1 / 71

Dependent Plurals and Three Levels of Multiplicity

Dependent Plurals and Three Levels of Multiplicity. Serge Minor CASTL, University of Tromsø. HSE Seminar Moscow, 11.04.2019. Encoding Co-Distributivity. Three girls watched three movies. Each girl watched a movie. All the girls watched movies. watched. (1). watched.

byerly
Download Presentation

Dependent Plurals and Three Levels of Multiplicity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dependent Plurals and Three Levels of Multiplicity Serge Minor CASTL, University of Tromsø HSE Seminar Moscow, 11.04.2019

  2. Encoding Co-Distributivity Three girls watched three movies. Each girl watched a movie. All the girls watched movies. watched (1) watched #Each girl watched movies. #All the girls watched three movies. (2) watched

  3. Ontological Plurality DPs with numerals introduce variables that range over collections of individuals (sums or sets) in a structured ontological domain: (3) *-operator (cf. Link 1983, Landman 1989, etc.): For anypredicateP, *P is the minimal predicatesatisfyingthefollowingconditions:

  4. Cumulativity a. Three girls watched three movies. ✓Co-distr **-operator (cf. Krifka 1989, Sternefeld 1993, Sauerland 1998 etc.) (4) b. For anyrelationR, **R is the minimal relationsatisfyingthefollowingconditions:

  5. Cumulativity a. Three girls watched movies. ✓Co-distr (5) (6) b.

  6. Distributivity a. (7) Each girl watched a movie. ✓Co-distr b. a. (8) Each girl watched three movies. ✗Co-distr b. a. (9) Each girl watched movies. ✗Co-distr b.

  7. The Puzzle: Dependent Plurals (10) a. All the girls watched movies. ✓Co-distr b. Most of the girls watched movies. ✓Co-distr c. Both girls watched movies. ✓Co-distr DPs with plural quantifiers (e.g. all, most, both) pattern with non-distributive DPs (e.g. the girls, three girls) Chomsky (1975), De Mey (1981), Kamp & Reyle (1993), Spector (2003), Zweig (2008, 2009) a.o.

  8. Dependent Plurals:Distributivity-based Analysis (11) a. All the girl watched three movies. ✗Co-distr b. Most of the girls watched three movies. ✗Co-distr c. Both girls watched two movies. ✗Co-distr Plural quantifiers (e.g. all, most, both) pattern with singular quantifiers (e.g. each, every)

  9. The Data: Overview ‘Bare plurals’ don’t have to be completely bare: (15) a. All the students handed in their papers. b. Most of the students read the papers they were assigned. c. Most ofthesegroups live permanentlyalongcertain coastlines.

  10. Dependent Plurals:Distributivity-based Analysis Partee (1975), Kamp & Reyle (1993), Spector (2003) • The plural feature on dependent plurals is semantically vacuous. • Semantically vacuous plural is licensed only in the scope of another plural feature: a. Mary watched movies. b. Every girl watched movies. (12) a. All the girls watched movies. b. (13)

  11. Dependent Plurals:Distributivity-based Analysis (12) a. All the girls watched movies. b. Incorrect prediction: Multiplicity Condition!

  12. Dependent Plurals:Cumulativity-based Analysis DeMey (1981), Bosveld-de Smet (1998), Swart (2006), Champollion (2010) DPs with plural quantifiers are not distributive: (13) a. All the girls watched movies. ✓Co-distr b. What about (14)? (14) a. All the girls watched three movies. ✗Co-distr b.

  13. Dependent Plurals:Cumulativity-based Analysis Zweig (2008, 2009), Champollion (2010) • Plurals are underlyingly number-neutral, singular imposes an atomicity condition: • Multiplicity for plurals is derived as a scalar implicature: a. (6) b. (7) a. A movie was playing. b. (8) a. Movies were playing. b.

  14. Dependent Plurals:Cumulativity-based Analysis Champollion (2010) DPs with all impose a presupposition on the predicate it combines with: (11) (12) All the girls watched three movies. ✗Co-distr a. b. (13) a. All the girls watched movies. ✓Co-distr b.

  15. Dependent Plurals:Cumulativity-based Analysis Champollion (2010) Problem: (14) All the girls watched fewer than five movies. ✗Co-distr a. b.

