Non-canonical comparatives: Syntax, semantics, & processing ESSLLI 2018 Roumyana Pancheva, Alexis Wellwood University of Southern California August 15, 2018 1 / 22
cardinality comparison Two generalizations about nominal comparatives (1) a. I bought more coffee than you did. volume, weight, *temperature b. I bought more coffees than you did. cardinality, *volume, *weight Monotonicity (Schwarzschild 2002, 2006) Comparatives with bare Ns show variable but constrained dimensionality, sensitive to part-whole relations. Number (Hackl 2001, Bale & Barner 2009) Comparatives with plural NPs may only be compared by number. There is a class of apparent counter-examples, the so-called mass plurals (e.g., muds). See Acquaviva 2008, Schwarzschild 2012, Solt 2015, among others. 2 / 22
Two generalizations about verbal comparatives The generalizations hold for VPs as well (Wellwood et al. 2012) (2) a. as much coffee volume, weight, *temperature b. too many coffees cardinality, *volume, *weight (3) a. run on the track as much distance, duration, *speed b. run to the track more/as many times cardinality, *distance, *duration 3 / 22
Capturing the monotonicity constraint Permissible values of the measure function µ encoded in many and much must be S(chwarzschild)-monotonic. S-monotonicity (Schwarzschild 2002, 2006) x, y D P, if x P y, then µ(x) < µ(y). (4) Let coffee = {..., c, c, c c,...} = D C (where c, c, etc. are non-atomic) Intuitively, for any x, y D C such that x P y, a. volume(x) < volume(y) b. weight(x) < weight(y) c. temperature(x) temperature(y) (5) Let coffees = {..., c, c, c c,...} = D C (where c, c, etc. are atomic) Intuitively, for any x, y D C such that x P y, cardinality(x) < cardinality(y) 4 / 22
An ambiguity theory of the plurality-cardinality link These patterns may be explained in part by an ambiguity in the morphosyntax of more, such that it spells out much plus -er with mass nouns, but many plus -er with plural nouns. (6) a. more 1 coffee much-er coffee b. more 2 coffees many-er coffee-pl Correspondingly, much contributes a variable over measure functions in general (with constraints), while many specifically contributes a cardinality function. (7) a. much = λd.λr η. µ quantity (r) d type η stands for e or v b. many = λd.λr η. µ cardinality (r) d 5 / 22
Some problems for the ambiguity theory One immediate issue with the ambiguity theory is that many never surfaces in the verbal domain, yet the cardinality-semantic plurality link still obtains for event comparison (8) a. too much coffee b. too many coffees (9) a. run on the track too much b. run to the track too much Similarly, the interpretation of object mass nouns is an issue, since they too do not surface with many but allow comparison by cardinality (10) too much traffic 6 / 22
Some problems for the ambiguity theory Another issue is that an adequate analysis of more 1 (i.e., much-er) must capture the fact that such comparatives display variable dimensionality both across and within predicates. (11) Variability across predicates a. more 1 coffee volume, *temperature b. more 1 global warming temperature, *volume (12) Variability within predicates a. more 1 coffee volume, weight b. run more 1 distance, duration 7 / 22
Little cross-linguistic support for the ambiguity theory If the distinction between primitive much and many was semantic, we would expect it to appear more robustly cross-linguistically, but this is not the case (13) Spanish (from Wellwood forthcoming) a. mucha cerveza volume b. muchas cervezas number (14) Bulgarian a. mnogo bira volume b. mnogo biri number 8 / 22
Little cross-linguistic support for the ambiguity theory Typologically more broadly, any way that a language has of indicating plurality marks a shift in interpretation from volume to number language volume number difference English much soup many cookies lexical Spanish mucha sopa muchas galletas agreement Italian molta minestra molti biscotti agreement French beaucoup de soupe beaucoup de biscuits morphology Macedonian mnogu supa mnogu kolaci morphology Mandarin henduo tang henduo kuai quqi classifier Bangla onek sup onek-gulo biskut classifier Table 1: Where many signals number with plural Ns in English, other languages combine a univocal form with (broadly) plural marking. (Wellwood 2014) 9 / 22
An alternative theory Wellwood 2014, 2015, forthcoming, building primarily on Schwarzschild 2002, 2006 and Bale & Barner 2009, argues for an alternative, univocal account, in which the patterns of constrained variability are captured by a new, stronger condition on the selection of measure functions. string morphosyntax semantics ambiguity more N much µ -er n... σ(µ)(x)... more Ns many-er n-pl... cardinality(xx)... univocality more N much µ -er n... σ(µ)(x)... more Ns much µ -er n-pl... σ(µ)(xx)... Table 2: Differences in the alignment between strings, morphosyntax, and semantics on the two accounts. By xx, yy, etc. in Table 2 and below, only visual clarity of talk of pluralities is intended - their nature isn t at issue. 10 / 22
An alternative theory Wellwood s proposal: the Number generalization is a special case of the Monotonicity generalization, and arises due to the semantics of much. The solution has two pieces: Surfacing many: many spells out much in the context of a nominal plural. Restricting much: permissible µs that much encodes are invariant under structure-preserving permutation. Claim: only number meets this and S-monotonicity for coffees and furniture. 11 / 22
An alternative theory What unifies plurals and object mass nouns, such that they require number comparisons in the comparative? Perhaps simply: their (ordered) domains have atomic minimal parts (Bale & Barner 2009). abc ab ac bc a b c Figure 1: Hypothetical extension for furniture and coffees in a context. Nodes represent pieces of furniture / containers of coffee and pluralities thereof, lines represent plural-part relations. 12 / 22
