Type-shifting and indefinites Type-shifting and indefinites

Henriëtte de Swart

Barcelona, May 2005

Advantages of GQ Advantages of GQ

Unified type for all NPs: <<e,t>,t>Unified interpretation for all NPs:PQ(P).Unified type for all Determiners:

<<e,t>,<<e,t>,t>>>. Unified interpretation for all Dets:PQ Det(P)(Q).

Disadvantages of GQ theoryDisadvantages of GQ theory

Not fine-grained enough to account for traditional classifications in terms of quantificational, predicative, referential.

Type-shifting (Partee 1987) has been proposed as a possible way to merge insights from GQ theory with other views.

Reference to individualsReference to individuals

Many type-shifting analyses have focussed on the availability of a type <e,t> or <<e,t>,<e,t>> reading for indefinites besides a type e or <<e,t>,t> reading.

Intermezzo Intermezzo

Type shifting (handout)

ApplicationsApplications

Empirical phenomena in which type <e,t> or <e,t>,<e,t>> denotations are relevant:

Intensional verbs (seek) ‘Light verbs’ (have, measurement phrases) Existential contexts (there is/are) Discourse anaphora Predicative constructions (to be (a) linguist) Incorporation Generic reference

Intensional verbs IIntensional verbs I

Zimmermann (1993): seek has <e,t> object. Cf. also Van Geenhoven & McNally (2005).

De re/de dicto distinction established with weak NPs; strong, quantificational NPs always get a de re interpretation.

Intensional verbs IIIntensional verbs II

Eve seeks a new book on semantics/two semanticists/no unicorns. [de re/de dicto]

Eve seeks every semanticist/most semanticists/neither unicorn. [de re only]

Eve seeks books on semantics [de dicto only]

‘‘Light’ verbs ILight’ verbs I

De Hoop (1992), de Hoop & van der Does (1998): object of ‘light’ verbs are preferably of type <e,t>. E.g.measurement verbs:

Ik heb gisteren enkele/vele/meer dan twintig/geen/… kilometer afgelegd. [Dutch]

I have covered some/many/more than twenty/no/… kilometers yesterday.

Light verbs IILight verbs II

This book weighs two kilos/many kilos/a few kilos/few kilos/nothing at all.

*This books weighs every kilo/most kilos/ neither kilo.

This book costs two euros/too much money/ very little/*everything/*most euros.

Light verbs IIILight verbs III

Verbs like have, consider:The house has a window/the most beautiful

window I have ever seen/two windows/ many/few/no windows.

*The house has all/most/windows/neither window.

John considers Bill a liar/the greatest liar he knows/*every liar.

Scrambling in Dutch IScrambling in Dutch I

Scrambled indefinites have a strong, quantificational interpretation. Unscrambled indefinites can have either a strong, or a weak (predicative) interpretation.

Je weet dat ik gisteren twee krakers heb gesproken. [indef, -scr, spec]

Je weet dat ik twee krakers gisteren heb gesproken. [indef, +scr, +spec]

You know that I spoke to two squatters yesterday.

Scrambling in Dutch IIScrambling in Dutch II

Definites scramble freely with light verbs: …omdat ik de was nog moet doen. [+scr] … omdat ik nog de was moet doen. [-scr] … because I still have to do the laundry. Indefinites do not scramble with light verbs: … omdat ik ook kinderen heb. [-scr] *… omdat ik kinderen ook heb. [+scr] … because I also have children.

All indefinitesAll indefinites

The restriction on scrambling with indefinites applies to all weak NPs, including mon NPs:

*…omdat Jan minstens/hoogstens twee kinderen ook heeft. … because Jan at least/at most two children also has. [+scr]

*… omdat Jan geen kinderen ook heeft. … because Jan no children als has. [+scr]

Minimal pairMinimal pair

Ik geloof dat ik ook de mazelen heb. [def,-scr]

Ik geloof dat ik de mazelen ook heb. [def,+scr]

Ik geloof dat ik ook mazelen heb. [ind, -scr]*Ik geloof dat ik mazelen ook heb. [ind, -scr]

I believe I have (the) measles too.

Definites and indefinitesDefinites and indefinites

Van der Does & de Hoop (1998): Definites can be independent of their semantic

context in a way indefinites cannot. Definites are naturally viewed as having a type e

interpretation (by means of the iota operator ). Indefinites are not; they have interpretations in the domain of type <e,t> (predicative) and type <<e,t>,t> (strong/quantificational) expressions.

A type-shifting explanationA type-shifting explanation

Restriction on scrambling: scrambling is incompatible with a type <e,t> denotation.

Light verbs prefer an object of type <e,t>, but are also compatible with type e.

Restriction on light verbs: light verbs block a type <<e,t>,t> interpretation for their object.

Result: light verbs do not allow scrambling of indefinites (type <e,t>), but freely allow scrambling of definites (in type e).

Scrambling of pronounsScrambling of pronouns

Van der Does and de Hoop assume that pronouns only have a denotation of type e.

This would make scrambling of pronouns obligatory with light verbs.

Ik geloof dat Jan keelpijn heeft. Ik geloof dat ik het ook krijg/ *dat ik ook het krijg.

I believe that John throat ache has (=has a sore throat). I believe that I it also get/ that I also it get.

Existential contextsExistential contexts

There is a child/someone/no one in the garden. There are children/two/at most five/many/no/few

children in the garden. *There is every/neither child in the garden. *There are all/most/both/neither children in the

garden. Weak determiners: symmetric, not ‘truly’

quantificational (Keenan).

A type-shifting approachA type-shifting approach

McNally (1998): use Partee’s BE operation to find all the NPs that have a type <e,t> denotation (= alle weak NPs).

Treat ‘there is’ as a one-place predicate of properties ‘to be instantiated’.

P there_be(P).Consequence: post-verbal NP has to denote

a property or a quantifier over properties.

Examples IExamples I

Truth conditions:[| NP |]M,g [| there be |]M,g. There was a book on display.There was every kind of book on display.(true iff every property that is in the

extension of every kind of book is in the extension of the existential predicate.)

Examples IIExamples II

There are at most three books on the table. At most there are three books on the

table.p [[C(p) true(p)] [ [| there are three

books on the table |] p].There are no books on the table. [| there are |] [| books on the table |].

EvaluationEvaluation

Type-shifting approach captures Keenan’s intuitions.

Problem: mon NPs are the default, mon NPs require special treatment (asymmetry). Is lexical decomposition desirable?

Question: how do we extend the property approach to weak readings of NPs in general?

CombinatoricsCombinatorics

Assume: all weak NPs have a type <e,t> denotation.

Do weak readings of NPs in ‘normal’ contexts have a type <e,t> denotation? If so, how do they combine with a verb that also takes GQs?

Susan ate an apple/two apples/no apples/ every apple/neither apples/most apples

Lexical ambiguityLexical ambiguity

Transitive verbs have a denotation (i) as a relation between two individuals and (ii) as a relation between an individual and a property (van Geenhoven 1998, van Geenhoven & McNally 2005).

Eat1: y x Eat(x,y)

Eat2: P x yEat(x,y P(y))

Evaluation IEvaluation I

Advantage: we can maintain function application as only combinatory rule.

Disadvantage (i): systematic ambiguity throughout the lexicon.

But maybe: lexical rule deriving two interpretations.

Evaluation IIEvaluation II

Disadvantage (ii): how to extend to monotone decreasing quantifiers (no existential closure!).

But: lexical decomposition (McNally 1998, Van Geenhoven & McNally 2005).

However: is lexical decomposition always correct and desirable?

Closure operations IClosure operations I

Alternative: maintain uniform interpretation of transitive verb as relation between two individuals. Enrich combinatorics: allows other modes of composition besides function application.

Heim (1982): existential closure.De Swart (2001): existential and universal

closure.

Closure operations IIClosure operations II

De Swart (2001):Existential closure applies to properties that

are derived from mon quantifiers (a, some, three, at least five, many, …).

Universal closure applies to properties that are derived from mon quantifiers (no, at no more than three, most five, few,.).

Existential closureExistential closure

C for predicative NPs derived from mon quantifiers: For Q a predicate of type <e,t>, and Pmin a predicative NP of type <e,t>, which denotes a minimal property derived from a mon quantifier:

C: x Q(x)(Pmin) C x(Q(x) P(x))

Universal closureUniversal closure

C for predicative NPs derived of mon quantifiers: For Q a predicate of type <e,t> and Pmax a predicative NP denoting a maximal property, derived from a mon quantifier, the combination of Q and Pmax introduces universal quantification:

C: x Q(x)(Pmax) C x(Q(x) P(x))

Evaluation IEvaluation I

Advantages: no lexical ambiguity of verbs, no lexical decomposition of NPs, no asymmetric treatment of mon and monNPs (rule based).

Disadvantage (i): how are monotonicity properties of the underlying NP recoverable?

Evaluation IIEvaluation II

Disadvantage (ii): complication in combinatorics (function application + two closure rules).

But: price to pay for have type <e,t> denotation at sentential level??

Recent accounts of e.g. incorporation also allow combinatory rules other than fa.

Discussion IDiscussion I

What is the class of expressions that has a type <e,t> denotation?

Largest class: all weak NPs (= all NPs that have a non-empty denotation after application of Partee’s type-shift BE, cf. Zimmermann 1993, McNally 1998, van der Does & de Hoop 1998); definites.

Relevant for: intensional verbs, ‘light’ verbs, existential contexts, weak readings of NPs in ‘normal contexts.’

Discussion IIDiscussion II

Class of indefinites that licenses discourse anaphora, and escapes from scope islands: a N, two N, some N; not no N, at least/at most two N, etc.

Discourse anaphora:A studenti came in. Shei had a question. Every studenti came in. #Shei had a question

about the exam.

Plurals and anaphoraPlurals and anaphora

Two studentsi came to see me. Theyi had a question about the exam.

Exactly two studentsi came to see me. #Theyi had a question about the exam.

Most studentsi came to see me. #Theyi had a question about the exam.

Quantificational NPs can take A B as their antecedent, but not simply A.

Scope islands IScope islands I

If a cousin of mine dies, I’ll inherit a fortune.

‘I have a cousin such that, if he dies, I’ll inherit a fortune.’

If every/no cousin of mine dies, I’ll inherit a fortune.

For every/no cousin of mine, if he dies, I’ll inherit a fortune.

Scope islands IIScope islands II

If three cousins of mine die, I’ll inherit a fortune.

‘I have three cousins, such that, if they (all die), I’ll inherit a fortune.’

‘I have three cousins, and for each of them, if he dies, I’ll inherit a fortune’

No escape from scope islands for true quantifiers, only for indefinites.

Choice function approachChoice function approach

Choice function approach: Reinhart (1997), Winter (1997), Kratzer (1998).

Indefinites like a cousin of mine, three cousins of mine, etc. denote choice functions: expressions of type <<e,t>,e>

The choice function picks an individual from a set. The choice function gets existential closure

outside of the scope island.

Choice functions denoting Choice functions denoting expressionsexpressions

Denote choice functions: singular indifinites like a cousin of mine; plural indefinites like three cousins of mine.

Do not denote choice functions: other weak quantifiers such as at least/at most three students of mine/no student of mine.

Do not denote choice functions: bare plurals (always narrow scope!).

Note on bare pluralsNote on bare plurals

Bare plurals introduce discourse anaphora:I bought booksi on semantics. Theyi are

very good.Bare plurals do not denote choice functions

(they never take wide scope!):If cousins of mine die, I will inherit a house.

Discussion IIIDiscussion III

Are property denoting: bare plurals and incorporated nominals (Van Geenhoven 1996).

Explains narrow scope of bare plurals:I didn’t see a spot on the floor. or I didn’t see spots on the floor. not Bare plurals and incorporated nominals are

somehow ‘deficient’.

IncorporationIncorporation

Incorporation in West Greenlandic, Hindi, Hungarian, etc, not in English, Romance: direct relation between verb and object.

Arnajarq eqalut-tur-p-u-q. [WG]

A.abs zalm-eet-Ind-[-tr]-3sg.

‘Arnajaraq eats salmon/is a salmon-eater.’

Lexical ambiguityLexical ambiguity

Van Geenhoven (1996): transitive verbs denote relations between individuals; incorporating verbs take a property denoting expression as their object.

Transitive verb: y x [V(x,y)]Incorporating verb: Px y [V(x,y) P(y)]Existential closure induced by the verb!

Bare and numberBare and number

In WG: incorporation of bare singulars.Plural interpretation allowed:Aani qimmi-qar-p-u-q. A.abs dogi-have-ind-[-tr]-3sg.

Kusana-q-a-a-t.Theyi are very nice.

Incorporation of pluralsIncorporation of plurals

In Hindi (Dayal 1999, 2005) and Hungarian (Farkas & de Swart 2003): incorporation of bare singulars and bare plurals.

Interpretation of bare singulars: number neutral (sg or pl, depending on context).

Interpretation of bare plurals: semantically plural.

Hungarian IHungarian I

Mari verset olvas.Mari poem.Acc read.Mari is reading a poem/poems.Mari verseket olvas.Mari poem.Pl.Acc read.

Hungarian IIHungarian II

Mari bélyeget gyüjt.Mari stamp.Acc collect.‘Mari collects stamps.’Feri feleségeket keres.Feri wife.Pl.Acc seek.‘Feri is looking for wives’ (pragm. odd)

New questionsNew questions

Questions about the distinction between bare NPs and NPs with a determiner: scope, licensing of anaphora, interpretation.

Questions about the distinction between bare singulars and bare plurals.

Implications for predicative constructions and generic reference.