: The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the others, in the scope of a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in tense semantics. The remainder of the paper is concerned with an interval based semantics of degree in relation to issues other than the comparative proper. The paper begins with a discussion of the role negative polarity has played in studies on the semantics of comparatives. 0.

The aim of this thesis is to investigate the linguistic phenomenon of polarity sensitivity. It is motivated by the belief that the complexity of the phenomenon requires a more articulated analysis than the standard one based on licensing conditions. Traditionally, the term of polarity sensitive is used to identify items whose distribution is considered to be affected by the positivity or negativity of the context of occurrence. The notion of negative context covers more than environments containing overt negation or negative quantifiers. Elements that induce a negative context are potential licensers for negative polarity sensitive items. The phenomenon of polarity sensitivity has been approached from a variety of perspectives in the literature. The cluster of data associated with it raises semantically and syntactically important questions. There is reduced agreement on the definition of pertinent negativity. Sensitive elements show meaning variations when taken in isolation or in con...

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2. The main ideas of Heim’s solution. (Chapter II) (Kamp’s is similar.).......................................................................4

2. Negation in natural language: syntax, semantics, pragmatics....................................................................... 2 2.1. Syntactic, semantic, pragmatic notions of negation.............................................................................. 2 2.1.1 Syntactic notions of S-Neg, C-Neg................................................................................................. 3 2.1.2 Semantic notions of “negation of”................................................................................................. 4

1. Introduction to the puzzle..........................................................................................................................................1 2. Background. “Scope ambiguity, ” NP interpretations, and the semantics of operators.............................................2 3. Natural language patterns – strategies of marking different interpretations differently............................................4 3.1. Some languages mark opaque readings, e.g. Romance languages- subjunctive................................................4

Note: No further parentheses are needed here, and according to the syntax on the handout, no further parentheses are possible. But “extra parentheses ” are in general considered acceptable, and if you find them helpful, I have no objection. So I would also count as correct any of the following: ∀x (love (Mary, x)), (∀x love (Mary, x)), (∀x (love (Mary, x))) 2. Mary loves everyone. [assuming D contains both humans and non-humans, so we need to be explicit about ‘everyone ’ as ‘every person’] ∀x (person(x) → love (Mary, x)) A wrong answer: ∀x (person(x) & love (Mary, x)) This says that everything in the universe is a person and loves Mary. 3. No one talks. [assume D contains only humans unless specified otherwise.] ¬∃x talk(x) or equivalently, ∀x¬talk(x) 4. Everyone loves himself. ∀x love (x, x) 5. Everyone loves everyone. ∀x∀y love (x, y) 6. Everyone loves everyone except himself. ( = Everyone loves everyone else.) ∀x∀y( ¬ x = y → love (x, y)) or ∀x∀y ( x ≠ y → love (x, y)) Or maybe it should be this, which is not equivalent to the pair above: ∀x∀y( ¬ x = y ↔ love (x, y)) or ∀x∀y ( x ≠ y ↔ love (x, y)) The first pair allows an individual to also love himself; the second pair doesn’t. 7. Every student smiles. ∀x (student(x) → smile ( x)) 8. Every student except George smiles. ∀x ((student(x) & x ≠ George) → smile ( x)) That formula allows the possibility that George smiles too; if we want to exclude it (this depends on what you believe about except; there are subtle differences and perhaps some indeterminacy among except, besides, other than and their nearest equivalents in other languages), then it should be the following, or something equivalent to it: ∀x ((student(x) → (x ≠ George ↔ smile ( x))) 9. Everyone walks or talks. ∀x (walk (x) ∨ talk (x)) 10. Every student walks or talks.