According to Wikipedia, "A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition." Sometimes, a paradox points out the dilemma, where two view-points or statements contradict each other.
One of the famous paradoxes is Russell's Paradox:
"Let R be the set of all sets that are not members of themselves. If R qualifies as a member of itself, it would contradict its own definition as a set containing all sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition."
Similarly,
"If God can do everything, He will be able to create a stone that he cannot lift. Then, He cannot lift that stone. Therefore, God cannot do everything."
In fact, whenever a statement refer to the absolute collective or general situation, such as everything, or anything, there may be a paradox. For example:
"Killing a living being is bad". Without referring to the situation or the circumstance, that statement cannot be a valid argument. However, "The Intention of killing a living being is bad" is a valid argument.
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