paradox

A paradox is a statement or concept that contains conflicting ideas. 

In logic, a paradox is a statement that contradicts itself; for example, the statement 

"I never tell the truth" is a paradox 
because if the statement is true (T), it must be false (F) and if it is false (F), it must be true (T). 

In everyday language, a paradox is a concept that seems absurd or contradictory, yet is true. 

In a Windows environment, for instance, 
it is a paradox that when a user wants to shut down their computer, it is necessary to first click "start".

contradict
～と矛盾する、相反する

You're contradicting yourself. 
君の言っていることは矛盾している。

conflict
対立する、矛盾する

absurd
ばかげた、ばかばかしい

absurd prediction
《an ～》でたらめの予測

absurd remark
ばかげた発言