Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them.
— George Orwell

Double-thought: as you believe things that should be self-contradictory. This is generally the result of some kind of propaganda.
James Dye contradictory quote

You may find many contradictory statements and philosophies within my writings. However, to this I will say such is life, for life is full of contradictions.
— Bryant H. McGill

A woman is sometimes fugitive, irrational, indeterminable, illogical and contradictory. A great deal of forbearance ought to be shown her, and a good deal of prudence exercised with regard to her, for she may bring about innumerable evils without knowing it. Capable of all kinds of devotion, and of all kinds of treason, monster incomprehensible, raised to the second power, she is at once the delight and the terror of man.
— Henri Frederic Amiel

Some people suggest that the problem is the separation of powers. If you had a parliamentary system, the struggle for power would not result in such complex peace treaties that empower so many different people to pursue so many contradictory aims.
— contradictory quotation by James Q. Wilson