contradictory

Etymology

Borrowed from Late Latin contradictorius, from Latin contradico.

adj

1. That contradicts something, such as an argument.
2. That is itself a contradiction.
   Our attitudes toward sharks are contradictory. We fear them and yet we seek them out. 1983, Richard Ellis, The Book of Sharks, Knopf, page 149
3. That is diametrically opposed to something.
4. Mutually exclusive.
5. Tending to contradict or oppose, contrarious.

noun

1. (logic) 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. 2001, Mark Sainsbury, chapter 1, in Logical Forms — An Introduction to Philosophical Logic, 2nd edition, Blackwell Publishing, §4, page 20