Typeshifting and indefinites

1
Type-shifting and indefinites

• Henriëtte de Swart
• Barcelona, May 2005

2
Advantages of GQ

• Unified type for all NPs ,t
• Unified interpretation for all NPs
• ?PQ(P).
• Unified type for all Determiners
  ,,t.
• Unified interpretation for all Dets
• ?P?Q Det(P)(Q).

3
Disadvantages 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.

4
Reference to individuals

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

5
Intermezzo

• Type shifting (handout)

6
Applications

• Empirical phenomena in which type or
  , 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

7
Intensional verbs I

• Zimmermann (1993) seek has 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.

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Intensional 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

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Light verbs I

• De Hoop (1992), de Hoop van der Does (1998)
  object of light verbs are preferably of type
  . 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.

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Light 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.

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Light 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.

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Scrambling 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.

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Scrambling 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.

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All 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

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Minimal 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.

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Definites 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 (predicative) and type
  ,t (strong/quantificational) expressions.

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A type-shifting explanation

• Restriction on scrambling scrambling is
  incompatible with a type denotation.
• Light verbs prefer an object of type , but
  are also compatible with type e.
• Restriction on light verbs light verbs block a
  type ,t interpretation for their object.
• Result light verbs do not allow scrambling of
  indefinites (type ), but freely allow
  scrambling of definites (in type e).

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Scrambling 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.

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Existential 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).

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A type-shifting approach

• McNally (1998) use Partees BE operation to find
  all the NPs that have a type 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.

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Examples 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.)

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Examples 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 .

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Evaluation

• Type-shifting approach captures Keenans
  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?

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Combinatorics

• Assume all weak NPs have a type
  denotation.
• Do weak readings of NPs in normal contexts have
  a type 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

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Lexical 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 ?y?Eat(x,y ? P(y))

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Evaluation 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.

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Evaluation 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?

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Closure 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.

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Closure 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,.).

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Existential closure

• ?C for predicative NPs derived from mon?
  quantifiers For Q a predicate of type , and
  Pmin a predicative NP of type , which
  denotes a minimal property derived from a mon?
  quantifier
• ?C ? ? x Q(x)(Pmin) ? ?C ?x(Q(x) ?P(x))

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Universal closure

• ?C for predicative NPs derived of mon?
  quantifiers For Q a predicate of type 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))

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Evaluation I

• Advantages no lexical ambiguity of verbs, no
  lexical decomposition of NPs, no asymmetric
  treatment of mon? and mon?NPs (rule based).
• Disadvantage (i) how are monotonicity properties
  of the underlying NP recoverable?

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Evaluation II

• Disadvantage (ii) complication in combinatorics
  (function application two closure rules).
• But price to pay for have type denotation
  at sentential level??
• Recent accounts of e.g. incorporation also allow
  combinatory rules other than fa.

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Discussion I

• What is the class of expressions that has a type
  denotation?
• Largest class all weak NPs ( all NPs that have
  a non-empty denotation after application of
  Partees 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.

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Discussion 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.

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Plurals 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.

37
Scope islands I

• If a cousin of mine dies, Ill inherit a fortune.
• I have a cousin such that, if he dies, Ill
  inherit a fortune.
• If every/no cousin of mine dies, Ill inherit a
  fortune.
• ? For every/no cousin of mine, if he dies, Ill
  inherit a fortune.

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Scope islands II

• If three cousins of mine die, Ill inherit a
  fortune.
• I have three cousins, such that, if they (all
  die), Ill inherit a fortune.
• ? I have three cousins, and for each of them, if
  he dies, Ill inherit a fortune
• No escape from scope islands for true
  quantifiers, only for indefinites.

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Choice 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
• The choice function picks an individual from a
  set.
• The choice function gets existential closure
  outside of the scope island.

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Choice functions denoting expressions

• 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!).

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Note 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.

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Discussion III

• Are property denoting bare plurals and
  incorporated nominals (Van Geenhoven 1996).
• Explains narrow scope of bare plurals
• I didnt see a spot on the floor. ?? or ??
• I didnt see spots on the floor. ?? not ??
• Bare plurals and incorporated nominals are
  somehow deficient.

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Incorporation

• 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.

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Lexical 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 ?P?x ?y V(x,y) ? P(y)
• Existential closure induced by the verb!

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Bare 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.

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Incorporation 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.

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Hungarian I

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

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Hungarian 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)

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New 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.