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In logic, the law of non-contradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "the house is white" and "the house is not white" are mutually exclusive.
As a demonstration of the principle, consider two contradictory statements—"All lemons are yellow" and "Not all lemons are yellow"—and suppose that both are true. If that is the case, anything can be proven, e.g., the assertion that " unicorns exist", by using the following argument:
Dialetheism – View that there are statements that are both true and false; Double standard – Inconsistent application of principles; Doublethink – Simultaneously accepting two mutually contradictory beliefs as correct; Graham's hierarchy of disagreement; Irony – Rhetorical device and literary technique; Law of noncontradiction
In other words: "two or more contradictory statements cannot both be true in the same sense at the same time": ¬(A∧¬A). In the words of Aristotle, that "one cannot say of something that it is and that it is not in the same respect and at the same time". As an illustration of this law, he wrote:
Ockham was opposed to the idea, arguing that whenever there is any distinction or non-identity in reality, then two contradictory statements can be made. But contradictory statements, he goes on arguing, cannot be truly asserted unless the realities they stand for are either (1) distinct real things (2) distinct concepts or (3) a thing and a ...
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
The tension between these two seemingly contradictory positions was massaged by Webbon in his correction of fellow Christian Nationalists Andrew Torba and Eric Conn. ... The Statement seeks to be ...
This can be written as: () An example of its use would be an attempt to prove two contradictory statements from a single fact. For example, if a person were to state "Whenever I hear the phone ringing I am happy" and then state "Whenever I hear the phone ringing I am not happy", one can infer that the person never hears the phone ringing.