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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."
To disprove opposing views about reality, he wrote a series of paradoxes that used reductio ad absurdum arguments, or arguments that disprove an idea by showing how it leads to illogical conclusions. [12] Furthermore, Zeno's philosophy makes use of infinitesimals, or quantities that are infinitely small while still being greater than zero. [14]
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.
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
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.
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 ...
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 ...