{"id":4362,"date":"2021-08-05T19:40:04","date_gmt":"2021-08-05T17:40:04","guid":{"rendered":"http:\/\/icar.cnrs.fr\/dicoplantin\/?p=4362"},"modified":"2025-08-07T09:54:24","modified_gmt":"2025-08-07T07:54:24","slug":"absurd-eng","status":"publish","type":"post","link":"https:\/\/icar.cnrs.fr\/dicoplantin\/absurd-eng\/","title":{"rendered":"Absurd"},"content":{"rendered":"

ABSURD<\/span><\/h1>\n

Latin absurdus<\/em>, \u201cabsurd\u201d. Arguments ad absurdum<\/em>, ab absurdo<\/em>, ex absurdo<\/em>.
\nAlso, reductio ad absurdum<\/em>, \u201creduction to absurdity\u201d, under different forms:
\nreductio ad impossibile<\/em>, \u201creduction to the impossible\u201d \u2014\u00a0 r. ad falsum<\/em>, \u201cr. to the false\u201d \u2014 r. ad ridiculum,<\/em> \u201cr. to the ridicule\u201d \u2014 <\/span>r. ad incommodum<\/em>; \u201cr. to the undesirable\u201d.<\/span><\/p>\n

1. The scheme<\/span><\/h1>\n
\n
\n
\n

The argumentation from the absurd<\/strong><\/span> is a form of indirect evidence based on contradiction. This lcategory of arguments concludes that an assertion or a proposal should be rejected based on the indefensible consequences which would result from its adoption.<\/p>\n

The general process of reduction to the absurd corresponds to the following mechanism:<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n
\n

1. A claim, a proposal is put forward, as a working hypothesis or possibility.
\n2. Consequences<\/strong> are drawn from this proposition, regardless of whether they are causal or logical.
\n3. One of these consequences is deemed \u201cabsurd\u201d based on certain criteria<\/strong>, cf. below
\n4. The initial proposal or hypothesis is rejected<\/strong>.<\/p>\n

Argumentation to the absurd<\/em> is not an argument from ignorance<\/a><\/em><\/strong>.
\n\u2014 An argument from ignorance<\/span><\/strong> concludes that P<\/strong> is true because\u00a0not-P has not been proven false.<\/strong>
\n\u2014 An argument to the absurd<\/span><\/strong> concludes that P<\/strong> is true because not-P<\/strong> has been proven false, and only one of P<\/strong> and not-P<\/strong>, can be true.
\nThis corresponds to a case-by-case argument in a situation where the number of cases is reduced to two, either P i<\/strong>s true or not-P<\/strong> is true; but not-P<\/strong> is false, so P<\/strong> is true, see apagogic<\/a> argument<\/a>; contradiction<\/a>.<\/p>\n

2. Varieties of absurdities<\/span>
\n<\/strong><\/span><\/h1>\n

There are as many kinds of reduction to absurdity as modes of deduction and reasons to evaluate a consequence as inadmissible. The qualification as absurd may thus apply to:
\n\u2014 Mathematical consequences.<\/strong> One clearly sees the variety and the diversity of what is called the \u201cabsurd\u201d in argumentation by contrasting these forms with the demonstration from the absurd, where absurd means \u201ccontradictory\u201d, cf. infra.<\/p>\n

\u2014 Logical or semantic consequences.<\/strong> Consequences derived, from the very meaning of an expression lead to a semantic difficulty, see dialectic<\/a>; opposites<\/a>.<\/p>\n

\u2014 Causal consequences.<\/strong> In the physical domain and natural experience, the effects predicted by the hypothesis are not observed, see. refutation by the opposite.<\/a> Refutation by an attested fact that differs from the theoretically expected fact, is a type of refutation from the absurd.<\/p>\n

\u2014 Practical consequences.<\/strong> However, as soon as one turns from the scientifically established causal link to the \u201ccausal story\u201d as constructed in a pragmatic argument<\/a>, however, the speaker intervenes through his or her positive or negative valuation of the consequences. The consequence is then:<\/p>\n

