Logic puzzle
- At least one of these statements is true.
- At most one of these statements is false.
- All three of these statements are true.
How many of the above statements are true?
Inspired by Logic puzzle T shirt, I considered logic puzzles of this general category. (I am easily amused.) Ayn Rand would call these statements floating abstractions. There is no ultimate subject matter; the statements have meaning only in relation to each other. Like the Oakland of Gertrude Stein’s day, there is no there there. The trick is to find an assignment of truth values that is mutually consistent.
With the T shirt puzzle, there is only one consistent assignment of truth values. My puzzle has more than one.
How many consistent truth assignments are there?
One is tempted to say that since there is no unique consistent truth value assignment, that all three statements are meaningless, neither true nor false. But if they’re all meaningless, then they’re all false. One can only say that “all three statements are meaningless” is not a consistent truth value assignment.