Ling 98a: The Meaning of Negation (Week 5)

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1 Yimei Xiang 15 October Review Negation in propositional logic, oppositions, term logic of Aristotle Presuppositions Projection and accommodation Three-valued logic External/internal negation, assertion operator A Presupposition-based account of neg-raising (NR) Implicatures Conventional implicatures Conversational maxims and conversational implicatures, SIs and Horn scale Exhaustification theory (EXH) SI-based account of NR Monotonicity NPIs DE, UE, NM Negation is a DE operator Monotonicity of determiners (e.g. every, some, three, no) Weak NPIs are licensed in DE environments NPI licensers Interveners Only John read any book. Strict NPIs are licensed in Anti-additive (AA) environments A function f is AA iff. f is DE, and [ f (X) f (Y ) f (X Y )] NOT [SOME( ) ( AA )] NOT [EVERY( ) ( DE, not AA )] Negated NR predicates (e.g. doesn t believe) Negated truth predicates (e.g. It is not the case that) 1

2 2 Preliminaries The following (a) sentences are ambiguous with respect to the hierarchical relation between operators (viz. negation, quantifiers). (1) a. Every boy saw some girl. i. Surface scope: x[b(x) y[g(y) S(x, y)]] ii. Inverse scope: y[g(y) x[b(x) S(x, y)]] b. John saw Mary. c. Every boy saw Mary. (2) a. John didn t read a book written by Gennaro. i. There is one book written by Gennaro that John didn t read. ii. John didn t read any book written by Gennaro. b. John didn t read Meaning and Grammar However, while having multiple operators, the following sentences (without considering any extra stress) are unambiguous. Why is that so? (3) a. John didn t read any book written by Gennaro. NEG >> any b. John didn t read some book written by Gennaro. some >> NEG Draw the tree-diagram for (1b) and (1c), identity the semantic type of each node. Keywords today: Generalized quantifiers and determiners Quantifier raising (QR) Positive polarity items (PPIs) 2

3 3 Generalized quantifiers and determiners Quantificational DPs (e.g. everything, something, every boy, some girl) differ from e type NPs/DPs (e.g. Mary) from many aspects: (see Heim & Kratzer 1998 pp ) - Law of contradiction (LC) (4) a. Mary is coming and Mary is not coming. is a contradiction b. Someone is coming and someone is not coming. isn t a contradiction - Law of Excluded Middle (LEM) (5) a. Mary is coming or Mary is not coming. is a tautology b. Everyone is coming or everyone is not coming. isn t a tautology - Monotonicity (6) a. Mary came yesterday morning. Mary came yesterday. b. At most one student came yesterday morning. At most one student came yesterday. Quantificational DPs are different from < e,t > type common nouns (e.g. student): student denotes a set of individuals that are students. everything, something and nothing are not sets of individuals. The semantic type of quantificational phrases: If quantificational subjects are not of type e, due to Montague (1973), subjects are not considered as the type-logical argument of the verb phrase. Rather, the verb phrase is the argument of the quantificational subject. Namely, quantificational subjects are second-order functions of type << e,t >,t >, referred as generalized quantifiers. (7) a. every boy: λ P. x[b(x) P(x)] b. some girl: λ P. x[g(x) P(x)] We will see later how this theory works with quantificational objects. In-class Exercise 1: Draw a tree-diagram for the following sentences (take no as a determiner): (8) a. Some student ran. b. No student ran. 3

4 The semantic type of determiners (e.g. every, some, no) Determiners combine with a noun phrase of type < e,t > to return a << e,t >,t >, and their type is therefore quite complex: << e,t >,<< e,t >,t >> (the type of functions that take a property, then take a second property, to return a proposition). (9) a. every = λq.λp x[q(x) P(x)] b. some = λq.λp. x[q(x) P(x)] c. no = λq.λp. x[q(x) P(x)] Discussion: How to interpret the determiner a? From the perspective of set theory, determiners can be understood as relations between sets. (10) a. R every = {< A,B > A B} b. R some = {< A,B > A B /0} c. R no = {< A,B > A B = /0} 4 Quantifier Raising (QR) When a sentence takes a quantificational DP as its object, there is a type-mismatch: (11) Bill admires everybody. admires: < e,< e,t >> everybody: << e,t >,t > admires everybody:? Quantifier Raising (QR): at LF, quantifiers can raise to adjoin to any propositional node, leaving behind a trace and introducing a lambda abstraction over the traces variable. 4

5 In-class Exercise 2: Draw the tree-diagrams for the following sentences. (12) a. Every boy saw some girl. b. John didn t read a book. Related readings: Heim & Kratzer (1998) Chapter 8. 5 Negation and Quantificational DPs Most quantifiers can take scope either below or above auxiliary negation. (13) John didn t read a book written by Gennaro. a. John read no book written by Gennaro. b. There were one book written by Gennaro that John didn t read. (14) John didn t attend more than two meetings. a. John attend no more than two meetings. b. There were more than two meetings from which John was absent. However, some quantificational DPs have to take scope over the auxiliary negation: (15) I didn t see someone. a. There is a person such that I didn t see it. some > not b. There is nobody that I saw. *not > some 6 Positive polarity items PPIs in the scope of clause-mate negation (or negative quantifiers or without) can only receive a wide scope reading. (16) a. John didn t call someone. *not > some b. No one called someone. *no one > some c. John came to the party without someone. *without > some The PPI some takes scope below the clause-mate auxiliary negation only when the negation has a metalinguistic use. (17) a. A: I heard John talked to someone at the party yesterday. 5

6 b. B: No, actually. John DIDN T talk to someone. Anti-licensers: clause-mate negation, negative quantifiers, without... The anti-licensing relation doesn t hold across sentence-boundaries. (18) a. It is not the case [that John called someone. not > [CP some b. I don t think [that John called someone. not > [CP some c. Nobody thinks [that he called someone. nobody > [CP some Licensers of weak NPIs Anti-licensers of PPIs (19) a. At most five boys called anyone/someone. b. I rarely get help from anyone/someone. c. Few boys talk to any/some girls. Generally, PPIs are anti-licensed is the local environment is AA. Such an anti-licensing relation can be salvaged by an intervening universal quantifiers (e.g. everyone, always) (20) a. John didn t give everyone something. not > every > some b. John doesn t always call someone. not > always > some PPIs do not occur in the immediate scope of a clause-mate anti-additive operator AA-OP (Szabolcsi 2004, simplified version) Related readings: Szabolcsi, Anna Positive polarity negative polarity. Natural Language and Linguistic Theory 22: