Both Uses

paradox
in
Into the Wild
(Auto-generated)

Such willful ignorance ....amounts to disrespect for the land, and paradoxically demonstrates the same sort of arrogance that resulted in the Exxon Valdez spill, just another case of underprepared, overconfident men bumbling around out there and screwing up because they lacked the requisite humility.†
p. 72.2

paradoxically = in a manner that seems (at least at first impression) to be impossible because things that seem true contradict each other
Perhaps the greatest paradox concerned his feelings about money.†
p. 115.4 *

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."