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assign-f - P. M K: L 20. F 2007. Assignment F [Week 9]...

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Unformatted text preview: P. M K: L 20. F 2007. Assignment F [Week 9] [F1.] (10 points) Adjectives have different behaviour. An adjective Adj is intersective if the following inferences are valid: (1) A is an Adj N. ∴ A is an N. A is an Adj N. ∴ A is Adj. A is Adj. A is an N. ∴ A is an Adj N. Determine whether the following adjectives are intersective: /blue/, /French/, /intelligent/. In each case, give an example and indicate, if necessary, how it proves your point (that is, either it is general enough to show that the inference is always valid, or you have given a counterexample). Try to present examples that are not contrived. [F2.] (10 points) We assume that there are four people in the universe: Paul, Quincy, Rodriguez, and Stuart (or P, Q, R, S, if you like). We can evaluate the meaning of a quantified expression in this way. Let S := {/Paul/, /Quincy/, /Rodriguez/, /Stuart/} Subject Quantifier Elimination The sentence /Someone V./ is true if and only if for some X ∈ S : /X V./ is true. The sentence /Everyone V./ is true if and only if for all X ∈ S : /X V./ is true. Object Quantifier Elimination The sentence /A V someone./ is true if and only if for some X ∈ S : /A V X./ is true. The sentence /A V everyone./ is true if and only if for all X ∈ S : /A V X./ is true. We assume that the following is true: P runs, Q runs, R runs, S does not run, P sees R, Q sees S, R sees R, R sees P and S sees P, no one else sees anyone else. 1. Determine whether /Someone runs./ is true. Determine whether /Everyone runs./ is true. Calculate explicitly, using the rules and facts given in this assignment. 2. There are two ways to understand the sentence /Everyone sees someone./ according to the clauses above. Show that on one of the readings the sentence is false and that it is true on the other. ...
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