Degree pluralities : distributive, cumulative and collective readings of comparatives

Transcription

1 Degree pluralities : distributive, cumulative and collective readings of comparatives Jakub Dotlačil (Groningen) & Rick Nouwen (Utrecht) February 14, 2014, Paris

2 1 John lifted the box.

3 1 John lifted the box. 2 The boys lifted a box.

4 1 John lifted the box. 2 The boys lifted a box. Collective reading Distributive reading

5 1 John lifted the box. 2 The boys lifted a box. Collective reading 3 Ten boys lifted five boxes. Distributive reading

6 Plural individuals Scha 1981, Link 1983, Landman 1996, Schwarzschild 1996, Sternefeld 1998, Landman 2000, Beck & Sauerland 2000, Winter 2002, Dotlacil 2010, Nouwen 2013

7 Plural individuals Scha 1981, Link 1983, Landman 1996, Schwarzschild 1996, Sternefeld 1998, Landman 2000, Beck & Sauerland 2000, Winter 2002, Dotlacil 2010, Nouwen 2013 Plural events Krifka 1989, Schein 1993, Landman 2000, Kratzer 2003

8 Plural individuals Scha 1981, Link 1983, Landman 1996, Schwarzschild 1996, Sternefeld 1998, Landman 2000, Beck & Sauerland 2000, Winter 2002, Dotlacil 2010, Nouwen 2013 Plural events Krifka 1989, Schein 1993, Landman 2000, Kratzer 2003 Plural information states Van den Berg 1996, Krifka 1996, Nouwen 2003, Nouwen 2007, Brasoveanu 2008 Plural propositions Sharvit & Beck 2002 Plural times Artstein 2003 Plural degrees...

9 Weak claim: the domain of degrees contains degree pluralities

10 Weak claim: the domain of degrees contains degree pluralities John, Peter and Bill are 20, 22 and 26 years old.

11 Weak claim: the domain of degrees contains degree pluralities John, Peter and Bill are 20, 22 and 26 years old. Strong claim: the comparative expresses a relation between degree pluralities comparison can be distributive, cumulative and, potentially, collective.

12 1 A simple framework for plural degree semantics 2 Quantifiers in than-clauses 3 Cumulative comparison 4 Collective comparison

13 1 A simple framework for plural degree semantics 2 Quantifiers in than-clauses 3 Cumulative comparison 4 Collective comparison

14 7 / 44 Distributivity & Cumulativity Two boys carried two boxes. distributive construal: there are two boys such that each of these boys carried two boxes

15 7 / 44 Distributivity & Cumulativity Two boys carried two boxes. distributive construal: there are two boys such that each of these boys carried two boxes cumulative construal: there are two boys and two boxes such that each boy carried at least one of those boxes and each box was carried by at least one of these boys

16 7 / 44 Distributivity & Cumulativity Two boys carried two boxes. distributive construal: there are two boys such that each of these boys carried two boxes cumulative construal: there are two boys and two boxes such that each boy carried at least one of those boxes and each box was carried by at least one of these boys

17 A semantic framework for distributivity & cumulativity Link, 1983, Landman, 1996, 2000, cf. Nouwen / 44

18 9 / 44 A semantic framework for distributivity & cumulativity Link, 1983, Landman, 1996, 2000, cf. Nouwen 2014 a b is the plural individual that has a and b as its parts Predicate cumulation: *X := the smallest set s.t. *X X & x, y *X : x y *X X = {a, b}, *X = {a, b, a b}

19 9 / 44 A semantic framework for distributivity & cumulativity Link, 1983, Landman, 1996, 2000, cf. Nouwen 2014 a b is the plural individual that has a and b as its parts Predicate cumulation: *X := the smallest set s.t. *X X & x, y *X : x y *X X = {a, b}, *X = {a, b, a b} Relation cumulation: **R := the smallest set s.t. **R R & x, x, y, y [ x, x, y, y **R x y, x y **R] R = { a, b, b, c }, **R = { a, b, b, c, a b, b c }

