Also found in: Dictionary, Thesaurus, Legal.

[ri¦dək·tē·ō äd ab′sərd·əm]
(mathematics)
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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

M. M. NOVOSELOV

References in periodicals archive ?
Really, today's LGBT activists, along with their sycophantic allies (like the frightened little toadies at Reuters) signify the embodiment of reductio ad absurdum. When one objectively contemplates the logical conclusion of each of their "progressive" propositions, one is left contemplating the absurd.
One of the most forceful and elegant arguments in favor of PTPTI is the--we think we can say famous--Misesian reductio ad absurdum. Mises delivers it in Human Action (in the chapter preceding the one dedicated to interest proper): Time preference is a categorical requisite of human action.
Moreover, Block attempts a reductio ad absurdum of my position on the basis of the following supposed analogy:
In the end, his is a variation on the poetics of the fragment, in which a reductio ad absurdum only demonstrates the futility of any attempt to construct the "grand narratives" of modernity.
This conclusion was purely a reductio ad absurdum (3), (4) on our part.
For critics of this approach to government, anarchism aims at a reductio ad absurdum: the libertarian argument will inevitably lead one to the conclusion that there should be no state at all.
There is even a discussion of Hume's reductio ad absurdum of miracles, and Augustine's view in contrast.
* In Tetrachordon, Milton uses, he believes, a reductio ad absurdum argument to ridicule those who fear abuses so much that they would forbid all divorce: "If the importation of wine and the use of all strong drink were forbid, it would both clean rid the possibility of committing that odious vice [of drunkenness], and men might afterwards live happily and healthfully, without the use of those intoxicating liquors.
The exercise is its own reductio ad absurdum, an exercise in comedy, like the high school game of adding "between the sheets" to the titles of hymns--high meeting low for yucks: "Amazing Grace Between the Sheets"; "Rock of Ages Between the Sheets"; or, given the news out of Boston lately, "Jesus Loves the Little Children Between the Sheets."
Con tinas dosis de humor e ironia y a traves de un uso magistral de la paradoja y de la reductio ad absurdum, Chesterton desenmascara la falsedad de algunas criticas extendidas contra la Iglesia catolica, o senala sin tapujos las afirmaciones erroneas sobre la religion, el sentido de la historia, la evolucion del hombre, etc., originadas en cosmovisiones cientificistas, materialistas o agnosticas.
This is a kind of reductio ad absurdum, but it points to the problem poets are experiencing in the early 21st Century.

Site: Follow: Share:
Open / Close