Modal concord Conditionals Disjunction Superlative and comparative quantifiers. At least et al. Bart Geurts. Bart Geurts: At least et al.

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1 At least et al. Bart Geurts

2 The story in a nutshell Superlative quantifiers ( at least 7 wombats ) are quite different from comparative ones ( more than 6 opossums ). Superlative quantifiers are modal expressions. In important ways, they resemble conditionals and disjunctions (which are modal expressions, too, naturally). So the plan is as follows: Background Modal concord Conditionals Disjunction Superlative vs. comparative quantifiers

3 Modal concord

4 Modal concord [1] Hij moet zeker in Brussel zijn. he must certainly in Brussels be Compositional reading: I suppose he has to be in Brussels. Concord reading: He (definitely) has to be in Brussels. [2] Hij moet misschien in Brussel zijn. he must perhaps in Brussels be Compositional reading: Perhaps he has to be in Brussels. Concord reading: none [3] Ze zou misschien wel eens dronken kunnen zijn. she could maybe wel eens drunk can be Compositional reading:... (she is drunk) [not available] Concord reading: (she is drunk)

5 A concise phenomenology of modal concord Modal concord items: beslist definitely, zeker certainly, wellicht probably, misschien possibly, etc. MC items can stand on their own: [1] Ze zou misschien dronken kunnen zijn. she could perhaps drunk can be [2] Ze is misschien dronken. she is perhaps drunk She might be drunk. MC items don t license each other: [3]?Ze heeft misschien mogelijkerwijs een delirium. she has maybe maybe a delirium

6 A concise phenomenology of modal concord MC items impose constraints on their licensers regarding force ( vs. ) and type (e.g. epistemic vs. deontic). Consequently, there are no MC readings for: [1] De kleine dinosaurus moet misschien weggaan. the little dinosaur must perhaps go-away Perhaps the little dinosaur has to go away. [2] Je mag verplicht een ijsje eten. you may obligatorily an ice cream eat You are allowed to obligatorily eat an ice cream.

7 Conditionals

8 The Lewis-Kratzer doctrine 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. Whenever there is no explicit operator, we have to posit one. [Kratzer 1991] Proposed exegesis: There are two strategies for dealing with if-clauses: [O] An if-clause may restrict the domain of an overt operator. [C] An if-clause may restrict the domain of a covert operator. Every conditional sentence with an overt modal is ambiguous.

9 Reframing the proposed exegesis An if-clause introduces a tacit operator M which: [O] may be unified with an overt operator N, if one is present ( modal concord), or [C] may be left to stand on its own, in which case M defaults to epistemic necessity ( compositional construal of MC items). Again, every conditional sentence with an overt modal in it will be ambiguous.

10 ... and ambiguous they are [1] If you re myopic, you should use contraceptives. (O) In all deontically accessible worlds in which you are myopic, you use contraceptives. [ ] (C) In all epistemically accessible worlds in which you are myopic, you should use contraceptives. [ ] [2] If Fred takes a biscuit, he may take two. [deontic] (O) Fred is allowed to take two biscuits. [ ] (C) I don t know how many biscuits Fred is allowed to take, but if he takes one, then that settles the matter, for then he is allowed to take two. [ ]

11 Inferential properties of conditionals The modal vs. the truth-functional account On a truth-functional construal, the following argument is valid: Plato wasn t Belgian If Plato was Belgian, Aristotle was Dutch On the modal account, it isn t. The following is valid on the default (epistemic) construal of the if-clause: If Plato was Belgian, Aristotle was Dutch Plato was Belgian Aristotle was Dutch

12 Disjunction

13 Disjunctions as modals Zimmermann 2000 Geurts 2005 Basic idea: A disjunction is actually a conjunction of alternatives: S 1 or S 2 means (really means) Maybe S 1 and maybe S 2. The interpretation of a disjunction begins with a rather abstract lexical meaning, which is restricted by various kinds of semantico-pragmatic constraints. The context-dependence of modal expressions plays a crucial role in the story. E.g. Alice might grow taller.

14 Disjunctions as modals Zimmermann 2000 Geurts 2005 The general form of a modal proposition is AMB, where M is a quantifier whose domain is A. Hence: A B, A B, etc. The logical form of S 1 or S 2 is: A 1 M 1 B 1 A 2 M 2 B 2 M 1/2 may be either overt or covert. The domain of M 1/2 is determined by the context. Further constraints: Disjointness: A 1 B 1 A 2 B 2 = Exhaustivity: C (A 1 B 1 ) (A 2 B 2 ) where C is the background set furnished by the context.

15 C-readings and O-readings [1] You may do this or you may do that. The tacit modal operators introduced by or either fuse with the overt modals, or else default to epistemic possibility: (O) A B A B You have permission to do this and you have permission to do that. (C) A B C A B C It may be that you have permission to do this and it may be that you have permission to do that.

