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 predicate, few cannot amount to all. (8) # Few egg-laying mammals suckle their young, perhaps because there are few. Since few can never amount to “all” on a proportional reading, and can on a cardinal reading, Huettner’s observation gives added support to the ambiguity hypothesis. This test, which applies directly only to few and not to many, has remained robust and useful. (Extending it to many involves showing or assuming that few and many are relevantly parallel.)
1.3. Analysis of Partee (1989), and problems noted Partee proposed capturing the observed phenomena via a lexical ambiguity in many and few. Cardinal many: starts out as adjective, shiftable to Det by composition with a null indefinite article. Proportional many: “essentially quantificational” Determiners like every and most, involving tripartite structures if given a Kamp-Heim style analysis.
The biggest issue that was noticed but not resolved concerned Westerståhl’s “reverse proportional reading”, in which the roles of A and B are switched; that reading was and for a long time remained a real puzzle. The classic example of the “reverse reading” is (9):
(9) Many Scandinavians have won the Nobel Prize in literature. (Westerståhl 1985b)
This is interpretable as true in a situation where as of 1984, out of a total of 84 winners, 14 came from Scandinavia. So it’s equivalent in truth conditions on that reading to (10) on a “standard-proportional” reading.
(10) Many of the winners of the Nobel Prize in literature have been Scandinavians.
So we have the possible reading (11):
(11) Reverse proportional reading of many(A,B): |A ∩ B| ≥ k |B|
RGGU1215.doc 3 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
If this is a real reading, then it is a counterexample to the universal that all determiners are conservative, and it is the only serious challenger, since other potential counterexamples like only and mostly have been argued not to be determiners. (12) A determiner D is conservative iff for all A, B, D(A,B) iff D(A, A ∩ B). Partee (1989) concluded on a worrisome note, trying to put a brave face on some crucial data noticed too late to rework the paper. [I repeat this here (condensed) as one possible response to such situations: don’t throw the paper away, but be honest about problems.]
I have left untouched some important proposals from Westerståhl (1984), who argues that there are proportional readings for many which are not based on proportion of the common noun set. These violate the constraint that determiner meanings are always conservative …, and it is partly for this reason that I have ignored them. But for honesty’s sake and as a pointer to an important area for future research, I mention new data that I noticed very recently, which offers potentially differing truth-conditions for testing the ambiguity of many, but which appears to clearly argue for the existence of a non-CN-based [non-NP-based] proportional reading as well. (37) There are more illiterate people in small rural towns than in large cities. (38) Small programs give financial support to more of their students than large programs do. (39) Some small programs support more students than some large programs do. Such sentences are valuable sources of data, since comparatives generally remove the ambiguity of vague predicates, and clear differences can then show up between cardinal and proportional readings. But judgments about the possible readings for (37-39) show a surprising range of possibilities, including a non-CN-based proportional reading for (37). I thus conclude the paper with a call for more work in this interesting area … 1.4. Two many’s in Russian. Babko-Malaya (1998) discussed two Russian translations for many, weak cardinal mnogo and strong proportional mnogie (See also (Paperno 2012).) Her analysis is summarized and discussed in (Partee 2001). We start with her reformulation of the two readings.
Partee (1989) (13) Cardinal: | ║ NP ║M,g ∩ ║ VP ║M,g | > n, where n is a relatively large context- dependent integer (14) Proportional: | ║ NP ║M,g ∩ ║ VP ║M,g | > c × | ║ NP ║M,g | , where c is a relatively large fraction.
Babko-Malaya (1998): (15) Proportional: |║NP║M,g ∩ ║VP║M,g | > f(║NP║M,g), where f(║NP║M,g) = c × |║NP║M,g | and c is a large proportion.
(16) Cardinal: |║NP║M,g ∩ ║VP║M,g | > f(C), where C is a context-dependent comparison set. This restatement distinguishes two separate problems in the semantics of many and few. The first: what determines the comparison set C in the case of cardinal many? The second: What is the nature of the comparing function f, and is it context-dependent? (“How many is many?”) Her answer: For cardinal many, C can be determined from focus structure. And the function f is not especially context-sensitive, or not relevantly so. Babko-Malaya argued that the existence of the two distinct quantifiers in Russian supported my ambiguity hypothesis, and
RGGU1215.doc 4 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
also that the range of readings possible for mnogie, including Westerståhl’s “reverse proportional” reading, supported Herburger’s focus-dependent analysis of proportional readings. Her main claim: the ambiguity proposed for English many is supported by fact that the two proposed readings correspond to two distinct quantifiers in Russian. mnogo : ‘many’ – ADV - weak. mnogie : ‘many’-ADJ. – strong.
(17) a. V lesu bylo mnogo ljudej. b. * V lesu byli mnogie ljudi.
(18) a. *Mnogo lingvistov inteligenty. b. Mnogie lingvisty inteligenty.
BUT: Is mnogie really an adjective?? And it’s the STRONG member of the pair??
Babko-Malaya’s paper was a very worrisome sort of support for the ambiguity hypothesis! I would have expected the weak one to be an adjective if either is, given what I had written about cardinals and weak many. Later, after discussions with my Russian students (Partee 2010, Partee 2011), I came to believe that neither one is an adjective (there is an adjective mnogočislennyj that means ‘numerous’, different from both, which is used to translate things like his many friends), and that mnogie is only one of several determiners to show such morphology (the demonstratives tot, ètot have similar endings). The morphology of Russian determiners, numerals, and quantifiers is rich and complex and puzzling, and I am no expert on it, so for years I just left that problem dormant. I was glad to see that there were two many’s in Russian, a weak and a strong one, but I clearly had no explanation of how their morphosyntax related to their semantic properties. But later work by Krasikova, and by Krasikova & Champollion (Section 4 below) argues that mnogie really is an adjective1, and mnogo a focus-sensitive measure adverbial, and argues for quite different principles than the ones I had suggested in my earlier work. Interestingly, their work leaves it open whether English many should be considered lexically ambiguous or not; both possibilities are compatible with their account of Russian (Section 4.)
1 Sveta Krasikova (p.c., March 2012) reports, “I've also always thought that 'the many N' cases are cardinal. But Stefanie [Solt]'s example [(23) below] seems really proportional, and I would translate it into Russian by using 'nemnogie': [BHP note: I never knew that mnogie or nemnogie could be used in this way! This is important!] (i) Тем немногим детям, которые любят шпинат, не надо принимать витамины. (the X, s.t. X is a small group of children and X like spinach, …) It's important that the relative clause should induce some kind of partitioning on the head noun children who like spinach and who don't). If no such partitioning is prominent, sentences with 'nemnogie' are odd. The following sentence sounds strange to me unless I put focus on 'he' and partition all the books into those written by him and by other people. ?Те немногие книги, которые он написал, были переведены на 10 языков. those nemnogie books which he wrote were translated into 10 languages (the X, s.t. X is a small group of books and he wrote X, …) I would use the cardinal variant with 'nemnogochislennye' (lit. non-numerous): Те немногочисленные книги, которые он написал, были переведены на 10 языков. (the X, s.t. X are books and he wrote X and X are small in number, …”
RGGU1215.doc 5 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
2. New issues and new theoretical approaches in newer work Partee (1989), Westerståhl (1985a, 1985b), Babko-Malaya, Herburger, and others working in the 1980’s and 1990’s in the framework of Generalized Quantifiers and related approaches concentrated on figuring out the meanings of various quantifiers, and sometimes on their syntactic properties as well, and how those meanings were connected with the kinds of properties studied by Barwise and Cooper, Keenan and Stavi, and with phenomena like the Definiteness Effect and the distribution of NPI’s. Great advances were made, but in subsequent years of course more has been sought and more achieved. 2.1. Don’t settle for “stipulated” lexical ambiguity. Partee (1989) simply stipulated the two meanings for few and many. In more recent work, the goal is to derive and explain the possible readings and distribution of many, mnogo, mnogie. Don’t accept “lexical ambiguity” as a solution unless there is no other solution. Sections 3,4.
2.2. Pay more attention to morphosyntax, and semantic types. Partee (1989) was attracted to Milsark’s idea that weak quantifiers were basically adjectival in nature, and got determiner-like meanings by the semantic combination of an existential quantifier with a predicate of pluralities. But Herburger and others showed by the mid-1990’s that that could not be right, because of non-monotone-increasing weak quantifiers like no, few, and at most n. And Partee (1989) did not include any “degree” morphology. (Not discussing today, but reflected in most recent research. And see (Giusti and Leko 2005) for more on Slavic quantifiers, especially their syntax.)
2.3. Compositionality issues about POS, comparative, and superlative degrees. Among much new work about all sorts of degree-related constructions and about scalar predicates of many sorts, there has been a lot that involves many, much, more, most. Not surprisingly, attempts to get comparative more and superlative the most right have had repercussions on how to treat many and much. (Hackl, Kotek & Sudo, Szabolcsi) Not discussing today.
2.4. What is the relation between focus structure and “reverse proportional” readings? Where do “comparison classes” enter the analysis? How are they constrained by syntax, by focus structure, by pragmatic principles? What is the explanation of the “reverse proportional” reading? (In 1989 I just said that n and k “come from the context”. I really didn’t believe there was anything systematic to be said about “how”.) Current work suggests that the “reverse proportional” reading is probably a subcase of the cardinal reading, and that only the cardinal reading is focus-sensitive. This fits well with the behavior of mnogo and mnogie and the account given by Krasikova, and by Krasikova & Champollion. Section 3.
