A paradox is a logically self-contradictory
statement.

In logic , many paradoxes exist which are known to be invalid arguments, but which are nevertheless valuable in promoting
critical thinking , [9] while other paradoxes have revealed errors in definitions which were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined.

Some examples of paradoxes are:
1) Crocodile dilemma: If a crocodile steals a child and promises its return if the father can correctly guess exactly what the crocodile will do, how should the crocodile respond in the case that the father guesses that the child will not be returned?

2) Liar paradox: "This sentence is false."
If "this sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.

3) Sorites paradox (also known as the
paradox of the heap): If one removes a single grain of sand from a heap, they still have a heap. If they keep removing single grains, the heap will disappear. Can a single grain of sand make the difference between heap and non-heap?

4) Irresistible force paradox : What would happen if an unstoppable force hit an immovable object?

5) Predestination paradox: A man travels back in time to discover the cause of a famous fire. While in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time. The bootstrap paradox is closely tied to this, in which, as a result of time travel, information or objects appear to have no beginning.

6) Hitler's murder paradox : One can travel back in time and murder Adolf Hitler before he can instigate World War II and
the Holocaust; but if he had never instigated that, then the murder removes any reason for the travel.

7) Paradox of free will : If God knows in advance how we will decide, how can there be free will?

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

9) Omnipotence paradox: Can an omnipotent being create a rock too heavy for itself to lift?

10) Problem of evil : (Epicurean paradox) The existence of evil seems to be incompatible with the existence of an omnipotent, omniscient, and morally perfect God.

11) Paradox of value, also known as
diamond-water paradox : Water is more useful than diamonds, yet is a lot cheaper.

12) Barber paradox: A male barber shaves all and only those men who do not shave themselves. Does he shave himself?

13) Knower paradox : "This sentence is not known."

14) Hedgehog's dilemma or Lover's paradox: Despite goodwill, human intimacy cannot occur without substantial mutual harm.

15) Paradox of place: If everything that exists has a place, that place must have a place, and so on ad infinitum.

Interesting