contradictory

That contradicts something, such as an argument.

This wide variety of genuinely contradictory holy sutras generated a serious problem in later Chinese and Japanese Buddhism. In the early period the Chinese and Japanese did not know that there were so many schools of Buddhism which disagreed with one another. Chinese and Japanese Buddhists assumed that every single Buddhist sutra was the actual words of the Buddha himself. As a result, Chinese Buddhists had to come up with some kind of explanation for the contradictory claims and assertions apparently made by the same holy person. The Chinese T’ien-t’ai school decided that the texts were spoken by the Buddha but tailored to different audiences of vastly different capabilities and insight.

That is itself a contradiction.

Our attitudes toward sharks are contradictory. We fear them and yet we seek them out.

That is diametrically opposed to something.

Schemes […] contradictory to common sense.

Mutually exclusive.

[White House deputy chief of policy Stephen] Miller has offered contradictory versions of Trump administration statements and court rulings.

Tending to contradict or oppose, contrarious.

Either of a pair of propositions, that cannot both be true or both be false.

If one proposition is the negation of another, it follows trivially from the definition that the two propositions are contradictories. The converse does not hold. Two propositions can be contradictories without either being the negation of the other. For example: 3) John is more than six feet tall and 4) John is either exactly six feet tall or else less than six feet tall are contradictories, but neither is the negation of the other. Negation is one way, but not the only way, of forming a contradictory.