  16. The Data: Overview

  17. Semantics with Plural Info States • Traditional semantic systems (Heim & Kratzer 1998, Groenendijk & Stokhof 1991, Muskens 1996): Expressions are evaluated with respect to single assignments. • Semantic systems with plural info states (van den Berg 1994, 1996, Nouwen 2003, Brasoveanu 2007, 2008, Brasoveanu & Farkas 2011, Henderson 2014) Expressions are evaluated with respect to sets of assignments, or plural info states.

  18. Plural Info States • I is a set of assignments, or plural info state, type st. • i1, i2, i3are assignments in I, type s. • u1, u2 … are variable, or discourse referents (drefs), modeled as functions from assignments to individuals, type se. • x11, x12 … are individuals, type e.

  19. DRSs Sentences are translated as DRSs, i.e. relations between an input and an output info state, type (st)((st)t) (= t). A typical DRS performs two functions: it introduces new drefs, and places conditions on the output info state. a. Au dog is barkingε. (15) b.

  20. Truth Truth of a DRS For a DRS D of type (st)((st)t) and an input info state I, such that I is a singleton set of assignments, D is true with respect to I iff there is an output info state J such that D(I)(J)=1.

  21. Truth a. Au dog is barkingε. (16) This DRS will be true with respect to a singleton input info state I, if there exists an output info state J of the following form: b. • x is a dog. • e is a barking event. • x is the agent of e. This is equivalent to stating that there is an x, such that x is a dog, and there is an e, such that e is a barking event, and x is the agent of e.

  22. Weak Distributivity Weak distributivity: distributivity across the assignments in a plural info state. x2 x3 y1 ⨁ y2 y1 ⨁ y2 x1 ⨁ ⨁ x3 y1 ⨁ y2 x1 x2 y1 ⨁ y2

  23. Strong Distributivity Strong distributivity: distributivity across multiple info states. x2 x3 y1 ⨁ y2 y1 ⨁ y2 x1 ⨁ ⨁ x3 y1 ⨁ y2 x1 x2 y1 ⨁ y2

  24. Assignment-level Plurality • Assignment-level, or ontological, plurality requires for each value of a discourse referent in a plural info state to be a sum of individuals with cardinality greater than 1.

  25. State-level Plurality • State-level, or non-ontological, plurality requires for a dref to return multiple distinct values in a plural info state.

  26. Proposal: Determiners • Non-quantificational determiners (e.g. the definite and indefinite articles) do not induce distributivity. • All/most encode weak distributivity. • Each/every encode strong distributivity.

  27. Proposal: Numerals • Numerals and cardinality modifier (e.g. several) introduce assignment-level cardinality conditions on the values of a dref, which apply distributively for each assignment in an info state.

  28. Proposal: Number Singular introduces two conditions: • An assignment-level atomicity condition,atom(u), which requires for each value of a dref in a plural info state to be an atomic individual. • A state-level uniqueness condition, unique(u), which requires for all the values of a dref across the assignments in a plural info state to be the same.

  29. Proposal: Number Plural is semantically vacuous (Krifka 2004, Sauerland et al. 2005). However, in non-downward entailing contexts a strengthened reading is derived for bare plurals as a scalar implicature, via negation of the singular alternative (Zweig 2008, 2009): • The values of a dref introduced by a bare plural must be either non-atomic or non-unique with respect to a plural info state, atom(u) unique(u).

  30. Allvs Non-Q (13) a. All the girls watched three movies. ✗Co-distr b. Three girls watched three movies. ✓Co-distr

  31. Allvs Non-Q Threeu the girls watchedεthreeu’ movies. • g1, g2, g3– are atomic girl-individuals. • e – is a sum of watching events. • m1, m2, m3– are atomic movie-individuals. • g1 ⨁ g2 ⨁ g3is the cumulative agent of e. • m1 ⨁ m2 ⨁ m3is the cumalative theme of e.

  32. Allvs Non-Q Allu the girls watchedεthreeu’ movies. All introduced weak distributivity with respect to u:

  33. Allvs Non-Q Allu the girls watchedεthreeu’ movies. • g1, g2, g3– are atomic girl-individuals. • e1, e2, e3– are watching events. • m1, m2, m3– are movie-individuals. • g1is the agent of e1; g2is the agent of e2; g3is the agent of e3. • m1is the theme of e1; m2is the theme of e2; m3is the theme of e3.

  34. Allvs Non-Q Allu the girls watchedεthreeu’ movies. • the values for u’ have a cardinality 3 for each assignment in K, i.e. each girl watched three movies.

