In opposition to Aristotelian logic is what one might call paradoxical logic, which assumes that A and non-A do not exclude each other as predicates of X. Paradoxical logic was predominant in Chinese and Indian thinking, in Heraclitus' philosophy, and then again under the name of dialectics in the thought of Hegel and Marx. The general principle of paradoxical logic has been clearly described in general terms by Lao-Tse: "Words that are strictly true seem to be paradoxical." And by Chuang-tzu: "That which is one is one. That which is not-one, is also one."
http://enlight.lib.ntu.edu.tw/FULLTEXT/JR-PHIL/ew25921.htm
http://en.wikipedia.org/wiki/List_of_paradoxes
-> Prisoner's dilemma: Two people might not cooperate even if it is in both their best interests to do so.
-> Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.
-> Catch-22 (logic): A situation where someone is in need of something that can only be had by not being in need of it.
http://www.martrix.org/1%20Paradox.pdf
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