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Which of These Sentences Express Propositions? What Do the Other Sentences Express?

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Solutions to Exercises on Modal Concepts 1

Q1: Which of these sentences express propositions? What do the other sentences express?

(Examples might be questions, commands, exclamations, wishes.)

1 Sydney is north of Melbourne.

Answer: Proposition

2 Is Edinburgh in Scotland?

Answer: Question

3 The moon is made of Swiss cheese.

Answer: Proposition

4 Did you see the eclipse?

Answer: Question

5 What an eclipse!

Answer: Exclamation

6 Would that I were good at logic.

Answer: Wish

7 Look at the eclipse.

Answer: Command

8 I wish that I were good at logic.

Answer: Wish

9 7+12=23

Answer: Proposition

10 If you get Kelly you will be rewarded.

Answer: Proposition

Q2. Are these statements true or false?

a) If something is impossible, then it does not actually happen

in the world.

True

b) If something actually happens in the world, then it is possible.

True

c) It is impossible for Dan to be both the fastest swimmer in the world and the slowest swimmer in the world

False, since I am both the fastest swimmer in the world and the slowest swimmer in the world in a possible situation in which I am the only swimmer in the world

d) It is possible for that 2 + 3 = 6

False

e) It is necessary that every square is a rectangle

True

f) It is necessary that Dan is Australian

False, since there is a possible situation in which Dan was born in Hong Kong and was a Hong Konger and not an Australian.

Q3 Are these statements true or false?

a) Being a boy is sufficient for being a male

True, since, in every possible situation, if an x is a boy then it is a male.

b) Being a boy is necessary for being a male

False, since there is a possible situation where an x is a male, but is not a boy (since he is a man).

c) Having a bag is sufficient for having either a bag or an umbrella

True, since in every possible situation where an x has a bag, x has either a bag or an umbrella

d) Having a bag is necessary for having either a bag or an umbrella

False, since there is a possible situation where something has an umbrella and not bag.

e) If X is necessary for Y, and Y is necessary for Z, then X is necessary for Z.

True.

Argument: Suppose  X is necessary for Y, and Y is necessary for Z. Suppose an object x has Z in situation s. Then, since Y is necessary for Z, x has Y in s. Then, since X is necessary for Y, x has X in s. Hence, in every situation where an object has Z, that object also has X. Hence, X is necessary for Z. Hence, (1g) is true.

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