  35. AllvsEach (15) a. All the girls watched movies. ✓Co-distr b. Each girl watched movies. ✗Co-distr

  36. AllvsEach Allu the girls watchedεmoviesu’. All introduces weak distributivity with respect to u:

  37. AllvsEach Allu the girls watchedεmoviesu’. • g1, g2, g3– are atomic girl-individuals. • e1, e2, e3– are watching events. • m1, m2, m3– are movie-individuals. • g1is the agent of e1; g2is the agent of e2; g3is the agent of e3. • m1is the theme of e1; m2is the theme of e2; m3is the theme of e3. • the values for u’ are either non-atomic or non-unique with respect to K, i.e. either at least one of the girls watched more than one movie, or at least two girls watched different movies (= Multiplicitiy Condition).

  38. AllvsEach Eachu girl watchedεmoviesu’. Each introduces strong distributivity with respect to u:

  39. AllvsEach Eachu girl watchedεmoviesu’. • g1, g2, g3– are atomic girl-individuals. • e1, e2, e3– are watching events. • m1, m2, m3– are movie-individuals. • g1is the agent of e1; g2is the agent of e2; g3is the agent of e3. • m1is the theme of e1; m2is the theme of e2; m3is the theme of e3.

  40. AllvsEach Eachu girl watchedεmoviesu’. • the values for u’ are either non-atomic or non-unique with respect to each info state. ⇒m1, m2, and m3 are each non-atomic, i.e. each girl watched more than one movie.

  41. Conclusions • A semantic system with plural info states allows for a natural formalization of a) the distinction between weak and strong distributivity, and b) ontological and state-level plurality. • These distinctions allow us to account for the three-way contrast between non-quantificational DPs (non-distributive), DPs involving plural quantifiers (weakly distributive), and DPs involving singular quantifiers (strongly distributive) • … and the contrast between cardinality modifiers (encode ontological cardinality conditions) and grammatical number features (make reference to state-level (non-)uniqueness).

  42. Collective Predication Two types of collective predicates generate a three-way distinction: (14) a. The students gathered in the hallway. b. All the students gathered in the hallway. c. #Each student gathered in the hallway. (15) a. The students are a good team. b. #All the students are a good team. c. #Each student is a good team. (Vendler 1967, Scha 1984, Dowty 1987, Winter 2000, Hackl 2002)

  43. Collective Predication Ideally, we should have a unified account for the availability of a co-distributive interpretation, and compatibility with the two types of collective predicates.

  44. Collective Predication Proposal: • Good team-type collective predicates apply distributively to each value of a variable in a plural info state (≈ cardinal modifiers). • Gather-type collective predicates apply to the sum of values of a variable across the assignments in a plural info state (≈ grammatical plural).

  45. Collective Predication Theu students are a good teamε. Theu students gatheredε in the hallway. • s1, s2, s3– are atomic student-individuals. • e – is an event/state of gathering/being a good team. • s1 ⨁ s2 ⨁ s3is the cumulative agent/holder of e.

  46. Collective Predication #Allu the students are a good teamε. • s1, s2, s3– are atomic student-individuals. • e1, e2, e3– are events (states) of being a good team. • s1is the holder of e1; s2is the holder of e2; s3is the holder of e3.

  47. Collective Predication Allu the students gatheredε in the hallway. • s1, s2, s3– are atomic student-individuals. • e1– is a gathering event. • s1⨁s2⨁s3is the agent of e1.

  48. Collective Predication #Eachu student gatheredε in the hallway. • g1, g2, g3– are atomic student-individuals. • e1, e2, e3– are gathering events. • s1is the agent of e1; s2is the agent of e2; s3is the agent of e3.

  49. Long-Distance Dependent Plurals Prediction: We should find cases where co-distributional relations between licensors and dependent plurals occur at a distance, e.g. across clausal boundaries: (17) a. Solipsists believe that only their own minds exist. b. Everyone loves to claim that their teams’ mascots are the best on the planet. It’s human nature. c. Both Managers Johnny Brady and Charley Givens expressed confidence that their teams would win Thursday’s game. (18) a. The students left the room immediately after receiving their grades. b. Each student left the room immediately after receiving his grade. (from Schwarzchild 1996)

  50. Long-Distance Dependent Plurals (18) Solipsists believe that only their own minds exist. If their own minds is interpreted as ontologically plural (i.e. referring to a non-atomic sum), we derive one of two readings: (19) a. Generally, a solipsist believes that only the minds of soliplsists exist. b. Generally, a solipsist believes that only her/his minds exist. But we want a co-distributive reading!

More Related