the comparative

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Sigrid Beck

and don’t double interpretive possibilities with a scoping mechanism. Next, we turn to all the complications. 3.2

Refinement I: Have to–type modals

This subsection concerns universal quantifiers that do not behave like every girl, predict and other apparent wide scope universals. Remember from Section 2 that modals like have to appear to favour a narrow scope interpretation rather than the apparent wide scope interpretation described and derived above for other universals. (97)

Mary wants to play basketball. The school rules require all players to be at least 1.70 m.

(970 )

a. b.

Mary is taller than she has to be. Mary’s actual height exceeds the degree of tallness which she has in all worlds compatible with the school rules; i.e. Mary’s actual height exceeds the required minimum, 1.70 m.

Keeping stable our assumptions about the meaning of than-clauses, we will assume (98) for this example. Selecting the maximum of the shortest than-clause interval will not yield the desired truth conditions this time, though: that would amount to the claim that Mary’s height exceeds the maximum height permitted. The sentence intuitively says that Mary is above the required minimum. Contrasts like the one between have to and predict are of course what motivates the scope analysis (apparent wide scope for predict, apparent narrow scope for have to). A different description of the facts is that the example with predict (and similar examples with every girl, should, etc.) has a ‘more than maximum’ interpretation while have to can have a ‘more than minimum’ interpretation. I see the task for my approach as having to explain how factors independent of comparative semantics may result in a ‘more than minimum’ interpretation rather than the expected ‘more than maximum’ reading. (98)

than she has to be tall = λD 0 . ∀w[wR@ → Mary’s height in w ∈ D0 ] intervals into which Mary’s height falls in all worlds compatible with the rules the beginning of this interval is below Mary’s actual height, i.e. Mary’s height exceeds the minimal element of the shortest than-clause interval 1:34


There are two analyses, as far as I am aware, that propose to reduce the variation in the interpretation of than-clauses with universal modals between maximum and minimum interpretation to independent factors, such that the readings collapse into one. Meier (2002) proposes that the ordering source that modal semantics uses is responsible for a contextually guided determination of the interpretation, explaining away apparent maxima and minima both. Krasikova (2008) examines the problem of have to–type modals in comparatives in particular and employs covert exhaustification to explain away apparent ‘more than minimum’ interpretations. While both approaches solve the problem at hand equally well for my purposes, I describe below Krasikova’s suggestions because they seem to me to offer more promise for identifying which modal operators give rise to which reading(s). Krasikova (2008) points out that whether we get a ‘more than minimum’ reading like the one illustrated above for this type of modal or a ‘more than maximum’ reading parallel to the reading illustrated for predict depends on the context an individual example is put into. Remember example (99) from above, which shows that have to–type modals may also give rise to a ‘more than maximum’ reading — the reading we expect under the present analysis.5 Thus what distinguishes have to–type modals from others is the availability of an apparent narrow scope reading (a ‘more than minimum’ reading under the present perspective). (99)

He was coming through later than he had to if he were going to retain the overall lead. (from Google, cited from Krasikova 2008)

Krasikova further observes that the universal modals that can give rise to the ‘more than minimum’/apparent narrow scope reading are just the ones that occur in sufficiency modal constructions (SMC). An example of an SMC is given below (von Fintel & Iatridou 2005). (100)

You only have to go to the North End (to get good cheese).

5 It is not at present clear to me under what circumstances a have to–type modal seems to permit a more-than-maximum interpretation. Relevant factors may be the choice of a negative polar adjective and a subjunctive-like interpretation (Danny Fox and Irene Heim, p.c.). Personally, I find this interpretation very hard to get.

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Sigrid Beck

(1000 )

Truth conditions:

Implicature:

You do not have to do anything more difficult than to go to the North End (to get good cheese). You have to go to the North End or do something at least as difficult (to get good cheese).

The combination of only and a modal in the SMC considers alternatives to the proposition that is the complement of have to, and ranks those alternatives on a scale. Plausible alternatives for our example and their ranking are given in (101). They provide the domain of quantification, C in (102); (102a) sketches a structure for the example, (102b) a meaning for ‘only have to’ and (102c) the outcome, which corresponds to the desired truth conditions (1000 ). Note that the SMC reading is one that identifies the point on a scale that is the minimum sufficiency point, as illustrated in (103). (101)

a. b.

(102)

a. b. c.

(103)

that you go to the nearest supermarket, that you go to the North End, that you go to New York, that you go to Italy SUPER < NE < NY < Italy (where ‘ ; with have to, we may apply Max> after exhaustification. This gives rise to a ‘more than minimum’/apparent narrow scope reading. If exhaustification does not apply, we get the regular ‘more than maximum’ = apparent wide scope reading (cf. example (99) above). Modals that do not permit an SMC reading do not permit a ‘more than minimum’ reading either, because the ‘more than minimum’ reading is an SMC reading. I refer the reader to Krasikova 2008 for further discussion. Crucially for present purposes the correlation with SMC use provides an independent criterion for when to expect which reading. The contrast between the different kinds of universal quantifiers is not analysed as a scope effect. The analysis argued for here makes the interpetation of have to–type modals a property of those particular lexical items. They are the only apparent narrow scope items requiring special attention since in contrast to the scope analysis’ procedure, apparent narrow scope existentials have already been taken care of. 3.3

Refinement II: Indefinites, numeral NPs and the like

This section concerns existential quantifiers that do not behave like NPI any and other apparent narrow scope existentials. The problem for the selection

1:38


strategy can be illustrated by the example below. (108)

John is taller than exactly five of his classmates are.

(1080 )

a. Exactly five of John’s classmates are shorter than he is. b. #John is taller than the tallest of his 5 or more classmates.

The intuitively available interpretation (1080 a) looks once more like a straightforward wide scope reading of the numeral quantifier. Application of the selection strategy predicts an interpretation that is unavailable, (1080 b), as illustrated below. (109)

λD 0 . for exactly 5 x : max(λd. x is d-tall) ∈ D 0 intervals into which the height of exactly 5 classmates falls Max> (m_inf([λD 0 . for exactly 5 x : max(λd. x is d-tall) ∈ D 0 ])) = the height of John’s tallest classmate, as long as there are at least 5 _ _ •_ _ _•_ _ _• _ _ _ _ •_ _ _•_ _ _• _ _ _• _ _ •_ _ _ _ _ _/

c1

c2

c3

c4

c5

c6

c7

c8

Max>

We face the combined challenge of (i) predicting the right interpretation and (ii) not predicting the non-existing one. I propose to tackle this problem through a more thorough analysis of numeral NPs. We will first consider indefinite NPs in the context of than-clauses and then move on to numerals and example (108). 3.3.1 Singular and plural indefinites Singular indefinites allow in principle two interpretations in than-clauses: an apparent wide scope and an apparent narrow scope reading. Which reading(s) is/are possible depends on the indefinite as well as the sentence context. We have seen examples with NPIs in which only the narrow scope reading is available. An example that has a wide scope reading is given in (110). (111) and (112) provide two examples which I take to be genuinely ambiguous (the English version of (111) probably is too, although native speakers seem to have some difficulty judging the example). (110)

a. b.

John is taller than one of the girls is. There is a girl x such that John is taller than x.

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Sigrid Beck

(111)

(1110 ) (112) (1120 )

Annett hat lauter gesungen als eine Sopranistin. Annett has louder sung than a soprano ‘Annett sang more loudly than a soprano did.’ a. b.

(German)

There is a soprano x such that Annett sang more loudly than x. Annett sang more loudly than any soprano did.

Sveta could solve this problem faster than some undergrad could. a. b.

There is an undergrad x such that Sveta could solve this problem faster than x could. Sveta could solve this problem faster than any undergrad could.

For examples with apparent narrow scope existentials it was demonstrated above (with an NPI indefinite, anyone else) how the selection analysis can derive an appropriate interpretation corresponding to the apparent narrow scope reading. What about the apparent wide scope reading? One option open to us is to acknowledge that indefinites quite often give rise to apparent wide scope readings — so-called specific readings — and to adopt whatever mechanism is appropriate for the analysis of specific readings in general for apparent wide scope indefinites in than-clauses. This is what I will do, and I use the choice function mechanism as the probably best known analysis of specific indefinites (e.g. Reinhart 1992; Kratzer 1998; but see Endriss 2009 for a different analysis). I illustrate with example (113a) from Heim 1982, where a friend of mine can have apparent scope over the conditional. (113)

a.

b.

If a cat likes a friend of mine, I always give it to him. There is a friend of mine such that if a cat likes him, I give it to him. ∃f : CH(f ) & [if a cat likes f(friend of mine), I give it to him] If a cat likes the friend of mine selected by f (f a choice function), I give it to him.

Furthermore, I will assume that indefinite NPs, e.g. with German ein (‘a’), are ambiguous between the ‘normal’ interpretation ‘∃x’ (existential quantification over individuals) and the ‘specific’ interpretation ‘∃f ’ (existential quantification over choice functions). Below I provide a selection analysis of the two readings of (111) under those assumptions.7 On this analysis, the apparent narrow scope reading amounts to a ‘∃x’ interpretation and 7 I use the German example because the larger English inventory of indefinites makes it hard for me to determine which examples are genuinely ambiguous.

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the apparent wide scope reading amounts to a ‘∃f ’ interpretation for the indefinite. (114)

a.

b.

[als [1 [einex Sopranistin t1 laut gesungen hat]]] = [λD 0 . ∃x[soprano(x) & max(λd. x sang d-loudly) ∈ D 0 ]] intervals that cover the loudness of soprano singers Annett sang more loudly than Max> (m_inf([λD 0 . ∃x[soprano(x)&max(λd. x sang d-loudly) ∈ D 0 ]])) = Annett sang more loudly than the loudest soprano. = Annett sang more loudly than any soprano did. [als [1 [einef Sopranistin t1 laut gesungen hat]]] = [λD 0 . max(λd. f (soprano)sang d-loudly) ∈ D 0 ] intervals that include the loudness of the soprano selected by f ∃f : CH(f ) & Annett sang more loudly than Max> (m_inf([λD 0 . max(λd. f (soprano) sang d-loudly) ∈ D 0 ])) = Annett sang more loudly than the soprano selected by f (f a choice function). = There is a soprano x such that Annett sang more loudly than x.

I further assume that the usual factors (in particular, the nature of the indefinite and what readings the sentence context permits) decide when we can get which reading(s) of a singular indefinite. I have nothing illuminating to say about the particulars of this; note, however, that I do assume that apparent narrow scope readings are possible with indefinites/existentials other than NPIs. My intuitions regarding German indefinites like jemand (someone) + anders/sonst (other/else), wh-word + other/else convince me of this in particular, because these indefinites are not, I believe, plausibly analysed as polarity items, nor are they plausibly analysed as generic (hence not existential). Other languages’ inventory of indefinites may make my view of what the interpretive possibilities of existentials in than-clauses are appear less obvious. I am grateful in particular to Sveta Krasikova for discussion of this point.

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Sigrid Beck

(115)

a.

b. (116)

a.

b.

Hier ist es schöner als anderswo. here is it nicer than elsewhere ‘It’s nicer here than it is elsewhere.’ possible reading: It is nicer here than it is anywhere else. Sam ist schneller als jemand anderes/sonstwer. Sam is faster than someone other/someone else ‘Sam is faster than another person.’ possible reading: Sam is faster than anyone else is.

Also, the data in (117) (in addition to (111) above) provide an indefinite, ein anderer (‘another’), that is ambiguous. Both (117a) and (117b) were collected informally from the web. Context makes it clear that (117a) is intended to mean ‘faster than everyone else’ and (117b) is intended to mean that someone was slower. (117)

a.

b.

Wir denken 7-mal schneller, als ein anderer reden kann. we think 7 times faster than an other talk can ‘We think seven times faster than anyone else can talk.’ Die meisten überholten mich, aber ab und zu war ich auch the most passed me but now and then was I also mal schneller als ein anderer. once faster than an other ‘Most people passed me, but now and then I was faster than someone.’

Matters look somewhat different when we consider plural indefinites. Beginning with bare plurals, note that many examples sound strange (thank you to Irene Heim for example (118)). (118)

a. John is taller than a giraffe. b. ??John is taller than giraffes.

(119)

a.

Prof. Shimoyama hat einen längeren Beitrag geschrieben Prof. Shimoyama has a longer contribution written als eine Doktorandin. than a Ph.D. student ‘Prof. Shimoyama wrote a longer contribution than a Ph.D. student.’ (ok: ∃x, ok: ∃f ) 1:42


b. ??Prof. Shimoyama hat einen längeren Beitrag geschrieben Prof. Shimoyama has a longer contribution written als Doktorandinnen. than Ph.D. students ‘Prof. Shimoyama wrote a longer contribution than Ph.D. students.’ (120)

a.

Hans Hans b. ??Hans Hans c. Hans Hans

ist schneller gelaufen als eine Schwester von Greg. ran faster than a sister of Greg’s. (ok: ∃x, ok: ∃f ) ist schneller gelaufen als Schwestern von Greg. ran faster than sisters of Greg’s. ist schneller gelaufen als einige Schwestern von Greg. ran faster than several sisters of Greg’s. (ok: ∃f )

The version with the singular indefinite can have an apparent narrow scope or an apparent wide scope interpretation (with some speaker variation regarding which interpretation is favoured). It is known that bare plurals prefer narrow scope interpretations — let’s say this implies that the choice function ‘∃f ’ interpretation is dispreferred. What the oddness of the plural data tells us, then, is that there is something unexpectedly wrong with the non-specific ‘∃X’ interpretation of the plural indefinite (I write capital ‘X’ to indicate plurality, in contrast to ‘x’ for singular). Note that the data (118)–(120) improve when some or several/einige is added to the plural indefinite. They then have an apparent wide scope or ‘∃f ’ interpretation. The following generalization emerges: (121)

Max> (m_inf(λD.∃X[. . . ])) is dispreferred relative to Max> (m_inf(λD.∃x[. . . ])). A plural indefinite ambiguous between ‘∃X’ and ‘∃f ’ will yield ‘∃f ’. A plural indefinite that prefers the ‘∃X’ interpretation will sound strange.

Why should a plural indefinite sound odd unless it can easily reveice a specific interpretation? The generalization is intuitively unsurprising once we examine the ‘∃X’ interpretation more closely. Careful consideration as to what it would mean in the case of (120), provided in (122a), reveals that (given that there is more than one sister of Greg’s) it would be true iff the sentence with the singular ‘∃x’ (’any sister of Greg’s) would be true. I suggest that this makes the interpretation (122a) somehow inappropriate for the example. Perhaps this can be seen as a matter of economy: the plural has no purpose,

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Sigrid Beck

hence cannot be used gratuitously. (122)

a. #Hans ran faster than Max> (m_inf([λD 0 . ∃X[∗sister(X) & ∀x ∈ X : x’s speed ∈ D 0 ])) = Hans ran faster than any sister of Greg’s. b. ∃f : CH(f ) & Hans ran faster than Max> (m_inf([λD 0 . ∀x ∈ f (∗sister) : max(λd. x ran d-fast) ∈ D 0 ])) = Hans ran faster than each of the sisters selected by f (f a choice function). (dispreferred with bare plural, ok with some/several)

(123) is a first shot at what the relevant constraint might effect. The reading that survives, (122b), is one in which, compared to the corresponding singular indefinite, the plural serves a purpose. (123)

Ban on Unmotivated Pluralization (BUMP): Do not quantify over a plurality if quantification over a singularity lets you infer the same reference.

It would be good to be able to reduce this phenomenon to other cases with a similar semantics.8 Below I relate than-clauses to definite descriptions and embedded questions (I am once more inspired by Danny Fox (p.c.) in making this connection). The idea is that all three constructions share some sense of maximality and/or maximal informativity (Fox & Hackl 2006 and the above considerations). So (124a) refers to the maximal, and in the sense of (85) above, the maximally informative speed that John ran; (124b) will require the maximally informative answer, i.e. the maximal speed John reached; and according to the analysis developed here, (124c) is of course analogous. (124)

a. b. c.

the speed that John ran how fast John ran than John ran

8 An anonymous reviewer and Danny Fox pointed out to me that a plural is not generally dispreferred when a singular yields the same interpretation, contrary to a claim I made in an earlier version of this paper. Negation and other downward monotone environments allow plural indefinites, as the example in (i) illustrates. I thank them for pointing out this flaw to me. (i)

We don’t sell apples (??an apple) in this store. There were no women present.

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The following three sets of data replace the proper name in (124) with various kinds of indefinites in the three constructions. The plain singular indefinite is fine and picks out the fastest speed in the definite description and the question as well as in the than-clause — in addition to a possible specific reading. The bare plurals are somewhat odd, which we can explain if a constraint like the BUMP above is operative (and the ‘∃f ’ interpretation is dispreferred). The last set with plural some indefinites are fine and have the specific reading. Plural indefinites with some are different from bare plurals in easily allowing an ‘∃f ’ interpretation. (125)

(126)

(127)

a. b. c.

the speed that a sister of Greg’s ran how fast a sister of Greg’s ran than a sister of Greg’s ran

a. ??the speed that sisters of Greg’s ran b. ??how fast sisters of Greg’s ran c. ??than sisters of Greg’s ran a. b. c.

the speed that some sisters of Greg’s ran how fast some sisters of Greg’s ran than some sisters of Greg’s ran

These data share the problem of having to determine unique reference from a set via maximality/informativity. They motivate the way that the BUMP is phrased above. Perhaps it is the nature of maximality/informativity as ‘glue’ that makes it sensitive to such a constraint: the step of postulating such operators is an inference one draws to have things make sense, and such inferences are subject to ‘making sense’-type of requirements like the BUMP. But I hasten to add that I am by no means confident that I understand what is at stake and that more work ought to be done in figuring out what the BUMP is really about. I conclude this subsection with a couple of comments on further kinds of indefinites. The first data point confirms the perspective on the data developed so far with the German example (128), where the obligatorily weak lauter (several/many) sounds very strange. Only einige (several) is acceptable, under an apparent wide scope reading. (128)

Annett hat lauter gesungen als einige/??lauter Sopranistinnen. Annett has louder sung than several sopranos ‘Annett sang more loudly than several sopranos.’

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Sigrid Beck

This can be understood if lauter disprefers a choice function analysis, permitting only the BUMP violating reading (1280 a), while einige yields an acceptable interpretation in terms of (1280 b). Our assumption about lauter vs. einige is confirmed by (129), where only the version with einige allows the specific interpretation of the NP ‘relatives of mine’. (1280 )

a. #Annett sang more loudly than Max> (m_inf([λD 0 . ∃X[∗soprano(X) & ∀x ∈ X : max(λd. x sang d-loudly) ∈ D 0 ])) = Annett sang more loudly than any soprano. b. ∃f : CH(f ) & Annett sang more loudly than Max> (m_inf([λD 0 . ∀x ∈ f (∗soprano) : max(λd. x sang d-loudly) ∈ D 0 ])) = Annett sang more loudly than each of the sopranos selected by f (f a choice function)

(129)

a. b.

Wenn einige Verwandte von mir sterben, erbe ich einen Bauernhof. Wenn lauter Verwandte von mir sterben, erbe ich einen Bauernhof. ‘If several relatives of mine die, I will inherit a farm.’

Similarly, we might expect that NPIs in than-clauses will only be licensed on the apparent narrow scope reading ‘∃x’ (perhaps they have no ‘∃f ’ interpretation, or perhaps that interpretation would fail to satisfy the licensing requirements on their context). This predicts that singular NPIs only have an apparent narrow scope reading. It also makes the interesting prediction that plural NPIs should be odd in than-clauses. (130b) is judged degraded compared to (130a) and (130c) by some speakers, but not by all. (130)

a. John solved this problem faster than any girl did. b. ??John solved this problem faster than any girls did. c. John solved this problem faster than any of the girls did.

I don’t understand why some people judge (130b) to be fine; I wonder whether a Free Choice interpretation of any girls is possible for those who accept the sentence. A final remark: it is not the case that plural indefinites in than-clauses are generally bad, not even narrow scope ones. The data in (131) embed the indefinite beneath another operator, and the BUMP does not apply.

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(131)

a. b.

More people bought books than read magazines. I buy books more often than I buy magazines.

To sum up: indefinites are semantically ambiguous, and this shows up in than-clauses just like it does elsewhere. Apparent wide scope of indefinites is analysed as pseudoscope: a specific reading. Sometimes one interpretation is excluded by independent factors. In particular an economy constraint BUMP can rule out ‘∃X’ for plural indefinites in than-clauses.9 The analysis rests on how the semantic glue interacts with intervals, and on how the interpretation is derived. I assume that the semantic glue is sensitive to BUMPy constraints, i.e. that it is a natural place for their application. 3.3.2

Numerals

With these results regarding indefinites in place, let us next be somewhat more precise in our semantic analysis of ‘exactly n’. Like Gajewski (2008), we employ a more elaborate analysis of these numerals (compare Hackl 2001a,b; 9 It is not clear to me that competing analyses of quantifiers in than-clauses can easily explain the pattern of singular vs. plural indefinites. To give an example, the Pi analysis (supposing it goes along with my assumptions about the semantics of plural indefinites) predicts for (ia) a narrow scope reading (ic) in addition to the wide scope reading (ib). (i)

a. b. c.

d. e.

John was faster than (some) sisters of Greg’s were. ∃X[∗ sister(X) & ∀x ∈ X : Speed(John) > Speed(x)] ‘Some sisters of Greg’s were slower than John.’ Speed(John)] > max(λd. ∃X[∗ sister(X) & ∀x ∈ X : Speed(x) ≥ d]) ‘John’s speed exceeds the speed reached by the slowest member of a plurality of sisters of Greg’s’ = John was faster than the second fastest sister of Greg’s. ∃d[Speed(John) ≥ d & NOT ∃X[∗ sister(X) & ∀x ∈ X : Speed(x) ≥ d]] Suppose Greg has three sisters:

_ _•_ _ _ _ _ _ _ _ •_ _ _ _ _ _ _ _ •_ _ _ _ _ _ _/ x1

x3

x2 largest speed reached by every member of a plurality of sisters of Greg’s

An interpretation corresponding to (ic) is not available and would have to be excluded — in the plural case, but not in the singular. The reading predicted by the NOT-theory, (id), is parallel. Depending on how hard it is to do so, an argument might be gained for the selection analysis from the pattern of singular vs. plural indefinites in than-clauses.

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Krifka 1999 on the semantics of such NPs). Remember the simple example (66) and its analysis. (66)

a. b.

Exactly three girls weigh 50 lb. [EXACT [XP (exactly) threeF girls weigh 50 lb.]]

(660 )

threeF girls weigh 50 lb.o = ∃X[∗ girl(X)&card(X) = 3&∗ weigh. 50. lb(X)] threeF girls weigh 50 lb.f = {∃X[∗ girl(X) & card(X) = n & ∗ weigh. 50. lb(X)] : n ∈ N}

(67)

EXACT(XPf )(XPo ) = 1 iffXPo = 1 & ∀q ∈ XPf : ¬(XPo → q) → ¬q ‘Out of all the alternatives of XP, the most informative true one is the ordinary semantics of XP.’

(68)

(66b) = 1 iff ∃X[∗ girl(X) & card(X) = 3 & ∗ weigh. 50. lb(X)] & ∀n[n > 3 → ¬∃X[∗ girl(X) & card(X) = n & ∗ weigh. 50. lb(X)]] iff max(λn. ∃X[∗ girl(X) & card(X) = n & ∗ weigh. 50. lb(X)]) = 3

This step does not immediately solve our problem. If we give the than-clause in (108) the semantics in (132), nothing changes: we still compare with the tallest of John’s classmates, as long as there are at least five. Notice, however, that this interpretation is just as strange as the plain plural indefinite ‘∃X’ interpretation above, since the number information serves no real purpose for the truth conditions. (108)

John is taller than exactly five classmates of his are.

(132)

λD 0 . max(λn. ∃X[∗ classmate(X)&card(X) = n&∗ Height(X) ∈ D 0 ]) = 5 Intervals into which the height of exactly five of John’s classmantes falls

(133)

John is taller than Max> (m_inf(λD 0 . max(λn.∃X[∗ classmate(X) & card(X) = n & ∗ Height(X) ∈ D 0 ]) = 5))

(1330 )

Presupposition: Assertion:

John has at least five classmates. He is taller than any of them.

This reading is thus ruled out by the same constraint BUMP. We should then alternatively consider a choice function analysis of the indefinite ‘n class-

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mates’. I combine this below with the assumption that exactly is evaluated in the matrix clause. In (134), we derive the desired interpretation. (134)

max(λn. ∃f [CH(f ) & John is taller than Max> (m_inf(λD 0 . ∀x ∈ f ((λX. ∗ classmate(X) & card(X) = n) : Height(x) ∈ D 0 ]) = 5 ’the largest number n such that John is taller than the tallest of the n classmates of his selected by some choice function f is 5.’

An LF of example (108) representing a version of Krifka’s analysis looks as in (135). (135)

a. b.

[EXACT [John is taller [than Max> m_inf [(exactly) 5f of his classmates are tall]]]] Out of all the alternatives of the form ‘John is taller than n of his classmates are’, the most informative true one is ‘John is taller than 5 of his classmates are’.

The applicability of the constraint BUMP to numeral indefinites is empirically supported by the data below, which behave in a parallel way to plural indefinites with some, for example. (136)

a. b. c.

the speed that two finalist drove how fast two finalist drove than two finalist drove

Thus I suggest that a proper semantic analysis of numeral NPs makes the facts compatible with a selection solution after all. 3.3.3

Further relevant cases

The analysis developed here for indefinite NPs in than-clauses needs to be extended to NPs with many and most, which show the same apparent wide scope interpretations we observed for numerals. (137)

a. b.

John is taller than many of his classmates are. There are many classmates of John’s such that he is taller than they are.

(138)

a. b.

John is taller than most of his classmates are. For most x, x a classmate of John’s: John is taller than x.

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I will make further use of the semantics developed by Hackl (2001a,b, 2009) for these NPs, according to which ‘many N’ is an indefinite NP including a gradable adjective in the positive form, and ‘most N’ is correspondingly a superlative. This makes feasible analyses that can be paraphrased in the following way:10 (1370 )

John is taller than the tallest of the many-membered group of classmates of his selected by f (f a choice function).

(1380 )

John is taller than the tallest of the group selected by f , which comprises a majority of his classmates (f a choice function).

More detailed analysis are given below ((139) provides the two potential readings of (137) and (140)–(142) analyse (138)). Besides being able to predict the existing readings, the BUMP constraint in (123) will rule out the ones that are intuitively unavailable. (139)

a. #John is taller than Max> (m_inf([λD 0 . ∃X[∗ classm(X) & many(X) & ∀x ∈ X : Height(x) ∈ D 0 ])) = John is taller than any classmate (as long as there are many). b. ∃f : CH(f ) & John is taller than Max> (m_inf([λD 0 . ∀x ∈ f (λX. ∗ classm(X) & many(X)) : Height(x) ∈ D 0 ])) = John is taller than each of the many classmates selected by f (f a choice function)

(140)

than [1 [X most of his classmates are t1 tall]] = [λD 0 . ∃X∃d[∗ classm(X)&d-many(X)&∀Y ∈ C[Y ≠ X&∗ classm(Y ) → ¬d-many(Y )] & ∀x ∈ X : Height(x) ∈ D 0 ] intervals that contain the heights of a majority of John’s classmates

(141)

than [1 [f most of his classmates are t1 tall]] = [λD 0 . ∀x ∈ f (λX. ∃d[∗ classm(X) & d-many(X) & ∀Y ∈ C[Y ≠

10 An anonymous reviewer points out that this predicts that these NPs can have the same specific readings we know from indefinites. I concur, but would like to point out that this prediction arises from an analysis of these quantifiers as indefinites, not from the application of that analysis to than-clauses. The empirical test cases include data like (i) below. (i)

a. b.

If many relatives of mine die, I will inherit a farm. If most relatives of mine die, I will inherit a farm.

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X & ∗ classm(Y ) → ¬d-many(Y )]) : Height(x) ∈ D 0 ] intervals that contain the heights of the majority of John’s classmates selected by f (142)

a. #John is taller than Max> (m_inf([λD 0 . ∃X∃d[∗ classm(X)&d-many(X)&∀Y ∈ C[Y ≠ X & ∗ classm(Y ) → ¬d-many(Y )] & ∀x ∈ X : Height(x) ∈ D 0 ])) = John is taller than the tallest of any majority of his classmates. = John is taller than any of his classmates. b. ∃f : CH(f ) & John is taller than Max> (m_inf([λD 0 . ∀x ∈ f (λX. ∃d[∗ classm(X) & d-many(X) & ∀Y ∈ C[Y ≠ X & ∗ classm(Y ) → ¬d-many(Y )]) : Height(x) ∈ D0 ] = John is taller than the tallest of the majority of John’s classmates selected by f (f a choice function) = For most x, x a classmate of John’s: John is taller than x.

To sum up: this subsection has analysed the available vs. unavailable readings of indefinite NPs in than-clauses using a choice function mechanism plus a constraint on unmotivated pluralization. The formulation of the BUMP in (123) is offered as a first version of the constraint we need; what we want to derive is that it is strange to say ‘John is taller than exactly three girls are’ if we meant, and might as well have said ‘John is taller than any girl is’. Since this seems eminently reasonable, I am hopeful that a good way of stating the relevant constraint exists. Given this, the present section has extended the selection analysis to apparent wide scope indefinite NPs of various kinds (including numerals, many and most), using a pseudoscope mechanism argued for extensively for indefinites independently of comparatives. The comparative semantics itself remains simple. 3.4

Refinement III: Differentials

The final kind of data that does not immediately fall out from the selection analysis is represented by example (143) below: a than-clause containing a universal quantifier in combination with a differential. (143)

a. b.

John is exactly 200 taller than every girl is. For every girl x: John is exactly 200 taller than x.

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Sigrid Beck

Compared to Heim, and also Schwarzschild & Wilkinson, we seem to have a problem. Heim’s analysis can derive the intuitive interpretation as shown below. (144)

[[than every girl is tall] [5 [John is exactly 200 taller t5 ]]]

(1440 )

[than [1 [every girl [2 [[Pi t1 ] [3 [t2 is t3 tall]]]]]]] = λD 0 . ∀x[girl(x) → Height(x) ∈ D 0 ] intervals into which the height of every girl falls

(145)

(144) = [λD 0 . ∀x[girl(x) → Height(x) ∈ D 0 ](λd. John is exactly 200 taller than d) = for every girl x: John is exactly 200 taller than x

Choice of Max> on the other hand predicts a different interpretation, which does not seem right for (143): (146)

John is exactly 200 taller than Max> (m_inf(than-clause)) = John is exactly 200 taller than the tallest girl.

The intuitively available reading of (143a) can be described as one in which we assume that all the girls reach the same height. I call this an assumption of equality among the individuals universally quantified over, EQ for short. The EQ appears to speak in favor of a scope solution since it is entailed by the truth conditions resulting from giving the universal wide scope over the comparison. It is not entailed by the truth conditions according to the selection analysis, although it is of course compatible with the truth conditions in (146) that the girls all have the same height. Sentence (143a) exemplifies a problem that arises when a than-clause containing a universal quantifier is combined with a differential that includes exactly, at most or almost. A differential including at least does not distinguish between the two sets of truth conditions. (147)

a. John is at most/almost 200 taller than every girl is. b. For every girl x: John is no more than 200 taller than x c. #John is no more than 200 taller than the tallest girl.

(148)

a. b. c.

John is at least 200 taller than every girl is. For every girl x: John is at least 200 taller than x John is at least 200 taller than the tallest girl.

An unmodified differential does not constitute evidence as strong as an exactly/at most-type differential, because, while it gives rise to the usual

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strengthening implicature that amounts to an exactly reading, this implicature can be canceled. If we suppose the implicature to be present, the unmodified differential is parallel to exactly. (149)

a. b. c.

John is 200 taller than every girl is. Implicature: John is no more than 200 taller than every girl is. John is 200 taller than every girl is, perhaps more.

To sum up the picture so far, differentials with exactly and at most, and perhaps simple differentials, seem to be problematic for the selection analysis as opposed to the scope analysis. However, there is more to say about this issue empirically and theoretically. Beginning with the theoretical side, note that the interpretation of the matrix clause in (144) was simplified in terms of not giving the differential quantifier exactly 200 independent scope.11 Data like (150) show that such expressions do take scope, however: (150) (151) (1500 )

You are allowed to be exactly 60 tall. exactly 60 = λD. max(D) = 60 a. b.

max(λd. ∃w[wAcc@& you are d-tall in w]) = 60 The largest permitted height for you is 60 . ∃w[wAcc@ & max(λd. you are d-tall in w) = 60 ] It is permitted that you be exactly 60 tall.

Hence, in addition to (a more elaborate version of) (144) above, the LF and interpretation in (152) become possible. For the Pi theory, this leads to availability of the analysis in (153). (152) (1440 )

(153)

[[exactly 200 ] [4 [[than every girl is tall] [5 [John is t4 taller t5 ]]]]] [than [1 [every girl [2 [[Pi t1 ] [3 [t2 is t3 tall]]]]]]] = λD 0 . ∀x[girl(x) → Height(x) ∈ D 0 ] intervals into which the height of every girl falls (152) = [exactly 200 ](λd0 . [λD 0 . ∀x[girl(x) → Height(x) ∈ D 0 ] (λd. John is d0 taller than d) = [exactly 200 ](λd0 . for every girl x: John is d0 taller than x) = max(λd0 . for every girl x: John is d0 taller than x) = 200 ‘The largest amount that John is taller than every girl is 200 .’

11 Thanks to Danny Fox for drawing my attention to this point.

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Sigrid Beck

Note that this LF no longer predicts all the girls to have the same height. It says that John is exactly 200 taller than the tallest girl — just like the selection analysis. It is thus not clear that the predictions of the scope analysis are really different from, and superior to, the selection analysis. Next, let’s take a closer look at the data. Above, we identified as a problem that EQ is not predicted, the assumption that all individuals universally quantified over have the same height (or whatever the gradable predicate measures). However, the data are quite difficult. While I agree with the perception in the literature that in (143a) the EQ is plausible, it is clear that it does not always arise. Below are some examples where it doesn’t; (154)–(156) are collected from the internet.12 The reader can convince her/himself that further relevant data can easily be found. The difficulty in determining the interpretation of data with nominal universal quantifiers is related to the point mentioned in Section 2 about differentials and intensional verbs. I mention in (1560 ) a suggestive example also collected from the web. (154)

Aden had the camera for $100 less than everyone else in town was charging.

(155)

WOW! Almost 4 seconds faster than everyone else, and a 9 second gap on Lance.

(156)

Jones was almost an inch taller than the both of them. (the both of them = John Lennon and Paul McCartney, Jones = Tom Jones. The author thinks that Jones was 50 1100 and that Paul McCartney was about 50 1000 . John Lennon is reported to be shorter than McCartney by about an inch.)

(1560 )

I finished 30 seconds faster than I expected. [. . . ] I know my 300 yard time more accurately now. (the continuation suggests that the speaker’s expectation was a range rather than a precise point in time.)

The examples are straightforwardly analysed using Max> to determine the relevant ‘point’ provided by the than-clause.13 The differential measures the 12 A naive Google search has not unearthed a clearly relevant example with an exactlydifferential. 13 A different type of example illustrated below is difficult for both a scope and a selection analysis. I find it hard to decide what such examples mean precisely. It seems plausible to me that we select some kind of ‘point’ from the meaning of the than-clause, but not in the way described in the text.

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distance between that and the main clause degree. This is demonstrated for (155) below. (1550 )

a. #For all x, x ≠ Z: (Z was) almost 4 seconds faster than x (wide scope) b. (Z was) almost 4 seconds faster than Max> (m_inf(λD 0 . for all x ≠ Z : Speed(x) ∈ D 0 )) = Z was almost 4 seconds faster than the next fastest person. (selection Max> )

We face the task of figuring out what distinguishes (143) from (154)–(156), i.e. why EQ arises in some data but not all. I would like to ask this question in terms of how the selection analysis might predict not only (154)–(156), but also (143). To this effect, let’s take a closer look at the combination of a differential with a comparative. Note that we understand a claim like (157a) relative to a plausible level of granularity. For us to judge (157a) to be true, it is in most contexts sufficient to be precise up to the level of a few millimeters. Suppose on the other hand that (157b) is about a sensitive piece of machinery. A one millimeter margin could very well not be acceptable. This means that what we call John’s height, or that rod’s length, is actually somewhat fuzzy: it is a ‘blob’ or an interval on the relevant scale whose size depends on context. The sensitivity to a level of precision is not represented in the standard truth conditions of the two examples given in (1570 ). (157)

a. b.

(1570 )

a. b.

Mary is exactly 2 cm taller than John is. This rod is exactly 2 cm longer than that rod is. Height(Mary) = Height(John) + 2 cm Length(this rod) = Length(that rod) + 2 cm

To capture this, I follow Krifka (2007) in assuming that a scale can be divided into different units. A unit on the scale then has to be identified that can count as a ‘point’ at the contextually relevant level of granularity. Which (i)

a.

Ben was almost a year older than everyone else in his class (because he had just missed the deadline for the previous school year). b. #For all x ≠ Ben: Ben was almost a year older than x. c. #Ben was almost a year older than the next oldest in his class. d. ?The others’ ages center around a point almost a year younger than Ben.

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Sigrid Beck

division we assume depends on context. Talking about a length of 1.80 m for example could then refer to a very short or a somewhat larger stretch of the scale, depending on the relevant standard of precision/unit size. I talk about unit size as granularity. (158)

. . . _ _ _ _ •_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _/ 1.80 m ... ... 5 cm 5 cm ... ... 2 cm 2 cm ... ... 1 cm

1 cm

I make use of Schwarzschild’s (1996) notion of a cover as a division of an entity into its contextually relevant parts, and apply it to scales in (159). Covers provide the relevant granularity. (159)

Let hS, >i be a scale. Then Cov is a cover of S if Cov is a set of subsets of S such that each d in S is in some set in Cov, each set in Cov is contiguous and no two sets in Cov overlap. Assume Cov to be the set of intervals that are of the contextually relevant size.

I furthermore revise the definition of an end “point” from (160) to (161) ((161b) is the informal version, (161c) the more precise version employing covers). Note that the distinction between points and intervals dissolves under this view because what we usually call a point is an interval on the scale whose size depends on context. (160)

a. b.

(161)

a. b. c.

Max> (phhd,ti,ti ) : = max> (max> (p)) = the end point of the interval that extends furthest Let S be a set ordered by R. Then maxR (S) = ιs[s ∈ S & ∀s 0 ∈ S[sRs 0 ]] Max> (phhd,ti,ti ) := end> (max> (p)) = the end ‘blob’ of the interval that extends furthest end> (D) := ιd. d ⊆ D & ¬∃d0 [d0 ⊆ D & d0 > d] & d counts as a point at the relevant level of granularity Let Cov be the set of intervals that are of the contextually relevant size. end>,Cov (D) := ιd. d ⊆ D & d ∈ Cov & ¬∃d0 [d0 ⊆ D & d ≠ d0 & d0 ∈ Cov &d0 > d]

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Supposing that we talk about what we roughly call 1.80 m, the meanings of our two than-clauses could (depending on context, i.e. the relevant cover) come out as in (162). It is thus in the nature of scales that they have a part/whole structure whose units are determined in a context dependent manner. (162)

a. b.

Max>,Cov1 (than John is tall) = [1.798–1.803] (a 0.5 cm unit) Max>,Cov2 (than that rod is long) = [1.7998–1.8002] (a 0.4 mm unit)

Let’s consider differentials under this refined understanding of scales. A differential measures the distance from the “point” referred to in the matrix to the “point” referred to in the than-clause, “point” being determined by the relevant unit size. Note that a plausible granularity for the than-clause has to match the granularity level suggested by the differential. If the two do not match, an odd sentence results. I call this a granularity clash. In the example below, we know that it is impossible to determine to the second the amount of time that it took John to learn French. The than-clause comes inherently with a coarse granularity, which clashes with the granularity of the differential in (163b). (163)

a. Mary learned arithmetic faster than John learned French. b. ?Mary learned arithmetic faster than John learned French by 7 minutes 23 seconds. c. Mary learned arithmetic faster than John learned French by several months.

We can generalize from the example as follows. In a comparative of the form (164a), it must at least be given that the cover of the relevant interval that the than-clause provides (via informativity) furnishes units that are smaller than the differential; i.e. (164b) is a requirement for the comparative to make sense. If that is the case, then the unit picked out as a “point” by Max> will also be smaller than the differential (164c). The comparative can then measure the gap between the main clause degree and the maximum of the than-clause with the differential ((164d)). If the maximum itself is larger, this will be impossible. In our example, suppose that we can with exceptional precision determine to the day how long it took Mary to learn arithmetic and John to learn French. We cannot reasonably measure the gap between two days in terms of the differential ‘7 minutes 23 seconds’. The level of

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Sigrid Beck

granularity relevant for the than-clause has to make sense in relation to the differential. (164)

a. b. c. d.

Main Clause Differential than D for all U ∈ Cov: U < Diff Since Max>,Cov (D) ∈ Cov : Max>,Cov (D) < Diff Max>,Cov (Main Clause) = Diff + Max>,Cov (D)

The reasoning works out given that the cover, and therefore the unit that counts as ‘maximal point’, is determined locally, i.e. than-clause internally, independently of the differential which will then either fit or clash.14 I think that granularity offers an explanation for the interpretive effect I call EQ. Consider the situation depicted below for (165). If we have no further information regarding the situation, the girls’ sizes can be far apart. This would indicate a large interval. The idea is that the semantics of the thanclause itself indicates possible Covers. There is then a danger that we have a x1 –x5 would be coarse-grained cover. A reasonable division of into relatively long units, hence Max> is long. This would be incompatible with the differential — a granularity clash. That is, a sentence in which the than-clause indicates a real spread (e.g. because of a universal quantifier) brings with it the danger of a granularity mismatch with a differential. John is exactly 200 taller than every girl is.

(165)

_ _ _• _ _ _• _ _ _ _ _ •_ _ _ •_ _ _ _ _ _• _ _ _ _ _• _ _ _ _/

(166)

x1

x2

x3

x5

x4

m_inf((than) every girl is tall) = {

J

x1 –x5

}

14 A similar effect can be observed with Covers in the plural domain in examples like (i) below. (i)

a. b.

The women and the men love their child. The Smiths and the Johnsons love their child.

Suppose we are talking about Angelina and Reginald Johnson and Mary and John Smith. Then the two subjects in (ia) and (ib) refer to the same group, but make different covers salient (Schwarzschild 1996). By virtue of the cover suggested by the subject, (ia) tends to be understood as ‘the women love their child and the men love their child’, which is unexpected. (ia) amounts to ‘the Smiths love their child and the Johnsons love their child’, which is more expected. The point is that the subject group autonomously makes salient a cover, whether this leads to a plausible interpretation of the whole or not.

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The Cover indicated by the than-clause may agree with the differential only under an additional assumption of closeness of the individual “points” covered by the than-clause interval. My suggestion is that if a potential granularity clash could only be avoided under an additional assumption of closeness, one tends to assume equality and a default Cover of the thanclause interval D in terms of the singleton set {D}. This is the EQ. In short, without an informative context, there is a danger of a granularity clash. The danger is avoided by the EQ. The EQ would under this analysis be an extra assumptions speakers make in order to ensure that a sentence is meaningful. (Note that the EQ is not the weakest assumption one could make to ensure that; perhaps it is the simplest assumption.) The data above for which the selection analysis automatically makes good predictions with Max> , (154)–(156), are such that we have a rather clear expectation about the kind of interval denoted by the than-clause — the range within which the individual degrees fall is fixed. The context is rich, and no problems with granularity arise. Thus a genuine Max> interpretation (i.e. one in which we pick out the maximum from a genuine spread) is possible without further assumptions. This distinguishes those data from our original example (165). I suggest that danger of a granularity clash leads to EQ: to supposing that the ‘points’ that are in danger of being spread over too large an interval in fact collapse into one. We expect that it should depend on the amount of information available on the interval covered by the thanclause whether we get an EQ interpretation or a genuine Max> interpretation. Additional information to the effect that the points are not the same, but close enough together for the purposes of the differential, may make the EQ unnecessary and thus make a genuine Max> interpretation possible for our EQ data. This appears to me to be correct: (167)

Background: we are running an experiment in which we vary the growth conditions of seedlings. In particular, we test different fertilizing agents (ViagraFlor, Dung™, ComposFix and GuanoPlus) and their effect on how fast our seedlings grow. After two weeks, it is reported that:

(168)

The ComposFix seedlings are exactly 200 taller than all the others. (Max> possible)

Danger of granularity clash arises in uninformative contexts and triggers EQ. I should be able to take the same than-clauses that occured in Max> examples

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Sigrid Beck

and place them into a less fortunate context, and trigger EQ. Again, this seems the right prediction. (169)

a. b.

This pot dries out exactly 40 min faster than all the others. (EQ likely) This T-Shirt dries exactly 20 min faster than all the others. (EQ likely)

We see that minimal pairs can be found that have essentially the same comparative (differential plus comparative adjective plus than-clause) but differ as to informativity of background context regarding the than-clause interval. An uninformative context makes us assume that the interval is point-like, so that Max> will be well defined and suitable — EQ. If we have enough background information to be sure that the Max> unit in the thanclause interval is suitable, we do not panic, make no extra assumptions, and can get a genuine Max> interpretation as expected. Things are different with an existential quantifier. Consider (170) against the same background as before. The minimal than-clause intervals will be the heights of the individual girls. Max> will be well defined and suitable without any additional assumptions, and will make this a comparison between John’s height and the height of the tallest girl, as desired. (170)

John is exactly 2 cm taller than any girl is. Max> (m_inf((than) any girl is tall))

(171)

_ _ _• _ _ _• _ _ _ _ _ •_ _ _ •_ _ _ _ _ _• _ _ _ _ _• _ _ _ _/

x1

x2

x3

x4

x5

J

I conclude that the selection strategy provides a reasonable perspective on differential comparatives. It depends on context whether we get an EQ interpretation or a genuine Max> interpretation, and the selection strategy can explain this. I will not investiate here what a scope strategy could say about the data. A more general remark: At this point in the analysis, a pragmatic element has entered the picture. The ‘glue’ I have been talking about so far is genuinely semantic and seems fully determined (as far as I can see) given the requirement of interpretability. But scales (following the insights represented by Krifka’s work) require reference to context and include a pragmatic element in the shape of the cover. In addition to the maximality/informativity

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operators themselves, we need the contextually relevant part/whole structure of the scale to interpret a particular example. Properties of the cover become relevant in particular in the presence of differentials, and speakers may be lead to make extra assumptions (EQ). The fuzzy nature of the data, in my opinion, speaks in favour of the idea that some kind of pragmatic glue is required to make things work out. Depending on the context, speakers may or may not have an easy time figuring out what the necessary glue is. That said, a remaining caveat is a more thorough empirical understanding of the data with differentials. 4 Summary and conclusions 4.1 Summary Building on work primarily by Schwarzschild & Wilkinson and Heim, I propose an analysis of quantifiers in than-clauses in which the quantifier is interpreted inside the than-clause. A shift from degrees to intervals of degrees makes this possible. Despite appearances, there is no scope interaction between quantifier and shifter or quantifier and comparison operator. Instead, there is uniformly selection of a point from the subordinate clause interval. The analysis takes from Schwarzschild & Wilkinson the step to intervals. It shares with Heim that comparison is ultimately reduced to comparison of points. Intervals are not directly compared. In contrast to Heim and the subsequent NOT-theory, apparent scope effects like the interpretation of have to–type modals and exactly n NPs have been explained away via recourse to alternative interpretational mechanisms, which have been argued for independently of than-clauses (in these two examples: exhaustification and an alternative semantics for exactly-numerals). My strategy is motivated by the lack of clear scope interaction in than-clauses. One feature of the proposal is that the semantics of the comparative operator is very simple. It is the same semantics that one needs for data like (172a), namely one in which the first argument of the comparative operator is a degree, (172c). Maximality is still used in clausal comparatives like the ones we have discussed, but it is independent of the comparative operator. (172)

a. b. c.

John is taller than 1.70 m. [[-er [than 1.70 m]] [2 [John is t2 tall]]] -er = λd1 . λd2 . d2 > d1

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It is in this sense the analysis developed here is in my opinion ‘simpler’ than Schwarzschild & Wilkinson’s. The complexity that is no doubt there in the present analysis consists in the assumption that general interpretive strategies like informativity and maximality are involved (plus in independent complications like the availability of specific readings for indefinites and the like). Also, the semantics is no longer completely determined by compositional semantics. Data with differentials could only be analysed by enriching the classical semantics with pragmatic notions (covers, contextual background). However, this aspect of the proposal is supported by contextual variability of the judgements and thus has to be part of a successful analysis. In order to ultimately evaluate the success of my proposals, the whole approach needs to also be extended to adverbials. I will not attempt to do so now. Other considerations concern a more detailed analysis of the various modals (including might) and an investigation of the interaction of several scope bearing elements inside a than-clause. I give some representative data below and acknowledge the need for further work on the subject (compare Schwarzschild & Wilkinson 2002, Heim 2006b, Schwarzschild 2008). Finally, I admit that I have no analysis for Sauerland’s (2008) example (174), for which he provides a solution in terms of Heim’s theory. (173)

(174)

a. b. c.

It is hotter here today than it often is in New Brunswick. It is hotter today than it might be tomorrow. Sveta solved this problem faster than someone else could have.

Ekaterina is an odd number of centimeters taller than each of her teammates.

These issues are left for future work. 4.2

Where do the intervals come from?

There is one important theoretical question left for the intervals-plus-selection analysis to answer: where do the intervals come from? In Section 3 I made the assumption that basic adjective meanings already contained intervals: (175)

tall = [λD. λx. Height(x) ∈ D]

I could alternatively have assumed that the operator Pi from Heim 2006b shifts the standard adjective meaning to (175).

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(176) (177)

Pi shifts from degrees to intervals: [1 [ AP [Pi t1 ] [3 [ AP t2 is t3 tall]]]] a. b. c.

tall = [λd. λx. Height(x) ≤ d] Pi = [λD. λP . max(P ) ∈ D] [λD. Pi(D)(tall(x))] = [λD. Height(x) ∈ D]

Since Pi on the analysis pursued here always takes scope immediately next to the adjective, this would have served no particular purpose and I simplified to (175). But a problem for assuming (175) as the basic meaning of a gradable adjective is that it is very weak. This creates problems for example for the negation theory of antonymy (compare e.g. Heim 2006a). (178a) analyses the negative polar adjective short as the negation of tall. I fail to be able to imagine how a parallel strategy for the interval based meaning (178b) could be successful. (178)

a. b.

short = [λd. λx. ¬ Height(x) ≥ d] = [λd. λx. Height(x) < d] short = λD. λx. Height(x) 6∈ D

So if the intervals do not come into the semantics via a motivated independent (since mobile) operator Pi, and nor are they plausibly basic, how do they come in? It would be attractive to say that intervals enter the semantics because, that is, if and only if, they are needed. That is what I would like to think, and (175) really was a simplification for the sake of uniformity that I think of as preliminary. An idea for how to bring intervals into the semantics when needed that is due to Heim (2009) is given below. We begin by observing that a relation can be expressed between a plurality and a part of a scale — a degree ‘blob’. (179)

a. b.

(You have to be 50 tall to enter.) Our children are that tall. (Bill’s GPA is 3.75.) Sam’s grades are that good, too.

We see a parallel to expressing a relation between a plurality and a mass noun. The example (180a) can be represented as in (180b) with the meaning in (180c) in mind for the relation between the two objects of drink — a cumulative interpretation (see e.g. Beck & Sauerland 2000 and all the earlier work cited there that they rely on). (180)

a. b.

Our children drank the milk. ∗ ∗ drank(M)(C)

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Sigrid Beck

c.

∀x ≤ C : ∃y ≤ M : drank(y)(x)&∀y ≤ M : ∃x ≤ C : drank(y)(x) All children participated in drinking the milk, and all parts of the milk were drunk by one of the children.

Transferring the analysis to our degree example yields (181). (181)

a. b. c.

Our children are that tall. ∗ ∗ tall(D)(C) ∀x ≤ C : ∃d ≤ D : tall(d)(x) & ∀d ≤ D : ∃x ≤ C : tall(d)(x) All the children’s heights fall into D, and all parts of D contain the height of a child.

It is easy to apply the same analysis to a than-clause containing a definite plural, and it yields the set of intervals that we need according to the analysis in Section 3. Comparison will be with the maximum point in that set and the sentence is predicted to mean that our children are shorter than John. (182)

a. b. c.

(John is taller) than our children are. λD. ∗ ∗ tall(D)(C) λD. ∀x ≤ C : ∃d ≤ D : tall(d)(x)&∀d ≤ D : ∃x ≤ C : tall(d)(x) intervals that contain the heights of all our children (and nothing else)

Note that the notion of degree ‘blobs’ that have a part/whole structure is anticipated by the reference to covers in Section 3. A cover provides us with the relevant parts of the degree scale. We are consistently assuming a mass like structure of the degree scale. To make the connection clear, (1820 ) provides a more complete formalisation of (180a) which includes covers (compare Beck 2001 for this kind of use for covers). (1820 )

a. b.

λD. [∗ ∗ λd. λx. d ∈ Cov &x ∈ Cov & tall(d)(x)](D)(C) λD. ∀x[x ≤ C & x ∈ Cov → ∃d[d ≤ D & d ∈ Cov & tall(d)(x)]] & ∀d[d ≤ D & d ∈ Cov → ∃x[x ≤ C & x ∈ Cov & tall(d)(x)]] (suppose that the relevant parts of ‘the children’ are the individual children, and that the relevant parts of the cover are the units according to granularity)

Example (182)/(1820 ) derives a set of intervals, as pluralities of degrees, as the meaning of a than-clause via plural predication. What would we need

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to do in order for this idea to apply to the range of data examined in this paper? I briefly discuss three issues for which this change in perspective is reelvant: (i) universal quantifiers, (ii) singular quantifiers, and (iii) maximal informativity. First, regarding universal quantifiers: The introduction of intervals analogously to (182) would have to happen with universal quantifiers of various kinds, in particular universal nominals and intensional verbs (cf. our two representative examples every girl and predict). Regarding intensional verbs, there is a proposal by Boškovi´ c & Gajewski (2008) that instead of universal quantification over worlds (183a) they (or at least some of them) involve sum formation (183b). (183)

a. b.

believex = λp. ∀w[w ∈ BELx → p(w)] believex = max(λW . W ∈ ∗BELx )

This makes possible the following analysis of a than-clause with an intensional verb (in the simpler version without covers): (184)

a. b. c.

(John is taller) than you believe. λD.[∗∗λw.λd. John is d-tall in w](max(λW .W ∈ ∗BELyou ))(D) λD.∀w ≤ max(λW .W ∈ ∗BELyou ) : ∃d ≤ D : tall(w)(d)(John)& ∀d ≤ D : ∃w ≤ max(λW .W ∈ ∗BELyou ) : tall(w)(d)(John) intervals that contain John’s height in all your belief worlds (and nothing else)

Nominal universal quantifiers, it has been observed, can sometimes be used to introduce a plurality, although this is not always easily possible. Perhaps (185) involves a reinterpretation as a plural definite NP. The same reinterpretation would be responsible for the interpretation of the than-clause in (186) in case the girls are of varying heights. This might make sense of my abovementioned intuition that a definite plural is more acceptable than a universal NP. (185) (186)

a. Everyone gathered in the hallway. b. ?Every student gathered in the hallway. a. b. c.

John is taller than every girl is. ‘every girl’ → G (the plurality of girls) λD.∗∗ tall(D)(G)

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Sigrid Beck

d.

h i λD. ∀x ≤ G : ∃d ≤ D : tall(d)(x) h i & ∀d ≤ D : ∃x ≤ G : tall(d)(x) intervals that contain the heights of all the girls (and nothing else)

Thus it can be argued that a plural analysis of intervals can capture these data15 The discussion from Section 3 is (almost — see below) unchanged; what changes is what happens below the level of AP, so to speak (the predication ‘x is d-tall’): what we assumed to be basic in (175) is now compositionally derived via pluralization mechanisms. Next, let’s reconsider data with singular quantificational elements: (187) (1870 )

a. Mary is taller than anyone else is. b. *John is taller than no girl is. a. b.

c.

John is taller than some girls are. h i λD. ∃X : ∀x ≤ X : ∃d ≤ D : tall(d)(x) h i & ∀d ≤ D : ∃x ≤ X : tall(d)(x) h i λD. ∀x ≤ f (∗ girl) : ∃d ≤ D : tall(d)(x) h i & ∀d ≤ D : ∃x ≤ f (∗ girl). tall(d)(x)

There would be no reason to introduce intervals in the data with singular indefinites and negative quantifiers. Remember from Section 3.1 that in these cases, we got rid of the intervals immediately anyway (maximal informativity reduced the contribution of the than-clause to the set of individual heights). Now, we could just revert to the classical analysis for those data. This is not an unwelcome result, since the classical analysis offers a successful solution for them. Pluralization as the trigger for the introduction of intervals will continue to play a role for plural indefinites (see example (1870 )); the discussion in Section 3.3 is thus also in important respects unchanged. Finally, we need to think once more about the role of maximal informativity. Plural semantics keeps intervals small. The truth conditions of cumulation are such that the pluralised relation holds between the plurality and the smallest interval that covers all the individuals in the plurality (cf. the second conjunct in (181c) and the following analyses). This may make 15 I am not sure at this point what to say about the have to–type modals. Perhaps (as non-negraising verbs) they do not have a plural analysis. We then revert to the classical analysis. If they do have a plural semantics, the story in Section 3.1 is maintained. The first version relates the behavior of a modal to neg-raising, the second to SMC use.

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m_inf unnecessary, leaving us with iterated maximality. Again this can be seen as a welcome result. The attraction of this approach is, as said above, that intervals enter the picture only when there is a real need for them. The idea is entirely compatible with the selection analysis and in my view very desirable. Why did I not set out in this fashion in Section 3? I am not quite confident enough of the story in (185), (186), and too many details remain to be worked out, plus the data need to be examined more carefully. As things stand, readers sceptical of the ideas sketched in this subsection may take Section 3 as it is, while others have the beginnings of an analysis of how and why intervals come into play at all. 4.3

Outlook

Let’s take a step back and think about what an analysis of quantifiers in than-clauses in terms of selection achieves — beyond the empirical coverage of the mostly well-known set of data that I have been concerned with above. Compared to its theoretical competitors, it primarily removes quantifiers in than-clauses from the realm of scope interaction phenomena. For example, the interpretive behaviour of quantifiers in than-clauses cannot be seen as an instance of the Heim/Kennedy generalization (Kennedy 1997; Heim 2001). The analysis I’ve given in Section 3 violates this generalization. (188)

Heim/Kennedy generalization: [ DegP . . . [ QP [. . . tDegP . . . ] . . . ]]

(189)

a. b.

than [1 [every girl is t1 tall]] λD. for every girl x : Height(x) ∈ D

The Heim/Kennedy generalization is motivated in particular by quantifiers in the matrix clause of comparatives. Suppose that the behaviour of quantifiers in the matrix clause relative to degree operators is regulated by a scope constraint deriving the Heim/Kennedy generalization. Then there would be no theoretical connection between this and than-clause quantifiers. We would accordingly expect empirical differences between quantifiers in main clause vs. than-clause. On the other hand, if one were to extend the requirement of finding a definite degree from the than-clause to the main clause (a good way of ensuring applicability of the lexical entry in (172c), note), a parallel analysis could still be pursued. (See once more Heim 2009 for a sketch of such an analysis.) There are some striking similarities between main clause and than-clause quantifiers that motivate such a step, in 1:67

Sigrid Beck

particular (190), (191) below: Both sentences in (190) have an interpretation that talks about the minimum requirement length of the paper, and neither sentence in (191) does. (190) (191)

a. b. a. b.

The paper is longer than it is required to be. The paper is required to be less long than that. The paper is longer than it is supposed to be. The paper is supposed to be less long than that.

But there are also apparent mismatches: (192)

a.

b.

Anderswo ist es weniger schön als hier. elsewhere is it less nice than here ‘It is less nice elsewhere than it is here.’ b. ??The most beautiful other place is less nice than it is here.

(193)

a.

(194)

a.

b. (195)

Hier ist es schöner als anderswo. here is it nicer than elsewhere ‘It is nicer here than it is elsewhere.’ ok: It is nicer here than it is in the most beautiful other place.

Sam war schneller als jemand anderes. Sam was faster than someone other ‘Sam was faster than another person.’ ok: Sam was faster than the fastest other person.

Jemand anderes war weniger schnell als Sam. Someone other was less fast than Sam ‘Another person was less fast than Sam.’ b. ??The fastest other person was less fast than Sam.

a.

At this point, I do acknowledge interesting empirical parallels, but I am also worried about apparent differences. I would not wish to be committed at present to claiming that quantifiers in the main clause behave in the same way as quantifiers in the than-clause, or that they don’t, and will remain neutral as to whether the analysis developed here should be extended to cover matrix clause quantifiers as well. Instead of making a connection to scope interaction phenomena, the present analysis is based on a plural/mass-semantics related vagueness plus semantic and pragmatic glue. It makes the interpretation of quantifiers in than-clauses more of a coercion-like phenomenon. Perhaps the variable and partly messy nature of the data can motivate the nature of the analysis.

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References Beck, Sigrid. 2001. Reciprocals are definites. Natural Language Semantics 9(1). 69–138. doi:10.1023/A:1012203407127. Beck, Sigrid. 2009. Comparatives and superlatives. To appear in Klaus von Heusinger, Claudia Maidenborn, and Paul Portner (eds.), Handbook of semantics: An international handbook of natural language meaning. Berlin: Mouton de Gruyter. Beck, Sigrid & Hotze Rullmann. 1999. A flexible approach to exhaustivity in questions. Natural Language Semantics 7(3). 249–298. doi:10.1023/A:1008373224343. Beck, Sigrid & Uli Sauerland. 2000. Cumulation is needed: A reply to Winter 2000. Natural Language Semantics 8(4). 349–371. doi:10.1023/A:1011240827230. Boškovi´ c, Željko & Jon Gajewski. 2008. Semantic correlates of the NP/DP parameter. Proceedings of the North East Linguistics Society 39. URL http://gajewski.uconn.edu/papers/NELS39paper.pdf. Cresswell, Max J. 1977. The semantics of degree. In Barbara H. Partee (ed.), Montague grammar, 261–292. Academic Press. Dalrymple, Mary, Makoto Kanazawa, Yookyung Kim, Sam Mchombo & Stanley Peters. 1998. Reciprocal expression and the concept of reciprocity. Linguistics and Philosophy 21(2). 159–210. doi:10.1023/A:1005330227480. Endriss, Cornelia. 2009. Quantificational topics: A scopal treatment of exceptional wide scope phenomena (Studies in Linguistics and Philosophy (SLAP) 86). Springer. doi:10.1007/978-90-481-2303-2. von Fintel, Kai & Sabine Iatridou. 2005. What to do if you want to go to Harlem: Anankastic conditionals and related matters. URL http://mit. edu/fintel/fintel-iatridou-2005-harlem.pdf. Ms, MIT. Fox, Danny. 2007. Free choice and the theory of scalar implicatures. In Uli Sauerland & Penka Stateva (eds.), Presupposition and implicature in compositional semantics, 537–586. New York: Palgrave Macmillan. Fox, Danny & Martin Hackl. 2006. The universal density of measurement. Linguistics and Philosophy 29(5). 537–586. doi:10.1007/s10988-006-9004-4. Gajewski, Jon. 2008. More on quantifiers in comparative clauses. Proceedings of Semantics and Linguistic Theory 18. doi:1813/13043. Hackl, Martin. 2001a. Comparative quantifiers. Ph.D. thesis, Massachusetts Institute of Technology. URL http://hdl.handle.net/1721.1/8765. Hackl, Martin. 2001b. A comparative syntax for comparative quantifiers.

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Proceedings of the North East Linguistics Society 31. Hackl, Martin. 2009. On the grammar and processing of proportional quantifiers: most versus more than half. Natural Language Semantics 17(1). 63–98. doi:10.1007/s11050-008-9039-x. Heim, Irene. 1982. The semantics of definite and indefinite noun phrases. Ph.D. thesis, University of Massachusetts at Amherst. URL http:// semanticsarchive.net/Archive/Tk0ZmYyY. Heim, Irene. 1994. Interrogative semantics and Karttunen’s semantics for know. In Rhonna Buchalla & Anita Mittwoch (eds.), The proceedings of the conference of the Israel Association for Theoretical Linguistics (IATL 1), 128–144. Hebrew University of Jerusalem. URL http://semanticsarchive. net/Archive/jUzYjk1O. Heim, Irene. 2001. Degree operators and scope. In Caroline Féry & Wolfgang Sternefeld (eds.), Audiatur vox sapientiae: A festschrift for Arnim von Stechow, 214–239. Berlin: Akademie Verlag. Heim, Irene. 2006a. Little. Proceedings of Semantics and Linguistic Theory 16. doi:1813/7579. Heim, Irene. 2006b. Remarks on comparative clauses as generalized quantifiers. URL http://semanticsarchive.net/Archive/mJiMDBlN. Ms, MIT. Heim, Irene. 2009. A unified account? Handout for ‘Topics in Semantics’, MIT. Heim, Irene & Angelika Kratzer. 1998. Semantics in generative grammar. Oxford: Blackwell. Hellan, Lars. 1981. Towards an integrated analysis of comparatives (Ergebnisse und Methoden moderner Sprachwissenschaft 11). Tübingen: Narr. Hoeksema, Jack. 1983. Negative polarity and the comparative. Natural Language and Linguistic Theory 1(3). 403–434. doi:10.1007/BF00142472. Jacobson, Pauline. 1995. On the quantificational force of English free relatives. In Emmon Bach, Eloise Jelinek, Angelika Kratzer & Barbara H. Partee (eds.), Quantification in natural languages (Studies in Linguistics and Philosophy (SLAP) 54), 451–486. Dordrecht: Kluwer. Kennedy, Chris. 1997. Projecting the adjective: The syntax and semantics of gradability and comparison. Ph.D. thesis, University of California, Santa Cruz. Klein, Ewan. 1991. Comparatives. In von Stechow & Wunderlich (1991), chap. 32, 673–691. Krasikova, Sveta. 2008. Quantifiers in comparatives. Proceedings of Sinn und Bedeutung 12. 337–352. URL http://www.hf.uio.no/ilos/forskning/

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konferanser/SuB12/proceedings/krasikova_337-352.pdf. Krasikova, Sveta & Ventsislav Zhechev. 2006. You only need a scalar only. Proceedings of Sinn und Bedeutung 10. URL http://www.sfb441.uni-tuebingen. de/b10/Pubs/KrasikovaZhechev_SuB05.pdf. Kratzer, Angelika. 1991. Modality. In von Stechow & Wunderlich (1991), 639–650. Kratzer, Angelika. 1998. Scope or pseudoscope? are there wide-scope indefinites? In Susan Rothstein (ed.), Events and grammar. Dordrecht: Kluwer. Krifka, Manfred. 1999. At least some determiners aren’t determiners. In Ken Turner (ed.), The semantics/pragmatics interface from different points of view (Current Research in the Semantics/Pragmatics Interface 1), 257–291. Elsevier. Krifka, Manfred. 2007. Approximate interpretation of number words: A case for strategic communication. In Gerlof Bouma, Irene Maria Krämer & Joost Zwarts (eds.), Cognitive foundations of interpretation (Verhandelingen der Koninklijke Nederlandse Akademie van Wetenschappen, Afd. Letterkunde 190), 111–126. Amsterdam: Royal Netherlands Academy of Arts and Sciences. Larson, Richard K. 1988. Scope and comparatives. Linguistics and Philosophy 11(1). 1–26. doi:10.1007/BF00635755. Link, Godehard. 1983. The logical analysis of plurals and mass terms: A lattice-theoretical approach. In Rainer Bäuerle, Christoph Schwarze & Arnim von Stechow (eds.), Meaning, use, and interpretation of language, Grundlagen der Kommunikation und Kognition, 302–323. de Gruyter. May, Robert. 1985. Logical form: Its structure and derivation (Linguistic Inquiry Monographs 12). Cambridge, MA: MIT Press. Meier, Cécile. 2002. Maximality and minimality in comparatives. Sinn und Bedeutung 6. 275–287. URL http://www.phil-fak.uni-duesseldorf.de/asw/ gfs/common/procSuB6/pdf/articles/MeierSuB6.pdf. Partee, Barbara H. 1984. Compositionality. In Fred Landman & Frank Veltman (eds.), Varieties of formal semantics (Groningen-Amsterdam Studies in Semantics (GRASS) 3), 281–311. Dordrecht: Foris. Reinhart, Tanya. 1992. Wh-in-situ: An apparent paradox. Proceedings of the Amsterdam Colloquium 8. 483–492. van Rooij, Robert. 2008. Comparatives and quantifiers. Empirical Issues in Syntax and Semantics 7. 423–444. URL http://www.cssp.cnrs.fr/eiss7/ van-rooij-eiss7.pdf.

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Rullmann, Hotze. 1995. Maximality in the semantics of wh-constructions. Ph.D. thesis, University of Massachusetts at Amherst. URL http://scholarworks. umass.edu/dissertations/AAI9524743/. Sauerland, Uli. 2008. Intervals have holes: A note on comparatives with differentials. Ms, ZAS Berlin. Schwarzschild, Roger. 1996. Pluralities (Studies in Linguistics and Philosophy (SLAP) 61). Kluwer. Schwarzschild, Roger. 2004. Scope splitting in the comparative. URL http: //www.rci.rutgers.edu/~tapuz/MIT04.pdf. Handout from a colloquium talk at MIT. Schwarzschild, Roger. 2008. The semantics of comparatives and other degree constructions. Language and Linguistics Compass 2(2). 308–331. doi:10.1111/j.1749-818X.2007.00049.x. Schwarzschild, Roger & Karina Wilkinson. 2002. Quantifiers in comparatives: A semantics of degree based on intervals. Natural Language Semantics 10(1). 1–41. doi:10.1023/A:1015545424775. Seuren, Pieter A.M. 1978. The structure and selection of positive and negative gradable adjectives. In Donka Farkas, Wesley M. Jacobsen & Karol W. Todrys (eds.), Papers from the Parasession on the Lexicon, Chicago Linguistic Society, April 14–15, 1978 (CLS 14), 336–346. von Stechow, Arnim. 1984. Comparing semantic theories of comparison. Journal of Semantics 3(1-2). 1–77. doi:10.1093/jos/3.1-2.1. von Stechow, Arnim. 1995. Lexical decomposition in syntax. In Urs Egli, Peter E. Pause, Christoph Schwarze, Arnim von Stechow & Götz Wienold (eds.), Lexical knowledge in the organization of language (Current Issues in Linguistic Theory 114), 81–118. John Benjamins. von Stechow, Arnim & Dieter Wunderlich (eds.). 1991. Semantics: An international handbook of contemporary research. Berlin: de Gruyter.

Prof. Dr. Sigrid Beck Chair of Descriptive and Theoretical Linguistics Englisches Seminar Universität Tübingen Wilhelmstr. 50 72074 Tübingen Germany [email protected]

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Two kinds of modified numerals∗ Rick Nouwen Utrecht University Received 2009-03-27 / First Decision 2009-07-19 / Revised 2009-08-18 / Second Decision 2009-09-08 / Revised 2009-09-29 / Accepted 2009-10-14 / Final Version Received 2009-10-15 / Published 2010-01-26

Abstract In this article, I show that there are two kinds of numeral modifiers: (Class A) those that express the comparison of a certain cardinality with the value expressed by the numeral and (Class B) those that express a bound on a degree property. The goal is, first of all, to provide empirical evidence for this claim and second to account for these data within a framework that treats modified numerals as degree quantifiers.

