Reductio Ad Absurdum

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reductio ad absurdum

[ri¦dək·tē·ō äd ab′sərd·əm]
A method of proof in which it is first supposed that the fact to be proved is false, and then it is shown that this supposition leads to the contradiction of accepted facts. Also known as indirect proof; proof by contradiction.

Reductio Ad Absurdum


the type of proof in which the proving of a judgment (the thesis of the proof) is achieved by the refutation of the judgment contradicting it—its antithesis. The refutation of the antithesis is achieved by establishing the fact that it is incompatible with any judgment whose truth has been established. The following pattern of proof corresponds to this form of reductio ad absurdum: if B is true and the falsity of B follows from A, then A is false.

Another, more general, form of reductio ad absurdum is proof by refutation (establishment of the falsity) of the antithesis according to the rule: having assumed A, we deduce a contradiction, consequently not-A. Here A can be either a positive or a negative judgment, and the deduction of the contradiction can be interpreted either as the deduction of the assertion of the identity of objects known to be different, or as the deduction of the pair of judgments B and not-B, or as the deduction of the conjunction of this pair, or as the deduction of the equivalency of this pair. The different interpretations of the concepts reductio ad absurdum and “contradiction” correspond to these different cases.

The method of reductio ad absurdum is especially important in mathematics: many negative judgments of mathematics cannot be proved by any means other than reduction to a contradiction. Besides those indicated above, there is another—paradoxical—form of reductio ad absurdum, which was used by Euclid in his Elements: judgment A can be considered proven if one can show that A results even from the asumption of the falsity of A.


References in periodicals archive ?
The theoretical, reductio ad absurdum, justification for time-preference as stated by Austrian authors is inadequate, while every seeming counter-example to it can, arguably, be squared with.
Is the reductio ad absurdum no longer a legitimate form of argument?
The other notable use of the reductio ad absurdum is Lincoln's response to Douglas's being in favor of adding territory to the United States without regard to its effect on the slavery question, Carry that to its logical conclusion, Lincoln says, and "the next thing will be a grab for the territory of poor Mexico, an invasion of the rich lands of South America, then the adjoining islands will follow .
6) This reductio ad absurdum interpretation (henceforth abbreviated, 'RAI') relies on the principle of non-contradiction.
Such a reductio ad absurdum is, however, probably inevitable when dealing with the sort of experimental imaginative writing to which Gottsche here doggedly attempts to bring critical order (Kafka, Musil, and Benjamin being but three outstanding practitioners of 'Kleine Prosa').
As with Houellebecq's other narrators, Daniel's story reads like a reductio ad absurdum of Schopenhauer, Darwin, and Freud.
Silver himself makes several reductio ad absurdum arguments: for example, his idea is that those who think a human embryo is a human being with moral worth should think the same of all living human cells, since they too are alive and genetically human.
He also necessarily holds that the steps from language to ontology are dramatic and the concept of realism corresponding to the concept of language is inferred through the process of reductio ad absurdum.
They accordingly drew the reductio ad absurdum conclusion that there is no evidence to support the belief that pregnancy results from sexual intercourse.
One of his chapters, "The Rage of Virginia Woolf," offers an account of the argument of Three Guineas that might be a useful example of the reductio ad absurdum for budding writers.
Estoy convencida de que todos aquellos que se acerquen a este libro encontraran en el muchos frutos de sabor exquisito y nutritivo alimento, que los llevara a compartir con Pessoa la embriagante conviccion de que: "La reductio ad absurdum es una de mis bebidas predilectas".
As the Chicago architect Stanley Tigerman says, we want buildings to please their users, not help architects make a philosophical point--a self-indulgent tendency in 20th-century architecture that reached its reductio ad absurdum with the "deconstructionist" architects, who deliberately designed buildings that no one would want to live in.