{"id":986,"date":"2011-09-15T12:09:00","date_gmt":"2011-09-15T15:09:00","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/2011\/09\/um-paradoxo-linear\/"},"modified":"2011-09-15T12:09:00","modified_gmt":"2011-09-15T15:09:00","slug":"um-paradoxo-linear","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2011\/09\/um-paradoxo-linear\/","title":{"rendered":"&gt;Um Paradoxo Linear"},"content":{"rendered":"<p>&gt;<\/p>\n<div style=\"text-align: justify\">Quase sempre, os paradoxos s\u00e3o paradoxais exatamente por apresentar uma certa circularidade auto-referencial (<i>cf.<\/i> o famoso Dilema de Tostines). O <i>quase <\/i>\u00e9 porque o conjunto das senten\u00e7as abaixo forma o que seu descobridor, Stephen Yablo, chama de paradoxo linear (e n\u00e3o apenas graficamente):<\/p>\n<\/div>\n<div>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<br \/>Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.<\/p>\n<p>&#8230;<i>ad infinitum<\/i>&#8230;<\/div>\n<div style=\"text-align: justify\">Apresentado por Yablo em 1993, esse arranjo consegue ser paradoxal sem ser circular, isto \u00e9, sem conter auto-refer\u00eancia. As senten\u00e7as n\u00e3o podem ser todas falsas, pois isso tornaria verdadeira a primeira delas, causando uma contradi\u00e7\u00e3o. Por outro lado, nenhuma delas pode ser verdadeira, pois uma \u00fanica afirmativa verdadeira teria que ser seguida por uma infinidade de senten\u00e7as falsas, e a falsidade de qualquer uma delas implica a verdade daquela que seguem.<\/p>\n<p>Em outras palavras, suponha que em algum lugar dessa sequ\u00eancia infinita de \u201cTodas as senten\u00e7as abaixo dessa s\u00e3o falsas.\u201d haja uma en\u00e9sima senten\u00e7a que seja verdadeira. Disso decorrem duas coisas:<\/p>\n<ul>\n<li><b>(a)<\/b> a en\u00e9sima-primeira senten\u00e7a \u00e9 falsa e&nbsp;<\/li>\n<li><b>(b)<\/b> qualquer senten\u00e7a que esteja al\u00e9m da en\u00e9sima-primeira \u00e9 falsa tamb\u00e9m.&nbsp;<\/li>\n<\/ul>\n<p>S\u00f3 que, segundo <b>(b)<\/b>, o que a en\u00e9sima-primeira senten\u00e7a diz \u2014&nbsp; que todas as senten\u00e7as que est\u00e3o abaixo dela s\u00e3o falsas \u2014 \u00e9 verdadeiro e, portanto, ao contr\u00e1rio do que se conclui por <b>(a)<\/b>, a en\u00e9sima-primeira senten\u00e7a \u00e9 verdadeira. Portanto, qualquer senten\u00e7a dada na sequ\u00eancia \u00e9 falsa. Mas as senten\u00e7as subsequentes a qualquer senten\u00e7a dada s\u00e3o todas falsas, o que valida a verdade da senten\u00e7a dada como verdadeira. <\/div>\n","protected":false},"excerpt":{"rendered":"<p>&gt; Quase sempre, os paradoxos s\u00e3o paradoxais exatamente por apresentar uma certa circularidade auto-referencial (cf. o famoso Dilema de Tostines). O quase \u00e9 porque o conjunto das senten\u00e7as abaixo forma o que seu descobridor, Stephen Yablo, chama de paradoxo linear (e n\u00e3o apenas graficamente): Todas as senten\u00e7as abaixo dessa s\u00e3o falsas.Todas as senten\u00e7as abaixo dessa [&hellip;]<\/p>\n","protected":false},"author":486,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"material-hide-sections":[],"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[198,254],"tags":[],"class_list":["post-986","post","type-post","status-publish","format-standard","hentry","category-logica","category-paradoxos"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>&gt;Um Paradoxo Linear - 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