16 Inferential properties of disjunctions The modal vs. the truth-functional account On a truth-functional construal, the following argument is valid: Plato was Belgian Either Plato was Belgian or Aristotle was Dutch On the modal account, it isn t. The following is valid on the default construal of or : Either Plato was Belgian or Aristotle was Dutch Plato was Belgian Aristotle was Dutch

17 Superlative and comparative quantifiers positive feedback to: negative feedback to:

18 Superlative and comparative quantifiers Superlative quantifiers: at least/most 4 sheep Comparative: more/fewer than 5 camels It is usually assumed that these quantifiers are interdefinable: at least 7 bath ducks = more than 6 bath ducks at most 7 bath ducks = fewer than 8 bath ducks Not so!

19 Superlative vs. comparative quantifiers NPs in superlative quantifiers may have specific readings: [1] I will invite at most 2 people, namely Jack and Jill. Jack and Jill will be invited. [2] I will invite fewer than 3 people, namely Jack and Jill. Jack and Jill will be invited. [3] I will invite fewer than 2 people, namely Jack and Jill. Inferential properties: [4] Barney ate 3 apples. Barney ate fewer than 4 apples. Barney ate at most 3 apples. Barney ate more than 2 apples. Barney ate at least 3 apples. By and large, the distribution of superlative quantifiers is much more restricted than that of their comparative counterparts.

20 Distributional restrictions Downward entailing contexts [1] Bach wrote {at least/most // more/fewer than} 27 fugues. [2] Bach didn t write {?at least/most // more/fewer than} 27 fugues. [3] No composer wrote {?at least/most // more/fewer than} 27 fugues. [4] Few composers wrote {?at least/most // more/fewer than} 27 fugues. Note that the variants with the superlative quantifiers, though infelicitous, are still interpretable.

21 Distributional restrictions Quantifiers [1] {All / Nearly all / Most /?Some /?About seven / None} (of the) children ate at least/most 2 sandwiches. [2] There were so many/few chocolates left that {everybody / almost everybody / most guests /?about seven guests / no one} got at least/most 3. [3] Before going to bed, she {always / nearly always / usually /?often / occasionally / rarely / never } says at least/most 4 prayers.

22 Outline of a proposal The standard analysis of comparative quantifiers is correct. Superlative quantifiers are modals: [1] Wilbur published at least 5 novels. x[#x = 5 Nx Pwx] x[#x > 5 Nx Pwx] [2] Wilbur published at most 5 novels. x[#x = 5 Nx Pwx] x[#x > 5 Nx Pwx] The modal operators are of the same type, and epistemic by default.

23 Fleshing out the proposal The two conjuncts introduced by the quantifier do not have the same status: primary operator x[#x = 5 Nx Pwx] } {{ } principal message x[#x > 5 Nx Pwx] If a superlative quantifier combines with an overt modal whose force is the same as that of its primary operator, the two operators will fuse by default ( modal concord O-reading). Otherwise, we will have a double modal ( compositional reading C-reading). The modal operators contributed by the quantifier are epistemic by default, hence will prefer to take wide scope.

24 Examples [1] You may take at most three chocolates. (O) x[cx #x = 3 Tyx] x[cx #x > 3 Tyx] (C) x[cx #x = 3 Tyx] x[cx #x > 3 Tyx] [2] You must take at least three chocolates. (O) x[cx #x = 3 Tyx] x[cx #x > 3 Tyx] (C) x[cx #x = 3 Tyx] x[cx #x > 3 Tyx] [3] You may take at least three chocolates. (O) (C) x[cx #x = 3 Tyx] x[cx #x > 3 Tyx] [4] You must take at most three chocolates. (O) (C) x[cx #x = 3 Tyx] x[cx #x > 3 Tyx]

25 Inferential properties Superlative vs. comparative quantifiers Barney ate 3 apples. [1] Barney ate fewer than 4 apples. [2] Barney ate at most 3 apples. [3] Barney ate more than 2 apples. [4] Barney ate at least 3 apples.

26 Modal modifiers If the modal analysis is correct, it makes sense that superlative modifiers sometimes alternate with overt modals: [1] Hij heeft voor zeker zes kranten gewerkt. he has for certainly six newspapers worked He has worked for at least six newspapers. [2] Hij heeft voor misschien drie kranten gewerkt. he has for maybe three newspapers worked He has worked for at most three newspapers.

27 Distributional restrictions If the modal analysis is correct, there should be restrictions on the distribution of superlative quantifiers just as there are on the distribution of bona fide modals (and epistemic ones in particular): {Each / Most /?About five / None} of the guests... [1]... may have dispatched the butler. [2]... had at least 3 cocktails. [3] Nabokov might not have written Lolita. (Only wide scope for.) [4] Nabokov didn t write at least/most 3 novels.

28 To be tested Implications for psychology Superlative quantifiers deviate from comparative ones in that: they are more complex, they are acquired later, and they license fewer inferences.

29 Summing up Superlative quantifiers are modal expressions, as witness: similar patterns of compositional and modal concord readings, similar inference patterns, and similar distributional restrictions.