{"id":987,"date":"2020-02-04T10:51:28","date_gmt":"2020-02-04T09:51:28","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=987"},"modified":"2020-02-04T10:51:28","modified_gmt":"2020-02-04T09:51:28","slug":"lunite-est-elle-un-nombre","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2020\/02\/04\/lunite-est-elle-un-nombre\/","title":{"rendered":"L’unit\u00e9 est-elle un nombre?"},"content":{"rendered":"

Les Grecs anciens refusaient de consid\u00e9rer l\u2019unit\u00e9 comme un nombre, comme on peut le lire dans La M\u00e9taphysique<\/em> d\u2019Aristote\u00a0:<\/p>\n

Il est, d\u2019ailleurs, de toute \u00e9vidence que c\u2019est l\u2019unit\u00e9 qui exprime la mesure\u00a0;\u00a0[\u2026] le nombre est une pluralit\u00e9 mesur\u00e9e\u00a0[\u2026] Aussi, n\u2019a-t-on pas moins raison de dire que l\u2019unit\u00e9 n\u2019est pas un nombre.<\/em><\/p>\n

Un ne fait pas nombre<\/h2>\n

Ce refus de consid\u00e9rer \u00ab\u00a0un\u00a0\u00bb comme un nombre vient de l\u2019assimilation du concept de nombre \u00e0 ceux de pluralit\u00e9 ou de multiplicit\u00e9. Cette confusion se retrouve en fran\u00e7ais ou \u00ab\u00a0nombreux\u00a0\u00bb ne peut signifier \u00ab\u00a0un\u00a0\u00bb.<\/p>\n

Une reconnaissance tardive<\/h2>\n

En 1585, Simon Stevin \u00e9crit dans les premi\u00e8res pages de La pratique d\u2019arithm\u00e9tique<\/em>\u00a0:<\/p>\n

Comme l\u2019unit\u00e9 est nombre par lequel la quantit\u00e9 d\u2019une chose expliqu\u00e9e se dit un.<\/em><\/p>\n

Alors que cela nous semble aujourd\u2019hui naturel, Simon Stevin se sent oblig\u00e9 de d\u00e9fendre cette position dans un long raisonnement de plusieurs pages, preuve que cette notion n\u2019est pas admise comme naturelle \u00e0 son \u00e9poque. Pourquoi\u00a0? Tout simplement parce qu\u2019elle s\u2019oppose \u00e0 la tradition philosophique du Moyen-\u00c2ge pour qui il n\u2019est point de v\u00e9rit\u00e9 en dehors d\u2019Aristote, d\u2019o\u00f9 le discours \u00e9tonnant\u00a0:<\/p>\n

Il est notoire que l\u2019on dit vulgairement que l\u2019unit\u00e9 n\u2019est pas nombre, mais seulement son principe [\u2026] ce que nous nions. Nous pouvons argumenter de la sorte\u00a0: La partie est de m\u00eame mati\u00e8re qu\u2019est son entier, unit\u00e9 est partie de multitude d\u2019unit\u00e9s, donc l\u2019unit\u00e9 est de m\u00eame mati\u00e8re qu\u2019est la multitude d\u2019unit\u00e9s. Mais la mati\u00e8re de multitude d\u2019unit\u00e9s est nombre donc la mati\u00e8re d\u2019unit\u00e9 est nombre.<\/em><\/p>\n

Le \u00ab\u00a0un\u00a0\u00bb est donc devenu nombre \u00e0 l\u2019\u00e9poque de Simon Stevin m\u00eame si certains, comme Diophante, un c\u00e9l\u00e8bre math\u00e9maticien grec du IIIe<\/sup> si\u00e8cle apr\u00e8s J\u00e9sus-Christ, l\u2019utilisaient d\u00e9j\u00e0 comme tel\u2026 mais apr\u00e8s avoir donn\u00e9 les d\u00e9finitions usuelles \u00e0 l’\u00e9poque, comme en sorte d’hommage \u00e0 la tradition.<\/p>\n

 <\/p>\n

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

Les Grecs anciens refusaient de consid\u00e9rer l\u2019unit\u00e9 comme un nombre, comme on peut le lire dans La M\u00e9taphysique d\u2019Aristote\u00a0: Il est, d\u2019ailleurs, de toute \u00e9vidence que c\u2019est l\u2019unit\u00e9 qui exprime la mesure\u00a0;\u00a0[\u2026] le nombre est une pluralit\u00e9 mesur\u00e9e\u00a0[\u2026] Aussi, n\u2019a-t-on pas moins raison de dire que l\u2019unit\u00e9 n\u2019est pas un nombre. Un ne fait pas … Continuer la lecture de L’unit\u00e9 est-elle un nombre?<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":992,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[63,29,104],"tags":[373,141,96,374,375],"class_list":["post-987","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-histoire","category-maths-2","category-philosophie","tag-arithmetique","tag-histoire","tag-philosophie","tag-un","tag-unite"],"yoast_head":"\nL'unit\u00e9 est-elle un nombre?, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2020\/02\/04\/lunite-est-elle-un-nombre\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"L'unit\u00e9 est-elle un nombre?, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Les Grecs anciens refusaient de consid\u00e9rer l\u2019unit\u00e9 comme un nombre, comme on peut le lire dans La M\u00e9taphysique d\u2019Aristote\u00a0: Il est, d\u2019ailleurs, de toute \u00e9vidence que c\u2019est l\u2019unit\u00e9 qui exprime la mesure\u00a0;\u00a0[\u2026] le nombre est une pluralit\u00e9 mesur\u00e9e\u00a0[\u2026] Aussi, n\u2019a-t-on pas moins raison de dire que l\u2019unit\u00e9 n\u2019est pas un nombre. 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