reductio ad absurdum

re·duc·ti·o ad ab·sur·dum

R0107800 (rĭ-dŭk′tē-ō ăd əb-sûr′dəm, -zûr′-, -shē-ō)n. pl. re·duc·ti·o·nes ad absurdum (-ō′nēz, -nās) Disproof of a proposition by showing that it leads to absurd or untenable conclusions.

[Medieval Latin reductiō ad absurdum : Latin reductiō, a bringing back, reduction + Latin ad, to + Latin absurdum, absurdity, from neuter of absurdus, absurd.]

reductio ad absurdum

(rɪˈdʌktɪəʊ æd æbˈsɜːdəm) n1. (Logic) a method of disproving a proposition by showing that its inevitable consequences would be absurd2. (Logic) a method of indirectly proving a proposition by assuming its negation to be true and showing that this leads to an absurdity3. application of a principle or proposed principle to an instance in which it is absurd[Latin, literally: reduction to the absurd]

re•duc•ti•o ad ab•sur•dum

(rɪˈdʌk tiˌoʊ ˈæd æbˈsɜr dəm, -ˈzɜr-, -ʃiˌoʊ)
n. a reduction to an absurdity; the refutation of a proposition by demonstrating that its logical conclusion is absurd. [1735–45; < Latin]

reductio ad absurdum

A Latin phrase meaning reduction to absurdity, used to mean carrying an argument to the point at which it becomes absurd.

Thesaurus

Noun

reductio ad absurdum - (reduction to the absurd) a disproof by showing that the consequences of the proposition are absurd; or a proof of a proposition by showing that its negation leads to a contradictionreductiodisproof, falsification, refutation - any evidence that helps to establish the falsity of something

Reductio Ad Absurdum

reductio ad absurdum

[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.

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.

M. M. NOVOSELOV

reductio ad absurdum

re·duc·ti·o ad ab·sur·dum

reductio ad absurdum

re•duc•ti•o ad ab•sur•dum

reductio ad absurdum

Reductio Ad Absurdum

reductio ad absurdum

Reductio Ad Absurdum

Reductio Ad Absurdum

Reductio Ad Absurdum

reductio ad absurdum

Synonyms for reductio ad absurdum

noun (reduction to the absurd) a disproof by showing that the consequences of the proposition are absurd

Synonyms

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