{"id":5162,"date":"2021-10-21T16:56:23","date_gmt":"2021-10-21T14:56:23","guid":{"rendered":"http:\/\/icar.cnrs.fr\/dicoplantin\/?p=5162"},"modified":"2025-06-03T15:01:46","modified_gmt":"2025-06-03T13:01:46","slug":"non-contradiction-principle","status":"publish","type":"post","link":"https:\/\/icar.cnrs.fr\/dicoplantin\/non-contradiction-principle\/","title":{"rendered":"Non-Contradiction Principle (e)"},"content":{"rendered":"

NON-CONTRADICTION PRINCIPLE<\/span><\/h2>\n

1. In logic<\/span><\/h2>\n

In logic, the principle of non-contradiction prohibits the affirmation of contradictory propositions. In other words:<\/p>\n

\u2014\u00a0The conjunction \u201cP<\/strong> and not-P<\/strong>\u201d is a contradiction, and, as such, is a self-destructive proposition, that is necessarily false<\/em>.<\/span>
\n\u2014\u00a0The disjunction \u201cP<\/strong> or not-P<\/strong>\u201d is necessarily true<\/em>.<\/span><\/p>\n

One of the two propositions P<\/strong> or not-P<\/strong> must be true, both cannot be true at the same time. The same thing cannot both be<\/em> and not be<\/em>. This principle is considered\u00a0 as a law of thought <\/em>in classical logic and an axiom<\/em> in contemporary logic. A logical system that respects the principle of non-contradiction contains no antinomies<\/em> and\u00a0 is said to be consistent<\/em>.<\/p>\n

Negation\u00a0\u2014\u00a0<\/strong>Using the truth table method, the negation operator is defined as follows:<\/p>\n\n\n\n\n\n
P<\/strong><\/td>\n\u00ac<\/strong>\u00a0P <\/strong><\/td>\n<\/tr>\n
T<\/td>\nF<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

This table expresses the principle of the excluded middle. It reads:<\/p>\n

Line 1: ‘if P is true, then not-P is false’.
\nLine 2: ‘if P is false, then not-P is true’.<\/p>\n

2. In natural language<\/span><\/h1>\n

The application of the non-contradiction principle to everyday language is complex, because:
\n\u2014 It presupposes that P<\/strong> is either unambiguously true or false, not far from true<\/em> or practically false<\/em>, true or not according to the circumstances<\/em>.
\n\u2014 There are natural language utterances that cannot be said to be either true or false, such as \u00ab\u00a0Come back tomorrow!<\/em>\u00a0\u00bb or \u00ab\u00a0I promise to come back tomorrow<\/em>.\u00a0\u00bb<\/p>\n

Many forms of argument appeal to the principle of non-contradiction , albeit under different names. See a<\/em>d hominem<\/em><\/a>; dialectic<\/a>; contradiction<\/a>; consistency<\/a>.<\/strong><\/p>\n

The principle of non-contradiction applies not only to logical and argumentative discourse, but to any kind of discourse. Inconsistent narratives<\/em> or descriptions<\/em> for example, are rejected as such.<\/p>\n

According to the basic rule of Aristotelian dialectic, any discourse that leads to a contradiction is irrational and must be abandoned. Hegelian dialectics sees the motor of history in the ongoing treatment of contradictions. Cynical politicians can invoke Hegel to hide their opportunism:<\/p>\n

Stalin’s speech on the Five-Year Plan serves as a passionate apology for contradiction as a \u201cvital value<\/em>\u201d and an \u201cinstrument of struggle<\/em>\u201d. One of Lenin’s great strengths was his ability never to feel imprisonned by what he had preached as true the day before. Mussolini’s famous words \u201cLet us beware of the deadly trap of coherence<\/em>\u201d could be endorsed by anyone intending to work within unpredictable currents they cannot.<\/span>
\nJulien Benda, [The Betrayal of the Intellectuals<\/em>], [1927][1]<\/a><\/span><\/p>\n

Affirming of a paradox as an oxymoron<\/em> enables one to endure the contradiction: \u201cO wound without scar!<\/em>\u201d. Rather than being deemed absurd or fallacious and dismissed, such a paradoxical assertion triggers a search for the deeper, symbolic meaning of the words wound<\/em> and scar<\/em> used in this context.
\nThis interpretive approach goes a step further than hastily dismissing it as a\u00a0 \u201cfallacy\u201d.<\/p>\n

\n

[1]<\/a> Julien Benda, La Trahison des Clercs<\/em>, [1927]. Excerpt from the preface<\/em> to the 1946 edition. Paris: Grasset, 1975, pp. 78-79.<\/span><\/p>\n

\n

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

NON-CONTRADICTION PRINCIPLE 1. In logic In logic, the principle of non-contradiction prohibits the affirmation of contradictory propositions. In other words: \u2014\u00a0The conjunction \u201cP and not-P\u201d is a contradiction, and, as such, is a self-destructive proposition, that is necessarily false. \u2014\u00a0The disjunction \u201cP or not-P\u201d is necessarily true. One of the two propositions P or not-P […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5162","post","type-post","status-publish","format-standard","hentry","category-non-classe"],"_links":{"self":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5162","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=5162"}],"version-history":[{"count":10,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5162\/revisions"}],"predecessor-version":[{"id":14326,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/posts\/5162\/revisions\/14326"}],"wp:attachment":[{"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/media?parent=5162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/categories?post=5162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icar.cnrs.fr\/dicoplantin\/wp-json\/wp\/v2\/tags?post=5162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}