\u2014 Contrary to the intended goals,<\/strong> the effects of the proposed action are perverse, the measure is counterproductive, contrary to various interests.<\/span>
\n\u2014 Inadmissible from the point of view of<\/strong> common sense, law, or morality, see apagogic<\/a>; <\/strong>ad Incommodum<\/a>.<\/span><\/p>\n

Pragmatic refutation by negative consequences is opposed to a measure by showing that it will have negative consequences unforeseen by the individual who proposes the measure, and that these drawbacks will prevail over any possible advantage.
\nThe argument is strengthened\u00a0 if the opponent can show that these\u00a0 alleged negative consequences are not just collateral effects, but are in fact diametrically opposed to the expected positive effects<\/strong>: the measure proposed to cure the patient will in fact strengthen her disease.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n
\n

3. Demonstration by Reduction to the Absurd<\/span>
\n<\/strong><\/h1>\n

Proof by the absurd (or by contradiction), is based on the principle of the excluded middle, according to which \u201cA<\/strong> or not-A<\/strong>\u201d is necessarily true. The reasoning is based not on the proposition A<\/strong> that we want to prove, but on its negation, not-A<\/strong>.
\nThe negation, not-A<\/strong>, is provisionally admitted and its consequences are deduced. These consequences lead to statement A, <\/strong>but the conjunction \u201cA<\/strong> and not-A<\/strong>\u201d contravenes the principle of contradiction. thus, not-A<\/strong> is false, and A<\/strong> is necessarily true.
\nIn the language of implication, we are in a situation where \u201cA<\/strong> \u2192 non-A<\/strong>\u2019. According to the principle of \u201cone can deduce anything from the false\u201d, this implication is true only if A<\/strong> is false.<\/p>\n

It can be shown by reduction to the absurd that \u201cthe square root of 2 (the number whose square is 2, noted by the symbol \u221a2) is not<\/u><\/em> a rational number\u201d (proposition A<\/strong>).<\/p>\n

(1) Suppose that \u201cthe number corresponding to \u221a2 is<\/u><\/em> a rational number\u201d (proposition not-A<\/strong>).
\n(2) By definition, a rational number can be written as a fraction \u201cp<\/strong> \/ q<\/strong>\u201d, where p<\/strong> and q<\/strong> are prime numbers (a prime number can only be divided by itself and 1<\/strong>).
\nFrom this hypothesis, it can be deduced that both p<\/strong> and q<\/strong> are even; Therefore, they have 2<\/strong> as a common divisor, which is contradicting the initial hypothesis.
\n(3) Conclusion: hypothesis (1) is false, and \u221a2<\/strong> is not a rational number.<\/p>\n

The demonstration by the absurd is an indirect<\/em> method of proof.\u00a0It does not directly prove that A<\/strong> is true, only that not-A<\/strong> is false. Not all specialists agree with this reasoning, \u201cwhile the classical mathematicians consider the proof by the absurd to be valid, the intuitionists reject it. They argue that in order to prove A<\/strong>, it is not enough to establish that not-<\/strong>(not-A<\/strong>)\u201d (Vax 1982, Absurd<\/em>).
\nWe see that the demonstrative character of a demonstration can be discussed.<\/p>\n

\n

\u00a0<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

ABSURD Latin absurdus, \u201cabsurd\u201d. Arguments ad absurdum, ab absurdo, ex absurdo. Also, reductio ad absurdum, \u201creduction to absurdity\u201d, under different forms: reductio ad impossibile, \u201creduction to the impossible\u201d \u2014\u00a0 r. ad falsum, \u201cr. to the false\u201d \u2014 r. ad ridiculum, \u201cr. to the ridicule\u201d \u2014 r. ad incommodum; \u201cr. to the undesirable\u201d. 1. The scheme […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4362","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/4362","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/comments?post=4362"}],"version-history":[{"count":18,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/4362\/revisions"}],"predecessor-version":[{"id":14652,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/4362\/revisions\/14652"}],"wp:attachment":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/media?parent=4362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/categories?post=4362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/tags?post=4362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}