Keywords: modified numerals, scalar quantification, modality

1 Introduction Modified numerals are most commonly exemplified by combinations of a numeral and a comparative, as in more than 100. Following Hackl (2001), I will refer to such expressions as comparative quantifiers. As (1) shows, however, apart from modification by a comparative, numerals combine with a striking diversity of expressions. (1)

more/fewer/less than 100 no more than 100, many more than 100

comparative quantifiers differential quantifiers

∗ I would like to thank two anonymous reviewers for their helpful comments. Many thanks, moreover, to S&P editors Kai von Fintel and, especially, David Beaver, for their painstaking efforts to point out ways in which to improve the article. A concise presentation of the main points of this article appeared under the same title in the proceedings of the thirteenth Sinn und Bedeutung conference (Nouwen 2009). Earlier ideas on this subject were presented at Semantics and Linguistic Theory 13 in Amherst (2008) and the Journées Sémantique et Modélisation in Toulouse (2008). I am grateful to the audiences of these events for useful discussion. Special thanks to Min Que and Luisa Meroni for some help with data. This work was supported by a grant from the Netherlands Organisation for Scientific Research NWO, which I hereby gratefully acknowledge. ©2010 R.W.F. Nouwen This is an open-access article distributed under the terms of a Creative Commons NonCommercial License (creativecommons.org/licenses/by-nc/3.0).

R.W.F. Nouwen

at least/most 100 100 or more/fewer/less under/over 100, between 100 and 200 from/up to 100, from 100 to 200 minimally/maximally 100, 100 tops

superlative disjunctive locative directional

quantifiers quantifiers quantifiers quantifiers other

For a long time, there seemed to be agreement in the formal semantic literature that there was little to be gained from a thorough investigation of these expressions. An especially dominant view, originating from generalised quantifier theory (Barwise & Cooper 1981), was that there was not much more to the semantics of such quantifiers than the expression of the numerical relations >, 10 fewer than 10 = λM. maxn (M(n)) < 10

The workings of this definition will become clear below, but one of the main motivations for an analysis along this line can be pointed out immediately. The semantics in (13) is simply that of a comparative construction, where cardinalities are seen as a special kind of degrees. That is, like the comparative, it involves a degree predicate M and a maximality operator that applies to 5 In a set-theoretic approach (12) would correspond to the perhaps more familiar (i). I discuss (12) rather than (i) since, in what follows, I will assume a framework that makes use of sum individuals. It is easy to see that, within their own respective frameworks, (12) and (i) ultimately yield the same truth-conditions. (i)

more than 10 = λX.λY .|X ∩ Y | > 10 fewer than 10 = λX.λY .|X ∩ Y | < 10

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Two kinds of modified numerals

this predicate (Heim 2000). In other words, (13) is completely parallel to other comparatives, like (14). While in (13), M is a predicate like being a number n such that Jasper invited n people to his party, in (14) M could, for instance, be filled in with something like being a degree d such that Jasper is tall to degree d. (14)

-er than d

= λM.maxd0 (M(d0 )) > d

Hackl assumes that argument DPs containing a (modified) numeral always contain a silent counting quantifier many: (15)

many = λnλP λQ.∃x[#x = n & P (x) & Q(x)]

(16)

10 sushis [ DP [ 10 many ] sushis ]

In this framework, the numeral (of type d, of degrees) is an argument of the silent quantifier many (of type hd, hhe, ti, hhe, ti, tiii, of generalised quantifier-style determiners parameterised for degrees). By applying [ 10 many ] to the noun (phrase), the standard generalised quantifier denotation of 10 sushis is derived: λQ.∃x[#x = 10 & sushi(x) & Q(x)]. The structure of a DP containing a modified numeral does not differ essentially. Modified numerals are also the argument of a counting quantifier, as illustrated in (17). (17)

fewer than 10 sushis [ DP [ [ fewer than 10 ] many ] sushis]

As was stated above, many is parametrised for cardinalities, which we take to be degrees. Fewer than 10, however, denotes a degree quantifier, not a degree constant. Thus, to avoid a type clash, the modified numeral in (17) has to move, leaving a degree trace and creating a degree property. (18)

Jasper ate fewer than 10 sushis. [ [fewer than 10] [ λn [ Jasper ate [ [ n many ] sushis ] ] ] ]

This leads to the following interpretation, which results in the desired simple truth-conditions. (19)

[λM.maxn (M(n)) < 10] ( λn.∃x[#x = n & sushi(x) & ate(j, x)]) =β maxn (∃x[#x = n & sushi(x) & ate(j, x)]) < 10

This might seem like a rather elaborate way of deriving the truth-conditions for such simple sentences. Using (12), we would have derived as truth-

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conditions ¬∃x[#x ≥ 10 & sushi(x) & ate(j, x)], which is equivalent to (19), but which does not require resorting to (moving) degree quantifiers and silent counting quantifiers. Importantly, however, Hackl’s theory makes some crucial predictions which are not made by theories assuming a semantics as in (12). If, like degree operators, modified numeral operators can take scope, we expect to find scope alternations that resemble those found with degree operators (Heim 2000). As Hackl observed, this prediction is borne out. For reasons explained in Heim 2000, structural ambiguity arising from degree quantifiers and intensional operators like modals is only visible with nonupward entailing quantifiers, which is why all the following examples are with upper-bounded modified numerals. The example in (20), for instance is ambiguous, with (20a) and (20b) as its two readings. (20)

(Bill has to read 6 books.) John is required to read fewer than 6 books. a. b.

‘John shouldn’t read more than 5 books’ ‘The minimal number of books John should read is fewer than 6’

One of the readings of (20) states that there is an upper bound on what John is allowed to read. The more natural interpretation, however, is a minimality reading, which is about the minimal number of books John is required to read. (That is, (20) would, for instance, be true if John meets the requirements as soon as he reads 3 or more books.) Following Heim (2000), Hackl analyses this ambiguity as resulting from alternative scope orderings of the modal and the comparative quantifier. The upper bound reading, (20a), corresponds to a logical form where the modal takes wide scope. The minimality reading involves the maximality operator intrinsic to the comparative construction taking wide scope over the modal (Heim 2000). (21)

[maxn (∃x[#x = n & book(x) & read(j, x)]) < 6] [require [ [fewer than 6] [ λn [John read n-many books] ] ] ]

(22)

maxn (∃x[#x = n & book(x) & read(j, x)]) < 6 [ [fewer than 6] [ λn [ require [John read n-many books] ] ] ]

A similar structural ambiguity can be observed with existential modals. The two readings of (23) are an upper bound interpretation as well as a reading

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which is very weak, stating simply that values below the numeral are within what is permitted, without stating anything about the permissions for higher values. (That is, the reading intended in (23b) is, for instance, verified by a situation where there are no restrictions whatsoever on what John is allowed to read. Clearly, (23a) would be false in such a situation.) (23)

John is allowed to bring fewer than 10 friends. a. b.

‘John shouldn’t bring more than 9 friends’ ‘It’s OK if John brings 9 or fewer friends (and it might also be OK if he brings more)’

As before, these readings can be predicted to exist on the basis of the relative scope of modal and comparative quantifiers. (24)

maxn (♦∃x[#x = n & friend(x) & bring(j, x)]) < 6 [ [fewer than 6] [ λn [ allow [John invite n-many friends] ] ] ]

(25)

♦[maxn (∃x[#x = n & friend(x) & bring(j, x)]) < 6] [ allow [ [fewer than 6] [ λn [John invite n-many friends] ] ] ]

The reader may check that Hackl’s predicted readings in (24) and (25) are indeed the attested ones. 3.2

Class B modifiers are different

These analyses are strongly supportive of an approach which treats comparative quantifiers as comparative constructions. The question now is whether class B quantifiers should be given a similar treatment. In other words, will the semantics in (26) do? (26)

up to / maximally / at most / etc... 10 =? λM. maxn (M(n)) ≤ 10

Choosing a semantics that is parallel to that of fewer than is partly unintuitive since the class B quantifiers are not comparative constructions. Yet, cases like maximally 10 suggest that the crucial ingredient of the semantics is the same, namely a maximality operator. The unsuitability of the analysis in (26) becomes immediately apparent, however, if we investigate examples with class B modified numerals embedded under an existential modal: these turn out not to be ambiguous (cf. Geurts & Nouwen 2007). Class B modifiers like maximally, up to and at most always yield an upper bound on what is allowed and resist the weaker reading that was found with comparative modifiers, as

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the contrast between (27) and (28) makes clear. (27)

John is allowed to bring fewer than 10 friends. But more is fine too.

(28)

John is allowed to bring {up to / at most / maximally} 10 friends. #But more is fine too.

A further interesting property of the interaction of class B modified numeral quantifiers and modals is that existential modals interfere with the inferences about speaker knowledge that we found for simple sentences. Above, I observed that (29) licenses the inference that the speaker does not know how many friends Jasper invited. In contrast, (30) does not license any such inference; it is compatible with the speaker knowing exactly what is and what is not allowed. (29)

Jasper invited maximally 50 friends.

(30)

Jasper is allowed to invite maximally 50 friends.

These observations add to the data separating class A from class B quantifiers. Summarising, the distinctions are then as follows. First of all, class B quantifiers, but not class A quantifiers, resist definite amounts, except when embedded under an existential modal. Second, class B quantifiers, but not class A quantifiers, resist weak readings when embedded under an existential modal. In the next section I will argue that the peculiarities of class B quantifiers can be explained if we assume that they are quite simply maxima and minima indicators. Basically, what I propose is that the semantics of maximally (minimally) is simply the operator maxd (mind ). This might be perceived as stating the obvious. What is not obvious, however, is how such a proposal accounts for the difference between class A and class B quantifiers. I will argue that the limited distribution of class B modifiers is due to the fact that they give rise to readings that are in competition with readings available for non-modified structures. I will show that, in many circumstances, the application of a class B modifier to a numeral yields an interpretation which is equivalent to one that was already available for the bare numeral. Before I can explain the proposal in detail, I therefore need to include an account of bare numerals in the framework.

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3.3

The semantics of numerals

Above, I adopted the semantics of Hackl 2001 for comparative modified numerals. An important part in that framework is played by the counting quantifier many. I will re-name this operator many1 , for, in what follows, I assume that for any numeral there are two counting quantifiers available. These two options are to account for the two meanings of numerals that may be observed: on the one hand the existential / weak / lower-bounded meaning and, on the other hand, the doubly bound / strong meaning. An example like (31), for instance, is ambiguous between (31a) and (31b). (31)

Jasper read 10 books. a. b.

the number of books read by Jasper ≥ 10 the number of books read by Jasper = 10

I assume that, like the meaning in (31a), the meaning in (31b) is semantic and not the result of a scalar implicature that results from (31a). See e.g. Geurts 2006 for a detailed ambiguity account, and for some compelling arguments in favour of it.6 In the current framework, that of Hackl 2001, the weak reading in (31a) is due to a weak semantics for the counting quantifier: i.e. many1 . I propose that the strong reading, (31b), is accounted for by an alternative quantifier many2 (taking inspiration from Geurts 2006.)7 (32)

many1 = λnλP λQ.∃x[#x = n & P (x) & Q(x)] many2 = λnλP λQ.∃!x[#x = n & P (x) & Q(x)]

Here, ∃!x[ϕ] abbreviates ∃x[ϕ & ∀x 0 [x 0 6= x → ¬ϕ[x/x 0 ] ]].8 In other words, ∃!x stands for ‘exactly one . . . ’. When x ranges over groups of individuals, ∃!x[#x = n & P (x)] is verified by assigning to x the maximal group of individuals with property P , where n is the cardinality of that group. This is because any smaller group will not be the unique group with property P of its cardinality. For instance, if our domain is {a, b, c, d}, all of which satisfy P , then ∃!x[#x = 3 & P (x)] is false, since several groups have three atoms and property P , among which a ⊕ b ⊕ c and a ⊕ c ⊕ d. However, ∃![#x = 4 & P (x)] 6 But see Breheny 2008 for a dissenting view. 7 Here is a mnemonic. The 1 in many1 represents the fact that this operator is unilaterally bound, namely lower-bounded only. Many2 on the other hand is bilaterally bound. 8 Here, ϕ[x/x 0 ] is the formula that is exactly like ϕ except that free occurrences of x have been replaced by x 0 . Moreover, it is assumed that ϕ contains no free occurrences of x 0 .

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is true, since apart from a ⊕ b ⊕ c ⊕ d there is no other group that has 4 atoms while satisfying P . Consequently, ∃!x[#x = n . . .] stands for ‘exactly n. . . ’. For instance, the doubly bound reading of Jasper read 10 books is (33). The truth-conditions of (33) are such that it is false if Jasper read fewer than 10 books (for then there would not be 10 books he read), but also false if Jasper read more than 10 books (for then there would be many groups of 10 books he read). (33)

∃!x[#x = 10 & book(x) & read(j, x)]

Not only does the option of two counting quantifiers, many1 and many2 , suffice to account for the ambiguity of bare numerals, it is moreover harmless with respect to the semantics of comparative quantifiers. A sentence like Jasper read more than 10 books is not ambiguous. It is important to show that the availability of two distinct counting quantifiers does not predict ambiguities in such examples. It will be instructive to see in somewhat more detail why this is indeed the case. The structure in (34) is exemplary of a simple sentence with a modified numeral object. As explained earlier, the modified numeral applies to the degree predicate that is created by moving the quantifier out of the DP. (34)

[ MOD n [ λd [ Jasper read d many1/2 books ] ] ]

Now that there is a choice between two counting quantifiers, the denotation of the degree predicate depends on which of many1 and many2 is chosen. The predicate in (35) is the result of a structure containing many1 ; the predicate in (36) is based on many2 . If, in the actual world, Jasper read 10 books, then (35) denotes {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. When, however, the predicate contains the many2 quantifier, the denotation is a singleton set: {10} if Jasper reads 10 books. This is because only the maximal group of books read by Jasper is such that it is the unique group of that kind of a certain cardinality. In general, the many2 -based degree predicate extension is a singleton set containing the maximum of the values in the denotation of the many1 -based degree predicate. (35)

λd.∃x[#x = d & book(x) & read(j, x)]

(36)

λd.∃!x[#x = d & book(x) & read(j, x)]

As discussed above, comparative quantifiers involve maximality operators. However, the maximal values for degree predicates like (35) and (36) are

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always equivalent. In simple sentences based on a structure like (34), the option of having two distinct counting quantifiers does therefore not result in any ambiguity. When we turn to cases where the degree predicate is formed by moving the modified numerals over a modal operator with universal force, something similar can be observed. If Jasper is required to read (exactly) 10 books, then the structure in (37) yields, again, the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Once more, the structure which contains the bilateral counting quantifier, the one in (38), yields the set containing the maximum of its weaker counterpart. (37)

[ λd [ require [ Jasper read d many1 books ] ] ] λd.∃x[#x = d & book(x) & read(j, x)]

(38)

[ λd [ require [ Jasper read d many2 books ] ] ] λd.∃!x[#x = d & book(x) & read(j, x)]

Given that the relation between (38) and (37) is once again one of a set and its maximal value, no ambiguities can be expected to arise when comparative quantifiers are applied to these two predicates. This is as is desired. Of course, it could be that the actual situation is not one containing a specific requirement, but one with for instance a minimality requirement. Say, for instance, Jasper has to read at least 4 books. In that case, (37) denotes the set {1, 2, 3, 4}. The extension of (38), however, is the empty set. (In such a context, there is no specific n such that Jasper has to read exactly n books.) Clearly, the maximal value for the predicate is undefined in such a case. This means that the logical form based on many2 will not lead to a sensible interpretation and, so, we again do not expect to find ambiguity. The case of predicates that are formed by abstracting over an existential modal operator is illustrated in (39) and (40). If Jasper is allowed to read a maximum of 10 books, then the two predicates are equivalent, both denoting the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.9 (39)

λd.♦∃x[#x = d & book(x) & read(j, x)]

(40)

λd.♦∃!x[#x = d & book(x) & read(j, x)]

In sum, the option of two counting quantifiers many1 and many2 is irrelevant when combined with a comparative quantifier. This is because the compara9 If there is in addition a lower bound, the two predicates are no longer equivalent, but their maximum will be.

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tive quantifier is based on maximality and the degree predicates containing the different counting quantifiers do not differ in their maximum value. 4 The semantics of class B quantifiers I now turn to the main proposal: class B quantifiers are maxima/minima indicators. I start with the upper-bounded modifiers. 4.1 Upper bound class B modifiers In the formula in (41), MOD↓B generalises over any of the class B modifiers at most, maximally, up to, etc.10 (41)

MOD↓B = λd.λM. maxn (M(n)) = d

If the semantics of upper bound class B quantifiers is as in (41), then why is their distribution so limited? What I think is the reason for the awkwardness of a lot of examples with class B quantifiers is the fact that, in many cases, (41) is a vacuous operator. To be precise, the two propostions in (42) are equivalent whenever the cardinality predicate M denotes a singleton set. In such a case, a bare numeral form is to be preferred over a numeral modified by a class B modifier, since the latter derives the same meaning from a much more complex linguistic form. (42)

a. b.

maxn (M(n)) = d M(d)

What I have in mind exactly is the kind of reasoning underlying Horn’s division of pragmatic labour (Horn 1984). The idea is that a maxim of brevity, 10 For modifiers like at most and maximally, one might wonder whether (41) is not too restricted, given that they are capable of modifying DPs more generally. However, it appears that there is a common mechanism to all uses of such modifiers. For instance, (i) could be assigned its intuitive meaning if we assume that at most has the semantics in (ii), where the operator ‘max’ compares properties on the rank order [assistant professor < associate professor < full professor]: (i)

Jasper is at most an associate professor.

(ii)

at most = λP .λx.maxP 0 (P 0 (x)) = P

It goes beyond the scope of this article to implement a formal connection between (ii) and (41), but it should be clear that the underlying mechanism is the same.

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part of Grice’s maxim of Manner (Grice 1975), steers toward minimising the form used to express something. This causes simple (unmarked) meanings to be typically expressed by means of simple (unmarked) forms. Marked forms which by convention could be given the same unmarked meaning as some unmarked form are instead given a more marked interpretation. There are many variations and implementations of this idea (McCawley 1978; Atlas & Levinson 1981; Blutner 2000; van Rooij 2004),11 but what is most relevant for this paper is the general idea that an unmarked meaning is blocked as an interpretation for the marked form. With this in mind, the equivalence of (42a) and (42b) whenever M denotes a singleton set has profound consequences for when it actually makes sense to state that the maximum of a degree predicate equals a certain value. That is, in cases where (42a) equals (42b), we expect that the use of maximally does not lead to an interpretation based solely on (42a), since the use of the bare numeral form would result in the same meaning. To illustrate this in some more detail let us carefully go through the following examples. We know from the discussion above that one of the interpretations available for (43) is (44). (43)

Jasper invited 10 people.

(44)

∃!x[#x = 10 & people(x) & invite(x)]

Now consider (45), which is interpreted either as (46) or as (47). (45)

Jasper invited maximally 10 people.

(46)

[ maximally 10 [ λd [ Jasper invited d many1 people ] ] ] maxn (∃x[#x = n & people(x) & invite(j, x)]) = 10

(47)

[ maximally 10 [ λd [ Jasper invited d many2 people ] ] ] maxn (∃!x[#x = n & people(x) & invite(j, x)]) = 10

The interpretations in (46) and (47) are equivalent. In fact, just like we do not expect ambiguities to arise with comparative quantifiers on the basis of the many1 /many2 choice, we do not expect any ambiguities to arise with MOD↓B quantifiers, for the simple reason that both such operators involve 11 In fact, there is a close resemblance between this prevalent idea in pragmatics and blocking principles in other parts of linguistics. The commonality is that two different expressions cannot have identical meanings. See, for instance, the Elsewhere Condition (Kiparsky 1973) in phonology or the Avoid Synonymy principle (Kiparsky 1983) in morphology.

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a maximality operator and that the maximal values of predicates based on many1 are always those of predicates based on many2 . In what follows, we will therefore gloss over the two equivalent options by representing the semantics following the general scheme in (48). (48)

[ maximally 10 [ λd [ Jasper invited d many1/2 people ] ] ] maxn (∃(!)x[#x = n & people(x) & invite(j, x)]) = 10

Importantly, the single reading of (45) is equivalent to (44), the strong reading of (43). The example in (43), however, reaches this interpretation by means of a much simpler linguistic form, one which does not involve a numeral modifier. I propose that this is why the reading in (48) of (45) does not surface: it is blocked by (43).12 As observed above, we can nevertheless make sense of (45) once we interpret the sentence to be about what the speaker holds possible. So, a further possible reading for (45) is that in (49). (49)

maxn (♦∃(!)x[#x = n & people(x) & invite(j, x)]) = 10

Crucially, this interpretation is not equivalent to (50), which is the result of interpreting (43) from the perspective of speaker possibility. (50)

♦∃!x[#x = 10 & people(x) & invite(j, x)]

12 An anonymous reviewer notes two complications with the proposed blocking mechanism. First of all, s/he wonders why exactly 10 is not blocked in a similar way to minimally 10, since the same reasoning seems to apply. I acknowledge that this is something that needs to be explained. Interestingly, this is something any theory that believes in the existence of an ‘exactly’ sense for numerals has to explain. One promising route has been proposed by Geurts (2006), who suggests that exactly is semantically empty and that its only function is “to reduce pragmatic slack” (p. 320). That is, whereas bare 100 allows for an imprecise rough construal (Krifka 2007a), exactly 100 enforces precision. If Geurts is on the right track, then there is no reason to expect that exactly 100 is blocked by 100. A further complication noted by the same anonymous reviewer is that if we assume that the ‘max’ operator is presuppositional, we might come to expect that maximally 100 blocks 100 instead of the other way around. This prediction appears to be made when at the same time we assume the Maximize Presupposition principle (Heim 1991). Since maximally 100 and 100 share the same meaning, but the former triggers a presupposition, the use of 100 would be blocked. This is a very interesting scenario, but since I have little to say about the kind of presuppositions (if any) expressions like maximally trigger and I furthermore have no thoughts on how maximize presupposition would interact with a brevity maxim, I will leave this issue to further research.

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In other words, the meaning in (49) for (45) is not blocked by the bare numeral form in (43) since (43) lacks this reading. To be sure, I do not claim that (50) would be an available reading for (43). That is, the particular kind of interpretation that examples like (45) receive is available only as a last resort strategy. Underlying this analysis is the assumption that there exist silent modal operators. I can offer no independent evidence for this assumption, but stress that the intuitions regarding examples like (45) quite clearly point into the direction of some sort of speaker modality. In work on superlative quantifiers, we find some alternatives to the present account. Such approaches are meant to deal with at most and at least only, but if my arguments above are on the right track, then we could reinterpret these proposals for the semantics of superlative quantifiers as applying to the whole of class B. For instance, the analysis of class B expressions presented here differs from that of superlative modifiers in Geurts & Nouwen 2007. According to the present proposal, the modal flavour of (45) is due to a silent existential modal operator. In Geurts & Nouwen, however, the modal was taken to be part of the lexical content of superlative quantifiers. Another alternative, proposed for superlative modifiers in Krifka 2007b and which is closer to the present proposal, is to analyse examples like (45) not as involving a modal operator, but rather a speech act predicate, like assert. In that framework, the analysis of (45) would say that n=10 is the maximal value for which ∃(!)x[#x = n & people(x) & invite(j, x)] is assertable, rather than possible.13 That is, according to Krifka, (45) is interpreted by assigning the modified numeral scope over an illocutionary force operator, rather than over a modal operator. I will return to a comparison of these approaches below. I would like to point out immediately, however, what I think are the major disadvantages of both alternatives. The main problem is with examples like (51), which contain an overt existential modal. (51)

Jasper is allowed to invite maximally/at most 10 people.

13 In his comments on the first version of this paper, David Beaver observed that it it is not necessarily the speaker’s knowledge that matters, as can be seen from (his) example (i). (i)

I know how many people were at the party, but I’ve been told not to reveal that number to the press. However, there were maximally 50 there.

It would be interesting to see if data like these help in reaching a synthesis of Krifka’s account and the present proposal.

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Its most salient reading is one in which 10 is said to be the maximum number of people Jasper is allowed to invite. That is, it places an upper bound on what is allowed. For Krifka, this is problematic since, here, the modified numeral is quite obviously not a speech act operator. For the proposal in Geurts & Nouwen 2007, such examples are problematic since the modal lexical semantics of at most predicts a reading with a double modal operator, one originating from the verb and one from the numeral modifier. To remedy this, Geurts and Nouwen provide an essentially non-compositional analysis of such examples as modal concord.14 In contrast, the current proposal deals effortlessly with examples, such as (51). What was crucial to my explanation of how (45) gets to be interpreted is that degree predicates based on modals with existential force denote non-singleton sets even when the counting quantifier associated with the numeral is many2 . This entails that saying that the maximum value for such a predicate is n is not equivalent to saying that the predicate holds for n. More formally, there is a contrast between (52a) and (52b). (52)

a. b.

maxn (∃(!)x[#x = n & people(x) & invite(j, x)]) = 10 a ∃!x[#x = 10 & people(x) & invite(j, x)]) maxn (♦∃(!)x[#x = n & people(x) & invite(j, x)]) = 10 i ♦∃!x[#x = 10 & people(x) & invite(j, x)])

As a result, whenever an upper bound class B modifier scopes over an existential modal, no blocking from the simpler bare numeral form will be able to take place. The application of an upper bound class B quantifier to a degree predicate is only felicitous if the resulting readings are not readings that can be expressed just as well by omitting the class B modifier. This is the case when a modal with existential force has scope inside the degree 14 A further problem I see with the proposal in Krifka 2007b is that the analysis does not appear to extend straightforwardly to illocutionary forces other than assertion, although in fairness this might be because (at the time of writing) no detailed exposition of this theory exists. For instance, nothing suggests that superlative modified numerals can scope over a question operator in questions. An additional disadvantage for the proposal of Geurts and Nouwen is that it does not yield an explanation of the lexical form of class B modifiers. Whereas the current proposal assigns to a modifier like maximally the semantics of a maximality operator, an extension of Geurts and Nouwen’s approach would have to take it to be a modal, thereby disassociating it from the intuitive meaning of maximal.

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predicate.15 Treating upper bound class B quantifiers as maxima indicators thus also predicts the absence of weak readings for examples like (51). Given the flexible scope of the numeral modifier we expect this sentence to have two corresponding logical forms, (54a) and (54b). (From here on, indicates deontic modality, to distinguish it from the (epistemic) speaker possibility ♦). (53)

Jasper is allowed to invite maximally/at most 10 people.

(54)

a. b.

maxn (∃(!)x[#x = n & people(x) & invite(j, x)]) = 10 [maxn (∃(!)x[#x = n & people(x) & invite(j, x)]) = 10]

If maximally 10 is taken to have wide scope over the modal, then we arrive at (54a), the reading that says that the maximum number of people Jasper is allowed to invite equals 10. This is not a semantic interpretation that is available for (55). Its many2 reading, for instance, says that inviting exactly 10 people is something that Jasper is allowed to do. This is much weaker than (54a). (The only way we can arrive at an equally strong reading for (55) is by means of implicature.) (55)

Jasper is allowed to invite 10 people.

If we take the modal in (51) to have widest scope, as in (54b), the resulting interpretation is one in which inviting exactly 10 people is allowed for Jasper. This is the reading for (55) discussed above, and so it is blocked. As a result, (54a) is the only interpretation available. An interesting side to the account presented here is that the upper bound class B quantifiers do not encode the ≤ relation. As maxima indicators, their application only makes sense if what they apply to denotes a range of values. Otherwise, using the strong reading of the bare numeral form will do just as well. Interestingly, the approach also predicts that some of the examples I discussed above do not only result in a blocking effect, but could moreover be predicted to be false. For instance, according to the approach set out above, the meaning of (56a) is that in (56b). 15 As far as I can see, assertability would have the same (crucially weak) properties as possibility. So, should a silent speech act predicate seem more plausible than a silent modal operator, then ♦ can just as well be interpreted as expressing assertability. It appears that such a move would be largely compatible with the proposal of Krifka 2007b.

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R.W.F. Nouwen

(56)

a. #A triangle has maximally 10 sides. b. ‘the maximum number of sides in a triangle is 10’

The reading in (56b) is not only blocked by A triangle has 10 sides, but it is moreover plainly false. I believe that this predicts that (56a) should be expected to have a somewhat different status from (57), which strictly speaking has a true interpretation, but one that can be expressed by simpler means. (57)

#A triangle has maximally 3 sides.

It is difficult to establish whether this difference in status is borne out, or even how this difference can be recognised. However, my own intuition tells me that while (56) is never acceptable, (57) could be used in a joking fashion. Native speakers inform me that (58) is marginally acceptable: (58) 4.2

?A triangle has minimally and maximally 3 sides. Lower-bound class B modifiers

Lower-bound class B modifiers correspond to minimality operators. Let MOD↑B correspond to any of the class B expressions at least, from, minimally, etc. (59)

MOD↑B = λd.λM. minn (M(n)) = d

Note first that minimality operators are sensitive to the many1 / many2 distinction. Consider the degree predicate [λd. John read d many1/2 books] and, say, that John read 10 books. In the many1 version of the logical form, the minimal degree equals 1. In fact, independent of how many books John read, as long as he read books, the minimal degree will always be 1. In the many2 version of the logical form, the predicate denotes a singleton set, {10} if John read 10 books. The minimal degree in that case is, of course, 10. These observations already straightforwardly account for our intuitions for an example like (60). (60)

John read minimally 10 books.

The many1 interpretation of (60) will be rejected, for it will always be false. The minimal value for any simple many1 -based degree predicate is always 1. The many2 interpretation of (60) will be rejected too, for it will correspond to an interpretation saying that John read (exactly) 10 books. This reading is

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blocked by the bare numeral. (In fact, (60) in the many2 variant is equivalent to John read maximally 10 books, which, as was explained above, is blocked for the same reasons.) We can save (60) by interpreting it with respect to an existential modal operator. This yields two readings: (61)

a. b.

mind (♦∃x[#x = d & read(j, x) & book(x)]) = 10 mind (♦∃!x[#x = d & read(j, x) & book(x)]) = 10

The form in (61a) is once more a contradiction: the minimal degree for which it is deemed possible that John read d-many1 books is always 1. The reading in (61b) is much more informative. It says that that the minimal number for which it is thought possible that John read exactly so many books is 10. In other words, this says that it is regarded as impossible that John read fewer than 10 books. This is exactly the reading that is available. 4.3

Beyond modals

Some words are in order on the interaction of numeral modifiers with nonmodal operators. Given the current proposal, any property that involves existential quantification would license the use of a class B modifier. However, it is known that degree operators (which we take modified numerals to be) cannot move to take scope over nominal quantifiers (cf. Kennedy 1997; Heim 2000).16 This explains why (62) does not have the reading in (63). (62)

Someone is allowed to invite maximally 50 friends.

(63)

the person who is allowed to invite most friends is allowed to invite 50 friends

As observed above, however, bare plurals do interact with class B quantifiers, as in for instance example (9). This would suggest that some intensional/modal analysis of the readings involved in such examples is in order. (Thanks to Maribel Romero for pointing this out to me.) I will leave a detailed analysis of these cases for further research. 16 In Heim’s formulation: If the scope of a quantificational DP contains the trace of a degree phrase, it also contains that degree phrase itself. See Heim 2000 for details.

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5 Maximal and minimal requirements As Hackl (2001) observed, there is an interesting interaction between modified numerals and modals. I have extended these observations by showing how existential modals have a tight connection to class B modifiers in that they license their (otherwise blocked) existence. What I have not discussed so far is how class B modifiers interact with universal modals. It turns out that this part of the story is not straightforward at all. Given my proposal in the previous section, we expect that there are in principle four logical forms that correspond to (64).17 (64)

Jasper should read minimally 10 books.

(65)

í >min: The minimum n such that Jasper will read n books should be 10 a. b.

(66)

í[minn (∃x[#x = n & book(x) & read(j, x)]) = 10] í[minn (∃!x[#x = n & book(x) & read(j, x)]) = 10]

many1 many2

min> í: The minimum n such that Jasper should read n books is 10 a. b.

minn (í∃x[#x = n & book(x) & read(j, x)]) = 10 minn (í∃!x[#x = n & book(x) & read(j, x)]) = 10

many1 many2

It turns out that none of these logical forms provide a reading that is in accordance to our intuitions regarding (64). First of all, notice that minn (∃x[#x = n & book(x) & read(j, x)]) = 10 is a contradiction. If there are 10 books that Jasper read, then there is also a singleton group containing a book Jasper read. The minimum number of books Jasper read is therefore either 1 (in case he read something) or 0 (in case he did not read anything). It could never be 10. Consequently, (65a) is a contradiction. For a similar reason, (66a) is a contradiction too. If there needs to be a group of 10 books 17 In this paper, I ignore readings which (for the case of at least) Büring (2008) calls speaker insecurity readings and which Geurts & Nouwen (2007) discuss extensively. Basically, this reading amounts to interpreting the modal statement with respect to speaker’s knowledge. Such readings are especially prominent with superlative quantifiers. For instance, the speaker insecurity reading of Jasper should read at least 10 books is: the speaker knows that there is a lower bound on the number of books that Jasper should read, s/he does not know what that lower bound is, but she does know that it exceeds 9. Furthermore, I also ignore a reading of (64) in which 10 books is construed as a specific indefinite. In that reading, (64) states that there are 10 specific books such that only if Jasper reads these books will he comply with what is minimally required.

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read by Jasper, then there also need to exist groups containing just a single book read by Jasper. Once again, the minimum number referred to in (66a) is either 0 or 1, never 10. Turning to (65b), notice that the minn -operator is vacuous here, since there is just a single n such that Jasper read exactly n books. This renders (65b) equivalent to the many2 reading of Jasper should read 10 books, and so we predict it to be blocked. The interpretation in (66b) does not fare any better. In fact, the minn -operator is vacuous here as well. This means that (65b) is equivalent to (66b) and that it is consequently also blocked. Even if no blocking were to take place, (65b)/(66b) offer the wrong interpretation anyway. They state that Jasper must read exactly 10 books (no more, no fewer), which is not what (64) means. One might think that the problems with (65b) and (66b) can be remedied by abandoning quantification over sums and instead using reference to (maximal) sums. For instance, (67) represents the truth-conditions we are after. (Here σx returns the maximal sum that when assigned to x verifies the scope of σ ). (67)

minn (í[#σx (book(x) & read(j, x)) ≥ n]) = 10

Still, here too the application of minn is not meaningful, since there is only a single n such that í[#σx (book(x) & read(j, x)) ≥ n] holds, which is 10 if (64) is true. As a consequence, it would not matter whether we applied a maximality or a minimality operator. We then wrongly predict that (68) should share a reading with (64). (Note that (65b) and (66b) suffer from the same odd prediction, given that the operator minn has no semantic impact there either.) (68)

Jasper should read maximally 10 books.

It appears then that the proposal defended in this article fails hopelessly on sentences like (64). As I will show, however, things are not so dire as they appear. In fact, I will argue that what we stumble upon here is a general, but poorly understood property of modals, which could be summarised as follows: (69)

Generalisation: universal modal operators are interpreted as operators with existential modal force when minimality is a stake

An illustration of (69) is (70), which is a satisfactory paraphrase for (64).

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R.W.F. Nouwen

What is striking is that this paraphrase contains allow instead of should. (70)

10 is the smallest number of books John is allowed to read

I will not offer an explanation for this generalisation (but see Nouwen 2010a for an attempt). I will simply show that if we look a bit closer at the interpretation of modal operators, then we come to understand that my theory actually yields a welcome analysis. 5.1 Previous analyses There is a precedent. In an earlier theory of at least, Geurts & Nouwen 2007, the correct predictions regarding its relation to universal modals are arrived at by an essentially non-compositional mechanism. A central claim made in that paper is that superlative quantifiers are modal expressions themselves. For instance, (71a) was proposed to correspond to (71b).18 Furthermore, it was assumed that there may be a non-compositional interaction between the modal that is implicitly contributed by a modified numeral and an explicit modal operator. For instance, (72a) is interpreted as an instance of modal concord, as in (72b), where the two modals fuse and the modal takes on the deontic flavour of need.19 (71)

a. b.

John read at least 10 books. ∃x[#x = 10 & book(x)& read(j, x)]

(72)

a. b.

