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Examples of these are the universal affirmative 'every man is white', and the universal negative 'no man is white'. These cannot be true at the same time. However, these are not contradictories because both of them may be false. For example, it is false that every man is white, since some men are not white.
For example, the word undevout appears in Webster's dictionary of 1828, while the pattern of non-person could conceivably be extended to non-platypus. Conversely, some words appear to be a prefixed form of an opposite, but the opposite term does not exist, such as inept, which appears to be in- + * ept; such a word is known as an unpaired word.
For example, something that is even entails that it is not odd. It is referred to as a 'binary' relationship because there are two members in a set of opposites. The relationship between opposites is known as opposition. A member of a pair of opposites can generally be determined by the question What is the opposite of X ?
Post's solution to the problem is described in the demonstration "An Example of a Successful Absolute Proof of Consistency", offered by Ernest Nagel and James R. Newman in their 1958 Gödel's Proof. They too observed a problem with respect to the notion of "contradiction" with its usual "truth values" of "truth" and "falsity". They observed that:
Technically, however, a logical contradiction is a proposition that is true and false in the same sense; a proposition which is true in one sense and false in another does not constitute a logical contradiction. (For example, although in one sense a man cannot both be a "father" and "celibate"—leaving aside such cases as either a celibate man ...
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.
The term "antithesis" in rhetoric goes back to the 4th century BC, for example Aristotle, Rhetoric, 1410a, in which he gives a series of examples. An antithesis can be a simple statement contrasting two things, using a parallel structure: I defended the Republic as a young man; I shall not desert her now that I am old. (Cicero, 2nd Philippic, 2 ...
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical argument, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.