Etymology
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paradox (n.)

1530s, "a statement contrary to common belief or expectation," from French paradoxe (14c.) 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" (see para- (1)) + doxa "opinion," from dokein "to appear, seem, think" (from PIE root *dek- "to take, accept").

Originally with notions of "absurd, fantastic." Meaning "statement that is seemingly self-contradictory yet not illogical or obviously untrue" is from 1560s. Specifically in logic, "a statement or proposition from an acceptable premise and following sound reasoning that yet leads to an illogical conclusion," by 1903.

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paradoxology (n.)

"the holding and defending of opinions contrary to those generally prevalent," 1640s; see paradox + -logy.

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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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koan (n.)
Zen paradox meant to stimulate the mind, 1918, from Japanese ko "public" + an "matter for thought."
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Cretan (n.)

Old English Cretense (plural), "natives or inhabitants of Crete, from Latin Cretanus (singular); see Crete. They were proverbial in ancient times as liars; compare Greek noun kretismos "lying," literally "Cretan behavior," and the classical sophism expressing the liar paradox (see one version below).  Alternative Cretic (c. 1600) was used especially of a form of verse.

Epimenides, the Cretan, says that all Cretans are liars.
If Epimenides' statement is not true, he is a liar; and if it is true, he is a liar, for he is a Cretan.
But his statement is either true or not true.
Therefore he is a liar.
But since he is a liar, his statement is not true that all Cretans are liars.
Therefore some Cretans are not liars.
But since some Cretans are not liars, Epimenides is not necessarily a liar because he is a Cretan.
Therefore, we may accept his statement that all Cretans are liars. And so on.
[John J. Toohey, "An Elementary Handbook of Logic," 1918]
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rule (n.)

c. 1200, "principle or maxim governing conduct, formula to which conduct must be conformed" from Old French riule, Norman reule "rule, custom, (religious) order" (in Modern French partially re-Latinized as règle), from Vulgar Latin *regula, from Latin regula "straight stick, bar, ruler;" figuratively "a pattern, a model," related to regere "to rule, straighten, guide" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule").

By mid-14c. as "control, government, sway, dominion." The meaning "regulation governing play of a game, etc." is from 1690s; the phrase rules of the game is by 1787. To bend the rules "interpret leniently, overlook infringement" is by 1680s.

The meaning "strip with a straight edge used for making straight lines or measuring" is from mid-14c. Typography sense of "thin strip cut type-high and used for printing continuous lines" is attested from 1680s. Rule of law "supremacy of impartial and well-defined laws to any individual's power" is from 1883. Rule of the road in reference to the fixed customs, formerly much varying from country to country, which regulate the sides to be taken by vehicles in passing each other, is by 1805.

The rule of the road is a paradox quite,
In driving your carriage along,
If you keep to the left you are sure to go right,
If you keep to the right you go wrong.
[Horne Tooke, "Diversions of Purley," 1805]
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