2.5. Is many intensional? (Keenan and Stavi 1986) argued that many and few are intensional, and therefore not Conservative, and therefore left them out of the category of quantifiers. I thought that their arguments could be answered just by invoking context-dependence of the “standard of comparison”. Others have argued that many is really intensional (sensitive to the intension and not just the extension of its arguments), and most recently Bastiaanse (2012) has argued that we can define a suitable intensional definition of Conservative and other crucial semantic properties, under which many can be intensional and still be Conservative. Section 5.
RGGU1215.doc 6 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
3. How to think about the “reverse proportional” reading? As noted above, the reverse proportional reading of many challenges the universal that all determiners are conservative, and is the only serious challenger to that universal. 3.1. Herburger 1997. On the analysis of (Herburger 1997), (see also (Babko-Malaya 1998), (Herburger 1993, 2000)) the reverse proportional reading, which she calls the “focus-affected (f-a) reading”, is given a serious treatment that accounts for many things left unaccounted for in Partee (1989), and it makes many and few conservative. But her treatment raised serious puzzles of its own, and I have always found it confusing. I discussed it in my Israel handout; here I will only give some of her most important examples, which are now classic.
Her “focus-affected” (f-a) reading is a generalization of Westerståhl’s “reverse proportional reading”. Her idea is that DPs containing many and few in some contexts are subject to focus- sensitivity in their interpretation: the choice of restrictor and nuclear scope is determined by focus structure, very much as it was already known to be for adverbs of quantification.
(19) Few COOKS applied. (Herburger 1997, p.61) (20) Focus-affected (f-a) readings: Focus inside a DP can give rise to a f-a interpretation, where the focused predicate serves as the matrix of the determiner and the nonfocused part as the restriction. (Herburger 1997, p.62)
One important feature of her account is her claim that it is only “weak” (in her sense, which is not quite the standard one) DPs that can get focus-affected readings, but those readings may be proportional readings. One crucial part of how she achieves that is by arguing that Strong Determiners always take their NP with them when they take scope by QR: the whole DP undergoes QR. Weak Determiners can stay in situ (“indefinite”), or raise with their whole DP, giving the “strong-like” interpretation, or just the D can raise alone, which can give a f-a reading.
3.2. Solt 2009. A “Relative proportional” which is a cardinal reading. One important recent addition to the literature is (Solt 2009). She builds on and also argues with influential work by Hackl (Hackl 2000, Hackl 2009), which I’m omitting from discussion because it doesn’t directly address the issues of how many many’s (but that question is addressed in more recent work by Hackl’s team (Kotek et al, 2011, 2012).)
Solt argues that reverse proportional readings are a species of cardinal reading. She emphasizes the role of the “Standard of Comparison” in degree-based approaches to gradability, building on (Cresswell 1976), unpublished work of von Stechow on times as degrees, and on (Heim 2006), to propose that the positive morpheme POS introduces a “neutral range”, an interval of values that count as neither large nor small on the given scale. POS interacts with a degree predicate to saturate its degree argument. The formulas in (21) need some interpreting, but for examples with many and few where the relevant scale is cardinal, they give results as in (22).
(21) a. ! ||many||"= λdλI#. d∈I b. ||few||" = λdλI#. d∈INV(I)
RGGU1215.doc 7 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
(22) a. Many students attended the lecture. b. The neutral range for the Standard of Comparison lies in the interval between 0 and the number of students who attended the lecture; i.e. the number who attended is above the upper end of the neutral range. c. Similarly, for few, the number who attended should be below the lower end of the neutral range.)
Solt goes into the issue of how the Standard of Comparison is determined; it is of course context-dependent, but she identifies some basic strategies and some linguistic constraints. POS forms are underspecified; the neutral range is introduced by POS, structured as a range of values around some “point of comparison” pC.. There are two main mechanisms for setting the range, exemplified by overt “compared to” phrases and overt “for” phrases (many cars in the parking lot for a Sunday), both of which are assumed to have covert counterparts.
When she turns to the cardinal/proportional distinction (Section 4.6), she shows that comparative more also has both cardinal and proportional readings. One of her arguments for that is that there exist overt comparisons of proportions with many and few, as in fewer than half of Americans think …, more than a quarter of adults in Ohio are …. She also shows that one can find proportional readings for clearly adjectival uses of many and few [!].
(23) The few children who like spinach do not need vitamin supplements. (p.208)
And she and Peters and Westerståhl (2006) have similar examples of proportional readings for many inside the NP of an existential sentence.
(24) a. There are many American presidents who are millionaires. (P & W. pp. 233-34) b. There are few children who like spinach. (Solt, p. 211)
Solt notes that the condition for getting proportional many, few in an existential sentence is the same as the condition for getting strong some, namely that there be a following relative clause with an I-level predicate.
(25) a. There are sm/*some children in the yard. b. There are *sm / some children who like spinach.
Solt contends that the cardinal/proportional distinction does NOT correspond to adjectival vs. quantificational few and many, but that the crucial distinction is between two kinds of scales, upper-bounded for proportional readings vs. open-ended for cardinal readings.
