I grabed some paradoxes from Wikipedia... 

Liar paradox: "This sentence is false."

Ship of Theseus:  It seems like you can replace any component of a ship, and it will still be the same ship. So you can replace them all, or one at a time, and it will still be the same ship. But then you can take all the original pieces, and assemble them into a ship. That, too, is the same ship you started with.

Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests.

Zeno's paradoxes: "You will never reach point B from point A as you must always get half-way there, and half of the half, and half of that half, and so on... ." (This is also a physical paradox.)  so motion should be impossible

Simpson's paradox: An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.

 bilene paradox: People can make decisions based not on what they actually want to do, but on what they think that other people want to do, with the result that everybody decides to do something that nobody really wants to do, but only what they thought that everybody else wanted to do.

Buridan's ass: How can a rational choice be made between two outcomes of equal value?

control paradox: No human is free from control, because even when they are free from the control of others, they are under their own control.

Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.

The Irresistible force paradox: what would happen if an unstoppable force hits an immovable object?

Here a just a few paradoxes...It seems our very understanding of logic lies in a realm seperate from reality, even though it is stems purely from it.  Why does logic that stems from our understanding of the universe often contradict the very conclusions that it comes to?

Just something to tink on...enjoy