History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012 Lecture 15: Case Study: History of the Semantics and Pragmatics of MANY, MNOGO, MNOGIE. 0. Introduction ......................................................................................................................................................... 1 1. The early work: Partee 1989 and Babko-Malaya 1998, vs. Löbner 1987.......................................................... 2 1.1. Partee 1989 – the cardinal/proportional ambiguity of many and few .......................................................... 2 1.2. Arguments for this ambiguity in Partee (1989) .......................................................................................... 2 1.3. Analysis of Partee (1989), and problems noted........................................................................................... 3 1.4. Two many’s in Russian................................................................................................................................ 4 2. New issues and new theoretical approaches in newer work............................................................................... 6 2.1. Don’t settle for “stipulated” lexical ambiguity............................................................................................ 6 2.2. Pay more attention to morphosyntax, and semantic types........................................................................... 6 2.3. Compositionality issues about POS, comparative, and superlative degrees. .............................................. 6 2.4. What is the relation between focus structure and “reverse proportional” readings?................................... 6 2.5. Is many intensional? .................................................................................................................................... 6 3. How to think about the “reverse proportional” reading?..................................................................................... 7 3.1. Herburger 1997............................................................................................................................................ 7 3.2. Solt 2009. A “Relative proportional” which is a cardinal reading. ............................................................ 7 4. Krasikova and Champollion on many, mnogo, mnogie....................................................................................... 9 4.1. Mnogie ....................................................................................................................................................... 10 4.2. Mnogo........................................................................................................................................................ 10 4.3. Many .......................................................................................................................................................... 11 5. Intensionality ..................................................................................................................................................... 12 6. Conclusions ....................................................................................................................................................... 12 Acknowledgments. ................................................................................................................................................ 13 References ............................................................................................................................................................. 13 Readings: (Partee 1989) Many quantifiers. (Krasikova 2011) On proportional and cardinal ‘many’. [treats mnogo, mnogie] (2011a, Krasikova and Champollion 2011b) Two many modifiers? [Abstract, Handout] (Bastiaanse 2012) The intensional many – Conservativity revisited Optional readings: (Westerståhl 1985b) Determiners and context sets (Herburger 1997) Focus and weak noun phrases (Babko-Malaya 1998) Context-dependent quantifiers restricted by focus [treats mnogo, mnogie] (Solt 2009) The Semantics of Adjectives of Quantity (Kotek et al. 2012) Many readings of most [deriving readings of most from readings of many] (Lappin 2000) An intensional parametric semantics for vague quantifiers. (Schwarzschild 2006) The role of dimensions in the syntax of noun phrases. 0. Introduction For the last lecture I’ve picked a “case study”: the history of the interpretation of many, and of Russian mnogo and mnogie. This is a topic that formal semanticists have argued about ever since the pioneering work of (Barwise and Cooper 1981); the debates and arguments have developed in interesting ways over the decades, the topic is of great current interest, and the differences between Russian and English are interesting and important. We saw in our study of quantifiers, and you verified in Homework 2, that Russian mnogo is a weak quantifier, and mnogie is a strong one. In English both are translated as many. When Barwise and Cooper did their study of the semantic properties of quantifiers, they left some question marks about the semantic properties of many and few, in part because they disagreed between themselves about the results of applying their tests. (Partee 1989) proposed that many is lexically ambiguous between a vague cardinal weak quantifier and a vague proportional strong quantifier, which could explain Barwise and Cooper’s disagreements. RGGU1215.doc 1 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012 Later (Babko-Malaya 1998) offered support for the ambiguity hypothesis with her work on mnogo and mnogie. But that work raised new questions, because it did not actually support my proposed explanation of the ambiguity, and there have been many hypotheses proposed and questions raised in the years since then, as we will see. I gave a talk on this topic in Israel in March 2012; I am omitting some of the things that were in that handout, and adding some things I learned later. Original handout available on request. 1. The early work: Partee 1989 and Babko-Malaya 1998, vs. Löbner 1987. 1.1. Partee 1989 – the cardinal/proportional ambiguity of many and few Partee 1989 argued that many and few are not only vague, but also ambiguous, and proposed the following cardinal and proportional readings: (1) Many aspens burned. (a) Cardinal: |A ∩ B| > n (b) Proportional: |A ∩ B| ≥ k k a fraction or % |A| (2) Few aspens burned. (a) Cardinal: |A ∩ B| ≤ n (b) Proportional: |A ∩ B| ≤ k |A| 1.2. Arguments for this ambiguity in Partee (1989) (Löbner 1987) had already argued for an explicitly anti-ambiguity account, arguing for a single semantic analysis, with context-dependent resolution of “relatively high/low”: (3) |N’ ∩ VP’| is relatively high/low Partee argued that despite the potential attractions of a no-ambiguity account, there really is a syntactic and semantic ambiguity. • Milsark’s generalizations (i) Only weak Det’s are allowed in existential there-sentences. (ii) Only strong Det’s co-occur with I-level predicates in simple NP VP sentences (4) a. *Sm people were Democrats. b. Some people were Democrats. Milsark: some determiners, including numerals, many, and few are weak but have “strong doublets”. He considered weak quantifiers not to be true quantifiers, but “cardinality words”. Many and few can clearly occur in both contexts, supporting an ambiguity, but not necessarily a lexical one. What’s important is that many and few in strong-only positions can have a proportional reading in addition to a possible cardinal reading. • Barwise & Cooper’s question marks. Barwise and Cooper noted some disagreements and uncertainties about the formal properties of few and many. Partee (1987) showed how those disagreements and uncertainties could be resolved by the ambiguity hypothesis. The ambiguity hypothesis also removed Barwise’s only counterexample to Cooper’s hypothesis that all weak determiners are intersective. • Explicit adjectives. Many and few in explicitly adjectival positions, as in the many women, the few third-year students in the class, have only the cardinal reading. This didn’t prove ambiguity, but added RGGU1215.doc 2 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012 support to the hypothesis that “there is a cardinal many which is adjective-like and patterns with the cardinal numbers in being able to be used as either an adjective or a determiner, and a proportional many which is only a determiner. In phrases like those in [(5a-b)] we find both at once; in these cases, the first is probably almost always construed proportionally, the second obligatorily construed cardinally” (Partee 1989). (5) a. few of the few jurors (from Westerståhl 1984) b. Many of the many protestors advocated violence. • Huettner’s test: When can few amount to all? Alison Huettner (1984) made the observation that there are some constructions in which “few NPs” can amount to all the NPs there are (though few certainly never means “all”), and others in which it cannot. Existential sentences like (6) are one such context; (6) could be true in a situation where all the faculty children were at the picnic, but there were few faculty children back then. (6) There were few faculty children at the 1980 picnic. NP-VP sentences with stage-level predicates, especially “existence-asserting” ones, also allow the possibility of few amounting to all. (7) Few egg-laying mammals turned up in our survey, perhaps because there are few. But in the subject of an individual-level