She finds two contexts that give rise to the proportional reading for many and few: a following I-level predicate, or a partitive. She hypothesizes that these two contexts share a “totalizing” property: The totality of the domain enters into the semantic computation. (She says this idea comes from a similar one used by Fiengo.)
She clearly distinguishes a weak cardinal reading from a strong proportional reading, but she does it without a lexical ambiguity in few, many. Her account is also not like those who try to do it with a single semantic reading and only pragmatic differences in setting a standard, like (Löbner 1987) and (Lappin 2000); she believes in the semantic ambiguity but derives it without a lexical ambiguity. Solt on the reverse reading: Solt devotes a section of her dissertation to the reverse reading. She reviews arguments against Herburger’s “focus-affected” reading account by Büring, de Hoop and Solà, and Cohen. She also notes that Westerståhl’s example is different from
RGGU1215.doc 8 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
Herburger’s examples: in Herburger’s cooks examples, the size of the set of all cooks does not matter for the truth conditions, but in Westerståhl’s example, the size of the set of Scandinavians IS relevant, as shown by Cohen’s examples (26a-b).
(26) a. Many Scandinavians have won the Nobel prize in literature. b. Many Andorrans have won the Nobel prize in literature.
A much smaller number of winners could make (26b) true than are needed for (26a); this was part of Cohen’s argument that we are dealing not with a “reverse proportional” reading but a “relative proportional” reading. As Solt notes, in both cases the number is being said to be “more than would normally be expected”. (Hence possibly intensional (Section 5).)
Solt’s proposal for the “relative proportional” reading makes it a CARDINAL reading; the term to the right of the greater-than relation is on her analysis a point of comparison pC.
(27) |Scandinavians ∩ winners| > | Scandinavians | × |All nationalities ∩ winners| (p.235) | All nationalities | If her arguments hold up, she has an analysis which derives the cardinal/proportional ambiguity without a lexical ambiguity, and on which there are no violations of any quantifier universals in any of the posited meanings for the lexical items or the DPs. But note that if all of (27) came from the semantics of many, it would violate Conservativity. It’s crucial that the part on the right-hand side is regarded as coming from principles for choosing an appropriate point of comparison. As Ariel Cohen (p.c.) notes, it’s not clear what the principles are for determining what to count as part of the semantics and what not; is Solt avoiding a violation of Conservativity by a questionable maneuver?
Some crucial aspects of Solt’s analysis: On her analysis, many and few are adjectives of quantity, expressing gradable predicates of scalar intervals. Their semantics requires that they be supplied with a value for a parameter specifying a standard of comparison; how that value gets supplied is constrained by grammar, not just “determined by context”. The adjective is not a predicate of the noun it combines with; that noun contributes rather to the setting of the standard of comparison. 4. Krasikova and Champollion on many, mnogo, mnogie Now we return to Russian. And at last there is a way to make sense of the fact that mnogie is an adjective but is proportional. Krasikova (2011) and Krasikova & Champollion (2011b) build on the work of Babko-Malaya, Hackl, Kayne, Herburger, Löbner, Milsark, Partee, Solt, and von Stechow to fashion an analysis that captures the similarities and differences between English many and Russian mnogo and mnogie, even deriving the difference in meaning between the two Russian quantifiers from their syntactic differences. (That part really impressed me, given how unprepared I was for an adjectival many to have a strong reading.)
What they take as common to all the meanings of many etc is roughly “large in number with respect to a comparison class”. If the comparison class is given by the NP in construction with many, the result is a proportional reading (PR); otherwise it is a cardinal reading (CR). The question is then what restricts the choices for mnogo and mnogie, whose distribution and interpretation are illustrated below.
