Quantifier Particles and Compositionality

In many languages, the same particles build quantifier words and serve as connectives, additive and scalar particles, question markers, existential verbs, and so on. Do the roles of each particle form a natural class with a stable semantics? Are the particles aided by additional elements, overt or covert, in fulfilling their varied roles? I propose a unified analysis, according to which the particles impose partial ordering requirements (glb and lub) on the interpretations of their hosts and the immediate larger contexts, but do not embody algebraic operations themselves. 1 The compositionality question Formal semanticists often treat even multi-morphemic words as compositional primitives. This paper examines a domain of data in which extending compositionality below the word level seems especially rewarding. English some, or, whether, every, both, and, even, too, and also look like a motley crew. But in many other languages, the same particles build quantifier words and serve as connectives, additive and scalar particles, question markers, existential verbs, and so on. It is natural to ask if they are really “the same” across their varied environments. Consider the following samples. Hungarian ki and Japanese dare, usually translated as ‘who’, are indeterminate pronouns in the terminology of Kuroda 1965. Ki and dare form ‘someone’ and ‘everyone’ with the aid of morphemes whose more general distribution is exemplified below. The joint distribution of Hungarian vala/vagy and etymologically unrelated -e corresponds, roughly, to that of Japanese -ka. The joint distribution of mind and is corresponds to that of -mo (see further in Szabolcsi, Whang & Zu 2013, Szabolcsi 2013). Slavic languages, Malayalam, Sinhala, and many others exhibit similar patterns. I will use upper-case KA and MO as generic cross-linguistic representatives. (1) Hungarian Japanese Gloss a. vala-ki dare-ka ‘someone’ b. A vagy B A-ka B(-ka) ‘A or B’ c. vagy száz hyaku-nin-to-ka ‘some 100 = approx. 100’ d. val-, vagy– ‘be’ participial & finite stems e. – dare-ga VP-ka ‘Who is VP-ing?’ f. [S-e] S-ka ‘whether S’ (2) Hungarian Japanese Gloss a. mind-en-ki dare-mo ‘everyone/anyone’ b. mind A mind B A-mo B-mo ‘A as well as B, both A and B’ [A is (és) B is] c. [A is] A-mo ‘also/even A’ ∗I thank Ivano Ciardelli, Marcel den Dikken, Salvador Mascarenhas, and Benjamin Slade for discussions. Proceedings of the 19th Amsterdam Colloquium Maria Aloni, Michael Franke & Floris Roelofsen (eds.) 27 Quantifier Particles and Compositionality Szabolcsi 2 A promising perspective: join and meet There is a beautiful generalization that caught the eyes of many linguists working with these data (Gil 2008, Haspelmath 1997, Jayaseelan 2001, 2011, among others; see Szabolcsi 2010: Ch 12). In one way or another, the roles of KA involve existential quantification or disjunction, and the roles of MO involve universal quantification or conjunction. Generalizing, (3) KA is lattice-theoretic join (∪), MO is a lattice-theoretic meet (∩). Alternative Semantics has thrown a new light on the signature environments of KA. Hamblin 1973, Kratzer & Shimoyama 2002, Alonso-Ovalle 2006, Aloni 2007, AnderBois 2012, and others proposed that not only polar and wh-questions but also declaratives with indefinite pronouns or disjunctions contribute sets of multiple classical propositions to interpretation. They contrast with declaratives that are atomic or whose main operations are negation, conjunction, or universal quantification, and contribute singleton sets of classical propositions. If the universe consists of Kate, Mary, and Joe, we have, (4) a. Who dances?, Someone dances, Kate or Mary or Joe dances {{w : dancew(k)}, {w : dancew(m)}, {w : dancew(j)}} b. whether Joe dances {{w : dancew(j)}, {w : ¬dancew(j)}} (5) a. Joe dances {{w : dancew(j)}} b. Everyone dances {{w : dancew(k) & dancew(m) & dancew(j)}} Inquisitive Semantics (say, Ciardelli et al. 2012) develops a notion of propositions as nonempty, downward closed sets of information states. The sentences in (4) and (5) are recognized as inquisitive and non-inquisitive propositions, respectively; disjunction and conjunction reemerge as Heyting-algebraic join and meet. The upshot is that the Alternative/Inquisitive Semantic perspective offers an even more interesting way to unify KA’s environments, and maintains the possibility to treat KA as a join and MO as a meet operator, although in a slightly modified algebraic setting. In other words, it looks like the core roles of KA and MO can be assigned a stable semantics, and a simple one at that. 3 Mismatches: Too few arguments, too many operators There are two general problems with this beautiful approach. The first problem is that both KA and MO may have just one argument. Schematically, (6) Hungarian (KA = vagy, MO = is), Russian (MO = i), Japanese (MO = mo): 10-KA boys ran. ‘Approximately/at least ten boys ran’ John-MO ran. ‘Also/even John ran’ The flip-side problem is that in some cases KA and MO occur on all their alleged arguments. In Sinhala, both inclusive disjunction hari and alternative question forming disjunction d@ Proceedings of the 19th Amsterdam Colloquium Maria Aloni, Michael Franke & Floris Roelofsen (eds.) 28 Quantifier Particles and Compositionality Szabolcsi attach to each disjunct, as illustrated in (7). Japanese mo, Russian i, and Hungarian mind as well as is all attach to each conjunct in the distributive construction illustrated in (8). (7) Sinhala (KA = hari / d@): John-KA Mary-KA ran. ‘John or Mary ran’ John-KA Mary-KA ran? ‘Did John run, or did Mary?’ (8) Japanese (MO = mo), Russian (MO = i), Hungarian (MO = mind / is) John-MO Mary-MO ran ‘John as well as Mary ran’ Russian li and Hungarian -e, the morphemes that mark alternative questions alternate with ‘or not’ in glorious justification of the Hamblin/Karttunen analysis of whether. But, embarrassingly, they also co-occur with ‘or not’ – which is in fact equally possible in the case of whether. (9) Russian (KA = li), Hungarian (KA = -e) . . . John ran-KA . . . John ran or not ‘whether (or not) John ran’ . . . John ran-KA or not The first problem might be explained away by assuming that the single argument represents or evokes a set of alternatives, to which join and meet can sensibly apply. But it is not clear how that assumption would explain the cases where KA and MO attach to each of the dis/conjuncts, i.e. where we have too many actors for one role. I conclude that KA is not join, and MO is not meet. But, in solving the problems I would like to preserve the insight that KA and MO occur precisely in contexts that are the least upper bound / greatest lower bound of the contribution of the host of KA/MO and something else. 4 The gist of the solution: KA/MO impose semantic requirements on the context There are three basic strategies for solving the mismatch problems: (10) a. KA and MO are meaningful, but their mission in the compositional process is not directly related to ∪ and ∩. b. KA and MO are meaningless syntactic elements that point to (possibly silent) meaningful ∪ and ∩ operators. Compare ± interpretable features. c. KA and MO are meaningful elements that point to least upper bounds (join) and greatest lower bounds (meet) in a semantic way. Compare presuppositions. The analysis of KA in Hagstrom 1998, Yatsushiro 2009, Cable 2010, and Slade 2011 can be seen to represent option (a). On this view, KA is a choice-function variable that eliminates alternatives. I will not pursue this analysis here, because it inherits the problems of choicefunctional analyses of indefinites, it offers no parallel insight for MO’s role, it assumes that alternatives (in general, sets as opposed to individuals) are bad for you, and it does not help with the “too many actors” problem. Proceedings of the 19th Amsterdam Colloquium Maria Aloni, Michael Franke & Floris Roelofsen (eds.) 29 Quantifier Particles and Compositionality Szabolcsi Variants of option (b) have been proposed in Carlson 1983, 2006 for all functional categories, in Ladusaw 1992 for negative concord, in Beghelli & Stowell 1997 for every/each, and in Kratzer 2005 for ka, mo, and more concord phenomena. Taking KA and MO to be meaningless syntactic pointers could be viable. But I’m going to argue that the semantic route is also viable and interesting. Option (c) says that KA and MO are meaningful elements that point to joins and meets in a semantic way. This is what I am going to pursue. My approach draws from Kobuchi-Philip 2009 and Slade 2011, works that took seriously some problems that other literature glossed over, and provided important elements of the solutions. MO is a good starting point, because the standard analysis of too easily extends to MO in John-MO ran ‘John, too, ran’ (I put scalar ‘even’ aside). John-MO ran is thought to assert that John ran and to presuppose that a salient individual distinct from John ran. So MO can be seen as a “semantic pointer” — it points to a fact not mentioned in the sentence, and ensures that the context is such that both John and another individual ran. Kobuchi-Philip’s insight is that in John-MO Mary-MO ran ‘John as well as Mary ran’, both MO’s can be seen as doing the same thing. John’s running and Mary’s running mutually satisfy the requirements of the two MOs. Similarly for Person-MO ran ‘Everyone ran’, with generalized conjunction. The mutual satisfaction of requirements is reminiscent of presupposition projection, and so a small amendment is called for. Presupposition projection works left-to-right, at least when it is effortless (Chemla & Schlenker 2012). If so, the symmetrical character of these constructions is a problem. I reclassify these definedness conditions as postsuppositions in the sense of Brasoveanu 2013: tests that are delayed and checked simultaneously after the at-issue content is established. This is utilized in John-MO Mary-MO ran. In contrast, if nothing in the at-issue content satisfies the test, it is imposed on the input context and emerges as a presupposition. The traditional analysis of John-MO ran is reproduced. For details see Brasoveanu & Szabolcsi 2013. Below, I will use the neutral term “requirement” instead of preor postsupposition. I assume that the same reasoning carries over to KA, whose semantics will be detailed in Section 6. 5 Ingredients of the analysis: Greatest lower bound / least upper bound requirements, pair formation, silent meet and join, defaults To summarize, the “mismatch cases” offer the best insight into the working of the particles. The particles do not embody algebraic operations, as examples of the form A Particle B would lead us to believe. Instead, I suggest, the particles require that interpretations of their hosts and of the immediately larger contexts stand in particular partial ordering relations. The core of the proposal is this. For simplicity, I pretend that the hosts of KA and MO are propositions.