Contradiction

• Date: 14th century

Definitions

• 1 : act or an instance of contradicting
• 2 a : a proposition, statement, or phrase that asserts or implies both the truth and falsity of something

b : a statement or phrase whose parts contradict each other <a round square is a contradiction in terms>

• 3 a : logical incongruity

b : a situation in which inherent factors, actions, or propositions are inconsistent or contrary to one another

Description

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other. Illustrating a general tendency in applied logic, Aristotle’s law of noncontradiction states that “One cannot say of something that it is and that it is not in the same respect and at the same time.”

By extension, outside of classical logic, one can speak of contradictions between actions when one presumes that their motives contradict each other.

History

By creation of a paradox Plato's Dialog of Euthydemus demonstrates the need for the notion of contradiction. In the ensuing dialog Dionysodorus denies the existence of "contradiction", all the while that Plato is contradicing him:

". . . I in my astonishment said: What do you mean Dionysodorus? I have often heard, and have been amazed to hear, this thesis of yours, which is maintained and employed by the disciples of Protagoras [a Sophist, the argument of whom Aristotle rebutts during his enunciation of the Law of Noncontradiction], and others before them, and which to me appears to be quite wonderful, and suicidal as well as destructive, and I think that I am most likely to hear the truth about it from you. The dictum is that there is no such thing as a falsehood; a man must either say what is true or say nothing. Is not that your position?

Indeed, Dionysodorus agrees that "there is no such thing as false opinion . . . there is no such thing as ignorance" and demands of Plato to "Refute me." Plato responds "But how can I refute you, if, as you say, to tell a falsehood is impossible?" [1]

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