John needs to read at least 10 books. í∃x[#x = 10 & book(x)& read(j, x)]

18 This is how I see the theoretical landscape: Although not immediately obvious, the proposal by Geurts and Nouwen already carries in it the idea that superlative quantifiers are minimality and maximality operators. For instance, (71b) is equivalent to stating that 10 is the minimal number of books John is allowed to read. Given the basic idea of treating class B operators as min/max-operators, one has a range of options to account for the distribution of such quantifiers and for their behaviour in intensional contexts. Geurts and Nouwen represent one extreme, where the lexicon specifies the exact behaviour of such quantifiers (together with the rule of modal concord). The present proposal puts forward the other extreme, where the lexical entry for superlative (and other class B) quantifiers is rather minimal, and where pragmatic mechanisms account for distribution and behaviour in intensional contexts. 19 I am simplifying the analysis here a little bit. Geurts & Nouwen (2007) propose that there is an additional conjunct to the meaning of sentences containing superlative quantifiers, for which they leave implicit whether it is entailed or implicated. For (71), for instance, there would be an additional condition in the truth-conditions saying: ¬∃x[#x > 10& book(x) & read(j, x)]. Similarly for (72).

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The approach of Geurts and Nouwen is the most broadly applicable approach to superlative quantifiers in the (admittedly small body of) literature on that topic. There are alternatives on the market, but they do not handle examples like these very well. As I mentioned above, Krifka (2007b) takes at least to be a speech act modifier. Basically, an example like (71) is analysed by Krifka in terms of what the speaker finds assertable and is paraphrased as follows: the lowest n such that it is assertable that John read n books is 10. When at least is embedded in an intensional context, however, it does not modify the strength of assertability, but rather the intensional operator. So, taking Krifka’s analysis as suitable not just for superlative, but rather for all class B quantifiers, (72a) would be paraphrased as (73). (73)

10 is the smallest value for n such that John should read n books

In such cases, Krifka’s analysis is identical to the one I have set out above and it runs in exactly the same problem: (73) is not the reading we are after. Rather, (72a) means that 10 is the smallest number of books John is allowed to read. 5.2

Minimal requirements

Geurts & Nouwen (2007) and Krifka (2007b) say nothing about the distinction between class A and class B expressions. However, if we extend their proposals for superlative quantifiers to cover all B-type quantifiers, then we have an interesting trio of competing characterisations of such expressions. At face value, the observations made so far in this section would appear to speak in favour of the modal concord proposal of Geurts & Nouwen (2007) (generalised to all class B quantifiers) and against the account defended here or in Krifka 2007b. As I will argue now, however, there are reasons to believe that the problematic predictions made by the latter two theories are not due to the semantics of the modified numeral, but are actually the result of an overly simplistic understanding of requirements. What I will do is discuss in some detail examples like (74). (74)

The minimum number of books John needs to read to please his mother is 10.

Notice, first of all, that on an intuitive level, (74) is equivalent to (75). (75)

John needs to read minimally 10 books to please his mother.

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R.W.F. Nouwen

Note, secondly, that (74) spells out the semantics I have proposed for (75). What I will show now is that when we look into the semantic details of (74), we will run into exactly the same problems as we did for (75). What this shows is that rather than thinking that my account of class B quantifiers is on the wrong track, there are actually reasons to believe that the proposal lays bare a hitherto unexplored problem for the semantics of modals like need, require, etc. Let us consider the semantics of (74). Say that, in fact, the minimal requirements for pleasing John’s mother are indeed John reading 10 books. That is, if John reads 10 or more books, she is happy. If he reads fewer, she will not be pleased. Standard accounts of goal-directed modality (von Fintel & Iatridou 2005) assume that statements of the form to q, need to p are true if and only if p holds in all worlds in which the goal q holds. Below, I refer to the worlds in which John pleases his mother as the goal worlds. It is instructive to see what we know about the propositions that are true in such worlds. The following is consistent with the context described above. (76)

a. b. c. d. e. f.

In all goal worlds: ∃x[#x = 10 & book(x) & read(j, x)] In all goal worlds: ∃x[#x = 9 & book(x) & read(j, x)] In all goal worlds: ∃x[#x = 1 & book(x) & read(j, x)] In some (not all) goal worlds: ∃x[#x = 11 & book(x) & read(j, x)] In some (not all) goal worlds: ∃x[#x = 12 & book(x) & read(j, x)] In no goal world: ¬∃x[book(x) & read(j, x)]

Let us now analyse some examples. First of all, (77a) and (77b) are intuitively true and are also predicted to be true ((77a) by virtue of (76a) and (77b) by virtue of (76c).) (77)

a. b.

To please his mother, John needs to read 10 books. To please his mother, John needs to read a book.

The example in (78) is intuitively false, and is also predicted to be false, for the context is such that there are goal worlds in which John reads only 10, and not 11, books. (78)

To please his mother, John needs to read 11 books.

So far, so good. If we turn to examples that place a bound on what is required, however, then the theory makes a wrong prediction. The example in (79) is intuitively false. If interpreted as (80), however, it is predicted to be true (by

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virtue of (76c)). (79)

The minimum number of books John needs to read, to please his mother, is 1.

(80)

minn [In all goal worlds: ∃x[#x = n & book(x) & read(j, x)]] = 1

In general, theories such as that of von Fintel & Iatridou (2005) predict that if S is an entailment scale of propositions, and p is a proposition on this scale, then if p is a minimal requirement for some goal proposition q, then a statement of the form “the minimum requirement to q is p” is always predicted to be false, except when p is the minimal proposition of S. This makes a devastating prediction, namely that minimal requirements could never be expressed, since they would always correspond to the absolute minimum. One might think that what is going wrong in the example above is that I assume that when we talk about how many books John read we should be talking about existential sentences, that is about at least how many books John read. The alternative would be to describe the number of books John read by means of the counting quantifier many 2 , that is, how many books John read exactly. I’m afraid this only makes the problem worse. Here is a description of the relevant context in terms of the exact number of books that were read by John. (81)

a. b. c. d. e.

In In In In In

some but not all goal worlds: John read exactly 10 books. no goal world: John read exactly 9 books. no goal world: John read exactly 1 book. some but not all goal worlds: John read exactly 11 books. some but not all goal worlds: John read exactly 12 books.

Now, there is no number n such that John read exactly n books in all goal worlds. So, the smallest number of books John needs to read does not refer. The upshot is that there is no satisfactory analysis of examples like (74) under the assumptions made here. In general, it seems that, under standard assumptions, there is no satisfactory analysis of minimal requirements. Whatever way we find to fix the semantics of cases like (74), however, this fix will work to save the account of class B quantifiers too, for (74) was a literal spell-out of the proposed interpretation of similar sentences with at least, minimally, etc. It goes beyond the scope of this article to provide such a fix. The overview in (81), however, can help to indicate where we should look for

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R.W.F. Nouwen

a solution.20 Given that there is no goal world in which John read exactly n books for n’s smaller than 10, it follows that 10 is the minimal number of books John could read to please his mother. In other words, examples like (74) show that, in the scope of a minimality operator, modals that are lexically universal quantifiers get a weaker interpretation. That said, it is time to revisit example (64), repeated here as (82). (82)

Jasper should read minimally 10 books.

My proposal generated four logical forms, two of which were contradictory and two of which were blocked by a non-modified form. Let us revisit one of these logical forms, namely the one with a narrow scope modal and a doubly bound counting quantifier, represented in (83). The resulting truth-conditions were presented above as (84). (83)

[ minimally 10 λn [ should [ Jasper read [ n-many2 books ] ] ] ]

(84)

minn (í∃!x[#x = n & book(x) & read(j, x)]) = 10

What the discussion in the current section suggests is that it is a misunderstanding to assume that (83) is interpreted as (84), and that it looks like there is a mapping to a form like (85), instead. (85)

minn (∃!x[#x = n & book(x) & read(j, x)]) = 10

This captures the intuitive meaning of (82). At this point I do not have anything to offer which provides the mechanism behind the generalisation that the combination of a universal modal and a minimality operator leads to a semantics which is existential in nature. What is relevant for the present purposes is that this is a general phenomenon. Interestingly, this means there are noteworthy connections to other areas where the semantics of a modal statement appear mysterious. Schwager (2005), for instance, notices that certain imperatives, which are standardly considered to have universal modal force, require a weaker semantics. Her key examples are German imperatives containing for example. (86)

Q: How can I save money? A: Kauf zum Beispiel keine Zigaretten! Buy for instance no cigarettes “For example, don’t buy any cigarettes!”

20 See Nouwen 2010a for a proposal along these lines.

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In the context of the question asked in (86), the imperative does not convey that to comply with the advice, the hearer has to stop buying cigarettes. Instead, it is interpreted as stating that one of the things one could do to save money is to stop buying cigarettes. Thus, examples like these display a mechanism that is similar to the interaction of numeral modifiers and modality. The mysterious interaction of modified numerals and modals is moreover reminiscent of the interaction of modals and disjunction (Zimmermann 2000; Geurts 2005; Aloni 2007), especially since, on an intuitive level at least, a class B modified numeral like minimally 10 (and, quite obviously, 10 or more) appears to correspond to a disjunction of alternative cardinalities, with 10 as the minimal disjunct.21 A central issue in the literature on modals and disjunction is that classical semantic assumptions fail to capture the entailments of sentences where a disjunctive statement is embedded under a modal operator (Kamp 1973). A detailed comparison of this complex issue with the discussion of minimal requirements that I presented here, however, will be left to further research. 6

More about the A/B distinction

In this section, I will attempt to give some initial answers to three empirical questions concerning the distinction between class A and B modified numerals that is central to this article. First of all, I turn to the issue of which expressions go with which class. So far, I have restricted my attention mostly to, on the one hand, comparative quantifiers (as proto-typical class A expressions) and, on the other hand, superlative, minimality/maximality and up to-modified numerals (as representatives of class B). What about expressions like the prepositional over n or under n or the double bound between n and m or from n to m? Below, I will turn briefly to such expressions. A second empirical question concerns the validity of the examples used so far. Although I believe that the intuitions concerning the constructed examples in this article are rather clear, my plea for two kinds of modified numerals would still benefit from some independent objective support. Below, I present the results of a small corpus study that clearly reflects the distinction argued for in this article. Finally, this section will turn to the cross-linguistic generality of the 21 See Nilsen 2007 and Büring 2008 for suggestions along this line for the modifier at least only.

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R.W.F. Nouwen

proposal. I will provide data from a more or less random set of languages that suggest that the class A/B distinction is not a quirk of English or Germanic, or even Indo-European, but is, in fact, quite general. 6.1 Filling in class A and B I will leave it an open question exactly which quantifiers belong to which class. Nevertheless, I can already offer some speculations on several quantifiers that I have so far not discussed. To start with disjunctive quantifiers, it appears that these are clear cases of class B expressions. (87)

a. #A triangle has 3 or more sides. b. #A triangle has 3 or fewer sides.

With disjunctive quantifiers in class B, one might wonder whether there are any examples of class A expressions which are not the familiar comparative quantifiers more/fewer/less than n. I think that locative prepositional modifiers are a likely candidate for class A membership, however. In fact, I believe that the locative/directional distinction in spatial prepositions corresponds to the class A/B distinction when these prepositions are used as numeral modifiers. Roughly, locative prepositions express the location of an object and are compatible with the absence of directionality or motion. Directional prepositions, on the other hand, cannot be used as mere indicators of location.

(88)

Locative: a. b. c.

(89)

John was standing under a tree. That cloud is hanging over San Francisco. Breukelen is located between Utrecht and Amsterdam.

Directional: a. #John was standing up to here. b. #John was standing from here. c. #Breukelen is located from Utrecht to Amsterdam.

Now, compare (90a) and (90b). (90)

a. b.

You can get a car for under €1000. You can get a car for maximally €1000.

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The example in (90b) is somewhat strange, since it claims that the most expensive car you can buy is €1000. The example in (89a), in contrast, makes no such claim. It clearly has a weak reading: there are cars that are cheaper than €1000 and there might be more expensive ones too. As explained above, such weak readings are typical for class A quantifiers and do not occur with class B quantifiers.22 Furthermore, under seems perfectly compatible with definite amounts, such as in (91). (91)

The total number of guests is under 100. To be precise, it’s 87.

Class A is then not restricted to comparative constructions only. In fact, other locative prepositions seem to behave similarly to under. (92)

The total number of guests is between 100 and 150. It’s 122.

The locative complex preposition between . . . and . . . contrasts with its directional counterpart from . . . (up) to . . . , which behaves like a class B modifier: it is incompatible with definite amounts, as in (93), but felicitous if it relates to a range of values. (93) (94)

#The ticket to the Stevie Wonder concert that I bought yesterday cost from €100 to €800. Tickets to the Stevie Wonder concert cost from €100 to €800.

It appears then that locative prepositions turn into class A modifiers, while directional ones turn into class B modifiers. A potential counterexample, however, is over, which apart from a (relatively rarely used) locative sense, as in (88b), has a directional sense, such as exemplified in (95). (95)

The bird flew over the bridge.

As a numeral modifier, however, over looks like a class A element. In (96), over 100 is clearly relating the precise weight 104kg with 100kg. Note in (97) how this contrasts with the directional 100 . . . and up, which is made 22 An anonymous reviewer notes a complication. It appears that under cannot take wide scope with respect to a modal. That is, it fails to display scope ambiguities such as the one in (20) above. For instance, (i) (which is an example given by the reviewer) is odd, since it misses an interpretation where the modified numeral has scope over require. (i)

#John is required to come up with under 6 brilliant ideas.

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R.W.F. Nouwen

felicitous by embedding it under an existential modal. (96)

He weighs over 100 kg. To be precise, he weighs 104 kg.

(97)

a. #He weighs 100 kg and up. b. He is allowed to weigh 100 kg and up.

A potential explanation for why the numeral modifier over lacks a directional/class B sense23 is that the use of prepositions in numeral quantifiers is restricted to prepositions that are vertically oriented. This is connected to the observation of Lakoff & Johnson 1980 that cardinality is metaphorically vertical: more is higher (as in a high number), less is lower (as in a low number). Prepositions in modified numerals follow this metaphor.24 What is interesting about over, however, is that only its locative sense is vertical. Its directional sense, as in (95), rather expresses a mainly horizontal motion. This could explain why there is no class B sense numeral modifier over. Further clues that this analysis is on the right track come from Dutch, where the preposition over lacks a locative sense. (98) (99)

#De wolk hangt over San Francisco. The cloud hangs over San Francisco. De vogel vloog over de brug. The bird flew over the bridge.

Instead of over in (98), boven (above) should be used for locative meanings. (100)

De wolk hangt boven San Francisco. The cloud hangs above San Francisco. ‘The cloud hangs over San Francisco.’

In Dutch, only boven can modify numerals. Over, which lacks a vertical sense, is unacceptable in modified numerals. (101)

Inflatie kan {boven / #over} de 10% zijn. Inflation can {above / over} the 10% be. ‘Inflation can be over 10%’

23 Thanks to Joost Zwarts for discussing this matter with me. 24 Up (to) and under are clearly vertical. Between and from . . . to are compatible with all possible axes.

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I will refrain from attempting to offer further evidence for my suggestion that there is a correspondence between the locative/directional and the A/B distinction. In any case, it should be clear that the set of prepositional quantifiers offers an interesting range of contrasts that support the existence of two classes of modified numerals. To summarise this subsection, I tentatively put forward the following classification for English modified numerals. (102)

Class A (Positive:) more than —, over — (Negative:) fewer than —, less than —, under — (Neutral:) between — and —

(103)

Class B (Positive:) at least —, minimally —, from — (up), — or more (Negative:) at most —, maximally — , up to —, — or fewer, — or less (Neutral:) from — and —

Missing from this classification are the negative comparative quantifiers like no more/fewer than 10. The reason for this is that the occurrence of negation complicates the comparison with other quantifiers. In fact, I think that such quantifiers are best treated as the compositional combination of a class A comparative modifier with a negative differential no. See Nouwen 2008b for the consequences of such a move and for more details on the interpretations available for sentences containing such quantifiers. 6.2 Support for the A/B distinction from a corpus study I now turn to a small corpus study I conducted which supports the division between class A and class B modifiers. Recall that one of the central observations in favour of the distinction connected to contrasts such as (104). Whereas (104a) can be interpreted with respect to a definite actual number of people invited by Jasper, (104b) does not allow such an interpretation and instead is evaluated in relation to what the speaker holds possible. (104)

a. b.

Jasper invited fewer than 100 people. 87, to be precise. Jasper invited maximally 100 people. #87, to be precise.

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R.W.F. Nouwen

I explained this contrast by proposing that upper bound class B quantifiers are indicators of maxima. The indication of the maximum of a single value leads to infelicity. Existential modals, however, introduce a range of (possible) values, which thereby license the application of the maxima indicator. For examples like (104b), where no overt modal is present, the hearer will have to accommodate an interpretation with respect to speaker possibility. Given that ♦-modals licenses the application of an upper bound class B modifier, one would expect, however, that class B modifiers co-occur with an overt modal operator relatively often. I conducted a corpus study to find out whether this expectation is fulfilled. 6.2.1

Method

I used the free service for searching the Corpus of Contemporary American English (COCA, 385 million words, a mix of fiction, science, newspaper and entertainment texts and spoken word transcripts) at americancorpus.org (Davies 2008). For each numeral modifier I took 100 quasi-random25 occurrences of the modifier with a numeral. For each of these cases I examined whether the modified numeral was in the scope of an explicit existential modal operator (such as can, could, might, possibly, allow, etc.) In other words, I only looked at the surface form and only counted the number of cases where a modal expression has a scope relation with a modified numeral. Given the theory presented in this article, the prediction is that this number is significantly higher with class B numerals than with class A expressions. I compared five modifiers: fewer than, under, between, at most and up to. Not all occurrences of these modifiers with a numeral in the corpus were taken into consideration. For instance, (105) was ignored because in this example up to is probably not a constituent.26 That is, this example contains the particle verb to lift up, rather than the verb to lift. (105)

Periodically we’d lift up to 60 kilometers where the temperatures and pressures are more like Earth’s.

I similarly disregarded occurrences of under n where under is a regular preposition rather than a preposition in a role of numeral modifier. (For instance, examples resembling He was known under 2 different names.) 25 ‘Quasi’, since the results are given in chronological order and I would just take the earliest hits. 26 From: “To boldly go. . . ”, Donald Robertson (1994), Astronomy, Vol. 22, Iss. 12; pg. 34, 8 pgs.

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6.2.2

Results

The results, summarised in the table in (106), support the proposal in this article. Here, P is the percentage of occurrences within a existential modal context, within a sample of 100 occurrences of that modifer.27 (106) P

Class A fewer than under 4% 3%

between 4%

Class B at most up to 23% 21%

The corpus thus shows a clear preference for combining class B quantifiers with existential modal operators, as was predicted.28 Whether the data are as clear as (106) for other expressions too remains to be seen. It will be difficult to extend this type of study to other modifiers. Maximally and from. . . to, for instance, were included in the present corpus search, but did not yield enough occurrences to make a meaningful comparison. 6.3 The cross-linguistic generality of the distinction The class A/B distinction is not a peculiarity of the English language. I will suggest in this subsection that, in fact, the distinction is quite general and that languages seem to fill in the two classes in roughly the same way. Dutch, for instance, mirrors the English data perfectly. To illustrate, (107) and (108) shows the A/B distinction in a contrast between comparative and superlative quantifiers. (107)

Een driehoek heeft meer dan 1 zijde. A triangle has more than 1 side.

(108)

#Een driehoek heeft minstens 2 zijdes. A triangle has at least 2 sides.

There are similar contrasts for other numeral modifiers. In a nutshell, the Dutch data suggests the two classes in (109), which is parallel to English.

27 I also counted the number of occurrences in a universal modal context. As would be predicted, this yielded no significant difference between class A and class B modifiers. For all modified numerals, this number was between 1 and 5. 28 The contrast between the Class A and Class B data is significant (χ 2 =41.2, df=1, p = 1.375×10−10 .)

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R.W.F. Nouwen

(109)

Dutch Class A (Positive:) meer dan — (more than), boven de — (above the) (Negative:) minder dan — (fewer/less than), onder de — (under the) (Neutral:) tussen de — en de — (between the. . . and. . . )

(110)

Dutch Class B (Positive:) ten minste —, minstens —, op z’n minst — (at least), vanaf — (from off), zeker — (certain), minimaal — (minimal) (Negative:) ten hoogste —, hoogstens —, op z’n hoogst — (at most),tot — (up to), maximaal — (maximal) (Neutral:) van — tot — (from — to —)

In other languages, we find similar data. For instance, the division between comparative and superlative modifiers appears to be cross-linguistically quite general. In Italian, for instance, the following contrast exists. (111)

Un triangolo ha piú di 1 lato. A triangle has more than 1 side.

(112) #Un triangolo ha almeno 2 lati. A triangle has at least 2 sides. In Chinese, there also exists a superlative form that behaves like a class B modifier. (113) #Sanjiaoxing zui-shao you liang-tiao bian. triangle most-little have 2-CL side On the other hand, there also exists an alternative form resembling English at least, which behaves differently. The form zhi-shao can be used as in a similar way as English at least is in sentences like At least it doesn’t rain!. Despite this parallel to the English superlative modifiers, the example in (114) appears to be fine, which suggests zhi-shao is of type A. (114)

Sanjiaoxing zhi-shao you liang-tiao bian. triangles to-little have 2-CL side

I leave a more detailed investigation of such data for further research. Whatever the outcome, however, the data first and foremost reveal that the type of contrasts that have been the central focus of this paper occur in Chinese and that, thereby, Chinese also appears to have the class A/B distinction.

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Above, I suggested that prepositional numeral modifiers are to be divided in two classes in accordance with the locative/directional distinction that exists for their spatial meanings. The clearest case of a class B directional prepositional modifier in English is up to. In many other languages, one and the same particle is used for indicating spatial, numerical and temporal extremes. (In English, up to cannot be used as a temporal operator, for which until exists.) In Dutch, for instance, the preposition tot has these three functions. Crucially, in all these three domains tot displays class B characteristics. (115) #Een driehoek heeft tot 10 zijdes. A triangle has up to/until 10 sides. (116) #Je auto stond tot hier geparkeerd. Your car stood up to/until here parked. ‘#Your car was parked up to here’ (117)

Je auto mag tot hier geparkeerd worden. Your car may up to/until here parked be. ‘You may park your car up to here’

(118) #Jasper kwam tot middernacht de kamer binnengelopen. J. came up to/until midnight the room inside-walked. ‘#J. entered the room until midnight’ (119)

Jasper mag tot middernacht de kamer binnen komen J. may up to/until midnight the room inside come lopen. walk. ‘J. is allowed to enter the room until midnight’

Similar data exist for German bis (zu), Hebrew ’ad, Catalan fins a, Spanish hasta and Italian fino a. In fact, in Italian it appears that (120) is generally awkward, resisting a reading that connects to speaker’s possibility. However, it becomes acceptable if an overt modal verb is inserted. (120) ??John ha invitato {al massimo / fino a} 50 amici. John has invited {at most / until} 50 friends. (121)

John può invitare {al massimo / fino a} 50 amici. John can invite {at most / until} 50 friends.

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7

Conclusion

The central aim of this article has been to put forward the empirical observation that numeral modifiers come in two classes: those that relate to definite amounts (class A) and those that resist association with definite cardinality (class B). Theoretically, I proposed that underlying this distinction is a difference in the kind of relations numeral modifiers encode: either a simple comparison relation between numbers (class A) or a relation between a range of values and its minimum or maximum (class B). I furthermore showed how this theory can be implemented in a framework where numeral modifiers are treated as degree quantifiers. While there already existed analyses of both type A and type B modifiers, the class difference that was the central focus of this article has not yet been discussed. For the treatment of class A quantifiers in this article I adopted the proposal of Hackl 2001. My account of class B modifiers, on the other hand, is original. It can be compared to two closely related proposals on the semantics of superlative modifiers: Geurts & Nouwen 2007, where superlative modified numerals are proposed to lexically specify modal operators, and Krifka 2007b, where superlative quantifiers are proposed to be speech act modifiers. Both works do not discuss the class A/B distinction, but I take it that both these proposals, in view of the main observations of this article, can be viewed as accounts not just of superlative quantifiers, but of class B members in general. As suggested in section 5, my proposal is in certain respects quite close to Krifka’s. It differs greatly, however, from Geurts & Nouwen 2007 in the way the interaction between modified numerals and modality is accounted for. In a way, the current article as well as Krifka 2007b represent a position where quantifiers lexically specify quite minimal functions, which consequently leads to much of the work being done by pragmatic mechanisms (such as blocking). For the proposal in Geurts & Nouwen 2007, on the other hand, the balance is different in that a much greater burden is placed on semantics. An in-depth comparison of these accounts of class B quantifiers, however, is left for further research. References Aloni, Maria. 2007. Free choice, modals, and imperatives. Natural Language Semantics 15(1). 65–94. doi:10.1007/s11050-007-9010-2. Atlas, Jay David & Stephen C. Levinson. 1981. It-clefts, informativeness, and

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logical form: Radical pragmatics (revised standard version). In Peter Cole (ed.), Radical pragmatics, 1–61. New York: Academic Press. Barwise, John & Robin Cooper. 1981. Generalized quantifiers and natural language. Linguistics and Philosophy 4(2). 159–219. doi:10.1007/BF00350139. Blutner, Reinhard. 2000. Some aspects of optimality in natural language interpretation. Journal of Semantics 17(3). 189–216. doi:10.1093/jos/17.3.189. Breheny, Richard. 2008. A new look at the semantics and pragmatics of numerically quantified noun phrases. Journal of Semantics 25(2). 93–140. doi:10.1093/jos/ffm016. Büring, Daniel. 2008. The least at least can do. In Charles B. Chang & Hannah J. Haynie (eds.), Proceedings of WCCFL 26, 114–120. Somerville, Massachusetts: Cascadilla Press. Corblin, Francis. 2007. Existence, maximality and the semantics of numeral modifiers. In Ileana Comorovski & Klaus von Heusinger (eds.), Existence: Semantics and syntax (Studies in Linguistics and Philosophy 84), Springer. Corver, Norbert & Joost Zwarts. 2006. Prepositional numerals. Lingua 116(6). 811–836. doi:10.1016/j.lingua.2005.03.008. Davies, Mark. 2008. The corpus of contemporary American English (COCA): 385 million words, 1990-present. Available online at http://www. americancorpus.org. von Fintel, Kai & Sabine Iatridou. 2005. What to do if you want to go to Harlem: Anankastic conditionals and related matters. Ms. MIT, available on http://mit.edu/fintel/www/harlem-rutgers.pdf. Geurts, Bart. 2005. Entertaining alternatives: disjunctions as modals. Natural Language Semantics 13(4). 383–410. doi:10.1007/s11050-005-2052-4. Geurts, Bart. 2006. Take five: the meaning and use of a number word. In Svetlana Vogeleer & Liliane Tasmowski (eds.), Non-definiteness and plurality, 311–329. Amsterdam/Philadelphia: Benjamins. Pre-published version available at http://ncs.ruhosting.nl/bart/papers/five.pdf. Geurts, Bart & Rick Nouwen. 2007. At least et al.: the semantics of scalar modifiers. Language 83(3). 533–559. Grice, Paul. 1975. Logic and conversation. In Peter Cole & Jerry L. Morgan (eds.), Syntax and semantics 3: Speech acts, 41–58. New York: Academic Press. Hackl, Martin. 2001. Comparative quantifiers: Department of Linguistics and Philosophy, Massachusetts Institute of Technology dissertation. doi:1721.1/8765. Heim, Irene. 1991. Artikel und Definitheit. In Arnim von Stechow & Dieter

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Wunderlich (eds.), Semantik: Ein internationales Handbuch der zeitgenössischen Forschung, Berlin: de Gruyter. Heim, Irene. 2000. Degree operators and scope. In Proceedings of SALT 10, Ithaca, NY: CLC Publications. Horn, Laurence R. 1984. Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature. In Deborah Schiffrin (ed.), Meaning, form and use in context, 11–42. Washinton: Georgetown University Press. Kamp, Hans. 1973. Free choice permission. Proceedings of the Aristotelian Society 74. 57–74. Kennedy, Christopher. 1997. Projecting the adjective: the syntax and semantics of gradability and comparison: UCSD PhD. Thesis. Kiparsky, Paul. 1973. "Elsewhere" in phonology. In Stephen R. Anderson & Paul Kiparsky (eds.), A festschrift for Morris Halle, 93–106. New York: Holt, Reinhart, & Winston. Kiparsky, Paul. 1983. Word formation and the lexicon. In Proceedings of the 1982 Mid-America Linguistics Conference, 47–78. Lawrence, Kansas: University of Kansas. Krifka, Manfred. 1999. At least some determiners aren’t determiners. In Ken Turner (ed.), The semantics/pragmatics interface from different points of view vol. 1, 257–291. Elsevier. Krifka, Manfred. 2007a. Approximate interpretation of number words: A case for strategic communication. In Irene Vogel & Joost Zwarts (ed.), Cognitive foundations of communication, Amsterdam: Koninklijke Nederlandse Akademie van Wetenschapen. Krifka, Manfred. 2007b. More on the difference between more than two and at least three. Paper presented at University of California at Santa Cruz, available at http://amor.rz.hu-berlin.de/~h2816i3x/Talks/SantaCruz2007. pdf. Lakoff, George & Mark Johnson. 1980. Metaphors we live by. University of Chicago Press. McCawley, James. 1978. Conversational implicature and the lexicon. In Peter Cole (ed.), Syntax and semantics 9: Pragmatics, New York: Academic Press. Nilsen, Øystein. 2007. At least: Free choice and lowest utility. Paper presented at ESSLLI workshop on quantifier modification. Nouwen, Rick. 2008a. Directionality in modified numerals: the case of up to. Semantics and Linguistic Theory 18. doi:1813/13056. Nouwen, Rick. 2008b. Upper-bounded no more: the implicatures of negative comparison. Natural Language Semantics 16(4). 271–295.

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doi:10.1007/s11050-008-9034-2. Nouwen, Rick. 2009. Two kinds of modified numerals. In T. Solstad & A. Riester (eds.), Proceedings of Sinn und Bedeutung 13, Available at http: //www.let.uu.nl/~Rick.Nouwen/personal/papers/sub09.pdf, 15 pages. Nouwen, Rick. 2010a. Two puzzles of requirement. In Maria Aloni & Katrin Schulz (eds.), The Amsterdam Colloquium 2009, Springer. http://www. hum.uu.nl/medewerkers/r.w.f.nouwen/papers/neccsuff.pdf. Nouwen, Rick. 2010b. What’s in a quantifier? In Martin Everaert, Tom Lentz, Hannah de Mulder, Øystein Nilsen & Arjen Zondervan (eds.), The linguistic enterprise: From knowledge of language to knowledge in linguistics (Linguistik Aktuell/Linguistics Today 150), John Benjamins. Pre-published version available at http://www.hum.uu.nl/medewerkers/r.w.f.nouwen/ papers/wiaq.pdf. van Rooij, Robert. 2004. Signalling games select Horn strategies. Linguistics and Philosophy 27(4). 493–527. doi:10.1023/B:LING.0000024403.88733.3f. Schwager, Magdalena. 2005. Exhaustive imperatives. In Paul Dekker & Michael Franke (eds.), Proceedings of the 15th Amsterdam Colloquium, Universiteit van Amsterdam. Solt, Stephanie. 2007. Few more and many fewer: complex quantifiers based on many and few. In Rick Nouwen & Jakub Dotlacil (eds.), Proceedings of the ESSLLI2007 Workshop on Quantifier Modification, . Takahashi, Shoichi. 2006. More than two quantifiers. Natural Language Semantics 14(1). 57–101. doi:10.1007/s11050-005-4534-9. Umbach, Carla. 2006. Why do modified numerals resist a referential interpretation? In Proceedings of SALT 15, 258 – 275. Cornell University Press. Zimmermann, Thomas Ede. 2000. Free choice disjunction and epistemic possibility. Natural Language Semantics 8(4). 255–290. doi:10.1023/A:1011255819284.

Dr. R.W.F. Nouwen Utrecht Institute for Linguistics OTS Janskerkhof 13, NL-3512 BL Utrecht, the Netherlands [email protected]

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Iffiness∗ Anthony S. Gillies Rutgers University

Received 2009-06-24 / First Decision 2009-08-07 / Revised 2009-09-13 / Second Decision 2009-09-21 / Revised 2009-10-14 / Accepted 2009-11-18 / Final Version Received 2010-01-17 / Published 2010-02-01

Abstract How do ordinary indicative conditionals manage to convey conditional information, information about what might or must be if such-and-such is or turns out to be the case? An old school thesis is that they do this by expressing something iffy: ordinary indicatives express a two-place conditional operator and that is how they convey conditional information. How indicatives interact with epistemic modals seems to be an argument against iffiness and for the new school thesis that if -clauses are merely devices for restricting the domains of other operators. I will make the trouble both clear and general, and then explore a way out for fans of iffiness.

Keywords: indicative conditionals, epistemic modality, if-clauses, conditionals, strict conditionals, dynamic semantics

1 An iffy thesis One thing language is good for is imparting plain and simple information: there is an extra chair at our table or we are all out of beer. But — happily — we ∗ This paper has been around awhile, versions of it circulating since 05.2006 and accruing a lot of debts of gratitude along the way. Chris Kennedy, Jim Joyce, Craige Roberts, Josef Stern, Rich Thomason, audiences at the Rutgers Semantics Workshop (October 2007), the Michigan L&P Workshop (Lite Version, November 2007), the Arché Contextualism & Relativism Workshop (May 2008), the University of Chicago Semantics & Philosophy Language Workshop (March 2009), and — especially (actually, especially∗ ) — Josh Dever, David Beaver, Kai von Fintel, Brian Weatherson, and the anonymous S&P referees have all done their best trying to save me from making too many howlers. But too many is surely context dependent, so caveat emptor. This research was supported in part by the National Science Foundation under Grant No. BCS-0547814. ©2010 A. S. Gillies This is an open-access article distributed under the terms of a Creative Commons NonCommercial License (creativecommons.org/licenses/by-nc/3.0).

A. S. Gillies

do not only exchange plain information about tables, chairs, and beer mugs. We also exchange conditional information thereof: if we are all out of beer, it is time for you to buy another round. That is very useful indeed. Conditional information is information about what might or must be, if such-and-such is or turns out to be the case. My target here has to do with how such conditional information manages to get expressed by indicative conditionals (not so called because anyone thinks that’s a great name but because no one can do any better). Some examples: (1)

a. b. c.

If the goat is behind door #1, then the new car is behind door #2. If the No. 9 shirt regains his form, then Barça might advance. If Carl is at the party, then Lenny must also be at the party.

Each of these is an ordinary indicative, two of them have epistemic modals in the consequent clause, and all of them express a bit of ordinary conditional information.1 What I am interested in is how well the indicatives play with the epistemic modals. What these examples say is plain. Take (1b). This says that — within the set of possibilities compatible with the information at hand — among those in which the star striker regains his form, some are possibilities in which Barça advance. Or take (1c). It says something about the occurrence of Lenny-is-at-the-party possibilities within the set of Carl-is-at-the-party possibilities — that, given the information at hand, every possibility of the latter stripe is also of the former stripe. So what sentences like these say is plain. How they say it isn’t. That’s my target here: How is it that the if s in our examples manage to express conditional information and do so in a way compatible with how they play with epistemic modals? The simplest story about how the if s in our examples manage to express conditional information is that each of them expresses the information of a conditional. Which is to say: what these conditional sentences mean can be read-off the fact that if expresses a conditional operator. Let’s say that a story about if is iffy iff it takes if to express a bona fide operator, a bona fide iffy operator (that is, a conditional operator properly so called), and the same bona fide iffy operator in each of the sentences in (1). We will have to sharpen that up by saying what it means for an operator to be a conditional 1 We ought to be careful to distinguish between conditional sentences (sentences of natural language), conditional connectives (two-place sentential connectives in some regimented language that may serve to represent the logical forms of conditional sentences), and conditional operators (relations that may serve as the denotations of conditional connectives).

