Possible Worlds: An introduction to Logic and Its Philosophy
Copyright © Raymond Bradley and Norman Swartz, 2010
Answers to selected exercises on pages 24-25
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- 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.
- noncontingent; true
- contingent
- noncontingent; true
- noncontingent; true
- contingent
- noncontingent; false
- contingent
- contingent
- contingent
- noncontingent; true
- Briefly explain why each of propositions k-o (p. 25) is false.
- 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.
- 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).
- 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).
- 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).
- 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).
- (There is no single answer to this question. There are an infinite
number of correct answers, and an infinite number of [different] incorrect
answers.)
- (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.)
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