(28) a. Mnogie deti prishli na prazdnik. ✓PR, *CR (with an i-level predicate) b. Vdol’ ruch’ja bylo mnogo velosepedistov. *PR, ✓CR (weak-only environment)
RGGU1215.doc 9 Informally: mnogo QRs like only in Rooth’s focus semantics. (24) a. ⟦mnogie⟧ = !N. !x. |x| ≥ standard(!x: N(x). !d. |x| ≥ d) & N(x) (19) Mnogo !d. [d-many girls are taking SEMANTICS] b. ⟦tall/vysokie⟧ = !N. !x. height(x) ≥ (9) a. mnogie/nemnogie studenty (13) V etom semestre mnogo studentok vybralo SEMANTIKU. = the number of ⟦girls (who) are taking semantics⟧ is significantly above standard(!x: N(x). !d. height(x) ≥ d) & N(x) many/few student.pl.Nom in this semester mnogo students.fem chose semantics ⟦ the average‘many/few of students’the focus alternatives to girls who are taking This may be different from world to world. So strictly speaking, “standard” takes SEMANTICS⟧ (14) Mnogomore studentokarguments, vybralo e.g. it semantikutakes an adjective v ETOM and semestre. a world, but we ignore this. b. vysokie studenty mnogo students.fem chose semantics in this semester = moretall girlsstudent.pl.Nom take semantics than the average number of girls in a course These3.2. sentences‘Mnogo’ mean the same as their English counterparts. (20) Mnogo‘tall !students’d. [d-GIRLS are taking semantics] First let’s account for the focus sensitivity of ‘mnogo’. We write ⟦X⟧-ordinary for And the= weak the number form patterns of ⟦girls with (who something) are taking else semantics altogether⟧ --is measuresignificantly phrases: above However, ‘mnogie’ is not focus sensitive: the ordinary (conventional) semantic value of X; ⟦X⟧-focus stands for its the average of the focus alternatives to ⟦GIRLS who are taking (15) Semantiku v etom semestre vybrali mnogie STUDENTKI. (10) a. mnogo/malo studentov focus value, see Rooth (1992). semanticsmany/few⟧ student.pl.Gen semantics in this semester chose mnogie students.fem = more girls take semantics than the average ofHistory semantics of Formal-taking Semantics, girls and Lecture 14 Preliminary entry: ‘many/few students’ Barbara H. Partee, RGGU, May 22, 2012 (16) V etom semestre mnogie studentki vybrali SEMANTIKU. semantics-taking boys b. dve tonny bobov (25in) this⟦mnogo semester⟧ = !mnogieD. max students.fem(⟦D ⟧-ordinary chose) ≥ standard semantics(⟦D⟧-focus) two tons bean.pl.Gen ‘two tons of beans’ (17)AgainMnogie we want studentki to give vybrali the standard semantiku function v ETOM some semestre. more information: Krasikova & Champollion’s summary of the pattern; “expected” refers to Partee (1989). mnogie students.fem chose semantics in this semester 3. Implementation (26) ⟦mnogo⟧ = !D. max(⟦D⟧-ordinary) ≥ In these examples, focus does not affect the proportional interpretation of 3.1.Form ‘Mnogie’Semantics Milsark test Expected syntax Actual syntax ‘Mnogiestandard studentki’(!x. is ! dinvariably : d ! "⟦ Dinterpreted⟧-focus. |x| as ≥ d“a) large proportion of female ⟦mnogimnogiee ⟧ combinesproportional with a nominalstrong of type
The resulting reading is Proportional. And it is not focus-sensitive. Changing the focus structure of a sentence with mnogie just gives contrastive interpretations, keeping the interpretation “a large proportion of female students”.
(32) a. Semantiku v etom semestre vybrali mnogie STUDENTKI. b. v etom semestre mnogie studentki vybrali SEMANTIKU. c. mnogie studentki vybrali semantiku v ETOM semestre.
4.2. Mnogo So why does mnogo have only a cardinal reading? They observe, following Babko-Malaya, that mnogo (like many adverbial quantifers) is focus-sensitive. And like Solt, they argue that its comparison class is determined by the focus value of the clause containing it. They assume that like focus-sensitive only, mnogo undergoes QR so that it takes the whole clause in its scope. And following (Schwarzschild 2006), in order for mnogo to compose with its syntactic complement in the same way as a measure phrase like dve tonny, they supply it with a type- shifter that applies to the noun and gives the noun a d argument and a measure function that measures the cardinality of the noun. I copy from their handout (p7):
2 There are exceptions to this for adjectives – see (Kamp and Partee 1995) and this year’s Lecture 14 – but apparently not for mnogie. They acknowledge this as an unexplained fact.
