Critical Thinking
Hard
4 min
A statement says: "All statements in this box are false." Is the statement true or false?
Hint
Consider what happens under each assumption.
Answer
The statement creates a self-reference paradox and cannot consistently be assigned simply true or false under ordinary classical interpretation.
Explanation
If the statement is true, then it says all statements in the box are false, including itself, which contradicts its truth. If it is false, then the claim that all statements are false is not true, meaning at least one statement is true; depending on the box contents, this may again create inconsistency. The classic form is a self-referential paradox.
Step-by-Step Solution
Assume true → contradiction.
Assume false → the claim is not universally true, requiring another true statement or interpretation.
Therefore the statement is paradoxical rather than a normal true/false puzzle.
Assume false → the claim is not universally true, requiring another true statement or interpretation.
Therefore the statement is paradoxical rather than a normal true/false puzzle.