An alternative theory The intuition: cardinality is the only permissible measure of such domains, because it uniquely characterizes these domains. That is, measures by cardinality assign all of the atomic minimal parts to 1, the 2-atom pluralities to 2, etc. A function like weight, in contrast, can assign different values to each atom, each 2-atom plurality, etc. Only a mapping by cardinality represents the structure of an atomic join semi-lattice. (Wellwood forthcoming) 13 / 22
An alternative theory A new constraint, augmenting S-monotonicity, which says that permissible σ assignments to µ must be A(utomorphism)-invariant i.e., they assign the same value to all x in P as to x s image under any structure-preserving permutation. A-invariance x D P, h Aut( D P, P ), µ(x) = µ(h(x)) (15) much µ σ (d)(x) = σ(µ)(x) d (Wellwood forthcoming) 14 / 22
An alternative theory Automorphism: a bijective function that maps a set, say D P, to itself, and meets the condition in (16). In effect, an automorphism maps elements of an ordered set to those same elements, such that all of the same ordering relations are preserved. (16) x, y D P, x P y iff h(x) P h(y) (Wellwood forthcoming) 15 / 22
An alternative theory An illustration: Let D P = {a, b, c, ab, ac, bc, abc} (the inclusive set of pluralities whose minimal parts are the individuals a, b, and c), and the ordering P on this set has all of the properties that we think the domains of plural nouns like toys or superordinate mass nouns like furniture have (i.e., they are atomic join semi-lattices). Then, h in (17) is an example of an automorphism on D P. (17) Automorphism h in Aut( D P, P ) a. h = [a b, b c, c a, ab bc, ac ab, bc ac, abc abc] b. range(h) = domain(h) [endomorphy] c. there is a function g such that domain(g) = range(h) [bijectivity] d. x, y[x P y h(x) P h(y)] [order preservation] (Wellwood forthcoming) 16 / 22
An alternative theory An illustration: Let D P = {a, b, c, ab, ac, bc, abc} (the inclusive set of pluralities whose minimal parts are the individuals a, b, and c), and the mereological ordering P on this set. There are many functions h that are not automorphisms on D P ; (18) gives some examples, along with reasons for their failure. (18) Functions h not in Aut( D P, P ) a. Any h = [a d,... ], since d D P [not endomorphic] b. Any h = [a b, c b,... ], since not invertible [not bijective] c. Any h = [a c, ab a,... ], since a P ab, but h(a) P h(ab) [not order-preserving] (Wellwood forthcoming) 17 / 22
An alternative theory Distinguishing cardinality and weight measures Since any automorphism h on atomic D P, P pairs singletons with singletons, doubletons with doubletons, etc., then any plurality xx D P is such that cardinality(xx) = cardinality(h(xx)). Thus, measures by cardinality are A-invariant with respect to such a domain. However, measures by weight are not; a counter-example is given in (19). (19) Let D P = {b, c, bc}, h an automorphism on D P such that h(b) = c, and weight : [b 120lbs, c 240lbs,...]. Then, since a. weight(h(b)) = weight(c), b. weight(h(b)) = 240lbs; therefore, c. weight(h(b)) weight(b), because 120lbs 240lbs. 18 / 22
An alternative theory Can A-invarience supplant S-monotonicity? It seems that the answer is no. There are measure functions that fail to preserve the structure of the domain for measurement, but which would satisfy A-invariance. Consider a hypothetical such function, one, that maps everything to the number 1. This function trivially satisfies A-invariance, since any x D P will be such that one(x) = 1, and of course one(h(x)) = 1, etc. Such a function will not satisfy S-monotonicity, however, since any case of some x, y D P such that x P y, it is not the case that one(x) one(y). 19 / 22
An alternative theory Does A-invarience apply in the case of measurement of mass nouns? It seems that the answer is yes. Suppose that the extension of coffee is a dense ordering of portions of coffee by inclusion. Any automorphism (hence, any h Aut( D C, C )) will preserve this structure exactly. It seems that just in the same way that cardinality can be said to represent essential structure of plural part-of relations, volume or weight do the same for material part-of relations. 20 / 22
References I Acquaviva, Paolo. 2008. Lexical plurals: A morphosemantic approach Oxford studies in theoretical linguistics. Oxford, UK: Oxford University Press. Bale, Alan & David Barner. 2009. The interpretation of functional heads: Using comparatives to explore the mass/count distinction. Journal of Semantics 26(3). 217 252. Hackl, Martin. 2001. Comparative quantifiers and plural predication. In K. Megerdoomian & Leora Anne Bar-el (eds.), Proceedings of WCCFL XX, 234 247. Somerville, Massachusetts: Cascadilla Press. Schwarzschild, Roger. 2002. The grammar of measurement. In B. Jackson (ed.), Proceedings of SALT XII, 225 245. Cornell University, Ithaca, NY: CLC Publications. Schwarzschild, Roger. 2006. The role of dimensions in the syntax of noun phrases. Syntax 9(1). 67 110. Schwarzschild, Roger. 2012. Neoneoneo Davidsonian Analysis of Nouns. Handout for the 2nd Mid-Atlantic Colloquium for Studies in Meaning, University of Maryland. 21 / 22
References II Solt, Stephanie. 2015. Q-adjectives and the semantics of quantity. Journal of Semantics 32(221-273). Wellwood, Alexis. 2014. Measuring predicates: University of Maryland, College Park dissertation. Wellwood, Alexis. 2015. On the semantics of comparison across categories. Linguistics and Philosophy 38(1). 67 101. Wellwood, Alexis. forthcoming. The semantics of more Studies in Semantics and Pragmatics. Oxford UK: Oxford University Press. Wellwood, Alexis, Valentine Hacquard & Roumyana Pancheva. 2012. Measuring and comparing individuals and events. Journal of Semantics 29(2). 207 228. 22 / 22