A logical paradox is a statement that, despite apparently valid reasoning from true premises, leads to a self-contradictory or logically unacceptable conclusion.
Examples of Logical Paradoxes
Here are a couple of examples of logical paradoxes, including those mentioned in the provided reference:
The Cretan Paradox
- Description: This paradox, also known as the liar paradox, is attributed to Epimenides, a Cretan. He states, "All Cretans are liars."
- The Problem:
- If the statement is true, then Epimenides, being a Cretan, is a liar. Therefore, his statement must be false.
- If the statement is false, then not all Cretans are liars. This implies that some Cretans may be truthful, meaning Epimenides could be telling the truth, thus contradicting the initial assumption of the statement being false.
- The Paradox: The statement leads to a contradiction regardless of whether it is assumed to be true or false.
The Crocodile Paradox
- Description: A crocodile steals a child and tells the child's father, "I will return her to you if you guess correctly whether I will do so or not." The father replies, "You will not return my child."
- The Problem:
- If the crocodile was going to return the child, the father's guess would be wrong and the child should not be returned.
- If the crocodile was not going to return the child, the father's guess would be right, and the child should be returned.
- The Paradox: The crocodile can neither return nor not return the child without violating the rules of the puzzle itself.
Table of Paradox Examples
| Paradox Name | Description | Key Issue |
|---|---|---|
| The Cretan Paradox | A Cretan states, "All Cretans are liars." | The statement contradicts itself if taken as true or false; creating a logical loop. |
| The Crocodile Paradox | A crocodile says it will return a stolen child if the father correctly guesses whether it will return the child. | The father's prediction (and the crocodile's promise) results in a no-win scenario regardless of the prediction and the crocodile's actions. |
These examples highlight how paradoxes can expose limitations in logic and language. They often serve as thought experiments and demonstrate the complexity of reasoning and self-referential statements.
