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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."
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]
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.
Dawkins presents the teapot as a reductio ad absurdum of this position: if agnosticism demands giving equal respect to the belief and disbelief in a supreme being, then it must also give equal respect to belief in an orbiting teapot, since the existence of an orbiting teapot is just as plausible scientifically as the existence of a supreme ...
The judgement of fallacy is therefore largely dependent on a normative judgement of the "absurd" conclusion. A charge of "proving too much" is thus generally invoked, rightly or wrongly, against normatively-opposed conclusions, and so such charges are often controversial at the time they are made, as in the following examples: [1]
For example, to prove there exists an n such that P(n), the classical mathematician may deduce a contradiction from the assumption for all n, not P(n). Under both the classical and the intuitionistic logic, by reductio ad absurdum this gives not for all n, not P(n).
For example, the contrariety of A and E statements, "All S are P," and "No S are P," follows by a reductio ad absurdum argument similar to the one given by Aristotle. Later logicians, notably Chrysippus, are also thought to have endorsed connexive principles. By 100 BCE logicians had divided into four or five distinct schools concerning the ...