Paradoxia
I like paradoxes I think they tell us something meanful about the nature of logic. Here are the most succinct paradoxes I know of. If you have any more please leave a comment.
Berry’s paradox: The smallest number that can not be expressed in less than 20 words.
Russell’s paradox: Does the set of all sets that do not contain themselves, contain itself?
The liar paradox: This statement is untrue.
Quine’s paradox: “Yields falsehood when preceded by its quotation” yields falsehood when preceded by it’s quotation.