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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.
Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one."
In general usage outside mathematics and philosophy, a reductio ad absurdum is a tactic in which the logic of an argument is challenged by reducing the concept to its most absurd extreme. Translated from Aristotle's "ἡ εις άτοπον απαγωγη" (hi eis atopon apagogi, "reduction to the impossible"). reductio ad Hitlerum
The phrase is distinct from reductio ad absurdum, which is usually a valid logical argument. ab abusu ad usum non valet consequentia: The inference of a use from its abuse is not valid: i.e., a right is still a right even if it is abused (e.g. practiced in a morally/ethically wrong way); cf. § abusus non tollit usum. ab aeterno: from the eternal
Appeal to ridicule (also called appeal to mockery, ad absurdo, or the horse laugh) [1] is an informal fallacy which presents an opponent's argument as absurd, ridiculous, or humorous, and therefore not worthy of serious consideration.
The heart of the dialogue opens with a challenge by Socrates to the elder and revered Parmenides and Zeno. Employing his customary method of attack, the reductio ad absurdum, Zeno has argued that if as the pluralists say things are many, then they will be both like and unlike; but this is an impossible situation, for unlike things cannot be like, nor like things unlike.
Isaac Barrow and Baermann used the notation Q.E.A., for "quod est absurdum" ("which is absurd"), along the lines of Q.E.D., but this notation is rarely used today. [12] A graphical symbol sometimes used for contradictions is a downwards zigzag arrow "lightning" symbol (U+21AF: ↯), for example in Davey and Priestley. [13]
Reductio ad absurdum, reducing to an absurdity, is a method of proof in polemics, logic and mathematics, whereby assuming that a proposition is true leads to absurdity; a proposition is assumed to be true and this is used to deduce a proposition known to be false, so the original proposition must have been false.