A paradox occurs when an entity has dual attributes A and not-A, whatever A might be. Aristotle called such a situation the ‘Law of Contradiction’, saying, “It is impossible for the same attribute at once to belong and not to belong to the same thing and in the same relation … as some imagine Heraclitus says.”
In contrast Heraclitus of Ephesus said, “The Hidden Harmony is better than the obvious” and “Opposition brings concord; out of discord comes the fairest harmony.”
We should not blame Aristotle for driving Western civilization into the cul-de-sac that it is in today. For he was merely expressing the orthodoxy of the fragmented mind and split psyche, seeking to defend an ego- and ethnocentric sense of identity.
So, despite paradoxes being found in mathematical logic and quantum physics, there is still a psychological reluctance to embrace a harmonious, both-and way of life, in contrast to the conflict-ridden, either-or approach of the patriarchal epoch.
1540, ‘a statement contrary to common belief or expectation’, from Middle French paradoxe and directly from Latin paradoxum ‘paradox, statement seemingly absurd yet really true’, from Greek paradoxon ‘incredible statement or opinion’, noun use of neuter of adjective paradoxos ‘contrary to expectation, incredible’, from para- ‘contrary to’, from PIE base *per-¹, and doxa ‘opinion, notion; delusion; glory, splendour’, from dokein ‘to appear, seem, think’, from PIE base *dek- ‘to take, accept’.