RGGU1215.doc 10 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
type
(31) ⟦d !card studentov⟧ = "x. students(x) & card(x) ≥ d (39) ⟦mnogo girls are TAKING SEMANTICS⟧ = the number of girls taking semantics exceeds the average size of a salient girl group. (32) ⟦d !card students came⟧ = "x. students(x) & card(x) ≥ d & came(x) Suppose that the salient groups of girls are semantics-takers and non-semantics (33) ⟦mnogo⟧ = "D. max(⟦D⟧-ordinary) ≥ standard("x. "d : takers. d ! "⟦D⟧-focus. |x| ≥ d) Actually this prediction is true – though this has not been observed before: (34) mnogo "d [d ! students CAME] := card (40) V etom semestre mnogo studentok VYBRALO semantiku. " " " max( d. #x: students(x) & card(x) ≥ d & came(x)) ≥ standard( x. d: in this semester mnogo students.fem chose semantics d ! "{ "d. #x: students(x) & card(x) ≥ d & Alt(x) | Alt ! ⟦came⟧-focus}. Reading: ‘More students are taking semantics than not taking it.’ |x| ≥ d) (The number of children who came is at least the average of the focus They paraphrase this last formula as “The number of students who came is at least the value of ⟦"d [d ! students CAME]⟧ (which are other situations in which average of the focus value of [[λd [d µ students CAME] ]] (which are other situations in 4. Outlook children did something) which students did something).” In English there is a debate on whether there is one or two ‘many’s. Now let’s consider why mnogo doesn’t have proportional readings in the normal A long-standing debate revolves around whether this behavior is due to lexical They showcase. that a proportional reading is never available if the Comparison Class, or more generally the topic of the utterance, is specified by means of prosodic prominence. In those ambiguity (Milsark (1974); Partee (1989)), pragmatic underdetermination (35) ⟦mnogo girls are taking semantics⟧ cases, one gets a “focus-affected” reading, which can only be a species of Cardinal reading. (Löbner (1978)), or differences in scale structure (Solt (2009)). But Russian has rigid word order, used in signaling topic-focus structure. Topics occur Solt (2009) has shown that English ‘many’ is not a gradable adjective syntactically. We assume that there are 100 girls and 100 boys and that the salient groups are sentence-initially. But weak mnogo studentov does not make a good topic and does not like to English might be like Russian – two ‘many’s – just that they sound the same. occur in girlssentence and boys. initial position; attempted ways to do it run into trouble. However: English might also only have one ‘many’ whose comparison class is Proportional reading: neither constrained by the head noun, nor by focus, i.e. it is pragmatically 4.3. Many (36) More than half the girls are taking semantics. (i.e. more than 50 girls) determined. The restriction on Comparison Class used in the explanation of mnogie is assumed by them to applyActual only readings: to attributive gradable adjectives. Why doesn’t it apply to many? They appeal to The distinction between English many and Russian mnogo might be analogous to Solt and(37) to⟦ Kaynemnogo toGIRLS argue arethat taking English semantics many differs⟧ = the fromnumber attributive of girls takinggradable adjectives. the one that Beaver and Clark (2008) propose for English only and always. Only the former is directly focus-sensitive. The focus-sensitivity of the latter semantics exceeds the average size of a salient semantics-group. (33) a. Many linguists like phonology, but many don’t. results from its dependency on context, and from the fact that focus also Supposeb. *Good that linguists 30 boys likeare takingphonology, semantics but bad and don’t. 40 girls are taking(Kayne semantics. 2005) The reflects what is given in the context. average size of a salient semantics-taking group is 35. The sentence is true (34) butmany/*good the proportional of the studentsreading is false. (Solt 2009)
They( follow38) ⟦mnogo Solt in girls analyzing are taking many SEMANTICS not as a gradable⟧ = the predicate number of of girls individuals taking but one of degrees. Theresemantics are many exceeds possib theilities average for size the ofComparison a salient girl Class group. for an example like (35).
(35) Many faculty children came to the party.
The Comparison Class may but need not be constrained by the extension of faculty children. It can but need not be affected by focus, which7 can restrict the choice of discourse topic. 8
They conclude their handout by saying that their analysis of Russian mnogie and mnogo leaves open the question of whether English has two lexical many’s, or whether it has just one many, whose Comparison Class is not constrained either by the head noun nor by focus, i.e. it is pragmatically determined. They suggest that the distinction between English many and Russian mnogo could be like the distinction proposed by (Beaver and Clark 2003, Beaver and Clark 2008) between English only and always. Only only is directly focus-sensitive. The
RGGU1215.doc 11 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
focus-sensitivity of always is indirect, and results from its context-dependency, and from the fact that focus also reflects what is “given” in the context.
So the question of whether English many (and similar quantifiers in other languages) is lexically ambiguous is still open, and this should be a rich area for continuing cross-linguistic study. 5. Intensionality There won’t be time to discuss this today, but I want to mention the issue of intensionality, raised by a number of authors in the history of discussion of the puzzles of many, starting with (Keenan and Stavi 1986) and including (Fernando and Kamp 1996, Lappin 2000). Bastiaanse (2012) assumes that it has indeed been established that many is intensional, citing an example of (Westerståhl 1985a) to illustrate the problem. Situation: In a certain class at a certain university, 10 out of 30 students got the highest possible grade on a certain exam, which is unusually many. Those same 10 students are the only ones in the class who are right-handed, which is unusually few. Let A be the set of students in the class. Let B1 be the set of students in the university who got the highest grade. Let B2 be the set of students in the university who are right-handed. According to these assumptions, we want to say that (a) is true, but (b) is false. (36) a. Many students in the class got the highest grade. b. Many students in the class are right-handed.
