What do you make of the following sentences?
1. This sentence is false.
What's the truth value of the above sentence? If the sentence is false, then it's true that the sentence is false, which makes the sentence true. But if the sentence is true, then that truth contradicts the literal import of the sentence... which makes the sentence false! You could blow your mind if you think about this too hard.
2. Police police police police police.
Yes, this is an actual sentence. Can you make sense of it? (With thanks to Malcolm.)
3. Colorless green ideas sleep furiously.
This is a classic example, often used in linguistics, of how a sentence can be grammatically correct and yet be total nonsense.