Etymology
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paradoxical (adj.)

"of the nature of a paradox," 1580s, from paradox + -ical. Meaning "inconsistent with itself" is by 1630s. Competing forms were paradoxal (1560s), paradoxial (1620s), but these survive in niches, if at all. Related: Paradoxically.

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Definitions of paradoxical

paradoxical (adj.)
seemingly contradictory but nonetheless possibly true;
it is paradoxical that standing is more tiring than walking
Synonyms: self-contradictory
From wordnet.princeton.edu