20 10 / 44 A semantic framework for distributivity & cumulativity Link, 1983, Landman, 1996, 2000, cf. Nouwen 2014 Predicate cumulation: *X := the smallest set s.t. *X X & x, y *X : x y *X 1 Two boys *[carried two boxes] distributivity If b1 carried two boxes and b2 carried two boxes, then b1 b2 *[carried two boxes]

21 11 / 44 A semantic framework for distributivity & cumulativity Link, 1983, Landman, 1996, 2000, cf. Nouwen 2014 Relation cumulation: **R := the smallest set s.t. **R R & x, x, y, y [ x, x, y, y **R x y, x y **R] 2 Two boys **carried two boxes cumulativity If b1 carried bx1 and b2 carried bx2, then b1 b2 **carried bx1 bx2

22 12 / 44 A semantic framework for distributivity & cumulativity Link, 1983, Landman, 1996, 2000, cf. Nouwen Two boys carried two boxes collective b1 and b2, as a group, carried bx1 and bx2

23 13 / 44 Plural degree semantics Novel assumptions: the structure of D e = the structure of D d cumulation (i.e. * and **) may apply to relations of any type 1 John, Peter and Bill are 20, 22 and 26 years old. **old(j p b, ) **> **> **

24 1 A simple framework for plural degree semantics 2 Quantifiers in than-clauses 3 Cumulative comparison 4 Collective comparison

25 15 / 44 The syntax of than clauses John is taller than Mary is. than Op i Mary is t i tall Evidence for Op movement in than-clauses (Chomsky, 1977) (i) *He found more marbles than Mary went to the store in order to buy t (ii) *What did Mary go to the store in order to buy t? (Adjunct islands)

26 16 / 44 The semantics of than clauses John is taller than Mary is. Op i Mary is t i tall.

27 16 / 44 The semantics of than clauses John is taller than Mary is. Op i Mary is t i tall. Adjectives are monotone tall = λdλx.x s height d

28 16 / 44 The semantics of than clauses John is taller than Mary is. Adjectives are monotone Op i Mary is t i tall. tall = λdλx.x s height d The interval strategy von Stechow 1984, Heim 2000 than Op Mary is t tall = λd.mary is d-tall John is taller than the maximum of than WH Mary is t tall

29 16 / 44 The semantics of than clauses John is taller than Mary is. Adjectives are monotone Op i Mary is t i tall. tall = λdλx.x s height d The interval strategy von Stechow 1984, Heim 2000 than Op Mary is t tall = λd.mary is d-tall John is taller than the maximum of than WH Mary is t tall The negation strategy Seuren 1973, Klein 1981, van Rooij 2011 than WH Mary is t tall = λd. Mary is d-tall John is tall to some degree satisfying than WH Mary is t tall

30 17 / 44 The semantics of than clauses John is taller than Mary is. Interval: the maximal degree to which John is tall exceeds the maximal degree to which Mary is tall Negation: there is a degree to which John is tall such that it is not the case that Mary is that tall

31 18 / 44 The semantics of than clauses John is taller than every girl is.

32 The semantics of than clauses John is taller than every girl is. λd.every girl is d-tall = (0,150] λd. every girl is d-tall = (150, ) 18 / 44

33 The semantics of than clauses John is taller than every girl is. Interval: the (maximal) degree to which John is tall exceeds the (maximal) degree to which every girl is tall Negation: there is a degree to which John is tall such that it is not the case that every girl is tall to that degree λd.every girl is d-tall = (0,150] λd. every girl is d-tall = (150, ) 18 / 44

34 19 / 44 The semantics of than clauses Notice: λd.every girl is d-tall = (0,150] λd. every girl is d-tall = (150, ) than every girl is tall = the shortest girl s height

35 20 / 44 The semantics of than clauses Wide-scope behaviour for the universal quantifier (von Stechow): John is taller than every girls is - For every girl: the maximal degree to which John is tall exceeds the maximal degree to which the girl is tall - For every girl: there is a degree to which John is tall such that it is not the case that this girl is so tall Problem: than-clauses are islands (cf. Schwarzschild & Wilkinson) *The room was painted precisely that shade of green which Raffaelo Di Sanzio would have bitten off his right hand rather than use (Douglas Adams) Solution: stipulate a scope pivot within the than-clause

