A paradox is a statement that contradicts itself, or that must be both true and untrue at the same time. However, a key part of paradoxes is that they sound reasonable.
Example:
If the bar is crowded, then lots of people are going. But if so many people are going, it makes no sense to say “nobody goes” there anymore.
In literary analysis, “paradox” can sometimes have a looser meaning: a person or situation that contains contradictions.
Example: