Harvard Linguistics 110 Handout 6

Ling 110, Section 6 (Semantics II) March 24, 2006. Next Homework: 8.1, 8.9, 8.10 due on Monday after the break (April 3rd) Announcements: Semantics quiz in class on Wednesday, April 5th Quiz review session to be held Tuesday, April 4th 6-7 pm, in Emerson 101 1. Conservativity - definition: A determiner Q is conservative iff Q (A)(B) = Q (A) (A∩B). - in other words, a determiner Q can make a reference to set A but not to the set B. Therefore, whenever you see set B mentioned in the meaning description of a quantificational determiner, it actually refers to A ∩ B, not the whole set B. Conservativity is shared by all natural language determiners. e.g.) (1) every (A)(B) = 1 (2) no (A)(B) = 1 (3) some (A)(B) =1 (4) at least n (A)(B) = 1 (5) at most n (A)(B) = 1 (6) most (A)(B) = 1 (7) exactly n (A)(B) = 1 (8) both (A)(B) = 1 (9) 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) = ∅

A test: The quantifier Q is conservative iff “Q NP VP” is equivalent to “Q NP is a NP which VP”. - a proposition p and a proposition q are equivalent iff p and q have exactly same truth-conditions. - in other words, for p and q to be equivalent, (i) p must entail q and (ii) q must entail p.

e.g.) Q: are ‘every’ and ‘no’ conservative ? (10) a. Every student is happy. b. Every student is a student who is happy. (10a) and (10b) are equivalent (i.e. (10a) entails (10b) and (10b) entails (10a)). Therefore, ‘every’ is a conservative determiner. (11) a. No student is happy. b. No student is a student who is happy. (11a) and (1b) are equivalent (i.e. (11a) entails (11b) and (11b) entails (11a)). Therefore, ‘no’ is a conservative determiner.

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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: Nevery triangle has stripes. : in plain English, “Everything which is not a triangle has stripes”. Nevery student in this room wears glasses. : in plain English, “Everything which is not a student in this room wears glasses”. Q2: Is nevery conservative? Defend your answer. To take a concrete example, let’s assume A = the set of triangles and B = the set of things which have stripes. For nevery to be conservative, [ nevery (A)(B) ] and [ nevery (A)(A∩B) ] must be equivalent. Is this the case? Suppose we have the following two sentences. (12) Nevery [[triangle]] [[has stripes]]. (= nevery (A) (B)) : in plain English, this means “Everything which is not a triangle has stripes”. (13) Nevery [[triangle]] [[is a triangle which has stripes]]. (= nevery (A) (A∩B)) : in plain English, this means “Everything which is not a triangle is a triangle which has stripes”. Are (12) and (13) equivalent? NO! Note that for two propositions to be equivalent, the two propositions must entail each other. In this case, (13) entails (12)1 but not vice versa. Therefore, (12) and (13) are NOT equivalent. nevery is NOT conservative. A determiner with the meaning of nevery given here cannot exist in natural languages. 2. Decreasingness and NPI-licensing •

Some determiners are decreasing in the following sense: - A determiner forms a decreasing DP if, whenever we have [[VP1]] ⊂ [[VP2]], D NP VP2 entails D NP VP1. - In other words, a decreasing determiner reverses the direction of entailment. (14) a. John sang a song by Bob Dylan John sang a song. Nobody sang a song. b. Nobody sang a song by Bob Dylan

Exercise) Which of the following determiners is decreasing: some and at most three? Construct examples to show your point.

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Because (13) is a contradiction, which is supposed to entail every proposition.

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Negative Polarity Item Licensing - An NPI may be licensed by a c-commanding lexical item that has the decreasing property.

(15) a. No teenagers ever drink prune juice b. Few teenagers ever drink prune juice c. Less than 3 people ever drink prune juice Exercise) “John left the party without saying anything.” is grammatical. Q1: Which word in the above sentence do you think is a NPI-licensor? Q2: Does this NPI-licensor have the decreasing property (as predicted by our theory)? Construct examples to defend your answer.

3. Scope Ambiguity Consider the truth conditions of the following sentence. (16) Two students talked to every professor. This sentence can be paraphrased in two ways: Paraphrase 1 (17) There are two students who talked to every professor. Paraphrase 2 (18) For every professor, there are two students who talked to him or her. This way, sentence (16), which contains more than one quantified expression, is semantically ambiguous. In accordance with our general strategy to capture semantic ambiguity, let us consider if there is any way to represent the semantic ambiguity of sentence (16) in terms of structural ambiguity. One of the strategies that are often adopted in the literature is an operation called Quantifier Raising (QR for short), which moves the lower quantifier up above the higher one covertly. Thus, sentence (16) has the following two representations: Representation 1 (no different from its surface structure) (19) Two students talked to every professor. Representation 2 (the lower quantifier undergoes QR up above the higher quantifier) (20) [Every professori [two students talked to ti]] These two representations are called Logical Form (LF for short), which is the input to the component for semantic interpretation.

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Which LF representation yields which reading? We need a principle of semantic interpretation. (21) When a quantified expression X c-commands another quantified expression Y at LF, X takes scope over Y. Of the two quantified expressions, the one that takes scope over the other plays a role of “sorting key” in the interpretation, as seen in (17) and (18). Thus, LF (19) yields the reading paraphrased in (17) and LF (20) the reading paraphrased in (18). Surface Scope and Inverse Scope There are names to refer to the two LF representations such as those in (19) and (20). Surface Scope (22) Surface scope is the relative scope relation of two quantified expressions that obtain from LF where QR did not apply and the surface c-commanding relation between the two quantified expressions are carried over to LF. Inverse Scope (23) Inverse scope is the relative scope relation of two quantified expressions that obtain from LF where the lower quantified expression underwent QR to a position from which it c-commands what used to be the higher one. Exercise Consider the truth conditions of the following sentences and draw LF representations that yield the relevant readings. Also consider how far quantified expressions can undergo QR as well as what kind of expressions can undergo QR. (24) At least one policeman was standing in front of every building. (25) Two students said that Bill talked to every professor. (26) John does not always sing.

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