Contents -- 0. Quantification -- 0.1 Some quantifier expressions of natural languages -- 0.2 Varieties of quantification -- 0.2.1 Syntactic variation in quantifier expressions -- 0.2.2 Semantic types of NL quantification -- 0.2.3 Quantirelations -- 0.3 Explicit and implicit quantification -- 0.4 Monadic and polyadic quantifiers -- I: THE LOGICAL CONCEPTION OF QUANTIFIERS AND QUANTIFICATION -- 1. A Brief History of Quantification -- 1.1 Early history of quantifiers -- 1.2 Quantifiers in early predicate logic -- 1.3 Truth and models -- 1.4 Postscript: Why quantifiers cannot denote individuals or sets of individuals -- 2. The Emergence of Generalized Quantifiers in Modern Logic -- 2.1 First-order logic versus first-order languages -- 2.2 First-order logic (FO) -- 2.3 Mostowski quantifiers -- 2.4 Lindström quantifiers -- 2.5 Branching quantifiers -- 2.6 Digression: why logicians like FO -- 2.7 Summary -- II: QUANTIFIERS OF NATURAL LANGUAGE -- 3. Type (1) Quantifiers of Natural and Logical Languages -- 3.1 Preliminary concepts and distinctions -- 3.2 Phrases denoting type (1) quantifiers -- 3.3 Isomorphism closure -- 3.4 Extension -- 3.5 How natural language quantifier expressions always denote global quantifiers -- 4. Type (1, 1) Quantifiers of Natural Language -- 4.1 Examples of determiners -- 4.2 On existential import and related matters -- 4.3 Boolean operations -- 4.4 Relativization -- 4.5 Conservativity, extension, and relativization -- 4.6 Definiteness -- 4.7 Type (1, 1, 1) quantifiers and beyond -- 4.8 ISOM and the number triangle -- 5. Monotone Quantifiers -- 5.1 Standard monotonicity -- 5.2 Monotonicity in type (1, 1) -- 5.3 Monotonicity universals -- 5.4 Monotonicity under ISOM -- 5.5 Six basic forms of monotonicity -- 5.6 Smooth quantifiers -- 5.7 Linguistic application 1: a peculiar inference scheme.

5.8 Linguistic application 2: LAA quantifiers -- 5.9 Linguistic application 3: polarity-sensitive items in natural languages -- 6. Symmetry and Other Relational Properties of Type (1, 1) Quantifiers -- 6.1 Symmetry -- 6.2 On the symmetry of many and few -- 6.3 Existential-there sentences -- 6.4 Other relational properties of CONSERV and EXT type (1, 1) quantifiers -- 7. Possessive Quantifiers -- 7.1 Possessive determiners and NPs -- 7.2 Number and uniqueness -- 7.3 Universal readings and others -- 7.4 Scope ambiguities? -- 7.5 Narrowing -- 7.6 The possessor relation -- 7.7 The meaning of possessive determiners -- 7.8 Alternative accounts -- 7.9 Semantic rules for possessives -- 7.10 Iterated possessives -- 7.11 Definites and possessives -- 7.12 Closure properties of Poss -- 7.13 Possessives and monotonicity -- 7.14 Some remaining issues -- 8. Exceptive Quantifiers -- 8.1 Connected and free exception phrases -- 8.2 The Generality Claim -- 8.3 The Inclusion Condition -- 8.4 Exception conservativity -- 8.5 The Negative Condition -- 8.6 Entailed or implicated? -- 8.7 Other quantifiers in exception sentences -- 8.8 The classical idea of universal claims with exceptions -- 8.9 The account in von Fintel 1993 -- 8.10 The account in Moltmann 1995 -- 8.11 Counter-evidence to the Quantifier Constraint -- 8.12 A modest proposal -- 8.13 Quantified exception phrases -- 8.14 Further issues -- 9. Which Quantifiers are Logical? -- 9.1 Logicality and ISOM -- 9.2 Two claims about ISOM and natural language quantification -- 9.3 Constancy -- 9.4 Logical constants -- 10. Some Polyadic Quantifiers of Natural Language -- 10.1 Iteration -- 10.2 Resumption -- 10.3 Branching -- 10.4 Reciprocals -- III: BEGINNINGS OF A THEORY OF EXPRESSIVENESS, TRANSLATION, AND FORMALIZATION -- 11. The Concept of Expressiveness -- 11.1 Preliminaries -- 11.2 A framework for translation.

11.3 Varieties of sameness -- 12. Formalization: Expressibility, Definability, Compositionality -- 12.1 Logical equivalence revisited -- 12.2 Compositionality -- 12.3 Requirements on definitions -- 12.4 Extending lexical mappings to compositional translations -- 12.5 Why formal definability results matter for natural languages -- IV: LOGICAL RESULTS ON EXPRESSIBILITY WITH LINGUISTIC APPLICATIONS -- 13. Definability and Undefinability in Logical Languages: Tools for the Monadic Case -- 13.1 Logics with quantifiers -- 13.2 Definability -- 13.3 Undefinability -- 13.4 EF-tools for the monadic case -- 14. Applications to Monadic Definability -- 14.1 The method -- 14.2 FO-undefinability -- 14.3 Undefinability in other logics -- 14.4 Monotonicity and definability -- 14.5 Exercises -- 15. EF-tools for Polyadic Quantifiers -- 15.1 EF-games -- 15.2 Hella's bijective EF-game -- 15.3 Application to branching quantification -- 15.4 Application to Ramsey quantifiers and reciprocals -- 15.5 Application to resumption and adverbial quantification -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z -- Index of Symbols.