36 21 / 44 Negation as a scope pivot Larson, Gajewski, van Rooij, Schwarzschild than every girl is than WH j every girl i NOT t i is t j tall λd.every girl is not d-tall = (190, ) = than the tallest girl is Notice: the original (problematic) reading is available on a different scoping

37 22 / 44 Beck s interval strategy (Beck 2010) Core idea: selection from sets of intervals I (Schwarzschild & Wilkinson 2002, Heim 2006) max(min(i)) Example I s (than clauses) λi.mary s height I λi.every girl s height I min picks the smallest interval from a set of intervals matrix-clause: John s height whole construction: matrix-clause > than-clause

38 23 / 44 Beck s interval strategy: example John is taller than Mary is max(min(λi.mary s height I)) = max([mary s height]) = Mary s height

39 24 / 44 Beck s interval strategy: example John is taller than every girl is max(min(λi.every girl s height I)) = the height of the tallest girl

40 A conservative reinterpretation of Beck s selection approach 25 / 44 λd.every girl s height d = ,..., ,..., ,... the minimum =

41 A conservative reinterpretation of Beck s selection approach 25 / > ?? 170 **>

42 A conservative reinterpretation of Beck s selection approach 26 / 44 John is taller than every girl (is) Beck s approach take the smallest interval that contains the height of every girl take the maximum of that interval John s height > the maximum of [150,190]

43 A conservative reinterpretation of Beck s selection approach 26 / 44 John is taller than every girl (is) Beck s approach take the smallest interval that contains the height of every girl take the maximum of that interval Our approach take the smallest plurality that contains the height of every girl this plurality is in the **> relation to the matrix clause John s height > the maximum of [150,190] John s height > each of the atoms in

44 27 / 44 Comparison of Beck s and our approach Beck s approach max(min(λi.every girl s height I)) min picks the smallest interval from a set of intervals Our approach min(λd.every girl s height d) min picks the smallest plurality from a set of pluralities John s height **> than-clause Immediate advantage: no excessive maximality Instead, we deal with pluralities in the standard way

45 28 / 44 Compositional derivation Cumulativity on relation

46 29 / 44 Compositional derivation Pluralization of degree predicate

47 30 / 44 Differentials Standard semantics for differential: John is exactly 2 inches taller than Bill. John s height 2in = Bill s height John is exactly 2 inches taller than every girl (is). every girl is the same height % Beck: John s height 2in = the height of the tallest girl " John s height 2in **= the plurality of heights of the girls

48 31 / 44 Interim summary The comparative as a potentially cumulative relation between degree pluralities Conservative reinterpretation of Beck s selection approach Slightly simplifies the selection procedure Empirical advantage for differentials If we really want to argue for our framework then we need to show that some examples could not be interpreted without cumulation

49 The relation between distributive and cumulative readings 32 / 44 Fact: If one of the arguments of a relation is singular, then the distributive and cumulative reading collapse into one. John and Bill know Sue. John and Bill **know Sue. (cumulative analysis) = John and Bill *[know Sue] (distributive analysis) John is taller than every girl is. John s height **> than-clause (cumulative analysis) = than-clause *λd.john s height > d (distributive analysis)

50 1 A simple framework for plural degree semantics 2 Quantifiers in than-clauses 3 Cumulative comparison 4 Collective comparison

51 Cumulative readings in phrasal comparatives 34 / 44 Scha & Stallard 1988, Schwarzschild 1996, Matushansky & Ruys 2006 (i) The frigates were faster than the carriers. Imagine [..] a context in which it is clear that these ships are sent out in teams to different areas of the globe with each team consisting of frigates and carriers. It may be that one area calls for very fast action while another will tolerate a sluggish response. If that were the case, I would judge [(i)] true just in case the frigates in a given area were faster than the carriers of that area, regardless of what speed relations obtained between ships of different areas. Schwarzschild 1996, p. 89

