One great way to look at a paradox is to compare it with other things. First, a paradox is not a contradiction. Contradictions simply are nonsense. No amount of reflection will get you anywhere. Second, a paradox is not a mystery. A mystery is something that cannot be explained. It is above reason.

A paradox is something that looks like a contradiction or a mystery on the surface, but under close reflection makes sense. There is a logic, but the logic is not apparent at first.

Here is an example from the New Testament: If you want to find your life, you must lose it.

Here is another example: The last shall be first and the first shall be last.

Here is a final example: To best way to be creative, is not to seek it.

There are at least a couple of ways to define a paradox.

1. A statement that seems like it is contradictory or nonsensical but might still be true.
2. A statement that does contradict itself but at first seems true.

So these are slightly different ideas.

Here are some paradoxical statements:

The only way to ensure peace is to prepare for war.

The only way to make money is to spend money.

But I'm pretty sure I didn't just make those up so I'm not sure they'd count as my own paradoxical statements.