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Exercise 1 | More Quantificational Determiners

Consider the sentence in (1).

(1) Sheldon offended [D more than three] physicists.

Spell out a compositional analysis that derives the interpretation of (1).

Your analysis should have the following three parts:

A. Logical Form and Semantic Types

B. Lexical Entries and Auxiliary Assumptions

C. Step-by-Step Derivation.

Simplify and treat more than three as a determiner.

Bonus. Propose a semantic analysis of more than three that compositionally derives the interpretation you have assumed to be lexically provided.

Exercise 2 | More Ambiguities

The sentence in (2) below is ambiguous.

(2) Leonard didn't publish [D more than three] papers.

a) Provide precise one-sentence paraphrases of the two readings that (2) has Describe or sketch a situation that would make one reading true but the other false.

b) Discuss whether our current grammar predicts this ambiguity. (Be maximally explicit and include a full compositional interpretation.)

Exercise 3: More Presuppositions

English both is a quantificational determiner and a presupposition trigger. Two examples are in (3).

(3) a. Both physicists admire [N Stephen Hawkin].

     b. Both physicists published more than ten papers.

The goal of this exercise is to explore the meaning of both and to develop an analysis that captures its meaning contribution. In order to do so, pursue the following steps:

a) Discuss why (3-b) provides evidence for an analysis of both as a quantificational determiner. Include paraphrases and annotated Logical Forms in your discussion.

b) Provide a one-sentence paraphrase of the presupposition that both triggers in (3-a). Describe a situation in which the presupposition is true, but the sentence is false. Provide evidence that this is indeed the presupposition of the sentence in (3-a), and not part of its assertion.

c) Assuming that the definedness conditions are met in an evaluation situation, draw and annotate a Venn diagramme that represents the truth conditions of (3-a).

d) Write down a lexical entry for both and apply it to the analysis of (3-a).