52 Cumulative readings in phrasal comparatives 34 / 44 Scha & Stallard 1988, Schwarzschild 1996, Matushansky & Ruys 2006 (i) The frigates were faster than the carriers. Imagine [..] a context in which it is clear that these ships are sent out in teams to different areas of the globe with each team consisting of frigates and carriers. It may be that one area calls for very fast action while another will tolerate a sluggish response. If that were the case, I would judge [(i)] true just in case the frigates in a given area were faster than the carriers of that area, regardless of what speed relations obtained between ships of different areas. Schwarzschild 1996, p. 89 F1 F2 F3 C1 C2 C3 the frigates, the carriers **λx.λy.x is faster than y

53 35 / 44 Cumulative readings in clausal comparatives the frigates The frigates were faster than the carriers were How do we get a cumulative relation? the carriers λi ** were faster than % QR is clause-bounded! t i were cf. Bale 2006

54 36 / 44 Cumulative readings in clausal comparatives Alternative (Winter 2000, cf. Beck & Sauerland 2000): cumulative readings are distributive readings (e.g. *) cumulative effects are due to dependent interpretation The frigates each i were faster than the carriers i were Where the carriers i functionally depends on quantification over the frigates. Each student managed to hand the essay in on time

55 37 / 44 Cumulative readings in clausal comparatives So far in summary: There are cumulative phrasal comparatives these can be handled using the ** operator There are cumulative clausal comparatives Using ** is unavailable: QR over a clause boundary Alternative: distributivity + dependency Next: there exist cases where the dependency analysis is also unavailable

56 The state economies of Ireland, the Netherlands and Australia all scored higher than they each did in the mid-1980s. from (simplified)

57 The state economies of Ireland, the Netherlands and Australia all scored higher than they each did in the mid-1980s. from (simplified)

58 The state economies of Ireland, the Netherlands and Australia all scored higher than they each did in the mid-1980s. from (simplified) A dependency analysis is out of the question, due to they each. (i) The boys all think they won the race (ii) #The boys all think they each won the race (iii) The boys all think that they each failed the course

59 39 / 44 Similar data (i) The students earned less than each of them hoped they would (ii) The Baltimore Ravens scored more points than each of their opponents did (the actual scores: 24-9; 38-35; 28-13)

60 39 / 44 Similar data (i) The students earned less than each of them hoped they would (ii) The Baltimore Ravens scored more points than each of their opponents did (the actual scores: 24-9; 38-35; 28-13) Cumulative readings in the comparative no dependency analysis possible - #The boys all think each of them won the race no relation as a target of ** available - QR is clause-bounded

61 The negation approach / Beck s approach The state economies of Ireland, the Netherlands and Australia all scored higher than they each did in the mid-1980s. We want pairwise comparison of the individual scores; neither the negation approach, nor Beck s could give us this They give us a single degree of comparison 40 / 44

62 41 / 44 Our analysis These sentences are genuinely cumulative but do not involve a cumulative e, e, t -relation but rather a cumulative relation on degrees The state economies of Ireland, the Netherlands and Australia all scored higher than they each did in the mid-1980s **> 4 5 7

63 42 / 44 Collective readings? WOW! John was almost 4 seconds faster than every opponent, and a 9 second gap on Lance. Beck John: Rui: Tony: Lance: Lars: 10m40s 10m44s 10m45s 10m49s 11m30s " max(min(λd. x[opponent(x) x s time-4s D])) = 10m40s % 10m40s 4s ** = (10m44s 10m45s 10m49s 11m30s) Collective reading: degree point representative of degree group

64 43 / 44 Collective readings? Ben was almost a year older than everyone else in class (because he had just missed the deadline for the previous school year). (Beck) - #For all x Ben: Ben was almost a year older than x - #Ben was almost a year older than the next oldest in the class -?The others ages center around a point almost a year younger than Ben.

65 44 / 44 Summary and conclusion There exists properly cumulative readings for comparatives problematic to all existing accounts Proposal: than-clauses with quantifiers receive their particular interpretation via a process of pluralisation The maximality associated with than-clauses is a consequence of plural semantics and the monotonicity of scales When the monotonicity is cancelled (differentials) plural semantics correctly derives the-same-height reading