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operator properly so called. But that is the gist: iffiness — a.k.a. the operator view — is the thesis that ordinary indicative conditionals manage to express conditional information because if expresses a conditional operator. Depending on your upbringing, the operator view of if may well seem either obvious or obviously wrongheaded. More on that below. Either way, it is a hard line to maintain: how conditional sentences play with epistemic modals seems to refute it. A seeming refutation isn’t quite the same as an actual one, though. I will show that the refutation isn’t quite right by showing how fans of iffiness can account for what needs accounting for. But before showing how the operator view can be made to account for how if s and modals interact I want to make it look for all the world like it can’t be done. 2

Doom and how to avoid it (sketches thereof)

The operator view is an old school story about indicatives. It says that if expresses some relation between the (semantic value of the) antecedent and consequent. So if takes its place alongside other connectives and expresses an operator — the same operator — on the semantic values of the sentences it takes as arguments.2 To tell a story like this we have to say exactly what that operator is. But not just any telling will do. I want to show how our simple examples cause what looks like insurmountable trouble (doom, even) for any version of the operator view. Here’s an informal sketch of the trouble, what rides on it, and how — eventually — we can and ought to get out of the mess. Take this sketch as a promissory note that a formally precise version of all that can be given; the rest of the paper makes good on that. Suppose if expresses the limit case conditional operator of material implication. Iffiness requires that in sentences like (1b) and (1c) either the epistemic modals outscope the conditionals or the conditionals outscope the modals. Neither choice gets the truth conditions right if the conditional operator is the horseshoe. That’s easy to see (and well known).3 Linguists grow up on arguments like that. That is one reason why even though the operator view is the first thing a logician thinks of, it is the last thing a linguist does. 2 If is a little word with a big history — a big history that we can’t adequately tour here. But there are guides for hire: for instance, Bennett (2003) and von Fintel (2009). 3 The material conditional analysis of ordinary indicatives is defended (in somewhat different ways) by, for example, Grice (1989), Jackson (1987), and Lewis (1976). A textbook version of this “no-scope” argument that has the horseshoe analysis as its target appears in von Fintel & Heim 2007.

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But (as I’ll show) this very same trouble holds no matter what conditional operator an iffy story says if expresses. To see that requires two things. First, we need to say in a precise way what counts as a conditional operator (Section 4). Given some pretty weak assumptions iffiness requires that if means all (well, all relevant). Second, there are some characteristic Facts about how indicatives and epistemic modals interact (Section 5). These neatly divide: there are some consistency facts and there are some intuitive entailment facts. The operator view requires that either the conditionals outscope the modals or the modals outscope the conditionals. Something general then follows: no matter what conditional operator we say if expresses, one scope choice is ruled out by the consistency facts, the other by the entailments (Section 6). That seems to be bad news for any fan of any version of the old school operator view. And there seems to be more bad news in the offing since the operator view isn’t the only game in town (in some circles, it’s a game played only on the outskirts of town). The anti-iffiness rival — a.k.a. the restrictor view — is a new school approach. It embraces Kratzer’s thesis that if is not a connective at all: it doesn’t express an operator, a fortiori not an iffy operator, and a fortiori not the same iffy operator in each of our example sentences it figures in.4 Instead, says the restrictor analysis, if simply restricts other operators. In the cases we will care about, it restricts (possibly covert) epistemic modals. The restrictor view makes embarrassingly quick work of the data that spells such trouble for the operator view (Section 7). But the success of the restrictor analysis is no argument against Chuck Taylors and skyhooks tout court. That’s because there are old school stories that say that if expresses a strict conditional operator over possibilities compatible with the context, and that it can do all the restricting that needs doing (Sections 8). Once we see just how, we can look back and see more 4 The restrictor view gets its inspiration from Lewis’s (1975) argument that certain if s (under adverbs of quantification) cannot be understood as expressing some conditional but rather serve to mark an argument place in a polyadic construction. Kratzer’s thesis is that this holds for if across the board. The classic references are Kratzer 1981, 1986. There is another rival, too: some take if to be an operator, but an operator that does not (when given arguments) express a proposition (Adams 1975; Gibbard 1981; Edgington 1995, 2008). Instead, they say, if s express but do not report conditional beliefs on the part of their speakers. I will ignore this view here: it doesn’t really start off as the most plausible candidate, the trouble I make here about how if s and modals interact makes it less plausible not more, and it will just take us too far afield.

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clearly what is at stake in the difference between new school and old, why iffiness is worth pursuing (Section 9), and how this version of the old school story relates to recent dynamic semantic treatments (Section 10). 3

Ground rules

Let’s simplify. Assume that meanings get associated with sentences by getting associated with formulas in an intermediate language that represents the relevant logical forms (lfs) of them. Thus a story, old school or otherwise, has to first say what the relevant lfs are and then assign those lfs semantic values. We will begin with an intermediate language L that has a conditional connective that will serve to represent the lfs of ordinary indicatives. So let L be generated from a stock of atomic sentence letters, negation (¬), and conjunction (∧) in the usual way. But L also has the connective (if ·)(·), and the modals must and might. What I have to say can be said about an intermediate language that allows that the modals mix freely with the formulas of the non-modal fragment of L but restricts (if ·)(·) so that it takes only non-modal sentences in its first argument. So assume that L is such an intermediate language. When these restrictions outlive their utility, we can exchange them for others.5 Iffiness requires that the if of English expresses something properly iffy. That leaves open just which conditional operator we say that the if of English means. But our choices here are not completely free, and some ground rules will impose some order on what we may say. These will constrain our choice by saying what must be true for a conditional operator to be rightfully so called. But before getting to that, I’ll start with what I will assume about contexts. First, a general constraint: assume that truth-values — for the if s and the modals (when we come to that), as well as for the boolean fragment of L — are assigned at an index (world) i with respect to a context. I will assume that W , the space of possible worlds, is finite. Nothing important turns on this, and it simplifies things. For the fragment of L with no modals and no if s, contexts are idle. It will be the job of the modals to quantify over sets of live possibilities and the job 5 Conventions: p, q, r , . . . range over sentences of L (subject to our constraints on L); i, j, k, . . . range over worlds; and P , Q, R, . . . range over sets of worlds. And let’s not fuss over whether what is at stake is the ‘if ’ of English or the ‘if ’ of L; context will disambiguate.

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of contexts to select these sets of worlds over which the modals do their job. What I want to say can be said in a way that is agnostic about just what kinds of things contexts are: all I insist is that, given a world, they determine a set of possibilities that modals at that world quantify over.6 The functions doing the determining need to be well-behaved. Given a context c — replete with whatever things contexts are replete with — an epistemic modal base C determined by it is just what we need: Definition 3.1 (modal bases). Given a context c, C is a modal base (for c) only if: C = λi. j : j is compatible with the c-relevant information at i Since the only context dependence at stake here will be dependence on such bases, we can get by just as well by taking them to go proxy for bona fide contexts, granting them the honorific “contexts”, and relativizing the assignment of truth-values to index–modal base pairs directly. So we’ll be saying just which function ·C,i : L → {0, 1} is, where C represents the relevant contextual information. No harm comes from that, and it makes for a prettier view.7 But not just any function from indices to sets of indices will do as a (proxy) context. So we constrain C’s accordingly, requiring that they are well-behaved — that is, reflexive and euclidean: 6 The problems and prospects for iffiness are independent of just whose information in a context — speaker, speaker plus hearer, just the hearer, just the hearer’s picture of what the speaker intends, and so on — counts for selecting the domains for the modals to do their job, and whether or not that information is information-at-a-context at all. So let’s keep things simple here. If you’d rather be reading a paper which has these (and other) complexities at the forefront, see von Fintel & Gillies 2007, 2008a,b and the references therein. 7 Three comments. First: take ·C to be shorthand for i : ·C,i = 1 . If p’s denotation 0 is invariant across contexts – if pC = pC no matter the choice for C and C 0 – let’s agree to conserve a bit of (virtual) ink and sometimes omit the superscript: so, e.g., the if s I am focusing on here have non-modal antecedents, and so those antecedents will be context-invariant. Second: it’s a little misleading to say that the only context dependence is dependence on modal bases since we will want to allow the possibility that what worlds are relevant to an if at a world can vary across contexts. But, in fact, we can (and will) still leave room for that possibility by constraining how contexts and the sets of if -relevant possibilities relate. Third: if I had different ambitions, we couldn’t simplify quite like this. If the interaction at center stage were how if s and quantifiers interact, or if the modals in the if /modal interaction were deontic, then we’d want our contexts to rightly characterize the kind of information at stake and taking them to determine sets of possibilities compatible with what is known would not do. But my ambitions here aren’t different from what they are.

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Definition 3.2 (well-behavedness). C is well-behaved iff: i. i ∈ Ci ii. if j ∈ Ci then Ci ⊆ Cj

(reflexiveness) (euclideanness)

C represents a (proper) context only if it is well-behaved. Observation 3.1. If C is well-behaved then Ci is closed — well-behavedness implies that if j ∈ Ci , then Cj = Ci . Proof. Suppose j ∈ Ci . Consider any k ∈ Cj . Since C is euclidean and j ∈ Ci , Ci ⊆ Cj . Since C is reflexive, i ∈ Ci and thus i ∈ Cj . Appeal to euclideanness again: since k ∈ Cj , Cj ⊆ Ck ; but i ∈ Cj and so i ∈ Ck . And once more: since i ∈ Ck , Ck ⊆ Ci . And now reflexiveness: k ∈ Ck and so k ∈ Ci . (The inclusion in the other direction just is euclideanness.) Gloss Ci as the set of live possibilities at i in C. That Ci is closed means that the live possibilities in Ci do not vary across worlds compatible with C.8 4 Conditional operators By saying something about what must be true of an operator for it to be a conditional operator properly so called we thereby say something about what must be true for a story to be iffy. Taking if to express a bona fide conditional operator requires, minimally, two things. Thing one: it requires, in the cases we’ll care about, that if such-andsuch, then thus-and-so doesn’t take a stand on whether such-and-such is the case and so conditionals like that are typically happiest being uttered in circumstances in which such-and-such is compatible with the context as it stands when the conditional is issued. I will take this as a definedness condition on the semantics for our conditional connective. Definition 4.1 (definedness). if p q C,i is defined only if p is compatible with Ci . This is a weak constraint.9 8 Given euclideaness, we could get by with different assumptions on C to the same effect. But reflexiveness is a constraint it makes sense to want since, when we come to them, epistemic modals — what might or must be in virtue of what is known — in a given context will quantify over the set of possibilities compatible with that context. 9 The motivating idea isn’t novel (see, e.g., Stalnaker 1975): if it’s ruled out that p in C, and you want to say something conditional on p in C, then you should be reaching for a

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Thing two: it requires that if expresses a relation between antecedent and consequent. Whether if such-and-such, then thus-and-so is true depends on whether the relevant worlds at which such-and-such is true bears the right relationship to the worlds where thus-and-so is true. Take an arbitrary conditional like if p q at i, in C. And let P and Q be the sets of antecedent and consequent possibilities so related by the if . Now we need to zoom in on the relevant worlds in P . So let Di be the set of if -relevant worlds at i. For if to express a conditional operator properly so called, its denotation must be a relation R between P -together-with-the-relevant-possibilities-Di and Q. Di is the set of possibilities relevant for the if at i. Since Di is a function of i, different worlds may be relevant for one and the same if when evaluated at different worlds. But, depending on your favorite theory, Di may be a function of more than just i: it may be a function of i, of C, of p, of q, or of your kitchen sink. We will return to that shortly. No matter your favorite theory, we can still ex ante agree to this much: i is always among the possibilities relevant for an if at i, and only possibilities compatible with the context are relevant for an if at i. That is: Di is the set of if -relevant worlds at i only if i ∈ Di and Di ⊆ Ci . The first requirement is a platitude: the facts at a world are always relevant to whether an indicative at that world is true. The second means that an indicative in a context is supposed to say something about the possibilities compatible with that context. Beyond this, what your favorite theory implementing the operator view says about Di may vary because what stories say counts as an if -relevant possibility varies. But what does not vary is that all such stories determine Di in a pretty straightforward way and so the denotation they assign to if can be put as a relation between the relevant antecedent possibilities and the consequent possibilities. Three examples: Example 1 (variably strict conditional). Suppose your favorite story takes if to be a variably strict conditional based on some underlying ordering of possibilities (Stalnaker 1968; Lewis 1973). For every world i, let i be an ordering of worlds, a relation of comparative similarity (at least) weakly centered on i. Given a conditional if p q at i in C, you will want to identify Di with the set of possibilities no more dissimilar than the most similar p-world to i, restricted by Ci . Example 2 (strict conditional). Suppose your favorite Lewis-inspired story counterfactual not an indicative. That can be implemented in any number of ways, including making it a presupposition of if -clauses (see, e.g., von Fintel 1998a).

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Iffiness

comes not from D.K. but from C.I. You thus take if to be strict implication (restricted to C). But that, too, can be put in terms of orderings: your ordering i is universal, treating all worlds the same. Whence it follows that — since the nearest p-world is the same distance from i as is every world — taking Di to be the set of possibilities no further from i as the nearest p-world amounts to taking Di to be the set of all worlds W , restricted by Ci . Example 3 (material conditional). Suppose you are smitten by truth-tables, and your favorite incarnation of the operator view is the material conditional story. Equivalently: you will have a maximally discerning ordering (every world an island) and take Di to be the set of closest worlds to i simpliciter according to that ordering. For an if at i you will thus take Di to be {i}. (For an if at some other world j, even an if with the same antecedent and consequent as the one at i, take Dj to be j .) Summing this all up: even before taking a stand on just what relation between relevant antecedent possibilities and consequent possibilities that if must express in order to express a conditional operator properly so called, we know that it must still express such a relation. So let’s insist that we can put things that way, parametric on just how Di gets picked out and so parametric on what counts as “relevant” antecedent possibilities and so parametric on the details of your favorite theory: Definition 4.2 (relationality). (if ·)(·) expresses a conditional only if its truth conditions can be put this way: if defined, if p q C,i = 1 iff R(Di ∩ P , Q) for some set of possibilities Di and relation R, where i ∈ Di and Di ⊆ Ci . But not just any relation between Di ∩ P and Q counts as a conditional relation properly so called. I insist on three minimal constraints on R, for any P and Q: (i) that Di ∩ P imposes some order on the set of Q’s so related; (ii) that Q matters to whether the relation holds; and (iii) that — plus or minus just a bit — only the relationship between the possibilities in Di ∩ P and the possibilities in Q matter to whether the relation holds. These are not controversial, but do bear some unpacking.10 First, the order imposed by the antecedent: 10 This general way of characterizing conditionality is not new: both the assumptions and the results here are inspired by van Benthem’s (1986: §4) investigation of conditionals as generalized quantifiers. There are, however, differences between his versions and mine.

4:9

A. S. Gillies

Definition 4.3 (order). R is orderly iff: i. R(Di ∩ P , P ) ii. R(Di ∩ P , Q) and Q ⊆ S imply R(Di ∩ P , S) iii. R(Di ∩ P , Q) and R(Di ∩ P , S) imply R(Di ∩ P , Q ∩ S) R is something (if ·)(·) at i could mean only if it is orderly. Such R’s are precisely those for which the set of Q’s a Di ∩ P bears it to form a filter that contains P .11 That is an aesthetic reason for constraining R this way. Such R’s also jointly characterize the basic conditional logic.12 The relational properties correspond to reflexivity, right upward monotonicity, and conjunction. That is another — only partly aesthetic — reason for constraining them this way. Second, R must care about consequents. This is just the requirement that conditional relations, like quantifiers, be active: Definition 4.4 (activity). R is active iff: if Di ∩ P 6= then there is a Q and Q0 such that: R(Di ∩ P , Q) but not R(Di ∩ P , Q0 ) R is something (if ·)(·) at i could mean only if it is active. This means that R cares about how Di ∩ P relates to Q. So long as there are some relevant P -possibilities, there have to be some Q’s for which the relation holds and some for which it doesn’t. And finally: R is a relation between the sets of possibilities. Thus if R holds at all between P -plus-the-relevant-possibilities-Di and the consequentpossibilities Q, R will hold between any two sets of things that play the right possibility role. Intrinsic properties of worlds don’t count for or against the relation holding. The idea is simple, the execution harder. That is because I have allowed you to choose your favorite iffy theory, and what goes into determining Di depends on your choice. What is important is this: suppose your favorite story posits some additional structure to modal space to find just the right worlds which, when combined with P , gives the set of worlds relevant for evaluating Q. That means that your favorite story cares about how P relates to Q but also about the distribution of the worlds in P compared to the distribution in Q — for 11 It follows straightaway that orderly R’s are fully reflexive in the sense that R(Di ∩ P , Di ∩ P ). 12 See Veltman 1985 for a proof.

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Iffiness

example, perhaps insisting that it is the closest worlds in P to i that must bear R to Q. If we systematically swap possibilities for possibilities in a way that preserves the relevant structure, then the conditional relation ought to hold pre-swapping iff it holds post-swapping. And mutatis mutandis for Di : since once the posited structure does its job determining Di , then any systematic swapping of possibilities that leaves the domain untouched should also leave the conditional relation untouched.13 Where π is such a mapping and P a set of worlds, let π (P ) be the set of worlds i such that π (j) = i for some j ∈ P . Then: Definition 4.5 (quality). R is qualitative iff: R(Di ∩ P , Q) implies R(π (Di ∩ P ), π (Q)) R is something (if ·)(·) at i could mean only if it is qualitative. This does generalize the familiar constraint on quantifiers — it allows conditional operators to care about both the relationship between P and Q and also where the satisfying worlds are. If i is the universal ordering then this requirement reduces to the more familiar quantitative one (restricted to Ci ). And if Di = {i}, it trivializes. I am insisting that a story is iffy only if the truth conditions for an indica tive if p q at i in Ci can be put as a relation between R between Di ∩ P and Q. And we have insisted that the relation be constrained in sensible ways — it must impose some order on sets of consequent possibilities, it must care about consequents, and it must not care about the intrinsic properties of possibilities. Each example of an instance of the operator view above — variably strict, strict, and material conditionals — lives up to these constraints. Still, it seems like for all we have said it is possible to take the conditional to be true just in case most/many/several/some/just the right possibilities in Di ∩ P are in Q. But that is not so: given our constraints, if must mean all.14 13 This is the natural extension of the familiar requirement that quantifiers be quantitative: for Q to be a quantifier (with domain E) it must be that QE (A, B) iff QE (f (A), f (B)) where f is an isomorphism of E. Once we have structure to our domain, this will not do. The more general constraint is then to require that Q be invariant under O-automorphisms of the domain, where O is the ordering that imposes the posited structure. We can get by with slightly less: namely, stability under Di -invariant automorphisms. 14 Well, all relevant. This was first proved by van Benthem — see, e.g., van Benthem 1986. The version I give is simpler (we’re ignoring the infinite case) and a bit more general (slightly weaker assumptions); the proof is based on one in Veltman 1985, but generalizes it slightly.

4:11

A. S. Gillies

Observation 4.1. Assume R is a conditional relation properly so called. Then R(Di ∩ P , Q) iff Di ∩ P ⊆ Q. Proof. I care about the left-to-right direction. Suppose — for reductio — that R(Di ∩ P , Q) but Di ∩ P 6⊆ Q. What we’ll see is: (i) R(Di ∩ P , P ∩ Q); (ii) the world that witnesses that Di ∩ P 6⊆ Q can be exploited (by quality) to show that no world in P ∩ Q plays a role in R(Di ∩ P , P ∩ Q) holding — from which it follows that R(Di ∩ P , ); (iii) from which it follows that Di ∩ P must be empty — a contradiction. (i): By hypothesis R(Di ∩ P , Q). By order it follows that R(Di ∩ P , P ) and hence that R(Di ∩ P , P ∩ Q). (iia): Claim: Di ∩ P ∩ Q 6= . Proof of Claim: Assume otherwise. order guarantees that R(Di ∩ P , Di ∩ P ). By hypothesis R(Di ∩ P , Q), and so by order R(Di ∩ P , Di ∩ P ∩ Q). Applying the assumption that Di ∩ P ∩ Q = : R(Di ∩ P , ). Appeal to order again and we have that R(Di ∩ P , S) for any S. But then Di ∩ P must be empty (activity), contradicting the assumption that Di ∩ P È Q and proving the Claim. (iib): Let j be a witness to Di ∩ P 6⊆ Q. So j ∈ Di ∩ P but j 6∈ Q. Now pick any confirming instance k — that is, any k ∈ Di ∩ P ∩ Q — and let π be the mapping that swaps k and j and leaves all else untouched:

• π (j) = k • π (k) = j • π (i) = i for every i 6∈ j, k By (i) R(Di ∩ P , P ∩ Q). Hence, by quality, R(π (Di ∩ P ), π (P ∩ Q)). But π doesn’t affect Di ∩ P . So: R(Di ∩ P , π (P ∩ Q)). That is: R holds between Di ∩ P and both P ∩ Q and π (P ∩ Q). Hence — by order — it holds also between Di ∩ P and their intersection: R(Di ∩ P , (P ∩ Q) ∩ π (P ∩ Q)). But π (P ∩ Q) = ((P ∩ Q) \ {k}) ∪ j , so their intersection is (P ∩ Q) \ {k}. So: R(Di ∩P , (P ∩Q)\{k}). Which is to say that k is irrelevant for R’s holding. But k was any world in Di ∩ P ∩ Q, so finiteness plus order implies R(Di ∩ P , ). (iii): Appeal to order again: since R(Di ∩ P , ), it holds that for any S whatever R(Di ∩ P , S). Whence, by activity, it follows that Di ∩ P = . And that contradicts the assumption that Di ∩ P 6⊆ Q. The intuitive version is just this: if R holds between Di ∩ P and Q then the former must be included in the latter. That is because if things didn’t go that way then the witnessing counterexample world could play the role of any one of the confirming worlds. But that would mean that confirming worlds

4:12

Iffiness

play no role. Nothing like that could be something a conditional properly so called could mean. So Di ∩ P must be included in Q after all. 5 Three facts Iffiness requires that if is a conditional connective that expresses a conditional operator, and that pretty much means that if has to mean all. It requires that no matter what other operators we might find in its neighborhood. That spells trouble because of three simple Facts about how indicative conditionals and epistemic modals play together.15 I have lost my marbles. I know that just one of them — Red or Yellow — is in the box. But I don’t know which. I find myself saying things like: (2)

Red might be in the box and Yellow might be in the box. So, if Yellow isn’t in the box, then Red must be. And if Red isn’t in the box, then Yellow must be.

Conjunctions of epistemic modals like Red might be in the box and Yellow might be in the box are especially useful when the bare prejacents partition the possibilities compatible with the context. The first fact is simply that if s are consistent with such conjunctions of modals. Fact 1 (consistency). Suppose S1 and S2 partition the possibilities compatible with the context. Then the following are consistent: i. might S1 and might S2 ii. if not S1 , then must S2 ; and if not S2 , then must S1 15 Three notes about the Facts. First: “Facts” may be laying it on a little thick. The judgments are robust, and the costs high for denying the generalizations as I put them. That’s all true even if what we may say about them is a matter for disputing. But it does not much matter: what I really care about is three characteristic seeming facts about if s, mights, and musts that at first blush look like the kind of thing our best story ought to answer to. So let’s agree to take them at face value and see where that leads. Later, if your English breaks with mine or if your old school pride overwhelms, you can deny the Facts or explain them away as your preferences dictate. Second: the Facts may seem eerily familiar. They are not far removed from the sorts of examples of the interplay between adverbs of quantification and if -clauses in Lewis 1975 and Kratzer 1986. That is no coincidence, as we’ll see (briefly) in Section 7. Third: since the operator view isn’t the only game in town and since predicting the Facts is something any story (old school or otherwise) must do, we should state the Facts in a way that is agnostic on the iffy thesis. So the Facts characterize what is true of sentences in (quasi-)English, not necessarily what is true of their lfs in our regimented intermediate language.

4:13

A. S. Gillies

I do not know whether Carl made it to the party. But wherever Carl goes, Lenny is sure to follow. So if Carl is at the party, Lenny must be — Lenny is at the party, if Carl is. We just glossed an if with a commingling epistemic must by a bare if with no (overt) modal at all. Thus: (3)

a. b.

If Carl is at the party, then Lenny must be at the party. ≈ If Carl is at the party, then Lenny is at the party.

This pair has the ring of (truth-conditional) equivalence. Fact 2 below records that. But there are also arguments for thinking that the truth-value of (3a) should stand and fall with the truth-value of (3b). For suppose that such if s validate a deduction theorem and modus ponens, and that must is factive.16 The left-to-right direction: assume that (3a) is true. And consider the argument: (4)

If Carl is at the party, then Lenny must be at the party. Carl is at the party. So: Lenny is at the party.

The first two sentences — intuitively speaking — entail the third. And that is pushed on us by the assumptions: from the first two sentences we have (by modus ponens) that Lenny must be at the party, which by factivity entails Lenny is at the party. Apply the deduction theorem and we have that If Carl is at the party, then Lenny must be at the party entails If Carl is at the party, then Lenny is at the party. Since we have assumed that (3a) is true, it follows that (3b) must be. There are spots to get off this bus to be sure — by denying either modus ponens or by denying the factivity of must — but those costs are high.17 The right-to-left direction: assume that (3b) is true and consider: 16 Remember that, for now, we are dealing with properties of sentences of (quasi-)English not properties of those sentences’ lfs in some regimented language. The argument here isn’t meant to convince you of Fact 2, it is meant to make some of the costs of denying the data vivid. Geurts (2005) also notes that bare conditionals and their must-enriched counterparts are “more or less equivalent”. 17 You have to troll some pretty dark corners of logical space for deniers of modus ponens, but that’s not true for deniers of the factivity of must. That view has something of mantra status among linguists (philosophers are surprised to hear that). Mantra or not, it is wrong. For an all-out attack on it see von Fintel & Gillies 2010. Here is just one sort of consideration: if must p didn’t entail p (because must is located somewhere below the top of the scale of epistemic strength), then you’d expect must to combine with only in straightforward ways the way might can:

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Iffiness

(5)

If Carl is at the party, then Lenny is at the party. Carl is at the party. So: Lenny must be at the party.

This is as intuitive an entailment as we are likely to find. Whence it follows by the deduction theorem that If Carl is at the party, then Lenny is at the party on its own entails If Carl is at the party, then Lenny must be at the party. So if (3b) is true so must be (3a): that’s why the former seems to gloss the latter. Fact 2 (if/must). Conditional sentences like these are true in exactly the same scenarios: i. if S1 , then must S2 ii. if S1 , then S2 The glossing that this pattern permits is a nifty trick. But that is only half the story since if can also co-occur with epistemic might. The interaction between if and might is different and underwrites a different glossing. Alas, my team are not likely to win it all this year. It is late in the season and they have made too many miscues. But they are not quite out of it. If they win their remaining three games, and the team at the top lose theirs, my team will be champions. But our last three are against strong teams and their last three are against cellar dwellers. Still, my spirits are high: if we win out, we might win it all. Put another way, within the (relevant) my-team-wins-out possibilities — of which there are some — lies a my-teamwins-it-all possibility; there is a my-team-wins-out possibility that is a myteam-wins-it-all possibility. But that is just to say that there are (relevant) my-team-wins-out-and-wins-it-all possibilities. Maybe not very many, and maybe not so close, but some.18 Apart from keeping hope alive, the example also illustrates that we can gloss an indicative with a co-occurring epistemic might by a conjunction under the scope of might: (6)

(i)

a. b.

If my team wins out, they might win it all. ≈ It might turn out that my team wins out and wins it all.

a. I didn’t say it is raining, I only said it might be raining. b. #I didn’t say it is raining, I only said it must be raining.

But it doesn’t. 18 For the record: the Cubs. Please don’t bring it up.

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A. S. Gillies

That gloss sounds pretty good. And for good reason: conjunctions that you would expect to be happy if the truth of (6a) and (6b) could come apart are not happy at all: (7)

a. #If my team wins out, they might win it all; moreover, they can’t win out and win it all. b. #It might turn out that my team wins out and wins it all, and, in addition there’s no way that if they win out, they might win it all.

That gives us the third Fact about how if s play with modals.19 Fact 3 (if/might). Sentences like these are true in exactly the same scenarios: i. if S1 , then might S2 ii. it might be that [S1 and S2 ] It’s now a matter of telling some story, iffy or otherwise, that answers to these Facts. Old school operator views will have trouble with them; the new school restrictor view predicts them trivially. 6

Scope matters

The operator view takes if to express an operator, an iffy operator, and the same iffy operator no matter whether we have a co-occurring epistemic modal or not and no matter whether the modal is must or might. In cases where there is a modal, scope issues have to be sorted out. Take a sentence of the form (8)

If S1 then modal S2

19 There is a wrinkle: Fact 3 implies that if S1 , then might S2 is true in just the same spots as if S2 , then might S1 . Seems odd: (i)

a. b.

If I jump out the window, I might break a leg. If I break a leg, I might jump out the window.

The first is true, the second an overreaction. I intend, for now, to sweep this under the same rug that we sweep the odd way in which Some smoke and get cancer/Some get cancer and smoke don’t feel exactly equivalent even though Some is a symmetric quantifier if ever there was one. (The rug in question seems to be the tense/aspect rug; similar considerations drive von Fintel’s (1997) discussion of contraposition of bare conditionals.)

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Iffiness

and let S10 (S20 ) be the L-representation for sentence S1 (S2 ), and modal the L-representation for modal. We have a short menu of options for the relevant lf for such a sentence — either the narrowscoped (9a) or the widescoped (9b):

(9)

a. b.

if S10 modal S20 modal if S10 S20

If you want to put your lfs in tree form, be my guest: opting for narrowscoping means opting for sisterhood between modal and S2 ; opting for widescoping means opting for sisterhood between modal and if S1 then S2 . The trouble for the operator view is that, since if has to express inclusion, neither choice will do. One choice for scope relations seems ruled out by consistency (Fact 1), the other by if/must (Fact 2) and if/might (Fact 3). To put the trouble precisely, we need one more ground rule. Contexts, we said, have the job of determining the domains the modals quantify over. Modals, I’ll assume, do their job in the usual way by expressing their usual quantificational oomph over those domains: must (at i, with respect to C) acts as a universal quantifier, and might as an existential quantifier, over Ci . Definition 6.1 (modal force). i. might pC,i = 1 iff Ci ∩ pC 6= ii. must pC,i = 1 iff Ci ⊆ pC Now suppose we plump for narrowscoping. Then, given the ground rules, we cannot predict the consistency of the likes of (2) and that means that we cannot square iffiness with Fact 1. That’s true no matter how you fill in the particulars of the iffy story. Here is the narrowscoped analysis of my lost marbles. We have a modal and two indicatives: (10)

a. b. c.

Red might be in the box and Yellow might be in the box. might p ∧ might q If Yellow isn’t in the box, then Red must be. if ¬q must p If Red isn’t in the box, then Yellow must be. if ¬p must q

Any good story has to allow that the bundle of if s in (10b) and (10c) is consistent with the conjunction in (10a). But, assuming narrowscoping,

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A. S. Gillies

this — even without taking a stand on how we choose Di and so without taking a stand on what counts as the set of if -relevant worlds — seems to be beyond what can be delivered by any version of the operator view. Observation 6.1. Suppose p and q partition the possibilities in C and that (10a) is true. Then the (narrowscoped) sentences in (10) can’t all be true. Proof. Suppose otherwise — that the regimented formulas in L are all true at a live possibility, say i, with respect to C. Just one of my marbles is in the box. So any world in Ci is either a p-world or a q-world, but not both; C is well-behaved, so i ∈ Ci . That leaves two cases. case 1: i ∈ ¬q. By hypothesis if ¬q must p C,i = 1, and so Di ∩ ¬qC ⊆ must pC . Since i ∈ Di , it then follows that i ∈ must pC — which is to say must pC,i = 1. Thus Ci has only p-worlds in it. But that is at odds with the second conjunct of (10a): that might q is true at i guarantees a q-world, hence a ¬p-world, in Ci . case 2: i ∈ ¬p. By hypothesis if ¬p must q C,i = 1, and so Di ∩ ¬pC ⊆ must qC . Since i ∈ Di , it then follows that i ∈ must qC — which is to say must qC,i = 1. Thus Ci has only q-worlds in it. But that is at odds with the first conjunct of (10a): that might p is true at i guarantees a p-world, hence a ¬q-world, in Ci . Narrowscoping has the virtue of taking plain and simple lfs to represent indicatives with apparently epistemic modalized consequents. But it has the vice of not squaring with consistency. This is true no matter the particulars of your favorite version of the operator view.20 So suppose instead that co-occurring modals scope over the if -constructions in which they occur. Now it is the generalizations if/must and if/might that cause trouble. Again, that’s true no matter how Di is chosen and so no matter what counts as an if -relevant possibility and so no matter what conditional operator we say if expresses. Here is a widescope analysis of the key examples (3) and (6): (11)

a. b.

If Carl is at the party, then Lenny must be at the party. must if p q If Carl is at the party, then Lenny is at the party. if p q

20 Thus by supplying how your favorite version of the operator view says Di is determined, you can use this proof to show how that story (assuming narrowscoping) departs from Fact 1.

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Iffiness

(12)

a. b.

If my team wins out, they might win it all. might if p q It might turn out that my team wins out and wins it all. might (p ∧ q)

The facts are that must if p q ≈ if p q and that might if p q ≈ might (p ∧ q). What we need is a semantics for the conditional connective (if ·)(·) that can predict both patterns. But paths that might lead to one pretty reliably lead away from the other. So far I have insisted that i is always among the relevant worlds to an if at i (i ∈ Di ) and also that only worlds compatible with the context are relevant (Di ⊆ Ci ). Here I am in good company. But perhaps there is even more interaction between domains of if -relevant worlds and contexts. Some theories say that there can be no difference in domains for conditionals between worlds compatible with the context, others disagree: Definition 6.2 (egalitarianism & chauvinism). i. A semantics is egalitarian iff if whenever j ∈ Ci then Dj = Di . ii. A semantics is chauvinistic iff it is not egalitarian. egalitarianism requires domains to be invariant across worlds compatible with a context. That means that distinctions between worlds made by D’s — this world is relevant, that one isn’t — are unaffected when those distinctions are made from behind the veil of ignorance (we don’t know which world compatible with C is the actual world). Chauvinistic theories allow differences from behind the veil to matter to what possibilities get selected for domainhood, and thus allow that a possibility j ∈ Ci may determine a different set of relevant possibilities than does i. Once we have agreed that, for any i, Di selects from the worlds compatible with C and must include i, it is a further question whether we want to be egalitarians or chauvinists.21 21 The history of the conditional is littered with chauvinists. The material conditional analysis is chauvinistic. It says that the only possibility relevant for the truth of an if at i in C is i itself. And similarly for an if at j: only j matters there. Thus, except in the odd case where the context rules out uncertainty altogether, we will have that Dj 6= Di , for any choice of i and j compatible with C. A variably strict conditional analysis, based on a family of orderings (one for each world), is chauvinistic if we do not impose an “absoluteness” condition — the requirement that orderings around any two worlds be the same. (Lewis (1973: §6) discusses absoluteness in the process of characterizing the V -logics.) What to say about absoluteness is optional and so there is room for agnosticism about chauvinism. Stalnaker’s (1975) treatment of indicatives is not officially agnostic about chauvinism, but

4:19

A. S. Gillies

It is hard to be a chauvinist. That is because, assuming the particulars of the chauvinistic theory are compatible with there being a (p ∧ ¬q)-world in Ci but not in Di , no such story will predict if/must. The data say that bare indicatives and their must-enriched counterparts are true in the same scenarios. But chauvinism plus widescoping guarantees that the domain the if quantifies over is properly included in the domain its must-enriched counterpart quantifies over. Thus the former says something strictly weaker than — true in strictly more spots than — the latter. That is at odds with Fact 2: Observation 6.2. Suppose that Di ⊂ Ci . There are scenarios in which the widescoped (11b) is true but (11a) isn’t. Thus chauvinism plus widescoping can’t explain Fact 2. Proof. Consider a (p ∧ ¬q)-world — call it j — and suppose that Ci does, but Di does not, contain j. Then every possibility in Di ∩ p is in q and the plain if is true (at i, in C): if p q C,i = 1. But not the widescoped mustenriched if . That is because there is a world in Ci — namely j — such that not every possibility in Dj ∩ p is a possibility in q. Thus if p q C,j = 0 and so it is not true that the plain if is true at every world in Ci and so must if p q C,i = 0. Again, this is true no matter how we fill in the particulars of the operator view. If we widescope the modals, and the story is chauvinistic, it will not square with Fact 2. Given widescoping, egalitarianism fares no better. But here it is if/might (Fact 3) that causes trouble. This time the issue is triviality: mustenriched if s are true iff their might-enriched counterparts are. Here is why. First, egalitarianism implies that Di covers Ci : Observation 6.3. egalitarianism implies that Di = Ci . Proof. Assume otherwise. Di ⊆ Ci , so there must be a j ∈ Ci such that j 6∈ Di . By egalitarianism, Dj = Di . But we know that j ∈ Dj . Contradiction. that is only because he requires that i induce a total order that is centered pointwise on i, and that rules against absoluteness. But the pragmatic mechanisms he develops there are agnostic on the chauvinism question — what he says about how the context constrains selection functions is compatible with both egalitarianism and chauvinism. I myself see little reason to go for chauvinism.