I.e., we want to say: Many(A,B1) but ¬Many(A,B2). Westerståhl shows that since A ∩ B1 and A ∩ B2 are the very same set (that set of 10 students), many cannot be Conservative on such a scenario. Bastiaanse accepts the data, argues that the heart of the problem is the intensionality of many – it depends on the properties involved, not just the sets in the actual world. He says “As already known, readings of many without an intensional component can only be Conservative at the price of being almost arbitrarily context dependent.” He resolves the problem by defining an intensional notion of Conservativity which is satisfied by some but not all suggested analyses of many in the literature, including (possibly modified versions of) those of Fernando and Kamp (1996), Lappin (2000), and Solt (2009). 6. Conclusions The ambiguity has been maintained, but it may be explainable without lexical ambiguity. The cardinal reading is associated with an adjective-like (but not really) many in English and with non-adjectival mnogo in Russian: the differences can be explained, but it has taken hard work to develop the ingredients for an explanation, including careful attention to the difference between gradable adjectives that are predicates of individuals and gradable non-adjectives that are predicates of degrees. Further work by Szabolcsi (Szabolcsi 2012) and others extends this careful compositional look at these words to their comparative and superlative form, arguing that superlatives “contain” comparatives and comparatives “contain” POS-marked adjectives. There is more about most and the most in (Krasikova to appear), including an account the two different sources of definite articles in relative and absolute readings (including the English ∅ article for “determiner” most.) And there is interesting and relevant recent work that I haven’t even mentioned, as always!
RGGU1215.doc 12 History of Formal Semantics, Lecture 14 Barbara H. Partee, RGGU, May 22, 2012
Acknowledgments. This handout is based on a talk given at a workshop on Slavic Semantics at Bar Ilan University in March 2012; see acknowledgments there to Vladimir Borschev, Elena Paducheva, Yakov Testelets, and Moscow classes of students, and to Angelika Kratzer, and to colleagues who helped me discover and get hold of relevant recent work this spring, including Lucas Champollion, Ora Matushansky, Sveta Krasikova, Martin Hackl, Hadas Kotek, Hana Filip, Denis Paperno, and Helen de Hoop. And thanks for discussion and more suggestions to Ariel Cohen, Susan Rothstein, Fred Landman, and Galit Sassoon.
References Babko-Malaya, Olga. 1998. Context-dependent quantifiers restricted by focus. In University of Massachusetts Occasional Papers in Linguistics 21: Proceedings of the Workshop on Focus, eds. E. Benedicto, M. Romero and S. Tomioka, 1-18. Amherst: GLSA. Barwise, Jon, and Cooper, Robin. 1981. Generalized quantifiers and natural language. Linguistics and Philosophy 4:159-219. Reprinted in Portner and Partee, eds., 2002, 75-126 http://newstar.rinet.ru/~goga/biblio/essential-readings/03-Barwise.Cooper- Generalized.Quantifiers.and.Natural.Language.djvu. Bastiaanse, Harald. 2012. The intensional many - Conservativity revisited. Ms. ILLC, Amsterdam. http://home.medewerker.uva.nl/h.a.bastiaanse/bestanden/Intensional%20Conservativity%20of%2 0Many.pdf. Beaver, David I., and Clark, Brady. 2003. Always and Only: Why not all focus sensitive operators are alike. Natural Language Semantics 11:323-362. http://semanticsarchive.net/Archive/zQ5YmVlZ/aao.pdf. Beaver, David I., and Clark, Brady. 2008. Sense and Sensitivity: How Focus Determines Meaning. Oxford: Blackwell. Cresswell, M.J. 1976. The Semantics of Degree. In Montague Grammar, ed. Barbara Partee, 261-292. New York: Academic Press. Fernando, Tim, and Kamp, Hans. 1996. Expecting Many. In Proceedings of SALT 6, 53–68. Giusti, Giuliana, and Leko, Nedžad. 2005. The categorial status of quantity expressions. In Lingvistički Vidici, ed. Nedžad Leko, 121-183. Sarajevo: Forum Bosniae. http://www.academia.edu/attachments/6299404/download_file. Hackl, Martin. 2000. Comparative Quantifiers, Linguistics and Philosophy, MIT: PhD Dissertation. http://web.mit.edu/hackl/www/papers/files/NThesis5.pdf. Hackl, Martin. 2009. On the grammar and processing of proportional quantifiers: Most versus more than half. Natural Language Semantics 17.1:63-98. http://web.mit.edu/hackl/www/papers/files/Hackl%20NALS%2027%20Revised%20Manuscript% 20web%20page.pdf (preprint) Heim, Irene. 2006. Remarks on comparative clauses as generalized quantifiers. Ms. Cambridge, MA. http://www.semanticsarchive.net/Archive/mJiMDBlN/comparatives%20as%20GQs.pdf. Herburger, Elena. 1993. Focus and the LF of NP quantification. In SALT III: Proceedings of the Third Conference on Semantics and Linguistic Theory 1993, eds. Uptal Lahiri and Adam Zachary Wyner, 77-96. Ithaca, N.Y.: CLC Publications, Department of Linguistics, Cornell University. Herburger, Elena. 1997. Focus and weak noun phrases. Natural Language Semantics 5:53-78. Herburger, Elena. 2000. What Counts: Focus and Quantification. Cambridge, Mass.: MIT Press. Huettner, Alison. 1984. Semantics seminar paper on few and many. Amherst, MA: University of Massachusetts. Kamp, Hans, and Partee, Barbara. 1995. Prototype theory and compositionality. Cognition 57:129- 191. http://bhpartee.narod.ru/kamp-partee95.pdf Kayne, Richard. 2005. In Movement and Silence. Oxford: Oxford University Press. Keenan, Edward, and Stavi, Jonathan. 1986. A Semantic Characterization of Natural Language Determiners. Linguistics and Philosophy 9:253-326. Kotek, Hadas, Sudo, Yasutada, and Hackl, Martin. 2012. Many readings of most (Handout). Ms., CLS 48. Chicago.
