Harvard Linguistics 110 Handout 5

Ling 110, Section 5 (Semantics I) March 17, 2006. Next Homework: 7.1, 7.2, 7.4, 7.11, 7.12, 7.14 due at 11 am on Monday (March 20) Announcements: Semantics quiz date has been changed to Wednesday, April 5th Quiz review session will be held Tuesday, April 4th 6-7 pm, in Emerson 101 1. Compositionality of Meaning (1) Thumbnail definition of semantics: The study of the relation between linguistic form and meaning. (2) Semantic compositionality – the key principle in linguistic semantics due to Gottlob Frege: Meaning is compositional – the meaning of an expression is determined by the meanings of its parts and by the ways in which those parts are assembled. In semantics, we want to model the way a speaker/hearer computes the meaning of a whole from the meanings of its parts in a compositional fashion. 2. Entailment Speakers have intuitions about truth-value relations between sentences. Any competent English speaker can recognize that if (S1) is true, then so is (S2), even without knowing anything about the historical figure Julius Caesar: (S1) Julius Caesar was a famous man. (S2) Julius Caesar was a man. (3) Entailment: Sentence S1 entails sentence S2 if, and only if whenever S1 is true in a situation, S2 is also necessarily true in that situation. S1 entails S2 =def whenever S1 is true in a situation, S2 is true in that situation. In other words, a situation describable by S1 must also be a situation describable by S2. E.g.)

(S1) Beidao is a Chinese poet entails (S2) Beidao is a poet (S1) Beidao killed his wife entails (S2) Beidao’s wife died

Part of our linguistic knowledge is knowing the entailment relations between certain sentences. (4) Some sentences are necessarily true (= tautology): e.g.) Either there is a book on the table, or there isn’t a book on the table. Every hedgehog is a hedgehog. Every six-pointed triangle is a six-pointed triangle. (5) ... or necessarily false (= contradiction): e.g.) Lois read the book, and Lois didn’t read the book.

1

No hedgehog is a hedgehog. Some hedgehog is not a hedgehog. (6) Tautology, Contradiction and Entailment: (i) It is said that every sentence entails tautologies. (ii) It is also said that contradiction entails every sentence.

Exercise: which entails which in the following pairs of the sentences (if entailment ever holds)? (7) a. Amy knows the answer. b. Only Amy knows the answer. (8) a. If Mary wins a fellowship, she can finish her thesis. b. If Mary does not win a fellowship, she can’t finish her thesis. (9) a. His speech disturbed me. b. His speech deeply disturbed me. 3. Assertion and Presupposition (10) Assertion—What the speaker is claiming to be true or false by uttering the sentence. (11) Presupposition—What the speaker assumes to be true, as ‘background’ to the sentence s/he is uttering. When a speaker utters a sentence, the speaker asserts trueness or falseness a certain proposition, but the speaker cannot make any claim about the trueness or falseness of what is already presupposed (= assumed to be true). E.g.) Q: Did you stop beating your wife? A: Yes/No Whether you answer the question with yes or no, you can’t help getting to admit that you used to beat your wife. This is because the verb ‘stop’ triggers presupposition that ‘beating your wife’ is assumed to be true as a background of this conversation. (12) The negation-test for presupposition: A sentence S1 presupposed S2 if S1 entails and ¬S1 entails S2, too! E.g.) the factive predicate ‘be surprised’ S1: I was (not) surprised that Brad and Jen separated. S2: Brad and Jen separated S1 presupposes S2 because both S1 and its negation entail S2. E.g.) the definite determiner ‘the’ S1: The Mayor of Manchester is (not) a woman. S2: There is a uniquely identifiable Mayor of Manchester. S1 presupposes S2 because both S1 and its negation entail S2.