4:20

Iffiness

Thus if Di reflects some measure of proximity to i, egalitarianism implies that the underlying ordering is centered not pointwise on i but setwise on the worlds compatible with C. So egalitarianism implies that if is really a strict conditional. That’s true whether Di is derived from some underlying ordering or not: if , might and must quantify over the same domain of possibilities, and an if is true at i iff all of the antecedent worlds in that domain are consequent worlds.22 That means that an if at i (in C) is true iff the corresponding material conditional is true at every possibility compatible with C. And that means that such an if is true at i iff the material conditional, widescoped by must, is true at i.23 But from this degree of fit between Di and Ci it follows straightaway that no two possibilities compatible with C can differ over an if issued in C. There is solidarity among if s; they stand and fall together: Observation 6.4. egalitarianism implies if p q C,i = 1 iff for every j ∈ Ci : if p q C,j = 1 Proof. if p q C,i = 1 iff Di ∩ p ⊆ q. By egalitarianism: iff, for any j ∈ Ci , Dj ∩ p ⊆ q. Equivalently: iff, for any j ∈ Ci , Cj ∩ p ⊆ q — that is, iff for every such j, if p q C,j = 1. Given widescoping, any story with this equivalence will have a hard time saying why conditionals like (12a) seem to be true iff modalized conjunctions like (12b) are and so will have trouble with if/might. That is because, given the usual story for the modals (Definition 6.1), we get triviality: Observation 6.5. egalitarianism implies: might if p q C,i = 1 iff must if p q C,i = 1 Thus widescoping plus egalitarianism implies that must if p q is true iff might(p ∧ q) is. Not even Cubs fans fall for that. 22 Strictness makes it easy to understand why negating a bare conditional sounds so much like saying the counterexample might obtain. For more on context-dependent strictness (of different flavors) see, e.g., Veltman 1985, von Fintel 1998a, 2001, and Gillies 2004, 2007, 2009. 23 Thus, given well-behavedness (Definition 3.2), explaining Fact 2 is easy for widescoping egalitarians: if p q is equivalent to must (p ⊃ q) which, given well-behavedness, is equivalent to must must (p ⊃ q). And that, in turn, is equivalent to must if p q .

4:21

A. S. Gillies

Proof. Note that might if p q C,i = 1 iff the plain conditional if p q is true somewhere in Ci . But by Observation 6.4 the plain if is true somewhere in Ci iff it is true everywhere in Ci . And it is true everywhere in Ci just in case must if p q C,i = 1. That trivializes rather than explains Fact 3. No matter the particulars, widescoping plus egalitarianism can’t predict Fact 3. Iffiness requires conditionals to have a structure that does not play nice with modals. That’s because no way of resolving the relative scopes will work.24 What causes the trouble is that the operator view requires if to mean all. But the Facts don’t seem to allow that. If we widescope, then sometimes that seems all right — if the modal in question happens to have universal quantificational force. But when the modal is existential, if looks more like conjunction than inclusion. And narrowscoping seems no better, rendering all manner of coherent bits of discourse inconsistent. That is pretty bad news for the operator view. True, we could save iffiness by denying some Fact or other. (With defenders like that who needs detractors?) Adding insult to injury: the Facts were chosen not at random but with an eye to the competition. They are Facts that the new school restrictor view predicts so easily hardly anyone has noticed. 7

Iffiness lost

Lewis (1975) famously argued that if s appearing in certain quantificational constructions (under adverbs of quantification) are not properly iffy, that the if in 24 Could we go for widescoping must-enriched indicatives and narrowscoping might-enriched indicatives? For all we’ve said so far: yes. But that strategy faces an uphill battle. It is ad hoc, three times over. First because there is no good reason to think we should settle for anything less than a uniform story. Second because it is not obvious what it says we should do when we consider ways in which the modal might be embedded. What if the modal is can’t (a possibility modal scoped under negation) or needn’t (a universal under negation)? (i)

a. b.

If my team doesn’t win out, they can’t win it all. If the gardener didn’t do it, the culprit needn’t be the butler.

Do we widescope or narrowscope these? What principled story is there that predicts, rather than stipulates, that the first is widescoped and the second narrowscoped? Third because as soon as we consider epistemic modals that lie between the existential might and the universal must — like probably and unlikely — it is doomed to failure anyway.

4:22

Iffiness

(13)

 Always   Sometimes if a man owns a donkey, he beats it.       Never    

is not a conditional connective with a conditional operator as its meaning but instead acts as a non-connective whose only job is to mark an argumentplace for the adverb of quantification. The relevant structure is not some Q-adverb scoped over a conditional nor some conditional with a Q-adverb in its consequent, he said, but instead something like (14)

Q-adverb + if-clause + then-clause

The job of the if -clause in (13) is merely to restrict the domain over which the adverb (unselectively) quantifies, and allegedly that restricting job is a job that cannot be done by treating if as a conditional connective with a conditional operator as its meaning. If Q-adverb is universal, maybe an iffy if will work; but if it is existential, then conjunction does better. I want to set the issue about adverbial (and adnomial, for that matter) quantifiers aside for two reasons. First because I doubt the allegation sticks. But that is another argument for another day.25 And second because it will do us good to focus on simple cases. Still, the trouble for the operator view that is center stage here does look quite a lot like the problem Lewis pointed out. We have to make room for interaction between if -clauses and the domains our modals quantify over. But that interaction is tricky. That is because it looks impossible to assign if the same conditional meaning — thereby taking its contribution to be an iffy one — in all of our examples. Indeed, when the modal is universal a conditional relation looks good; but when the modal is existential, conjunction looks better. This is pretty much the same trouble Lewis saw for if s occurring under adverbs of quantification, and led him to conclude that such if s do not express operators at all (and a fortiori not conditional operators).26 Just as with adverbial quantifiers, there is a fast and easy solution to the problem if we get rid of the old school idea that if is a conditional connective and plump instead for anti-iffiness. The most forceful way of putting the anti-iffy thesis is Kratzer’s (1986: 11): 25 There are ways to get the restricting job done after all. The operator-based stories in, e.g., Belnap 1970, Dekker 2001, and von Fintel & Iatridou 2003 all manage. 26 For recent and more thorough-going defenses of if s-as-quantifier-restrictors see, e.g., Kratzer 1981, 1986 and von Fintel 1998b. But see Higginbotham 2003 for a dissenting view.

4:23

A. S. Gillies

The history of the conditional is the history of a syntactic mistake. There is no two-place “if. . . then” connective in the logical forms for natural languages. “If”-clauses are devices for restricting the domains of various operators. The thesis is that the relevant structure for the conditionals at issue here is not some modal scoped over a conditional nor some conditional with a modal in its consequent, but is instead something like (15)

modal + if-clause + then-clause

Or, closer to the way we’ve been putting things: (16)

modal(if-clause )(then-clause )

The job of the if -clause is to restrict the domain over which the modal quantifies. So instead of searching for a conditional operator properly so called that if contributes whether it commingles with a modal or not, we search for an operator for if to restrict. And, for indicative conditionals, we do not have to search far: the operators are (possibly covert) epistemic modals.27 So it is the modals, not the if s, that take center stage. They have logical forms along the lines of modal(p)(q), with the usual quantificational force: Definition 7.1 (modal force, amended). i. if defined, might (p)(q)C,i = 1 iff (Ci ∩ p) ∩ qC 6= ii. if defined, must (p)(q)C,i = 1 iff (Ci ∩ p) ⊆ qC This plus two assumptions gets us the now-standard and familiar restrictor view. It easily accounts for consistency (Fact 1), if/must (Fact 2), and if/might (Fact 3). First assumption: assume that when there is no if -clause and so no restrictor is explicit — as in Blue might be in the box or Yellow must be in the box — the first argument in the lf of the modal is filled by your favorite tautology (>). In those cases there is nothing to choose between an analysis that follows our earlier Definition 6.1 and an analysis that follows Definition 27 Officially, our intermediate language now also goes in for a change. L had one-place modals might and must and a two-place connective (if ·)(·). That won’t do to represent the restrictor view. Instead, we need the two-place modals might (·)(·) and must (·)(·) and have no need for a special conditional connective that expresses a conditional operator.

4:24

Iffiness

7.1, and so the latter generalizes the former. Second assumption: assume that the job of if -clauses is to make a (nontrivial) restrictor explicit. If there is no overt modal — as in a bare conditional — the if restricts a covert must. Collecting the pieces: Definition 7.2 (anti-iffiness). For any sentence S, let S 0 be its lf in our intermediate language. Then: i. A sentence of the form if S1 then S2 has lf: a. modal(S10 )(R 0 ) if S20 = modal R 0 b. must (S10 )(S20 ) otherwise ii. Truth conditions as in Definition 7.1 Return to the case of my missing marbles. Taking the if -clauses to be restrictors in the example: (17)

a. b. c.

Red might be in the box and Yellow might be in the box. might (>)(p) ∧ might (>)(q) If Yellow isn’t in the box, then Red must be. must (¬q)(p) If Red isn’t in the box, then Yellow must be. must (¬p)(q)

It’s modals all the way down. And the modals can all be true together. Observation 7.1 (anti-iffiness & consistency). Assume anti-iffiness (Definition 7.2). And suppose, in C, that (17a) is a partitioning modal. Then the sentences in (17) can all be true together. Proof. I am in i and there are just two worlds compatible with the facts I have, i and j. The first is a (p ∧ ¬q)-world, the second a (q ∧ ¬p)-world. The restrictors in (17a) are trivial, so it is true at i iff Ci has a p-world in it and a q-world in it; i witnesses the first conjunct, j the second. The restricting if -clause of (17b) makes sure that the must ends up quantifying only over the ¬q-worlds compatible with C: (17b) is true at i iff all of the worlds Ci ∩ ¬q are p-worlds. And the only one, i, is. Similarly for the must in (17c): it quantifies over the ¬p-worlds in Ci , checking to see that they are all q-worlds. It is just as easy to square this picture with if/must (Fact 2) and if/might (Fact 3). Here are the examples with their new school lfs:

4:25

A. S. Gillies

(18)

a. b.

(19)

a. b.

If Carl is at the party, then Lenny must be at the party. must (p)(q) If Carl is at the party, then Lenny is at the party. must (p)(q) If my team wins out, they might win it all. might (p)(q) It might turn out that my team wins out and wins it all. might (>)(p ∧ q)

Observation 7.2 (anti-iffiness, if/must, & if/might). Assume anti-iffiness (Definition 7.2). Then: i. If S1 , then S2 ≈ If S1 , then must S2 ii. If S1 , then might S2 ≈ might [S1 and S2 ] Proof. anti-iffiness assigns the same lf to a bare conditional like (18b) and its must-enriched counterpart (18a): must (p)(q). It would thus be hard, and pretty undesirable, for their truth conditions to come apart. That explains if/must. Now consider the if -as-restrictor analysis of the sort of examples behind if/might in (19). If (19b) is true at i in C then Ci has a (p ∧ q)-world in it. But then that same world must be in Ci ∩ p. It is a q-world, and that will witness the truth of (19a) at i. Going the other direction: if (19a) is true at i in C, then there are some q-worlds in Ci ∩ p. Any one of those will do as a (p ∧ q)-world in Ci , and that is sufficient for (19b) to be true at i. That explains if/might. These explanations are easy. And, given the trouble for the operator view, it looks like the only game in town is to say that if doesn’t express an operator and so not an iffy operator. That stings. 8

Iffiness regained

The problem for iffiness is that there is an interaction between if -clauses and the domains our modals quantify over. That is an interaction that seems hard to square with the thesis that if is a binary connective with a conditional meaning if we assume that it has the same meaning in each of the cases we care about here.

4:26

Iffiness

But we have overlooked a possibility. We insisted that for a story to be iffy it must say that if p q at i in C expresses some relation R between Di ∩ P and Q, where Di ∩ P is the set of (relevant) worlds where the antecedent is true and Q the set of worlds where the consequent is true. That is all right. But we unthinkingly assumed that the context relevant for figuring out what these sets of worlds are must always be C just because that was the context as it stood when the if was issued. That was a mistake. Setting it straight sets the record straight for old school iffiness. The Ramsey test — the schoolyard version, anyway — is a test for when an indicative conditional is acceptable given your beliefs. It says that if p q is acceptable in belief state B iff q is acceptable in the derived or subordinate state B-plus-the-information-that-p. You zoom in on the portion of B where p is true and see whether q throughout that region. But our job is to say something about the linguistically encoded meanings of indicatives not to dole out epistemic advice. Still, the Ramsey test (plus or minus just a bit) can be turned into a strict conditional story about truth-conditions. Here’s how (in three easy steps). Step one: sentences get truth-values at worlds in contexts. So swap C’s for B’s. Step two: embrace egalitarianism. The worlds compatible with the context are the if -relevant worlds. These first two steps give us a strict conditional analysis of indicatives, requiring that if p q is true at i in C iff all the p-possibilities in Ci are possibilities at which q is true. But truth depends on both index and context. Question: What context is relevant for checking to see whether q is true at these p-possibilities? Answer: The Ramseyan derived or subordinate context Cplus-the-information-that-p, or C + p for short. That’s step three. The Ramsey test invites us to add the information carried by the antecedent to the contextually relevant stock of information C and check the fate of the consequent. What we fans of iffiness overlooked was that this assigns two jobs to if -clauses, and we only paid attention to one of them. One job is the index-shifting job. The if -clause tells us to shift to various alternative indices — the antecedent-possibilities compatible with C — to see whether the consequent is true at them. This job is familiar and most versions of the operator view do a fine job tending to it. But there is another job. When we add the information carried by the antecedent to C we also add to the context relevant for figuring out whether the consequent is true. That is the context-shifting job. The if -clause tells us to shift to an alternative derived or subordinate state to see whether the consequent is true. We fans of old school iffiness made the mistake of only making sure that the first job

4:27

A. S. Gillies

got done. So far this isn’t a story about the meaning of if (much less an iffy one). It is a blueprint for how to construct a semantics that gives a uniform and iffy meaning to if s whether or not those if s mix and mingle with other operators. To construct a story using it we need to take a stand on what it means to add the information carried by an antecedent to the contextually relevant stock of information. Taking that stand depends on the aspirations of the theory since different constructions may depend on different sorts of contextually available information and there is every reason to think that augmenting information of different sorts goes by different rules. But our aspirations are pretty modest here: how indicatives interact with epistemic modals. So we can opt for an equally simple stand on what it means to add information to a context. Even before getting all the details laid out, we can see how the doubly shifty behavior of if -clauses will be able to predict what needs predicting about how indicatives and epistemic modals interact. The difference between interpreting q against the backdrop of the prior context C and against the backdrop of C + p is a difference that makes no difference if q has no context sensitive bits in it. No wonder we missed it! But if q does have context sensitive bits in it — like might or must, whose semantic value depends non-trivially on C — then this is a difference that makes all the difference. For example: consider a modal like must q. The contexts C and C + p may well determine different sets of possibilities. Since must q depends exactly on whether that set of possibilities has only q-worlds in it, we then get a difference. Thus if must q is the consequent of an indicative, contextshiftiness matters. Here is the simplest way of constructing a semantics around the blueprint: Definition 8.1 (iffiness + shiftiness). i. if defined, if p q C,i = 1 iff Ci ∩ pC ⊆ qC+p ii. C + p = λi.Ci ∩ pC Such a story about if is iffy: if expresses a relation between relevant antecedent and consequent worlds and that relation lives up to all the constraints we insisted on earlier. Hence if means all. And it expresses that no matter whether it scopes over a universal modal or an existential modal or no modal at all in the consequent. It is also doubly shifty. It is index-shifty since the truth of if p q at i depends on the truth of the constituent q

4:28

Iffiness

at worlds other than i. It is context-shifty since the truth of if p q in C depends on the truth of the constituent q in contexts other than C. The if /modal interactions that were such trouble were only trouble because we forgot to keep track of the context-shifting job of if -clauses. And doing that, even in the simple context-shifting in Definition 8.1, is enough to make iffiness sit better with the Facts. I know that just one of my marbles is in the box — either Red or Yellow — but do not know which it is. Narrowscope the modals. Then all of these can be true together: (20)

a. b. c.

Red might be in the box and Yellow might be in the box. might p ∧ might q If Yellow isn’t in the box, then Red must be. if ¬q must p If Red isn’t in the box, then Yellow must be. if ¬p must q

Observation 8.1 (iffiness & consistency). Assume iffiness + shiftiness (Definition 8.1). Suppose p and q partition the possibilities in C. The (narrowscoped) sentences in (20) can all be true together in C. Proof. Here is why. Suppose — for concreteness and without loss of generality — that C contains just two worlds: i, a (p ∧ ¬q)-world and j, a (q ∧ ¬p)world. So (20a) is true at i. Now take (20b). It is true at i in C, given iffiness + shiftiness, iff all the possibilities in Ci ∩ ¬q are possibilities that must pC+¬q maps to true. Thus we have to see whether the following holds: if k ∈ Ci ∩ ¬q then must pC+¬q,k = 1 Iff this is so is (20b) true at i in C. But Ci ∩ ¬q = {i}, so we have to see whether or not must pC+¬q,i = 1. Equivalently: the if is true at i iff (C + ¬q)i ⊆ p. And since i is in fact a p-world the if is true at i in C. And mutatis mutandis for (20c). The operator view isn’t at odds with consistency after all. It is also easy to predict if/must (Fact 2) and if/might (Fact 3). Here are the narrowscoped analyses of the motivating examples: (21)

a.

If Carl is at the party, then Lenny must be at the party. if p must q

4:29

A. S. Gillies

(22)

b.

If Carl is at the party, then Lenny is at the party. if p q

a.

If my team wins out, they might win it all. if p might q It might turn out that my team wins out and wins it all. might (p ∧ q)

b.

Observation 8.2 (iffiness, if/must, & if/might). Assume iffiness + shiftiness (Definition 8.1). Then: i. If S1 , then S2 ≈ If S1 , then must S2 ii. If S1 , then might S2 ≈ might [S1 and S2 ] Proof. If must q is true then so is q, no matter the world and context. So it’s easy to see that when (21a) is true so is (21b). Now suppose (21b) is true at i (with respect to C). Then all of the p-worlds in Ci are q-worlds (Ci ∩ p ⊆ qC+p ). But if they are all worlds at which q is true, then i — and so, given well-behavedness, every world in Ci — is equally a world at which must q is true (with respect to C + p). And so (21a) is true, at i in C, if (21b) is. That’s just what if/must requires. if/might is no different. The noteworthy part is seeing how iffiness + shiftiness predicts that when (22a) is true then so is (22b). Note that (22a) is true at i (with respect to C) just in case all of the p-worlds in Ci are worlds where might q, evaluated in C + p, is true. By well-behavedness we have that: if j, k ∈ Ci ∩ p then (C + p)j = (C + p)k = Ci ∩ p If there is a q-world in (C + p)j , then might q is true throughout this set. Since might q is an existential modal, if it is true with respect to C + p it must also be true with respect to C. (Updating contexts with + is monotone.) Whence it follows that the if with a commingling might is true at i iff among the p-worlds in Ci lies a q-world. And any such q-world will do to witness the truth of might (p ∧ q) at i in C. That’s just what if/might requires. Indicatives play well with epistemic modals. That interaction seemed hard to square with old school views that take if to express a conditional operator. No way of sorting out the relative scopes between the modals and the conditional seemed right. But that is because we mistakenly thought that antecedents of conditionals only have one job to do. They shift the index at which we check to see if the consequent is true. But they also contribute to the

4:30

Iffiness

context that is relevant when we do that checking. Once we let antecedents do both their index-shifting and context-shifting jobs we can safely narrowscope and there is no special problem posed for old school iffiness. The if in if p modal q means the same iffy thing — inclusion! — saying that all the (relevant) worlds where p is true are worlds where modal q is true. That’s so whether the oopmh of modal is universal or existential or null and does nothing to get in the way of explaining the Facts. That is something we fans of iffiness ought to dig.28 9

What is at stake

Given the success of anti-iffiness why bother with iffiness at all? A fair question. Given the context-shifting I’m advocating for fans of iffiness, what’s the difference between old school and new school? Another fair question. I owe some answers. I make three (not wholly unrelated) claims. First, even if the shifty version of the operator view and the basic version of the restrictor view covered the same ground, there is still reason to explore the operator view. Second, the views have different conceptual roots and different allegiances. Third, the views don’t cover the same ground. I need to argue for each of these. Suppose that — at least when it comes to accounting for data about the sorts of constructions at issue here — there’s nothing to choose between iffiness + shiftiness and anti-iffiness. Even under that assumption there is reason to take this version of the operator view seriously. That is because it is important to set the record straight. Maybe you don’t like skyhooks, Chuck Taylors, and conditional connectives expressing iffy operators in your lfs. It is important to know that whatever your reasons, it can’t be because iffiness can’t be squared with the Facts about how if s and modals interact. The Ramsey test intuition leads naturally to a story according to which if expresses a bona fide conditional operator that captures the restricting behavior of if -clauses. Thus the restricting behavior of if -clauses can be a 28 Before I said that I wanted to ignore issues about how this version of the operator view can meet Lewis’s challenge about the ways if -clauses and adverbs of quantification interact, saving that argument for another day. I want to stick to that (it really is an argument for another day), but the general idea is straightforward. First, adjust the kinds of information represented by a context so that we can sensibly quantify over individuals and the events they participate in. Second, allow that quantificational domains can be restricted by material in if -clauses — those domains play the role of the subordinate or derived context. Adverbs of quantification appear under the conditional and have their usual denotations.

4:31

A. S. Gillies

part of, rather than an obstacle to, their expressing something iffy. That is cool. But what’s the real difference between the views? One view says we have no conditional operator, just a complicated modal with a slot for a restrictor. The other says we have a conditional operator but that its antecedent shifts the context thereby acting like a restrictor. Tomato/tom˘ ato, right? Wrong! Here is one way of seeing that. Consider three indicatives: (23)

a. b. c.

If Scorpio succeeds, then the end must be near. If Scorpio succeeds, then the end is near. If Jimbo is in detention, then Nelson might be.

Compare (23a) and (23c). The restrictor view says these have different modals and different arguments for each of the slots in those modals. So, apart from the fact that each is a modal expression of some flavor or other, there is nothing much in common between the two. They are as different as Some students smoke and All dogs bark: each is a quantificational expression of some flavor or other. The operator view says something different. It says that, despite their different antecedents and different consequents, they still share a common iffy core: there is a conditional connective in common between them and it contributes the same thing to each of the sentences it occurs in. Or compare the must-enriched (23a) with its bare counterpart (23b). The restrictor view says the bare indicative just is the must-enriched version in disguise. That is how it predicts if/must (Fact 2). It thus treats bare indicatives as a special case, dealt with by positing a covert and inaudible necessity modal. Maybe there is reason to posit such an operator, and an independent and principled reason to posit the necessity modal instead of an existential one or some different modal with different quantificational force, and maybe those reasons outweigh the cost of the positing. The operator view adopts a very different stance here and that is what I want to point out. It says that bare indicatives like (23b) are ordinary conditionals and their counterparts with must-ed consequents like (23a) are ordinary conditionals that happen to have must in their consequents. No special cases, no positing of inaudible operators, and if/must comes out as a prediction not as a stipulation. None of this is a knock-down argument for or against either of the views — it’s not meant to be — but it does highlight their difference in worldview. All of this has been under the assumption that both the doubly shifty iffy view and the anti-iffy restrictor view cover the same ground about how if s

4:32

Iffiness

and modals interact. But that’s not quite right.29 So far we have only worried about how it is that a conditional sentence manages to express what might be if such-and-such or how it manages to express what must be if such-and-such. But conditional information can be more economically expressed than that. We can just as well have a single conditional sentence that expresses what must be and what might be if such-and-such. A case in point: although I have lost my marbles, I know that some of them — at least one of Red, Yellow, and Blue — are in the box. In fact I know a bit more. I know that Yellow and Blue are in the same spot and so that Red can’t be elsewhere if Yellow isn’t in the box. Another example: arriving at the party, I’m not sure who’s there and who isn’t. I do know that Lenny goes wherever Carl goes (but sometimes Lenny goes alone), but Monty never goes where Lenny goes. (24)

a. b.

If Yellow is in the box, then Red might be and Blue must be. If Lenny is at the party, then Carl might be but Monty isn’t.

These are not exotic, each conditional is a true thing to say in the circumstances, and there is space for the iffy view and incarnations of the anti-iffy restrictor view to differ on the truth conditions they assign to conditionals like these — and so the two views can’t be stylistic variants. Here is the issue: (24a) and (24b) have glosses: (25)

a.

If Yellow is in the box, then Red might be and if Yellow is the box, then Blue must be.

29 There are reasons independent of interaction with epistemic modals to think that antiiffiness, in its purest if -only-restricts form, can’t be the whole story. If it were, and if -clauses and when-clauses have the same restricting behavior, then we wouldn’t expect differences in cases like this: (i)

a. b.

If the Cubs get good pitching and timely hitting after the break, they might win it all. When the Cubs get good pitching and timely hitting after the break, they might win it all.

But we do detect a difference. I can say something true-if-hopeful with (ia). But (ib) passes optimistic and heads straight for delusional. It’s hard to see where to locate the difference — whether it’s semantic or pragmatic — if the semantic contribution of if and when is purely to mark the restrictor slot for the common operator might. (Lewis (1975) noticed that sometimes a restricting if is odd when its corresponding restricting when is fine. But he labeled these differences “stylistic variations”.) Some arguments along these lines are pushed by von Fintel & Iatridou (2003).

4:33

A. S. Gillies

b.

If Lenny is at the party, then Carl might be but if Lenny is at the Party, then Monty isn’t.

These swap a single conditional with a complicated consequent for a conjunction of simple conditionals. The simple incarnation of the anti-iffy restrictor view in Definition 7.2 says we do one thing when a conditional consequent has an overt modal, and do another when there isn’t. But we didn’t say how out in the open a modal must be to count as overt. Depending on what we say, we can get divergence between the operator view and the restrictor view for cases like these. Assume — for now — that a modal is overt in a sentence iff it is the connective featured in (the lf of) that sentence.30 Under that assumption, it is then easy to see that the two stories come apart: iffiness + shiftiness predicts that (24a) is equivalent to (25a) and so true (in the relevant context) and anti-iffiness does not. That is because the consequent of (24a) isn’t decorated with a leading modal (it’s a conjunction of modals), and so we have to posit one. So (24a) gets an L-representation like (26)

must (p)(might (>)(q) ∧ must (>)(r ))

But the truth conditions of (26) do not match the truth conditions of (25a) and so do not match the truth conditions of the original (24a): (26) is false in the context as we set it up even though both (24a) and (25a) are true. Now assume, instead, that a modal is overt iff it is pronounced — no matter how arbitrarily deeply embedded. Then (26) isn’t the right anti-iffy lf for (24a). Instead, we get something more sensible: (24a) and (25a) have the same lf. There’s no in-principle problem with that.31 But what about conditionals like (24b)? We don’t want to posit a must that outscopes the pronounced might. So we have to posit a narrowscoped one. In order to get the posited modal appropriately restricted — so that (24b) comes out equivalent to (25b) — we have two obvious options. Option (i): Argue that conditionals like those in (24) are not single conditionals at all, that they are really conjunctions of two simple modals. That way there is no difference at all between the conditionals in (24) and the glosses in (25). Option (ii): Enrich our intermediate language to allow for explicit domain-restricting variables, and provide a mechanism for the inheriting of those restrictions 30 In this sense, a modal is any (non-equivalent) stack of musts, mights, and negations. 31 Though it doesn’t come free: it puts strain on the process of assigning formulas of L to serve as the lfs of sentences of natural language.

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Iffiness

across intervening operators like conjunction. Both options are open, and party line proponents of anti-iffiness are free to pursue them. But they do require work. Option (i) posits movement we’d not like to have to posit, treats conditionals with apparent conjoined consequents as yet another special case, and describes rather than explains why the conditionals in (24) are glossable by those in (25). Option (ii) requires more expressive resources for L than we thought necessary and requires something over and above the anti-iffy story as it stands to say when and how domain restriction gets inherited over distance and across intervening operators. That’s not an argument against this option but a description of it.32 But none of that really matters: my point was that iffiness + shiftiness and anti-iffiness aren’t notational variants. And they are not: the iffy story takes conditionals like (24) in perfect stride. No special cases, no positing of inaudible operators, no stress on the parser in assigning formulas of L to serve as the lfs of conditional sentences, no movement. We get the right truth conditions, and we get as a prediction not a stipulation that the conditionals in (24) are equivalent to those in (25). 10

Context and dynamics

Not every fan of old school iffiness will want to follow me this far. But there is a cost to cutting their trip short since they must then deny or explain away one of the Facts. Iffiness, they’ll no doubt point out, is not without its own costs: the price of iffiness is shiftiness twice over. I reply that there are costs and then there are costs. Embracing contextshiftiness may be a cost, but I want to point out that it is not a new cost: it makes the analysis here a broadly dynamic semantic account of indicatives.33 So shiftiness is a cost you may already be willing to bear. I want to (briefly) point out how it is that this shiftiness amounts to a four-fold dynamic perspective on modals and conditionals. 32 Something in the neighborhood of Option (ii) is developed (though not with an eye to conjoined consequents) in von Fintel (1994). For a recent discussion see Rawlins 2008. 33 The general idea that consequents are evaluated in a subordinate or derived context is standard in dynamic semantics — see, e.g., dynamic treatments of donkey anaphora (Groenendijk & Stokhof 1991) or dynamic treatments of presupposition projection in conditional antecedents and consequents (Heim 1992; Beaver 1999) or dynamic treatments of counterfactuals (Veltman 2005; von Fintel 2001; Gillies 2007). But exploiting a derived context isn’t quite a litmus test for dynamics since that is something shared by a lot of Ramsey-inspired accounts, whether or not they count as ‘dynamic’.

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A. S. Gillies

The version of the operator view I’m advocating for fans of iffiness takes the truth of an indicative (at an index, in a context) to be doubly shifty. That doubly shifty behavior makes the semantics dynamic in the sense that interpretation both affects and is affected by the values of contextually filled parameters. Whether if p q is true at i in C depends on C; the indicative can be true at i for some choices of C and false at i for others. So interpretation is context-dependent. Whether if p q is true at i in C also depends on the subordinate context C + p. Interpreting the indicative in C affects — temporarily — the context for interpreting some subparts of it. So interpretation is also context-affecting. This analysis is also dynamic in a second sense. It makes certain sentences unstable — the truth-value a sentence gets in a context C is not a stable or persistent property since it can have a different truth-value in a context C 0 that contains properly more information. Definition 10.1 (persistence). 0

i. p is t-persistent iff pC,i = 1 and C 0 ⊆ C imply pC ,i = 1 0 ii. p is f -persistent iff pC,i = 0 and C 0 ⊆ C imply pC ,i = 0 p is persistent iff it is both t- and f -persistent. The boolean bits are, of course, both t- and f -persistent and so persistent fullstop. But not the modals: might, being existential, is f - but not t-persistent; must goes the other way. And since if is a strict conditional, equivalent to a necessity modal scoped over a material conditional, its pattern of persistence is just like that for must.34 These two senses in which the story is dynamic are two sides of the same coin. Together they explain how it is that the narrowscoped conditionals if ¬p must q and if ¬q must p are consistent with the partitioning modals in might p ∧ might q. From the fact that i ∈ if ¬p must q C and i ∈ ¬pC it does not follow that i ∈ must qC . Indeed, with my marbles lost, this is sure to be false at i in C since might p is true. What is true at i is that — in the subordinate or derived context C + ¬q — must q is true. That is allowed because must isn’t f -persistent. But that is not at odds with the might claim. And mutatis mutandis for the other if . 34 This pattern makes the treatment of indicatives here similar in some respects to Veltman’s (1985) data semantic treatment of indicatives. But there are important differences between the two stories. Here’s one: if p might q is data semantically equivalent to if p q . That won’t do given Fact 3.

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Iffiness

So we have dynamics twice over. But so far none of this looks quite like what is usually called “dynamic semantics”. In that sense of dynamics meaning isn’t associated with truth conditions or propositions but with context change potentials, effects on relevant states of information. Take an information state s to be a set of worlds, and say that what a sentence means is how its lf updates information states. That assigns to sentences the semantic type usually reserved for programs and recipes; they express relations between states — intuitively, the set of pairs of states such that executing the program in the first state terminates in the second. We can think of all sentences in this way, thereby treating them as instructions for changing information states. Thus: the meaning of a sentence p is how it changes an arbitrary information state. We might put that by saying the denotation [p] applied to s results in state s 0 ; in post-fix notation s[p] = s 0 .35 Now say that p is true in s iff s[p] = s, for then the information p carries is already present in s.36 Having gone this far, we can make good on the Ramsey test this way: Definition 10.2 (Dynamic Iffiness). s[ if p q ] = i ∈ s : q is true in s[p] Some programs have as their main point to make such-and-such the case; others to see whether such-and-such. Programs of the latter type are tests and they either return their input state (if such-and-such) or fail (otherwise). That is the kind of program Definition 10.2 says if is.37 It says an if tests s to see whether the consequent is true in s[p]. But — in good Ramseyian spirit — s[p] is just the subordinate context got by hypothetically adding p to s. Truth isn’t persistent here, either. That is because a state may pass a test posed by an existential (Are there p-possibilities?) and yet have 35 For the fragment without if s the updates are as you would expect (Veltman 1996). For the if -free fragment of L, define [·] as follows: i. s[patomic ] = i ∈ s : i(patomic ) = 1 ii. s[¬p] = s \ s[p] iii. s[p ∧ q] = s[p][q] iv. s[might p] = i ∈ s : s[p] 6= It then follows straightaway that — for the if - and modal-free fragment — s[p] = s ∩ p. 36 This generalizes the plain vanilla story about satisfaction we were taught when first learning propositional logic: as the story usually goes, a boolean p is true relative to a set of possibilities s iff all the possibilities in s are in p. But that is equivalent to saying that adding p to the information in s produces no change: s ∩ p = s iff s ⊆ p. 37 See, e.g., Gillies 2004.

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A. S. Gillies

some narrower, less uncertain state fail it (No more p-possibilities!). And dually for the universal must and if . An iffy account like the one in Definition 10.2 is dynamic in this third sense. But the doubly-shifty operator view iffiness + shiftiness doesn’t look much like a dynamic semantics in that sense. That analysis looks static, assigning truth-conditions to indicatives at a world in a context. And we can recover propositions if the mood strikes us. But the two stories are in fact the same: lack of persistence plus the global behavior of the modals and if s in the doubly shifty story make it equivalent to a dynamic story of the indicative that dispenses with the assignment of propositions of the normal sort from the beginning.38 Even though I told the story about truth-values assigned at contexts and indices, it is equivalent to a story about changing information states. So we have dynamics thrice over. We have gotten this far, and found ways to predict the Facts about how indicatives and epistemic modals interact, without taking a stand on when one sentence entails another. (Having said nothing about entailment we couldn’t have said anything about modus ponens either.) Entailment is usually taken to be preservation of truth at a point of evaluation: iff q is true at a point if p1 , . . . , pn are all true at that point do the latter entail the former. Not necessarily so in a dynamic semantics. Often enough, what is important and what an entailment relation ought to capture is not preservation of truth but preservation of information flow — what must be true after adding the information carried by the premises. That is an updateto-test entailment relation.39 Similarly, since the story as I have told it turns out to be a dynamic one, we ought to expect a larger menu of options for what it takes for a collection of premises to entail a conclusion. That is because truth is sensitive to both context and index and contexts can shift about as we move from the pi ’s to q. To make sure entailment is sensitive to those shifts, we shouldn’t merely require preservation of truth-at-a-point. Instead, just as in a more explicitly dynamic set-up, we want to augment the 38 The standard benchmark for dynamics is whether the interpretation function [·] is either non-introspective (Can it be that s[p] 6⊆ s?) or non-continuous (Can it be that s[p] 6= S i∈s {i} [p]?). In set-ups like the one in Definition 10.2, the behavior of indicatives is not continuous. See Gillies 2009 for the details on how the iffy story as I have put it is equivalent to a more directly dynamically iffy semantics, and how the right notions of entailment coincide in the two set-ups. 39 For more about the space of options for entailment relations in dynamic semantics see van Benthem 1996 and Veltman 1996. Update-to-test entailment is a lot like Stalnaker’s (1975) notion of reasonable inference.

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Iffiness

context with the information of the premises, evaluating q not in C but in (C + p1 ) + · · · + pn ). And that corresponds exactly to the dynamic update-totest entailment relation over our language L. That is the fourth way in which the semantics here is dynamic. So the doubly shifty behavior of indicatives reflects this four-fold dynamic perspective. That is useful to know for two reasons. First because it makes clear what the costs of iffiness are and it makes clear that some of those costs are not completely new. Second because it makes clear that the dynamic perspective on modals and conditionals is broader than we may have thought. The senses in which the story here reflects a dynamic perspective are familiar senses, but the mechanisms of that iffy story aren’t the usual mechanisms in a dynamic semantics. The semantics traffics in things like truth conditions and propositions, not in things like support or programs or context change potentials. So nothing in the dynamic perspective on modals and conditionals requires the latter sort of semantic trafficking at the expense of the former sort. It’s broader than that. 11 An iffy upshot My preferred version of the operator view says that an indicative is a doublyshifty strict conditional over sets of live possibilities. It assigns two jobs to if -clauses. They have the index-shifting job of shifting the point at which we check for a consequent’s truth, but they also have the context-shifting job of shifting the context relevant for deciding at such a point whether a consequent is true. That is how if can mean the same iffy thing no matter whether the consequent is modal, and no matter the quantificational force of that modal, without running afoul of the Facts. We began with the iffy thesis that conditional information is information of a conditional. Then we showed that — given some broad constraints for what counts as a conditional operator properly so called — apparently no operator view could be squared with the Facts since no way of sorting out the scopes would work. But all of that assumed that antecedents have no context-shifting role. So if you want to plump for an incarnation of the operator view, and you want to square your story with the Facts, you had better allow for context-shifting. It’s easy to get the idea that how if s and operators like epistemic modals interact is an argument for anti-iffiness. But since some iffy stories — this one! — can account for that data, that’s not right. Nothing about shiftiness

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rules out anti-iffiness, of course. And so it’s open to go for a restrictor view that co-opts context-shifting to account for the way that conditionals with conjoined consequents turn out equivalent to conjunctions of simpler conditionals. So if you want to toe the anti-iffy line, you might want to allow for context-shifting anyway. Of course, that makes toeing the line a bit like not toeing the line. References Adams, Ernest W. 1975. The logic of conditionals. Dordrecht: Reidel. Beaver, David. 1999. Presupposition accommodation: A plea for common sense. In Larry Moss, Jonathan Ginzburg & Martin de Rijk (eds.), Logic, language, and information vol. 2, 21–44. Stanford, CA: CSLI Publications. https://webspace.utexas.edu/dib97/itallc.pdf. Belnap, Nuel D. 1970. Conditional assertion and restricted quantification. Noûs 4(1). 1–12. doi:10.2307/2214285. Bennett, Jonathon. 2003. A philosophical guide to conditionals. Oxford University Press. van Benthem, Johan. 1986. Essays in logical semantics (Studies in Linguistics and Philosophy 29). Dordrecht: Reidel. van Benthem, Johan. 1996. Exploring logical dynamics. Stanford, CA: CSLI Publications. Dekker, Paul. 2001. On if and only. Semantics and Linguistics Theory [SALT] 11. 114–133. http://staff.science.uva.nl/~pdekker/Papers/OIAO.pdf. Edgington, Dorothy. 1995. Conditionals. Mind 104(414). 235–329. doi:10.1093/mind/104.414.235. Edgington, Dorothy. 2008. Conditionals. In Edward N. Zalta (ed.), The Stanford encyclopedia of philosophy, Winter 2008 edn. http://plato.stanford.edu/ archives/win2008/entries/conditionals/. von Fintel, Kai. 1994. Restrictions on quantifier domains. Amherst, MA: University of Massachusetts dissertation. http://semanticsarchive.net/ Archive/jA3N2IwN/fintel-1994-thesis.pdf. von Fintel, Kai. 1997. Bare plurals, bare conditionals, and only. Journal of Semantics 14(1). 1–56. doi:10.1093/jos/14.1.1. von Fintel, Kai. 1998a. The presupposition of subjunctive conditionals. In Uli Sauerland & Orin Percus (eds.), The interpretive tract (MIT Working Papers in Linguistics 25), 29–44. http://mit.edu/fintel/fintel-1998-subjunctive. pdf.

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von Fintel, Kai. 1998b. Quantifiers and if -clauses. Philosophical Quarterly 48(191). 209–214. doi:10.1111/1467-9213.00095. von Fintel, Kai. 2001. Counterfactuals in a dynamic context. In Michael Kenstowicz (ed.), Ken Hale: A life in language, 123–152. Cambridge, MA: MIT Press. von Fintel, Kai. 2009. Conditionals. Ms, to appear in Semantics: An international handbook of meaning, edited by Klaus von Heusinger, Claudia Maienborn, and Paul Portner. http://mit.edu/fintel/ fintel-2009-hsk-conditionals.pdf. von Fintel, Kai & Anthony S. Gillies. 2007. An opinionated guide to epistemic modality. In Tamar Szabó Gendler & John Hawthorne (eds.), Oxford studies in epistemology: Volume 2, 32–62. Oxford University Press. von Fintel, Kai & Anthony S. Gillies. 2008a. CIA leaks. The Philosophical Review 117(1). 77–98. doi:10.1215/00318108-2007-025. von Fintel, Kai & Anthony S. Gillies. 2008b. Might made right. In Brian Weatherson & Andy Egan (eds.), Epistemic modals, Oxford University Press (to appear). http://rci.rutgers.edu/~thony/fintel-gillies-2008-mmr.pdf. von Fintel, Kai & Anthony S. Gillies. 2010. Must... stay... strong! Natural Language Semantics to appear. http://mit.edu/fintel/fintel-gillies-2010-mss. pdf. von Fintel, Kai & Irene Heim. 2007. Intensional semantics. Lecture Notes, MIT. http://tinyurl.com/intensional. von Fintel, Kai & Sabine Iatridou. 2003. If and when if -clauses can restrict quantifiers. Manuscript, MIT. http://web.mit.edu/fintel/www/lpw.mich. pdf. Geurts, Bart. 2005. Entertaining alternatives: Disjunctions as modals. Natural Language Semantics 13(4). 383–410. doi:10.1007/s11050-005-2052-7. Gibbard, Allan. 1981. Two recent theories of conditionals. In William L. Harper, Robert Stalnaker & Glenn Pearce (eds.), Ifs, 211–248. Dordrecht: Reidel. Gillies, Anthony S. 2004. Epistemic conditionals and conditional epistemics. Noûs 38(4). 585–616. doi:10.1111/j.0029-4624.2004.00485.x. Gillies, Anthony S. 2007. Counterfactual scorekeeping. Linguistics and Philosophy 30(3). 329–360. doi:10.1007/s10988-007-9018-6. Gillies, Anthony S. 2009. On truth-conditions for if (but not quite only if ). The Philosophical Review 118(3). 325–349. doi:10.1215/00318108-2009-00. Grice, Paul. 1989. Indicative conditionals. In Studies in the way of words, 58–85. Cambridge, MA: Harvard University Press.

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Groenendijk, Jeroen & Martin Stokhof. 1991. Dynamic predicate logic. Linguistics and Philosophy 14(1). 39–100. doi:10.1007/BF00628304. Heim, Irene. 1992. Presupposition projection and the semantics of attitude verbs. Journal of Semantics 9(3). 183–221. doi:10.1093/jos/9.3.183. Higginbotham, James. 2003. Conditionals and compositionality. Philosophical Perspectives 17(1). 181–194. doi:10.1111/j.1520-8583.2003.00008.x. Jackson, Frank. 1987. Conditionals. Oxford University Press. Kratzer, Angelika. 1981. The notional category of modality. In Hans-Jurgen Eikmeyer & Hannes Rieser (eds.), Words, worlds, and contexts: New approaches in word semantics (Research in Text Theory 6), 38–74. Berlin: de Gruyter. Kratzer, Angelika. 1986. Conditionals. Proceedings of the Chicago Linguistics Society [CLS] 22(2). 1–15. Lewis, David. 1973. Counterfactuals. Cambridge, MA: Harvard University Press. Lewis, David. 1975. Adverbs of quantification. In Edward Keenan (ed.), Formal semantics of natural language, 3–15. Cambridge University Press. Lewis, David. 1976. Probabilities of conditionals and conditional probability. The Philosophical Review 85(3). 297–315. doi:10.2307/2184045. Rawlins, Kyle. 2008. (Un)Conditionals. Santa Cruz, CA: UC Santa Cruz dissertation. Stalnaker, Robert. 1968. A theory of conditionals. In Nicholas Rescher (ed.), Studies in logical theory (American Philosophical Quarterly Monograph Series 2), 98–112. Blackwell. Stalnaker, Robert. 1975. Indicative conditionals. Philosophia 5(3). 269–286. doi:10.1007/BF02379021. Veltman, Frank. 1985. Logics for conditionals. Amsterdam: University of Amsterdam dissertation. Veltman, Frank. 1996. Defaults in update semantics. Journal of Philosophical Logic 25(3). 221–261. doi:10.1007/BF00248150. Veltman, Frank. 2005. Making counterfactual assumptions. Journal of Semantics 22(2). 159–180. doi:10.1093/jos/ffh022.

Anthony S. Gillies Department of Philosophy Rutgers University [email protected]

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Cross-linguistic variation in modality systems: The role of mood∗ Lisa Matthewson University of British Columbia

Received 2009-07-14 / First Decision 2009-08-20 / Revision Received 2010-02-01 / Accepted 2010-03-25 / Final Version Received 2010-05-31 / Published 2010-08-06

Abstract The St’át’imcets (Lillooet Salish) subjunctive mood appears in nine distinct environments, with a range of semantic effects, including weakening an imperative to a polite request, turning a question into an uncertainty statement, and creating an ignorance free relative. The St’át’imcets subjunctive also differs from Indo-European subjunctives in that it is not selected by attitude verbs. In this paper I account for the St’át’imcets subjunctive using Portner’s (1997) proposal that moods restrict the conversational background of a governing modal. I argue that the St’át’imcets subjunctive restricts the conversational background of a governing modal, but in a way which obligatorily weakens the modal’s force. This obligatory modal weakening — not found with Indo-European non-indicative moods — correlates with the fact that St’át’imcets modals differ from Indo-European modals along the same dimension. While Indo-European modals typically lexically encode quantificational force, but leave conversational background to context, St’át’imcets modals encode conversational background, but leave quantificational force to context (Matthewson, Rullmann & Davis 2007, Rullmann, Matthewson & Davis 2008).

Keywords: Subjunctive, mood, irrealis, modals, imperatives, evidentials, questions, free relatives, attitude verbs, Salish ∗ I am very grateful to St’át’imcets consultants Carl Alexander, Gertrude Ned, Laura Thevarge, Rose Agnes Whitley and the late Beverley Frank. Thanks to David Beaver, Henry Davis, Peter Jacobs, the members of the UBC Pragmatics Research Group (Patrick Littell, Meagan Louie, Scott Mackie, Tyler Peterson, Amélia Reis Silva, Hotze Rullmann and Ryan Waldie), three anonymous reviewers, and audiences at New York University, the University of British Columbia and the 44th International Conference on Salish and Neighbouring Languages for helpful feedback and discussion. Thanks to Tyler Peterson for helping prepare the manuscript for publication. This research is supported by SSHRC grants #410-2005-0875 and #410-2007-1046. ©2010 Lisa Matthewson This is an open-access article distributed under the terms of a Creative Commons NonCommercial License (creativecommons.org/licenses/by-nc/3.0).

Lisa Matthewson

1 Introduction Many Indo-European languages possess both modals, lexical items which quantify over possible worlds, and subjunctive moods, agreement paradigms which usually require a licensing modal element. The contrast is illustrated for Italian in (1)–(2). (1) contains modal auxiliaries; (2) contains subjunctive mood agreement which is licensed by the matrix attitude verb. (1)

a.

deve essere nell’ ufficio must+3sg+pres+ind be in.the office ‘He must be in the office.’

b.

puo essere nell’ ufficio may+3sg+pres+ind be in.the office ‘He may be in the office.’

(2)

(Italian; Palmer 2006: 102)


dubito che impari I.doubt that learn+3sg+pres+sbjn ‘I doubt that he’s learning.’


Previous work on the Salish language St’át’imcets (a.k.a. Lillooet; see Matthewson et al. 2007, Rullmann et al. 2008, and Davis, Matthewson & Rullmann 2009) has established the existence of a set of modals in this language, which differ in their semantics from those of Indo-European. Indo-European modals typically lexically encode distinctions of quantificational force, but leave conversational background (in the sense of Kratzer 1981, 1991) up to context. (1a), for example, unambiguously expresses necessity, while (1b) unambiguously expresses possibility. However, both modals allow either epistemic or deontic interpretations, depending on context. In contrast, modals in St’át’imcets lexically encode conversational background, but leave quantificational force up to context. (3a), for example, is unambiguously epistemic, but is compatible with either a necessity or a possibility interpretation, depending on context. (3b) is unambiguously deontic, but similarly allows differing quantificational strengths. See Matthewson et al. 2007, Rullmann et al. 2008, and Davis et al. 2009 for extensive discussion.1 1 All St’át’imcets data are from primary fieldwork unless otherwise noted. Data are presented in the practical orthography of the language developed by Jan van Eijk; see van Eijk & Williams 1981. Abbreviations: adhort: adhortative, caus: causative, circ: circumstantial modal, col: collective, comp: complementizer, cond: conditional, conj: conjunctive, counter: counter to expectations, deic: deictic, deon: deontic, demon: demonstrative, det:

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Cross-linguistic variation in modality systems: The role of mood

(3)

a.

wá7=k’a s-t’al l=ti=tsítcw-s=a be=epis stat-stop in=det=house-3sg.poss=exis s=Philomena nom=Philomena ‘Philomena must / might be in her house.’

b.

only epistemic

lán=lhkacw=ka áts’x-en ti=kwtámts-sw=a already=2sg.subj=deon see-dir det=husband-2sg.poss=exis ‘You must / can / may see your husband now.’

only deontic

A simplified table representing the difference between the two types of modal system is given in Table 1:

Indo-European St’át’imcets Table 1

quantificational force

conversational background

lexical context

context lexical

Indo-European vs. St’át’imcets modal systems

In this paper I extend the cross-linguistic comparison to the realm of mood. I argue that St’át’imcets possesses a subjunctive mood, and show that it induces a range of apparently disparate semantic effects, depending on the construction in which it appears. One example of the use of the subjunctive is given in (4): it weakens the force of a deontic modal proposition (in a sense to be made precise below). Other uses include turning imperatives into polite requests, and turning questions into statements of uncertainty (cf. van Eijk 1997 and Davis 2006). (4)

a.

gúy’t=Ø=ka ti=sk’úk’wm’it=a sleep=3indic=deon det=child=exis ‘The child should sleep.’

determiner, dir: directive transitivizer, ds: different subject, epis: epistemic, erg: ergative, exis: assertion of existence, foc: focus, fut: future, impf: imperfective, inch: inchoative, indic: indicative, infer: inferential evidential, irr: irrealis, loc: locative, mid: middle intransitive, nom: nominalizer, obj: object, prt: particle, pass: passive, perc.evid: perceived evidence, pl: plural, poss: possessive, prep: preposition, real: realis, red: redirective applicative, rem.past: remote past, sbjn: subjunctive, sg: singular, sim: simultaneous, stat: stative, temp.deic: temporal deictic, ynq: yes-no question. The symbol - marks an affix boundary and = marks a clitic boundary.

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Lisa Matthewson

b.

guy’t=ás=ka ti=sk’úk’wm’it=a sleep=3sbjn=deon det=child=exis ‘I hope the child sleeps.’

I will show that the St’át’imcets subjunctive differs markedly from IndoEuropean subjunctives, both in the environments in which it is licensed, and in its semantic effects. I propose an analysis of the St’át’imcets subjunctive which adopts insights put forward by Portner (1997, 2003). For Portner, moods in various Indo-European languages place restrictions on the conversational background of a governing modal. I argue that the St’át’imcets subjunctive mood can be analyzed within exactly this framework, with the twist that in St’át’imcets, the restriction the subjunctive places on the governing modal obligatorily weakens the force of the proposition expressed. This has an interesting consequence. While we can account for the St’át’imcets subjunctive using the same theoretical tools as for Indo-European, at a functional level the two languages are using their mood systems to achieve quite different effects. In particular, St’át’imcets uses its mood system to restrict modal force — precisely what this language does not restrict via its lexical modals. At a functional level, then, we find the same kind of cross-linguistic variation in the domain of mood as we do with modals. This idea is illustrated in the simplified typology in Table 2:

Indo-European St’át’imcets Table 2

lexically restrict quant. force

lexically restrict convers. background

modals moods

moods modals

Modal and mood systems

These results suggest that while individual items in the realm of mood and modality lexically encode different aspects of meaning, the systems as a whole have very similar expressive power. The structure of the paper: Section 2 introduces the St’át’imcets subjunctive data. I first illustrate the nine different uses of the relevant agreement paradigm, and then argue that this agreement paradigm is a subjunctive, rather than an irrealis mood. Section 3 shows that the St’át’imcets subjunctive is not amenable to existing analyses of more familiar languages.

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Section 4 reviews the basic framework adopted, that of Portner (1997), and Section 5 provides initial arguments for adopting a Portner-style approach for St’át’imcets. Section 6 presents the formal analysis, and Section 7 applies the analysis to a range of uses of the subjunctive. Section 8 concludes and raises some issues for future research. 2

St’át’imcets subjunctive data

St’át’imcets possesses a complex system of subject and object agreement. There are different subject agreement paradigms for transitive vs. intransitive predicates. For intransitive predicates, there are three distinct subject paradigms, one of which is glossed as ‘subjunctive’ by van Eijk (1997) and Davis (2006).2

1sg 2sg 3sg 1pl 2pl 3pl Table 3

indicative indicative nominalized

subjunctive

tsút=kan tsút=kacw tsut=Ø tsút=kalh tsút=kal’ap tsút=wit

tsút=an tsút=acw tsút=as tsút=at tsút=al’ap tsút=wit=as

n=s=tsut s=tsút=su s=tsút=s s=tsút=kalh s=tsút=lap s=tsút=i

Subject agreement paradigms for the intransitive predicate tsut ‘to say’ (adapted from van Eijk 1997: 146)

With transitive predicates, the situation is similar, except that there are four separate paradigms, one of which is subjunctive.3,4 2 The cognate forms are often called ‘conjunctive’ in other Salish languages, primarily in order to disambiguate the abbreviations for ‘subject’ and ‘subjunctive’. See for example Kroeber 1999. 3 The traditional terms for the first two columns are ‘indicative’ and ‘nominalized’ respectively. The nominalized endings are identical to nominal possessive endings, and are glossed as ‘poss’ in the data. The choice between these first two paradigms is syntactically governed: the so-called ‘indicative’ surfaces in matrix clauses and relative clauses, while the nominalized paradigm appears in subordinate clauses. Both these sets contrast semantically, in all syntactic environments, with the subjunctive, hence my overall categorization of the first two paradigms as ‘indicative’. 4 See Kroeber 1999 and Davis 2000 for justification of the analysis of subject inflection

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Lisa Matthewson

In subsection 2.1 I illustrate the uses of the paradigms glossed as subjunctive, and in subsection 2.2 I argue that these paradigms more closely approximate familiar subjunctives, rather than irrealis moods. 2.1 Uses of the St’át’imcets subjunctive The mood I am glossing as ‘subjunctive’ has a wide range of uses, which at first glance are not easily unifiable. I illustrate all of them here. First, the subjunctive functions to turns a plain assertion into a wish (Davis 2006: chapter 24).5 (5)

a.

nilh s=Lémya7 ti=kél7=a foc nom=Lémya7 det=first=exis ‘Lémya7 is first.’

b.

nílh=as s=Lémya7 ku=kéla7 foc=3sbjn nom=Lémya7 det=first ‘May Lémya7 be first.’

(6)

a.

ámh=as ku=scwétpcen-su! good=3sbjn det=birthday=2sg.poss ‘May your birthday be good!’

b.

ámh=as ku=s=wá7=su! good=3sbjn det=nom=be=2sg.poss ‘Best wishes!’ [‘May your being be good.’]

(Davis 2006: ch. 24)

This use of the subjunctive is very restricted (see van Eijk 1997: 147). Minimal pairs cannot usually be constructed for ordinary assertions, as shown in (7)–(9). (7)

a.

kwis lhkúnsa rain today ‘It’s raining today.’

b.

*kwís=as lhkúnsa rain=3sbjn today intended: ‘May it rain today.’

assumed here. I do not provide the transitive paradigms, as subject markers vary based on the person and number of the object and the table is excessively large. See van Eijk 1997 and Davis 2006 for details. 5 The determiner alternation between (5a) and (5b) (ti=. . . =a vs. ku=) is predictable, but irrelevant for current concerns. See Matthewson 1998, 1999 for discussion.

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(8)

a.

áma ti=sq’ít=a good det=day=exis ‘It is a good day.’

b.

*ámh=as ti=sq’ít=a good=3sbjn det=day=exis intended: ‘May it be a good day.’

(9)

a.

guy’t ti=sk’úk’wm’ita sleep det=child=exis ‘The child is sleeping.’

b.

*guy’t=ás ti=sk’úk’wm’ita sleep=3sbjn det=child=exis intended: ‘I hope the child sleeps.’

In general, the subjunctive seems only to add to a plain assertion either in a cleft structure, as in (5), or in conventionalized wishes, as in (6). I return to this issue below. The more usual case of the subjunctive creating a wish-statement is when it co-occurs with the deontic modal ka, as in (10)–(11). (10)

a.

plan=ka=tí7=t’u7 wa7 máys-n-as already=deon=demon=prt impf fix-dir-3erg ‘He should have fixed that already.’

b.

plan=as=ká=tí7=t’u7 wa7 máys-n-as already=3sbjn=deon=demon=prt impf fix-dir-3erg ‘I wish he had fixed that already.’

(11)

a.

gúy’t=ka ti=sk’úk’wm’it=a sleep=deon det=child=exis ‘The child should sleep.’

b.

gúy’t=ás=ka ti=sk’úk’wm’it=a sleep=3sbjn=deon det=child=exis ‘I hope the child sleeps.’

When used with the deontic modal ka, in addition to the ‘wish’ interpretation shown in (10)–(11), the subjunctive can also render a ‘pretend to be ...’ interpretation.6 6 The data in (12) are from the Upper St’át’imcets dialect; in Lower St’át’imcets, (12a) is corrected to (i), which has the subjunctive but lacks the deontic modal. This independent

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Lisa Matthewson

(12)

a.

skalúl7=acw=ka: saq’w knáti7 múta7 em7ímn-em owl=2sg.sbjn=deon fly deic and animal.noise-mid ‘Pretend to be an owl: fly around and hoot.’ (Davis 2006: chapter 24)

b.

snu=hás=ka ku=skícza7 2sg.emph=3sbjn=deon det=mother ‘Pretend to be the mother.’ (Whitley, Davis, Matthewson & Frank (editors) no date)

The fourth construction which licenses the subjunctive is the imperative; the subjunctive weakens an imperative to a polite request (Davis 2006: chapter 24). In each of (13)–(15), the subjunctive imperative in (b) is construed as ‘more polite’ than the plain imperative in (a). The subjunctive is particularly common in negative requests, as in (15). (13)

a.

lts7á=malh lh=kits-in’=ál’ap! deic=adhort comp=put.down-dir=2pl.sbjn ‘Just put it over here!’

b.

lts7á=has=malh lh=kits-in’=ál’ap deic=3sbjn=adhort comp=put.down-dir=2pl.sbjn ‘Could you put it down here?’/‘You may as well put it down over here.’7 (adapted from Davis 2006: chapter 24)

(14)

a.

nás=malh áku7 pankúph=a go=adhort deic Vancouver=exis ‘You’d better go to Vancouver.’

b.

nás=acw=malh áku7 pankúph=a go=2sg.sbjn=adhort deic Vancouver=exis ‘You could go to Vancouver.’

pronoun construction is argued by Thoma (2007) to be a concealed cleft. I return to this issue below. (i) nu=hás ku=kalúla7 2sg.emph=3sbjn det=owl ‘Pretend to be an owl.’ 7 The third person subjunctive ending appears here because the structure is bi-clausal, involving a third-person impersonal main predicate: ‘It is here that you could put it down.’

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(15)

a.

cw7aoz kw=s=sek’w-en-ácw ta=nk’wanústen’=a neg det=nom=break-dir-2sg.erg det=window=exis ‘Don’t break the window.’

b.

cw7áoz=as kw=s=sek’w-en-ácw ta=nk’wanústen’=a neg=3sbjn det=nom=break-dir-2sg.erg det=window=exis ‘Don’t break the window.’

Fifth, in combination with an evidential or a future modal, the subjunctive helps to turn wh-questions into statements of uncertainty or wondering. (16)

a.

kanem=lhkán=k’a do.what=1sg.indic=infer ‘What happened to me?’

b.

kanem=án=k’a do.what=1sg.sbjn=infer ‘I don’t know what happened to me.’ / ‘I wonder what I’m doing.’8

(17)

a.

kanem=lhkácw=kelh múta7 do.what=2sg.indic=fut again ‘What are you going to be doing later?’

b.

kanem=ácw=kelh múta7 do.what=2sg.sbjn=fut again ‘I wonder what you are going to do again.’

(18)

a.

(van Eijk 1997: 215)

nká7=kelh lh=cúz’=acw nas where=fut comp=going.to=2sg.sbjn go ‘Where will you go?’

b.

nká7=as=kelh lh=cúz’=acw nas where=3sbjn=fut comp=going.to=2sg.sbjn go ‘Wherever will you go?’ / ‘I wonder where you are going to go now.’ (adapted from Davis 2006: chapter 24)

The same effect arises with yes-no questions. In combination with the evidential k’a or a future modal, the subjunctive also turns these into statements of uncertainty which are often translated using ‘maybe’ or ‘I wonder’. 8 For expository reasons, k’a was glossed as ‘epistemic’ in (3a) above, but from now on will be glossed as ‘inferential’. Matthewson et al. (2007) analyze k’a as an epistemic modal which carries a presupposition that there is inferential evidence for the claim.

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Lisa Matthewson

(19)

a.

lán=ha kwán-ens-as already=ynq take-dir-3erg ni=n-s-mets-cál=a det.abs=1sg.poss-nom-write-act=exis ‘Has she already got my letter?’

b.

lan=as=há=k’a kwán-ens-as already=3sbjn=ynq=infer take-dir-3erg ni=n-s-mets-cál=a det.abs=1sg.poss-nom-write-act=exis ‘I wonder if she’s already got my letter.’/’I don’t know if she got my letter or not.’

(20)

wa7=as=há=k’a tsicw impf=3sbjn=ynq=infer get.there i=n-sésq’wez’=a, cw7aoz kw=en det.pl=1sg.poss-younger.sibling=exis neg det=1sg.poss zwát-en know-dir ‘Perhaps my younger siblings went along, I don’t know.’ (Matthewson 2005: 265)

In combination with a wh-indefinite and the evidential k’a, the subjunctive creates free relatives with an ‘ignorance/free choice’ reading; see Davis 2006 for discussion. (21)

a.

qwatsáts=t’u7 múta7 súxwast áku7, t’ak aylh áku7, leave=prt again go.downhill deic go then deic nílh=k’a s=npzán-as foc=infer nom=meet(dir)-3erg k’a=lh=swát=as=k’a káti7 ku=npzán-as infer=comp=who=3sbjn=infer deic det=meet(dir)-3erg ‘So he set off downhill again, went down, and then he met whoever he met.’ (van Eijk & Williams 1981: 66, cited in Davis 2009)

b.

o, púpen’=lhkan [ta=stam’=as=á=k’a] oh find=1sg.indic [det=what=3sbjn=exis=infer] ‘Oh, I’ve found something or other.’ (Unpublished story by “Bill” Edwards, cited in Davis 2009)

When used in combination with the scalar particle t’u7, the subjunctive creates a statement translated as ‘might as well’ or ‘may as well’.

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(22)

a.

wá7=lhkan=t’u7 wa7 k’wzús-em impf=1sg.indic=prt impf work-mid ‘I am just working.’

b.

wá7=an=t’u7 wa7 k’wzús-em impf=1sg.sbjn=prt impf work-mid ‘I might as well stay and work.’

(23)

a.

wá7=lhkacw=t’u7 lts7a lhkúnsa ku=sgáp be=2sg.indic=prt deic now det=evening ‘You are staying here for the night.’

b.

wá7=acw=t’u7 lts7a lhkúnsa ku=sgáp be=2sg.sbjn=prt deic now det=evening ‘You may as well stay here for the night.’

And finally, in combination with a wh-word and the scalar particle t’u7, the subjunctive creates free relatives with a universal / indifference reading. (24)

a.

wa7 táw-em ki=smán’c=a, ns7á7z’-em impf sell-mid det.col=tobacco=exis trade-mid ku=stám’=as=t’u7 det=what=3sbjn=prt ‘He was selling tobacco, trading it for whatever . . . ’ (van Eijk & Williams 1981: 74, cited in Davis 2009)

b.

wa7 kwám=wit ku=káopi, ku=súkwa, ku=saplín, impf take(mid)=3pl det=coffee det=sugar det=flour [stám’=as=t’u7 cw7aoz [what=3sbjn=prt neg kw=s=ka-ríp-s-tum’-a det=nom=circ-grow-caus-1pl.erg-circ l=ti=tmícw-lhkalh=a] on=det=land-1pl.poss=exis] ‘They got coffee, sugar, flour, whatever we couldn’t grow on our land. . . ’ (Matthewson 2005: 105, cited in Davis 2009)

c.

[stám’=as=t’u7 káti7 i=wá7 [what=3sbjn=prt deic det.pl=impf ka-k’ac-s-twítas-a i=n-slalíl’tem=a] circ-dry-caus-3pl.erg-circ det.pl=1sg.poss-parents=exis] wa7 ts’áqw-an’-em lh=as sútik impf eat-dir-1pl.erg comp(impf)=3sbjn winter 9:11

Lisa Matthewson

‘Whatever my parents could dry, we ate in wintertime.’ (Matthewson 2005: 141, cited in Davis 2009) The nine uses of the St’át’imcets subjunctive are summarized in Table 4: environment

indicative meaning

subjunctive meaning

plain assertion deontic modal deontic modal imperative wh-question + evidential/future yes-no question + evidential/future wh-word + evidential scalar particle t’u7 wh-word + scalar particle t’u7

assertion deontic necessity/possibility deontic necessity/possibility command question

wish wish ‘pretend’ polite request uncertainty/wondering

question

uncertainty/wondering

question ‘just/still’ N/A

ignorance free relative ‘might as well’ indifference free relative

Table 4

Uses of the St’át’imcets subjunctive

These are all the cases where the subjunctive has a semantic effect; in the next sub-section we will also see some cases where the subjunctive is obligatory and semantically redundant. I will not aim to account for the entire panoply of subjunctive effects in one paper. However, the analysis I offer will explain the first seven uses, setting aside for future research only the two uses which involve the particle t’u7. See Section 8 for some speculative comments about the subjunctive in combination with t’u7. 2.2

This is a subjunctive mood

In this sub-section I justify the use of the term ‘subjunctive’ for the subject agreements being investigated. The choice of terminology is intended to reflect the fact that the St’át’imcets mood patterns with Indo-European subjunctives, rather than with Amerindian irrealis moods, in several respects. However, we will see below that the St’át’imcets subjunctive also differs

9:12


semantically in important ways from Indo-European subjunctives.9 Palmer (2006) observes that there is a broad geographical typology, such that European languages often encode an indicative/subjunctive distinction, while Amerindian and Papuan languages often encode a realis/irrealis distinction. A typical irrealis-marking system is illustrated in (25). (25)

a.

ho bu-busal-en age qo-in pig sim-run.out-3sg+ds+real 3pl hit-3pl+rem.past ‘They killed the pig as it ran out.’

b.

(Amele; Palmer 2006: 5)

ho bu-busal-eb age qo-qag-an pig sim-run.out-3sg+ds+irr 3pl hit-3pl-fut ‘They will kill the pig as it runs out.’

(Amele; Palmer 2006: 5)

According to Palmer (2006: 145), the indicative/subjunctive distinction and the realis/irrealis distinction are ‘basically the same’. The core function of both a subjunctive and an irrealis is to encode ‘non-assertion’.10 However, there are differences in distribution and in syntactic functions. First, Palmer observes that subjunctive is not marked independently of other inflectional categories such as person and number. Instead, there is typically a full subjunctive paradigm. On the other hand, irrealis is often marked by a single element. In this respect, the St’át’imcets mood patterns like a subjunctive; see Table 3 above. Second, in main clauses, irrealis marking is often used for questions, futures and denials; this is not the case for main clause subjunctives. In this respect also, the St’át’imcets mood patterns like a subjunctive. It is not used to mark questions, futures or denials. (26)–(28) all have indicative marking. 9 This raises a terminological issue which arises in many areas of grammar. Should we apply terms which were invented for European languages to similar — but not identical — categories in other languages? For example, should we say ‘The perfect / definite determiner / subjunctive in language X differs semantically from its English counterpart’, or should we say ‘Language X lacks a perfect / definite determiner / subjunctive’, because it lacks an element with the exact semantics of the English categories? I adopt the former approach here, as I think it leads to productive cross-linguistic comparison, and because it suggests that the traditional terms do not represent primitive sets of properties, but rather potentially decomposable ones. 10 Palmer does not provide a definition of ‘non-assertion’. He observes that common reasons why a proposition is not asserted are because the speaker doubts its veracity, because the proposition is unrealized, or because it is presupposed (Palmer 2006: 3). See Section 3 below for discussion.

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Lisa Matthewson

(26)

t’íq=Ø=ha kw=s=Josie? arrive=3indic=ynq det=nom=Josie ‘Did Josie arrive?’

(27)

t’íq=Ø=kelh kw=s=Josie arrive=3indic=fut det=nom=Josie ‘Josie will arrive.’

(28)

cw7aoz kw=s=t’iq=s s=Josie neg det=nom=arrive=3poss nom=Josie ‘Josie didn’t arrive.’

Third, Palmer notes that subjunctive marking is obligatory and redundant only in subordinate clauses, while irrealis marking is often obligatory and redundant in main clauses. Here again, the St’át’imcets mood patterns like a subjunctive. It is obligatory and redundant only in three cases. The first is when embedded under the complementizer lh=. lh= is glossed by van Eijk (1997) as ‘hypothetical’, and analyzed by Davis (2006) as a complementizer which introduces subjunctive clauses, including if -clauses, as in (29a) and (29b), temporal adjuncts (29b), locative adjuncts (29c), and complements to the evidential k’a when this is used as a (focused) adverb (29d). (29)

a.

lh=cw7áoz*(=as)=ka kw=s=gúy’t=su, comp=neg*(=3sbjn)=irr det=nom=sleep=2sg.poss lán=ka=tu7 wa7 xzum i=n’wt’ústen-sw=a already=irr=then impf big det.pl=eye-2sg.poss=exis ‘If you hadn’t slept, your eyes would have been big already.’ (van Eijk & Williams 1981: 12)

b.

xwáyt=wit=ka lh=wa7=wit*(=ás)=t’u7 qyax many.people.die=3pl=irr comp=be=3pl*(=3sbjn)=prt drunk múta7 tqálk’-em lh=w*(=as) qyáx=wit and drive-mid comp=impf*(=3sbjn) drunk=3pl ‘They would die if they got drunk and drove when they were drunk.’ (Matthewson 2005: 367)

c.

lts7a lh=wa7*(=as) qwál’qwel’t deic comp=impf*(=3sbjn) hurt ‘It is here that it is hurting.’

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d.

k’a lh=7án’was*(=as) sq’it, maybe comp=two*(=3sbjn) day ka-láx-s-as-a n-skícez7=a circ-remember-caus-3erg-circ 1sg.poss-mother=exis na=s-7ílacw-em-s=a det=nom-soak-mid-3poss=exis ta=n-qéqtsek=a det=1sg.poss-older.brother=exis ‘Maybe two days later, my mother remembered the fish my brother had been soaking.’ (Matthewson 2005: 152; cited in Davis 2006: chapter 23)11

The second case where the St’át’imcets subjunctive is obligatory and redundant is when embedded under the complementizer i= ‘when’, as in (30). i= has a similar distribution to lh=, but is restricted to past-time contexts. See van Eijk 1997: 235-6 and Davis 2006: chapter 27 for discussion. (30)

a.

i=kél7=at tsicw, áts’x-en-em when.past=first=1pl.sbjn get.there see-dir-1pl.erg i=cw7ít=a tsitcw det=many=exis house ‘When we first got there, we saw lots of houses.’ (Matthewson 2005: 74)

b.

wá7=lhkan lexláx-s i=kwís*(=as) impf=1sg.indic remember-caus when.past=fall*(=3sbjn) na=n-sésq’wez’=a, s=Harold Peter det.abs=1sg.poss-younger.sibling=exis nom=Harold Peter ‘I remember when my little brother was born, Harold Peter.’ (Matthewson 2005: 354-5)

11 Incidentally, Davis (2006: chapter 23) observes that ‘two or more k’a lh= clauses strung together form the closest equivalent in [St’át’imcets] of [English] “either...or”.’ An example is given in (i). (i)

k’a lh=xw7utsin-qín’=as, k’a lh=tsilkst-qín’=as=kelh maybe comp=four-animal=3sbjn maybe comp=five-animal=3sbjn=fut ‘It’ll either be a four point or a five point buck.’

(Davis 2006: chapter 23)

As Davis implies, St’át’imcets lacks any lexical item which renders logical disjunction, and constructions like (i), although used to translate English ‘or’, are literally two ‘maybe’-clauses strung together.

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Lisa Matthewson

Finally, the subjunctive is obligatory when it appears in combination with the perceived-evidence evidential =an’. =an’ is analyzed by Matthewson et al. (2007) as an epistemic modal which is defined only if the speaker has perceived indirect evidence for the prejacent proposition. (31)

a.

*táyt=kacw=an’ hungry=2sg.indic=perc.evid ‘You must be hungry.’

b.

táyt=acw=an’ hungry=2sg.sbjn=perc.evid ‘You must be hungry.’

(32)

a.

*nílh=Ø=an’ s=Sylvia ku=xílh-tal’i foc=3indic=perc.evid nom=Sylvia det=do(caus)-top ‘Apparently it was Sylvia who did it.’

b.

nílh=as=an’ s=Sylvia ku=xílh-tal’i foc=3sbjn=perc.evid nom=Sylvia det=do(caus)-top ‘Apparently it was Sylvia who did it.’ (Matthewson et al. 2007: 208)

The perceived-evidence evidential is the only environment in the language where the subjunctive is obligatory in a matrix clause. I assume that the subjunctive lacks semantic import here, as an otherwise very similar evidential lákw7a does not allow the subjunctive in cases parallel to (31)–(32) (Matthewson 2010, to appear). The conclusion is that St’át’imcets, in spite of being an Amerindian language, has a mood which patterns, at least morpho-syntactically, like a subjunctive rather than an irrealis. This fits with how van Eijk (1997) and Davis (2000, 2006) gloss the relevant forms. However, we will see in the next section that the St’át’imcets subjunctive differs semantically in interesting ways from European subjunctives. 3

Why previous analyses do not work for St’át’imcets

The vast majority of formal research on the subjunctive deals with IndoEuropean. In languages such as the Romance languages, the subjunctive mood is used for wishes, fears, speculations, doubts, obligations, reports, unrealized events, or presupposed propositions. Some examples are provided in (33)–(34).

9:16


(33)

a.

creo que aprende I.believe that learn+3sg+pres+indic ‘I believe that he is learning.’

b.

dudo que aprenda I.doubt that learn+3sg+pres+sbjn ‘I doubt that he’s learning.’

(34)

(Spanish; Palmer 2006: 5)


potessi venire anch’ io can+1sg+pres+sbjn come also I ‘If only I could come too.’


In this section I briefly discuss some of the main approaches to the subjunctive. I cannot do justice to the full array of proposals in the literature; the goal is to provide enough background to establish that the St’át’imcets subjunctive is not amenable to a range of existing approaches. One pervasive line of thought is that subjunctive encodes a general semantic contribution of ‘non-assertion’ (Bolinger 1968, Terrell & Hooper 1974, Hooper 1975, Klein 1975, Farkas 1992, Lunn 1995, Palmer 2006, Haverkate 2002, Panzeri 2003, among others). One recent formal proposal in this line is that of Farkas (2003). Farkas argues that there is a correlation between indicative mood and complements which have assertive context change potential relative to the embedded environment. Assertive context change for a matrix clause is defined as in (35); the context set of worlds Wc is narrowed. (35)

Assertive context change c + φ is assertive iff Wc 0 = Wc ∩ p, where c 0 is the output context. (Farkas 2003: 5)

Farkas provides an analysis of assertion in embedded contexts which predicts that positive epistemic predicates like believe or know take indicative complements, as these complements are asserted relative to the matrix subject’s epistemic state.12 Predicates of assertion (‘say’, ‘assert’) and of fiction (‘dream’, ‘imagine’) similarly introduce complements which are assertively added to the embedded speech context, and also take indicative complements. On the other hand, complements to desideratives (‘want’, ‘wish’, ‘desire’) and directives (‘command’, ‘direct’, ‘request’) are not assertive. Rather than eliminating 12 Predicates like believe take subjunctive complements in Italian; see Giorgi & Pianesi 1997, among many others, for discussion.

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Lisa Matthewson

worlds in the context set where the complement is false, these predicates eliminate worlds in the context set which are low on an evaluative ranking.13 Thus, these predicates take the subjunctive: (36)

Maria vrea s˘ a-i r˘ aspund˘ a Maria wants subj-cl answer.sbjn ‘Maria wants to answer him.’

(Romanian; Farkas 2003: 2)

Giannakidou (1997, 1998, 2009) offers an alternative characterization of the distribution of the subjunctive, according to which it appears in nonveridical contexts, while indicative appears in veridical contexts. The relevant definition is given in (37): (37)

A propositional operator F is veridical iff from the truth of F p we can infer that p is true relative to some individual x (i.e., in some individual x’s epistemic model) . . . If inference to the truth of p under F is not possible, F is nonveridical. (Giannakidou 2009: 1889)

According to this analysis, the division between indicative-taking and subjunctive-taking predicates relies on whether at least one epistemic agent is committed to the truth of the embedded proposition. Giannakidou’s approach predicts a similar division between indicative- and subjunctivetaking predicates to Farkas’s. In Modern Greek, the indicative is found in complements to predicates of assertion or fiction, epistemics, factives and semi-factives. The subjunctive is found in complements to volitionals, directives, modals, permissives, negatives, and verbs of fear (Giannakidou 2009: 9).14 An approach which aims to derive mood selection directly from the semantics of subordinating predicates is that of Villalta (2009). Villalta argues 13 The complements of desideratives are also not ‘decided’ relative to their context set, which is what is actually crucial here for Farkas (2003). Farkas proposes an Optimality Theory account involving the two constraints in (i): (i) *SUBJ/+Decided

*IND/-Assert

Different rankings of these two constraints give rise to different mood choices in Romanian vs. French for emotive factive predicates like ‘be sorry/happy’, ‘regret’. Emotive factives are +Decided but -Assertive, and take the indicative in Romanian and the subjunctive in French. 14 Giannakidou (2009) proposes that the Modern Greek subjunctive complementizer na contributes temporal semantics (introducing a ‘now’ variable). The generalization is still that subjunctive appears in non-veridical contexts; see Giannakidou 2009 for details.

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that subjunctive-selecting predicates are those whose embedded propositions are compared to contextual alternatives on a scale encoded by the predicate. The contribution of the subjunctive is to evaluate the contextual alternatives. Quer (1998, 2001), looking mainly at Catalan and Spanish, argues that the subjunctive signals a shift in the model of the evaluation of the truth of the proposition. For unembedded assertions, the anchor is the Speaker and the model is the epistemic model of the Speaker. Operators which introduce subjunctive introduce buletic models, or other models which create comparative relations among worlds. This predicts we will find subjunctive in purpose clauses, and predicts indicative/subjunctive alternations in restrictive relative clauses, concessives, and free relatives. Quer (2009) also discusses indicative/subjunctive alternations in conditionals, claiming that indicative appears in protases that are ‘realistic in the sense that they quantify over worlds which are close enough to the actual one’ (2009: 1780). Subjunctive is used when the worlds are further away from the actual one or even disjoint from it. An approach to mood which draws on notions from noun phrase semantics is offered by Baker & Travis (1997). Baker and Travis argue that in Mohawk, mood marks a division between ‘verbal specificity’ (‘factive’ mood) and Kamp/Heim-style indefiniteness (two variants of non-factive mood, previously called the ‘future’ and the ‘optative’). Indefinite/non-factive mood appears in future contexts, in past habituals, in negative clauses, under the verbs ‘promise’ and ‘want’, and in free relatives with a non-specific reading. What links all these indefinite-mood environments, according to Baker and Travis, is the same feature that characterizes indefinite noun phrases in the Kamp/Heim system: a free variable (in the Mohawk case, an event variable) which undergoes existential closure in the scope of various operators. This ends our brief tour through some major formal approaches to the subjunctive.15 The reader is referred to Portner (2003) for further overview and discussion. In the next sub-section I show that the St’át’imcets subjunctive does not behave like the Indo-European or Mohawk subjunctives, and that a new approach is required. 15 I defer discussion of Portner’s (1997) analysis to Section 5, since I will be adapting Portner’s approach for St’át’imcets.

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The St’át’imcets subjunctive is not amenable to existing approaches

3.1

The St’át’imcets subjunctive differs from familiar subjunctives in both its distribution and semantic effects. Although there are some initial similarities, such as the fact that both St’át’imcets and Indo-European subjunctives can be used to express wishes and hopes, St’át’imcets mood displays no sensitivity to the choice of matrix predicate. Thus, unlike in Romance or Greek, predicates of assertion, belief and fiction are not differentiated from desideratives or directives. All attitude verbs in St’át’imcets take the indicative, as illustrated for a representative range in (38).16,17 (38)

a.

tsut k=Laura kw=s=t’iq=Ø k=John say det=Laura det=nom=arrive=3indic det=John ‘Laura said that John came.’

b.

tsut-ánwas k=Laura kw=s=t’iq=Ø k=John say-inside det=Laura det=nom=arrive=3indic det=John ‘Laura thought that John came.’

c.

zwát-en-as k=Laura kw=s=t’iq=Ø k=John know-dir-3erg det=Laura det=nom=arrive=3indic det=John ‘Laura knew that John came.’

16 Interestingly, the same is not true of the related language Skwxwú7mesh (Squamish). In Skwxwú7mesh, the subjunctive (glossed as ‘conjunctive’; see fn. 2) is obligatory under ‘tell someone to do something’ (as in (i)), but is optional under ‘I think’, depending on whether the speaker knows that the event did not take place (ii-iii) (all data from Peter Jacobs, p.c.). (i) chen tsu-n-Ø-Ø mi as uys I tell-dir-dat-3obj come 3conj come.inside ‘I told him to come inside.’ (ii) chen ta7aw’n kwi s-Ø-s mi uys I think det nom-real-3poss come come.inside ‘I think he came inside.’ (iii) chen ta7aw’n k’-as mi uys I think irr-3conj come come.inside ‘I thought he came inside (but then I found out that he’s still outside playing).’ Jacobs (1992) analyzes the mood distinction in Skwxwú7mesh as encoding speaker certainty, which suggests that it differs from the St’át’imcets mood system. 17 The expected subject inflection in the embedded clauses in (38) would actually be possessive =s; see van Eijk 1997 and Davis 2006. However, many modern speakers prefer to omit the possessive ending and to use matrix indicative =Ø in these contexts. This does not affect the point at hand, as the variation is between two forms of indicative marking.

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d.

kw7íkwl’acw k=Laura kw=s=t’iq=Ø k=John dream det=Laura det=nom=leave=3indic det=John ‘Laura dreamt that John came.’

e.

xát’-min’-as k=Laura kw=s=t’iq=Ø k=John want-red-3erg det=Laura det=nom=arrive=3indic det=John ‘Laura wanted John to come.’

f.

tsa7cw k=Laura kw=s=t’iq=Ø k=John glad det=Laura det=nom=arrive=3indic det=John ‘Laura was happy that John came.’

g.

tsún-as k=Laura k=John kw=s=ts7as=Ø say(dir)-3erg det=Laura det=John det=nom=come=3indic ‘Laura told John to come.’18

The St’át’imcets subjunctive is also not used under negated verbs of belief or report, as it is in many European languages (cf. Palmer 2006: 116). Compare Spanish (39a) with St’át’imcets (39b) and (39c). (39)

a.

no creo que aprenda not I.think that learn+3sg+pres+sbjn ‘I don’t think that he is learning.’

b.


cw7aoz kw=en=tsut-ánwas kw=s=zwátet-cal=s neg det=1sg.poss=say-inside det=nom=know-act=3poss ‘I don’t think that he is learning.’

c.

cw7aoz kw=s=tsut=s kw=s=Aggie neg det=nom=say=3poss det=nom=Aggie kw=s=t’cum=s i=gáp=as det=nom=win=3poss when.past=evening=3sbjn ‘Aggie didn’t say she won last night.’

Nor does the St’át’imcets subjunctive give rise to interpretive differences inside relative clauses. In some Indo-European languages, an indicative/subjunctive contrast in restrictive relatives gives rise to a distinction which has variously been analyzed as referential/attributive, specific/nonspecific, or wide-scope/narrow-scope (see Rivero 1975, Farkas 1992, Giannakidou 1997, Beghelli 1998, Quer 2001, among many others). This is illustrated in 18 The predicate in (38g) differs from that in (38a)–(38f) because the ‘ordering’ environment in (38g) requires an unergative embedded verb.

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(40) for Catalan. Quer’s analysis of these examples involves a shifting of the model in which the descriptive condition in the relative clause is interpreted; the effect is one of apparent ‘wide-scope’ for the descriptive condition in the indicative (40a), as opposed to in the subjunctive (40b). (40)

a.

necessiten un alcalde [que fa grans need.3pl a mayor that make.indic.prs.3sg big inversions] investments ‘They need a mayor that makes big investments.’ (Catalan; Quer 2001: 90)

b.

necessiten un alcalde [que faci grans need.3pl a mayor that make.sbjn.prs.3sg big inversions] investments ‘They need a mayor that makes big investments.’ (Catalan; Quer 2001: 90)

In St’át’imcets, nominal restrictive relatives uniformly take indicative marking, as shown in (41). The distinction which is in Catalan is encoded by mood, is achieved by means of determiner choice in St’át’imcets (see Matthewson 1998, 1999 for analysis). (41)

a.

wa7 xat’-min’-ítas ti=kúkwpi7=a wa7 impf want-red-3pl.erg det=chief=exis impf ka-nuk’wa7-s-tanemwít-a k=wa=s mays circ-help-caus-3pl.pass-circ det=impf=3poss fix ku=tsetsítcw det=houses ‘They need a (particular) chief who can help them build houses.’ [wide-scope indefinite]

b.

wa7 xat’-min’-ítas ku=kúkwpi7 wa7 impf want-red-3pl.erg det=chief impf ka-nuk’wa7-s-tanemwít-a k=wa=s mays circ-help-caus-3pl.pass-circ det=impf=3poss fix ku=tsetsítcw det=houses ‘They need a(ny) chief who can help them build houses.’ [narrow-scope indefinite]

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The mood effects seen in conditionals in some Indo-European languages are also absent in St’át’imcets. The antecedents of both notionally indicative and subjunctive conditionals are obligatorily marked with the subjunctive, as shown in (42), a paradigm borrowed from Quer 2009: 1780. Although there are ways to distinguish the different types of conditionals, they do not involve an indicative-subjunctive mood alternation. (42)

a.

Context: I’m looking for John. You say: lh=7áts’x-en=an, nílh=t’u7 s=qwál’-en-tsin comp=see-dir=1sg.sbjn foc=prt nom=tell-dir-2sg.obj ‘If I see him, I’ll tell you.’

b.

Context: I’m looking for John, and I suspect you know where he is but you haven’t been telling me. You say: lh=7ats’x-en=án=ka, sqwal’-en-tsín=lhkan=kelh comp=see-dir=1sg.sbjn=irr tell-dir-2sg.obj=1sg.indc=fut ‘If I saw him, I would tell you.’

c.

Context: I was looking for John, but he left town before I could find him. You say: lh=7ats’x-en=án=ka=tu7 comp=see-dir=1sg.sbjn=irr=then qwal’-en-tsín=lhan=ka tell-dir-2sg.obj=1sg.indic=irr ‘If I had seen him, I would have told you.’

The St’át’imcets subjunctive is also not like the Mohawk one. Unlike in Mohawk, St’át’imcets futures take the indicative, as shown in (43); so do past habituals, as shown in (44), and plain negatives, as in (45). (43)

a.

ats’x-en-tsí=lhkan=kelh lh=nátcw=as see-dir-2sg.obj=1sg.indic=fut comp=one.day.away=3sbjn ‘I’ll see you tomorrow.’

b.

*ats’x-en-tsín=an=kelh lh=nátcw=as see-dir-2sg.obj=1sg.sbjn=fut comp=one.day.away=3sbjn ‘I’ll see you tomorrow.’

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(44)

a.

wa7=lhkalh=wí7=tu7 n-záw’-em ku=qú7 impf=1pl.indic=emph=then loc-get.water-mid det=water lhel=ta=qú7qu7=a múta7 lhel=ta=tswáw’cw=a from=det=water(pl)=exis and from=det=creek=exis ‘We used to fetch water from the spring and the creek.’ (Matthewson 2005: 370)

b.

*wa7=at=wí7=tu7 n-záw’-em ku=qú7 impf=1pl.sbjn=emph=then loc-get.water-mid det=water lhel=ta=qú7qu7=a múta7 lhel=ta=tswáw’cw=a from=det=water(pl)=exis and from=det=creek=exis ‘We used to fetch water from the spring and the creek.’

(45)

a.

áy=t’u7 kw=en=gúy’t ku=pála7 sgap neg=prt det=1sg.poss=sleep det=one evening ‘I didn’t sleep one night.’

b.

(Matthewson 2005: 267)

*áy=t’u7 kw=s=gúy’t=an ku=pála7 sgap neg=prt det=nom=sleep=1sg.sbjn det=one evening ‘I didn’t sleep one night.’

Finally, there are the cases where the St’át’imcets subjunctive does appear, with a predictable meaning difference, which are not attested in other languages. These include the use of the St’át’imcets subjunctive to weaken an imperative to a polite request, or to help turn a question into a statement of uncertainty (see examples in (13)–(15) and (16)–(20) above). I will argue below that in spite of these major empirical differences between the St’át’imcets subjunctive and that of familiar languages, the basic framework for mood semantics advanced by Portner (1997) can be adapted to capture all the St’át’imcets facts. This will support Portner’s proposal that moods are dependent on modals and place restrictions on the modal environments in which they appear. 4 Basic framework: Portner 1997 Portner’s (1997) leading idea is that moods place presuppositions on the modal environment in which they appear. More precisely, moods typically restrict properties of the accessibility relation associated with a governing modal operator (see also Portner 2003: 64). The modal operator may be

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provided by a higher attitude verb or modal; it may also, in unembedded situations, be provided by context. For illustration, let us first see how Portner analyzes English ‘moodindicating may’. In each of the examples in (46), the may is not the ordinary modal may; it is not asserting possibility. (46b), for example, does not mean ‘it is possible that it is possible that Sue wins the race.’ (46)

a.

Jack wishes that you may be happy.

b.

It is possible that Sue may win the race.

c.

May you have a pleasant journey!

(Portner 1997: 190)

Portner argues that mood-indicating may presupposes that p is doxastically possible (possible according to someone’s beliefs). For example, (46a) presupposes that Jack believes it is possible for you to be happy. He provides the analysis in (47). (47)

For any reference situation r , modal force F , and modal context R,

Jmay dep (φ)Kr ,F ,R is only defined if φ is possible with respect to

Doxα (r ), where α is the denotation of the matrix subject. When defined, Jmay dep φKr ,F ,R = JφKr ,F ,R

(Portner 1997: 201)

Portner further argues that there are actually two mood-indicating may’s, with slightly different properties. Mood-indicating may under wish, pray, etc. (as in (46a)) or in unembedded clauses (as in (46c)) has an extra requirement: it presupposes that the accessibility relation R is buletic (deals with somebody’s wishes or desires). The discussion of mood-indicating may illustrates an important aspect of Portner’s analysis, namely that moods place presuppositions on the modal accessibility relation (a type of conversational background). With English mood-indicating may, there is a doxastic and sometimes a buletic restriction. For the English mandative subjunctive, which appears in imperatives as well as in embedded contexts as in (48), R must be deontic, as shown in (49). (48)

Mary demands that you join us downstairs at 3pm. (Portner 1997: 202)

(49)

For any reference situation r , modal force F , and modal context R, Jm-subj(φ)Kr ,F ,R is only defined if R is a deontic accessibility relation. When defined, Jm-subj(φ)Kr ,F ,R = JφKr ,F ,R

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(Portner 1997: 202)

Lisa Matthewson

For Italian moods, Portner claims that R is restricted to being (non-)factive.19 The idea that moods restrict modal conversational backgrounds is common to several other modal-based analyses of mood (e.g., Farkas 1992 and Giorgi & Pianesi 199720 ), and is also found in James 1986. What James calls ‘manners of representation’ are root vs. epistemic conversational backgrounds: The ambiguity of the modal auxiliaries . . . supports the hypothesis that there are two separate manners of representation. Moods . . . signify manners of representation. They are not ambiguous, however; they signify one modality or the other (James 1986: 15). In the analysis to follow, I will adopt Portner’s idea that moods place restrictions on a governing modal operator. I will argue that the empirical differences between the St’át’imcets subjunctive and Indo-European subjunctives derive from the fact that the former restricts the conversational background of the modal operator in such a way that the modal force is weakened. 5 Adapting Portner’s approach for the Statimcets subjunctive I deal here only with the constructions where the subjunctive has a semantic effect; I will not address the cases of obligatory subjunctive agreement which were presented in subsection 2.2.21 My analysis will account for all meaningful uses of the St’át’imcets subjunctive except the two uses which contain the particle t’u7. See Section 8 for some discussion of the t’u7-constructions. 19 Interestingly, the Italian indicative imposes a modal force restriction as well as a conversational background restriction; it is only used with a force of necessity (Portner 1997: 197). 20 According to Giorgi and Pianesi, the subjunctive indicates that the ordering source is nonempty; this is a restriction on a conversational background. 21 The analysis presented below is actually compatible with the obligatory presence of the subjunctive in if -clauses introduced by lh=, and may even help to explain why lh= obligatorily selects the subjunctive when it means ‘if’, but selects indicative when it means ‘before’. Thanks to Henry Davis for discussion of this point, and see Davis 2006: chapter 26. (See also van Eijk 1997: 217, although van Eijk analyzes the subjunctive-inducing lh= as distinct from (e)lh= ‘before’.) As for the other obligatory cases of subjunctive, these may be grammaticized, semantically bleached relics of original meaningful uses, aided by the fact that subjunctive marking is intertwined with person agreement.

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5.1 The St’át’imcets subjunctive presupposes rather than asserts a modal semantics The first thing to establish is that like Portner’s moods, the St’át’imcets subjunctive does not itself assert a modal semantics, but is dependent on a governing modal operator. One piece of evidence for this is that the St’át’imcets subjunctive must co-occur with an overt modal in almost all its uses. Of the seven uses of the subjunctive being analyzed here, five of them have an overt modal (the deontics, ‘pretend’, wh-questions, yes-no questions, ignorance free relatives), one of them is plausibly analyzed as containing a covert modal (imperatives), and only one is non-modal (plain assertions). As noted above, the addition of the subjunctive to plain assertions is extremely restricted and at least semi-conventionalized. If the subjunctive were itself independently modal, it would be difficult to explain the minimal contrasts in (50)–(51).22 (50)

a.

*gúy’t=as ti=sk’úk’wm’it=a sleep=3sbjn det=child=exis Attempted: ‘I hope the child sleeps.’

b.

gúy’t=as=ka ti=sk’úk’wm’it=a sleep=3sbjn=deon det=child=exis ‘I hope the child sleeps.’

(51)

a.

*skalúl7=acw: saq’w knáti7 múta7 em7ímnem owl=2sg.sbjn fly deic and make.animal.noise ‘Pretend to be an owl: fly around and hoot.’

b.

skalúl7=acw=ka: saq’w knáti7 múta7 em7ímnem owl=2sg.sbjn=deon fly deic and make.animal.noise ‘Pretend to be an owl: fly around and hoot.’

Furthermore, just like with English mood-indicating may, the interpretation of St’át’imcets subjunctive clauses indicates that the mood does not 22 As noted above, Portner’s analysis does allow for unembedded uses of non-indicative moods, with the modal accessibility relation being provided by context. So there is no problem with the cases where the St’át’imcets subjunctive can appear without a c-commanding modal (as in (5)–(6)). Of course, we would eventually like to explain when these unembedded subjunctives can and cannot appear. Portner (1997: 201) notes for mood-indicating may and the mandative subjunctive that ‘Neither of these have a completely predictable distribution, in that neither occurs in every context in which a purely semantic account would predict that it could . . . it must be admitted that lexical and syntactic idiosyncracies come into play.’

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itself contribute modal semantics. For example, (50b) does not mean ‘It should be the case that the child should sleep’. The St’át’imcets subjunctive also patterns morphosyntactically like a mood rather than like real modals in the language. As shown above, the subjunctive is obligatorily selected by some complementizers, unlike modals. The subjunctive is also fused with subject marking into a full paradigm, unlike the modals, which are independent second-position clitics.23 I therefore conclude that the St’át’imcets subjunctive does not itself introduce a modal operator, but requires one in its environment. The St’át’imcets subjunctive does not presuppose a particular conversational background

5.2

The Statimcets subjunctive differs from most Indo-European moods in that it cannot be analyzed as being restricted to a certain type of conversational background. This is illustrated by the fact that it allows deontic, buletic or epistemic uses. Deontic conversational backgrounds arise with imperatives, as in (52) or (14b), repeated here in (53): (52)

ets7á=has=(malh) lh=xílh-ts=al’ap deic=3sbjn=(adhort) comp=do-caus=2pl.sbjn ‘Could you do it like this, you folks?’

(53)

nás=acw=malh áku7 pankúph=a go=2sg.sbjn=adhort deic Vancouver=exis ‘You could go to Vancouver.’

Buletic conversational backgrounds arise with the modal ka: (54)

plan=as=ká=ti7=t’u7 wa7 máys-n-as already=3sbjn=deon=demon=prt impf fix-dir-3erg ‘I wish he had fixed that already.’

(55)

guy’t=ás=ka ti=sk’úk’wm’it=a sleep=3sbjn=deon det=child=exis ‘I hope the child sleeps.’

23 Or in one case, a circumfix on the verb; see Davis et al. 2009.

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And epistemic conversational backgrounds arise with questions. (56)

nká7=as=kelh lh=cúz’=acw nas where=3sbjn=fut comp=going.to=2sg.sbjn go ‘Wherever will you go?’ / ‘I wonder where you are going to go now.’ (adapted from Davis 2006: chapter 24)

(57)

lan=as=há=k’a kwán-ens-as already=3sbjn=ynq=infer take-dir-3erg ni=n-s-mets-cál=a det.abs=1sg.poss-nom=write-act=exis ‘I wonder if she’s already got my letter.’ / ‘I don’t know if she got my letter or not.’

These data suggest that the St’át’imcets subjunctive is not analyzable in the same way as the European moods discussed by Portner (1997), which hardwire a restriction to a particular type of conversational background. 5.3

Instead, the St’át’imcets subjunctive functions to weaken the modal force

The core idea of my proposal is that the St’át’imcets subjunctive restricts its governing modal only in such a way as to weaken the force of the proposition expressed. The intuition that the St’át’imcets subjunctive weakens the proposition it adds to was already expressed by Davis (2006: chapter 24): The best way to characterize this meaning difference is in terms of the ‘force’ of a sentence. With ordinary indicative subjects, a sentence expresses a straightforward assertion, question or command; but with subjunctive subjects, the effect is to weaken the force of the sentence, so that an assertion becomes a wish, a question becomes a conjecture, and a command becomes a request. The important question is what exactly is meant by ‘weakening’ in this context, and how to derive the various effects of the subjunctive in a unified way. I will claim that the St’át’imcets subjunctive restricts the conversational background of a governing modal in such a way that the modal imparts a force no stronger than weak necessity. Since there are no modals which

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lexically encode quantificational force in St’át’imcets, this will mean that the subjunctive must appear in the scope of a variable-force modal, and will restrict it to a weakened interpretation. 6

Analysis

The idea to be pursued is that the St’át’imcets subjunctive restricts the domain of quantification of a c-commanding modal, so that the interpretation which obtains is weaker than pure necessity.24 Rullmann et al. (2008) argue that St’át’imcets possesses no modals which are lexically restricted for a pure necessity reading (see also Matthewson et al. 2007 and Davis et al. 2009). Instead, all St’át’imcets modals seem to allow both weak and strong interpretations (see (3) above, and see the references cited for many more examples). So, what we need to say is that the subjunctive forces an already potentially weak c-commanding modal to have a weak reading. In order to see how this will work, I first very briefly review the basics of a Kratzerian analysis of modals, and then outline how modals in St’át’imcets are analyzed. We will then add the subjunctive. Modals in a standard analysis introduce quantifiers over possible worlds. The set of worlds quantified over is narrowed down by two conversational backgrounds. First, it is narrowed down by the modal base, and then it is ordered and further narrowed down by the ordering source. The modal base and the ordering source are both usually provided by context in English, although there are systematic contributions of tense and aspect to the conversational background (see e.g., Condoravdi 2002 for discussion). A simple example is given in (58). (58)

Chris must do his homework. Modal base (circumstantial): The set of worlds in which the relevant facts are the same as in the actual world (e.g., we ignore worlds where Chris is not in school). Ordering source (normative): Orders worlds in the modal base so that the best worlds are those which come closest to the ideal represented by the school’s homework regulations. Universal quantification: In all the best worlds, Chris does his homework.

24 I would like to thank David Beaver and three anonymous reviewers for helping me clarify aspects of the analysis and its presentation.

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Rullmann et al. (2008) argue that there are two differences between English universal modals like must and St’át’imcets modals. First, the St’át’imcets modals place presuppositions on the conversational backgrounds. Second, the set of best worlds is further narrowed down by a choice function which picks out a potentially proper subset of the best worlds to be quantified over. This can lead to a weaker reading, depending on context. The idea is illustrated informally in (59).25 (59)

gúy’t=ka ti=sk’úk’wm’it=a sleep=deon det=child=exis ‘The child must/should/can sleep.’ Modal base (presupposed to be circumstantial): Worlds in which the relevant facts about our family are the same as in the actual world. Ordering source (presupposed to be normative): The best worlds are those in which my desire for an early night is fulfilled. Choice function: Picks out a potentially proper subset of the best worlds. Universal quantification: In all worlds in the subset of the best worlds picked out by the choice function, the child sleeps.

Since the quantification is over a potentially proper subset of the best worlds, sentences like (59) can be interpreted with any strength ranging from a pure possibility (‘The child can/may sleep’) to a strong necessity (‘The child must sleep’). The apparent variable quantificational force of St’át’imcets modals is thus derived not by ambiguity in the quantifier itself, but by restricting the size of the set of worlds quantified over by the universal quantifier. The larger the subset of the best worlds selected by the choice function, the stronger the proposition expressed. As a limiting case, the choice function may be the identity function. This results in a reading that is equivalent to the standard analysis of strong modals like must in English. Now we turn to the subjunctive. In order to capture the idea that the subjunctive weakens the c-commanding modal, I analyze the subjunctive as presupposing that at least one world in the set of best worlds is a world in which the embedded proposition is false. This will prevent the choice 25 A very sensible suggestion that we should replace Rullmann et al.’s choice function with an(other) ordering source has been made independently by Kratzer (2009), Portner (2009), and Peterson (2009, 2010). I will in fact do this below when I compare the current analysis to that of von Fintel & Iatridou (2008).

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function from being the identity function.26 This is illustrated informally for a deontic case in (60). (60)

guy’t=ás=ka ti=sk’úk’wm’it=a sleep=3subj=deon det=child=exis ‘I hope the child sleeps.’ Modal base (presupposed to be circumstantial): Worlds in which the relevant facts about our family are the same as in the actual world. Ordering source (presupposed to be normative): The best worlds are those in which my desire for an early night is fulfilled. Choice function (must pick out a proper subset of the best worlds, to avoid a contradiction with the presupposition of the subjunctive): The very best worlds are those in which my spouse’s desire for an early night is also fulfilled. Universal quantification: All the very best worlds are worlds in which the child sleeps.

(59) allows a strong interpretation which (60) disallows. If the choice function in (59) is the identity function, the speaker will be satisfied only if the child sleeps (‘in all the worlds where my desire for an early night is fulfilled, the child sleeps’). In (60), the speaker will certainly be satisfied if the child sleeps, but there are also other ways to make him/her happy. (60) asserts only that ‘in all the worlds where my and my spouse’s desires for an early night are fulfilled, the child sleeps’ — so the speaker’s desires may be satisfied if the speaker’s spouse looks after the child while the speaker goes to sleep. The requirement that (60) places on the child is thus weaker than a strong necessity. In the remainder of this section I provide a more formal implementation of this idea, and in Section 7 I show how the analysis accounts for a wide range of uses of the St’át’imcets subjunctive, including imperative-weakening, question-weakening, and ignorance free relatives. 26 Thanks to Hotze Rullmann (p.c.) for discussion of this point. The requirement that p be false in at least one of the best worlds appears reminiscent of a nonveridicality-style analysis, and there may be some deep significance to this. However, the analyses are different. For Giannakidou, the issue is always epistemic, as veridicality is defined in terms of a truth entailment in an individual’s epistemic model; see (37). Thus, subjunctive is predicted under verbs like ‘want’, as propositions under ‘want’ are not entailed to be true in any individual’s epistemic model. Under my analysis, the subjunctive has an anaphoric modal base and ordering source. I will show in subsection 7.5 that my analysis correctly predicts the indicative under verbs like ‘want’ in St’át’imcets.

9:32


I adopt the following basic definitions from von Fintel & Heim 2007. (61) shows the ordering of worlds according to how well they satisfy the set of propositions in the ordering source, and (62) shows how the best worlds are selected. (61)

Given a set of worlds X and a set of propositions P , define the strict partial order

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