Possible Worlds: An introduction to Logic and Its Philosophy
Copyright © Raymond Bradley and Norman Swartz, 2010
Answers to exercises on pages 8-9
- Yes. There is a logically possible world in which Frederick
has reached the age of 21 years after only 5 birthdays. It is a world
in which Frederick is born on Leap Day (Feb. 29). It is not the actual
world, however, since Frederick is a fictional character (and hence does
not exist in the actual world).
- Yes. A square house built at the North Pole would have all its walls
facing south. Again, we are not describing the actual world, since there
is no house at the North Pole.
- No. Epimenides can certainly utter the sentence "Everything that
Cretans say is false". But the proposition he is asserting in uttering
that sentence cannot be true if he, himself, is a Cretan.
- No. Any two of these three propositions can be true (together);
but not all three.
- No. Statements of arithmetic are necessarily true or necessarily
false. (See page 20, section 4.)
- Yes. The Pope (like anyone else) can believe a necessary falsehood.
- No. Only propositions which are true can be known (to be true).
No one – neither the Pope nor anyone else – can know that 2 + 2 is not equal
- Yes. Although very unlike ours, there is a possible world in which
no objects are subject to the law of gravitation. The ancients (in this
world) believed that the tiny parts of material objects are held together
by hooks and eyes. Even though their theories were wrong (about this world),
such a(n imagined) world is not self-contradictory; hence it is logically
- No. While there can be a mountain which is higher than every other
mountain, there cannot be mountain which is higher than every, since
that would entail its being higher than itself!
- The answer to this question depends on how one interprets "disappears".
A grin is a certain disposition (arrangement or placement) of the lips. If
the rest of the cat disappears, but the lips remain, then what is being
described is logically possible, but it is not physically possible.
But if by "disappears" one means that the lips, too, disappear, then
the grin cannot remain: the situation is logically impossible. And whatever
is logically impossible is physically impossible.
- The situation described is logically possible, but not physically
- Provided that Nat Bartlett is an ordinary human being (who never had more
than two arms), and who has not grown a new arm since losing his right arm,
and is not wearing a prosthetic arm when he sits down at the table,
the situation described is
self-contradictory and hence logically impossible. (My own personal
guess is that Eugene O'Neill, by the time he wrote the later scene, had
simply forgotten what he had written some six pages earlier. I doubt that
he knowingly, or intentionally, gave self-contradictory stage directions.)