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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 impossibile.
An oxymoron (plurals: oxymorons and oxymora) is a figure of speech that juxtaposes concepts with opposite meanings within a word or in a phrase that is a self-contradiction. As a rhetorical device, an oxymoron illustrates a point to communicate and reveal a paradox. [ 1 ][ 2 ] A general meaning of "contradiction in terms" is recorded by the ...
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 arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
List of paradoxes. Outline of public relations – Overview of and topical guide to public relations. Map–territory relation – Relationship between an object and a representation of that object (confusing map with territory, menu with meal) Mathematical fallacy – Certain type of mistaken proof.
Malapropism. A malapropism (/ ˈmæləprɒpɪzəm /; also called a malaprop, acyrologia, or Dogberryism) is the incorrect use of a word in place of a word with a similar sound, either unintentionally or for comedic effect, resulting in a nonsensical, often humorous utterance. An example is the statement attributed to baseball player Yogi Berra ...
The alternative origin given is that the word "prove" is used in the archaic sense of "test", [3] a reading advocated, for example, by a 1918 Detroit News style guide: The exception proves the rule is a phrase that arises from ignorance, though common to good writers. The original word was preuves, which did not mean proves but tests. [4]
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
A system will be said to be inconsistent if it yields the assertion of the unmodified variable p [S in the Newman and Nagel examples]. In other words, the notion of "contradiction" can be dispensed when constructing a proof of consistency; what replaces it is the notion of "mutually exclusive and exhaustive" classes.