### Possible Worlds: An introduction to Logic and Its Philosophy

Copyright © Raymond Bradley and Norman Swartz, 2010
Answers to selected exercises on pages 24-25

1. For each of the propositions a-j (pp. 24-25), say (1) whether it is contingent or noncontingent, and (2) if noncontingent, then whether it is true or false.

1. noncontingent; true
2. contingent
3. noncontingent; true
4. noncontingent; true
5. contingent
6. noncontingent; false
7. contingent
8. contingent
9. contingent
10. noncontingent; true

2. Briefly explain why each of propositions k-o (p. 25) is false.

1. The claim in the textbook is (in effect) that all actually true propositions are (also) contingent.
The claim is false because there is a counterexample (i.e. are exceptions), viz. necessary truths. Necessary truths are actually true, but they are not contingent.
2. The claim in the textbook is (in effect) that every possibly true proposition is (also) possibly false.
The claim is false because there is a counterexample (i.e. are exceptions), viz. necessary truths. Necessary truths are possibly true (i.e. are true in at least one possible world), but they are not possibly false (i.e. false in at least one possible world).
3. The claim in the textbook is (in effect) that all actually false propositions are possibly true.
The claim is false because there is a counterexample (i.e. are exceptions), viz. necessary falsehoods. Necessary falsehoods are actually false (i.e. are false in this world), but they are not possibly true (i.e. true in at least one possible world).
4. The claim in the textbook is (in effect) that all noncontingent propositions are actually true.
The claim is false because there is a counterexample (i.e. are exceptions), viz. necessary falsehoods. Necessary falsehoods are noncontingent propositions, but they are not actually true (i.e. true in this world).
5. The claim in the textbook is (in effect) that all possibly true propositions are contingent.
The claim is false because there is a counterexample (i.e. are exceptions), viz. necessary truths. Necessary truths are possibly true propositions (i.e. are true in at least one possible world), but they are not contingent (i.e. true in at least one possible world and false in at least one possible world).
3. (There is no single answer to this question. There are an infinite number of correct answers, and an infinite number of [different] incorrect answers.)

4. (Again, there is no single answer to this question. There are an infinite number of correct answers, and an infinite number of [different] incorrect answers.)