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Krasikova, Sveta. 2011. On proportional and cardinal 'many'. In GG@G (Generative Grammar in Geneva) 2011. Geneva. https://udrive.oit.umass.edu/partee/Semantics_Readings/Krasikova2011- Many.pdf. Krasikova, Sveta. to appear. Definiteness in superlatives. In Post-Proceedings of the 18th Amsterdam Colloquium, eds. Maria Aloni et al.: Springer. http://www.illc.uva.nl/AC/AC2011/Proceedings (pre-proceedings version). Krasikova, Svetlana, and Champollion, Lucas. 2011a. Two many modifiers? (Handout). Ms., Workshop on Modification MDF 2011. Madrid. https://udrive.oit.umass.edu/partee/Semantics_Readings/Krasikova- Champollion2011madrid_handout.pdf. Krasikova, Svetlana, and Champollion, Lucas. 2011b. Two many modifiers? (Abstract). Ms., Workshop on Modification MDF 2011. Madrid. http://www.congresos.cchs.csic.es/mdf2011/sites/congresos.cchs.csic.es.mdf2011/files/mdf2011_ krasikova-champollion.pdf. Lappin, Shalom. 2000. An intensional parametric semantics for vague quantifiers. Linguistics and Philosophy 23:599-620. Löbner, Sebastian. 1987. Quantification as a major module of natural language semantics. In Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers, GRASS 8, eds. J. Groenendijk, D. de Jongh and M. Stokhof, 53-85. Dordrecht.: Foris. Paperno, Denis. 2012. Quantification in Standard Russian. In Handbook of Quantifiers in Natural language, eds. Edward L. Keenan and Denis Paperno. http://paperno.bol.ucla.edu/russian.pdf. Partee, Barbara H. 1989. Many quantifiers. In ESCOL 89: Proceedings of the Eastern States Conference on Linguistics, eds. Joyce Powers and Kenneth de Jong, 383-402. Columbus, OH: Department of Linguistics, Ohio State University. Reprinted in Partee, Barbara H. 2004. Compositionality in Formal Semantics: Selected Papers by Barbara H. Partee. Oxford: Blackwell Publishing, 241-258 https://udrive.oit.umass.edu/partee/Partee1989Many- quantifiers.pdf. Partee, Barbara H. 2001. Lecture 10: Many, mnogo, mnogie. Cardinal and proportional quantifiers and their semantics. Class Handout. Ms. https://udrive.oit.umass.edu/partee/Semantics_Readings/RGGU0110-mnogo-mnogie-many.pdf. Partee, Barbara H. 2010. Lecture 4, 2010: Noun Phrases and Generalized Quantifiers. Class handout. Ms., Formal Semantics of Noun Phrases. Spring semester, RGGU. Moscow. https://udrive.oit.umass.edu/partee/RGGU%202010%20materials/RGGU104.pdf. Partee, Barbara H. 2011. Lecture 4, 2011: Noun Phrases and Generalized Quantifiers. Class handout. Ms., Formal Semantics and Semantic Universals. Spring semester, MGU. Moscow. https://udrive.oit.umass.edu/partee/MGU_Web_11/materials/MGU114.pdf. Peters, Stanley, and Westerståhl, Dag. 2006. Quantifiers in Language and Logic. Oxford: Oxford University Press. Schwarzschild, Roger. 2006. The role of dimensions in the syntax of noun phrases. Syntax 9.1:67-110. http://www.rci.rutgers.edu/~tapuz/Role%20of%20Dimensions%20in%20Syntax%20of%20Noun %20Phrases.pdf. Solt, Stephanie. 2009. The Semantics of Adjectives of Quantity, Linguistics, CUNY. http://www.zas.gwz-berlin.de/fileadmin/mitarbeiter/solt/Solt_Dissertation.pdf. Szabolcsi, Anna. 2012. Word-less compositionality: case studies in quantification. Slides for UCLA talk, Feb 24, 2012. https://files.nyu.edu/as109/public/szabolcsi_word-less_ucla.pdf. Westerståhl, Dag. 1985a. Logical constants in quantifier languages. Linguistics and Philosophy 8:387- 413. Westerståhl, Dag. 1985b. Determiners and context sets. In Generalized Quantifiers in Natural Language, eds. Johan van Benthem and Alice ter Meulen, 45-71. Dordrecht: Foris.
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