All 5 Uses

paradox
in
Ulysses, by James Joyce
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Is it some paradox?†
Chpt 1
We have grown out of Wilde and paradoxes.†
Chpt 1 *

paradoxes = situations or statements that may be true but are surprising or seem impossible because parts of them seem to contradict each other
Quoth littlejohn Eglinton: —I was prepared for paradoxes from what Malachi Mulligan told us but I may as well warn you that if you want to shake my belief that Shakespeare is Hamlet you have a stern task before you.†
Chpt 9
Of course it's all paradox, don't you know, Hughes and hews and hues, the colour, but it's so typical the way he works it out.†
Chpt 9
—Do you think it is only a paradox?†
Chpt 9

Definitions:

(1) (paradox)
a situation or statement that seems to contradict itself but may still be true
(2) (meaning too rare to warrant focus)
More rarely, paradox may refer to a statement that contradicts itself -- such as "I always lie."