2

Exercise: Discuss what presupposition each of the following sentences has. (13) a. John realizes that syntax deals with sentence structure. b. Sue regrets getting a Ph.D. in art history.

c. Bill managed to kiss Mary. 4. Extensions vs. Intensions (14) The thing or the set of the things which bear a property X is called the extension of X: [[ Romeo ]] = the individual by the name of Romeo [[ student ]] = the set of all entities that are students [[ vegetarian ]] = the set of all entities that are vegetarians Q: Can two expressions have the same extension but different meanings? e.g. ) the first person to walk on the moon Neil Armstrong Q: Do they pick out the same entity in the world? I.e., do they have the same extension? Q: Do they have the same meaning? (S1) My crazy aunt thought she was the first person to walk on the moon. (S2) My crazy aunt thought she was Neil Armstrong. (S1) Everyone knows Venus is the morning star. (S2) Everyone knows Venus is Venus. (15) Frege’s observation: Expressions with identical extensions can produce different truth values. (16) To express this difference, semanticists contrast extensions with intensions: Extension: The entity or the set of entities in the world to which an expression refers. (its referece) Intension: The ‘inherent sense’ conveyed by an expression. 5. Fundamentals of Extensional Semantics (17) Extension of Proper Names: [[ Ann ]] = Ann [[ John ]] = John [[ Fido ]] = Fido etc. (18) Extension of Predicates: [[ smoke ]] = the set of all individuals that smoke [[ smart ]] = the set of all individuals that are smart [[ boy ]] = the set of all individuals that are boys

3

etc. (19) Set-Theoretic Denotations of VPs - [[ VP ]] denotes a set of entities - In general, when DP is a proper name, a sentence of the form [DP VP] is true iff [[ DP ]] ∈ [[ VP ]]. e.g.) Lois is happy is true iff

[[ Lois ]] ∈ [[ (be) happy ]]

Exercise: Given the extensions of proper names and predicates and the general principle in (19), how can we derive the fact the sentence “John dances and sings” entails the sentence “John sings”? 6. Modifiers (S1) I bought a green sweater entails (S2) I bought a sweater [[ sweater ]] = the set of all sweaters [[ green ]] = the set of all green things We can model the contribution of “green” using set theory: “green sweater” refers to anything which is in the intersection of these two sets (Venn diagram): [[ sweater ]] ∩ [[ green ]] •

Modifiers which function like this are called intersective.

(20) A rule of meaning composition: If AP is intersective, then the constituent [NP AP NP ] is interpreted as [[ AP ]] ∩ [[ NP ]] Q: Are all adjectives intersective? Observe the following adjectives: e.g.) a former teacher a fake gun a small elephant vs. a big flea 7. Meaning of Determiners What do quantificational determiners contribute to the meaning of an expression? (21) Relational view of quantifying determiners: Determiners specify relations between sets. (22) every (A)(B) = 1 (23) no (A)(B) = 1 (24) some (A)(B) =1 (25) at least n (A)(B) = 1 (26) at most n (A)(B) = 1 (27) most (A)(B) = 1 (28) exactly n (A)(B) = 1 (29) both (A)(B) = 1 (30) neither (A)(B) = 1

iff iff iff iff iff iff iff iff iff

A⊆B (in other words, (A ∩ B) = A ) (A ∩ B) = ∅ (A ∩ B) ≠ ∅ | A ∩ B| ≥ n | A ∩ B| ≤ n | A ∩ B| > 1/2 |A| | A ∩ B| = n | A | = 2 & A ⊆ B (i.e. | A | = 2 & (A ∩ B) = A) | A | = 2 & (A ∩ B) = ∅

4

…etc. (31) Conservativity (shared by all natural language determiners) - definition: A determiner Q is conservative iff Q (A)(B) = Q (A) (A∩B). •

A test: The quantifier Q is conservative iff “Q NP VP” can be paraphrased as “Q NP is a NP which VP” and the truth-condition of the sentence remains the same.

(32) a. Every student is happy b. Every student is a student who is happy (32a) and (32b) are equivalent (i.e. (32a) entails (32b) and (32b) entails (32a)). ‘Every’ is a conservative determiner. (33) a. No student is a happy b. No student is a student who is happy (33a) and (33b) are equivalent (i.e. (27a) entails (27b) and (27b) entails (27a)). ‘No’ is a conservative determiner. ... -> Conservativity seems to be a universal property of natural language determiners. Exercise :Let’s invent a hypothetical determiner: nevery definition: nevery NP VP = Everything which is not in [[ NP ]] is in [[ VP ]] or nevery (A) (B) = 1 iff (E - A) ⊆ B ( E is the universe/domain of discourse) Q1: Paraphrase the following sentences in plain English: e.g.) Nevery triangle has stripes. Nevery student in this room wear glasses.

Q2: Is nevery conservative? Defend your answer.

5