{"id":2455,"date":"2025-06-27T10:56:09","date_gmt":"2025-06-27T10:56:09","guid":{"rendered":"https:\/\/lapalabrarazonada.es\/?p=2455"},"modified":"2025-06-27T12:33:58","modified_gmt":"2025-06-27T12:33:58","slug":"la-logica-formal","status":"publish","type":"post","link":"https:\/\/lapalabrarazonada.es\/ca\/la-logica-formal\/","title":{"rendered":"La l\u00f3gica formal"},"content":{"rendered":"<div class=\"yoast-breadcrumbs\"><span><span><a href=\"https:\/\/lapalabrarazonada.es\/ca\/\">Portada<\/a><\/span> \u00bb <span><a href=\"https:\/\/lapalabrarazonada.es\/ca\/category\/filosofia-1o-bach\/\">Filosof\u00eda (1\u00ba BACH)<\/a><\/span> \u00bb <span><a href=\"https:\/\/lapalabrarazonada.es\/ca\/category\/filosofia-1o-bach\/sa5\/\">SA5<\/a><\/span> \u00bb <span class=\"breadcrumb_last\" aria-current=\"page\">La l\u00f3gica formal<\/span><\/span><\/div>\n\n\n<h2 class=\"wp-block-heading\">\u00bfQu\u00e9 es la l\u00f3gica?<\/h2>\n\n\n\n<p>La l\u00f3gica es la disciplina filos\u00f3fica que estudia las reglas del pensamiento v\u00e1lido. Se ocupa de analizar c\u00f3mo razonamos, c\u00f3mo inferimos conclusiones a partir de premisas y c\u00f3mo podemos evitar errores o falacias en nuestras argumentaciones.<\/p>\n\n\n\n<p>En t\u00e9rminos generales, la l\u00f3gica busca responder a preguntas como: \u00bfqu\u00e9 hace que un argumento sea correcto?, \u00bfc\u00f3mo distinguimos un razonamiento v\u00e1lido de uno inv\u00e1lido?, \u00bfcu\u00e1les son las estructuras b\u00e1sicas del pensamiento riguroso?<\/p>\n\n\n\n<p>Aprender l\u00f3gica no significa memorizar f\u00f3rmulas, sino adquirir herramientas para pensar con claridad, identificar supuestos, evaluar ideas y participar en debates con argumentos s\u00f3lidos. En esta unidad nos centraremos en la l\u00f3gica formal, que analiza la forma (estructura) de los razonamientos, independientemente de su contenido.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u00bfQu\u00e9 es una proposici\u00f3n l\u00f3gica?<\/h2>\n\n\n\n<p>Una proposici\u00f3n l\u00f3gica es un enunciado que afirma algo que puede ser verdadero o falso. Por ejemplo, \u00abHoy llueve\u00bb o \u00ab2 + 2 = 4\u00bb son proposiciones, porque podemos comprobar si son ciertas o no. En cambio, expresiones como \u00ab\u00a1Llueve ya!\u00bb o \u00abOjal\u00e1 no llueva\u00bb no lo son, porque no afirman nada que podamos evaluar l\u00f3gicamente.<\/p>\n\n\n\n<p>La l\u00f3gica proposicional estudia la forma de los razonamientos partiendo de este tipo de afirmaciones. Su objetivo no es determinar si una proposici\u00f3n es verdadera en un caso concreto, sino analizar si el razonamiento en su conjunto es v\u00e1lido.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Conectivas l\u00f3gicas b\u00e1sicas<\/h2>\n\n\n\n<p>Las conectivas l\u00f3gicas permiten combinar proposiciones simples para formar proposiciones compuestas. Las principales son:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Negaci\u00f3n ( \u00ac )<\/strong>: niega una proposici\u00f3n. Si p es \u00abLlueve\u00bb, entonces \u00acp es \u00abNo llueve\u00bb.<\/li>\n\n\n\n<li><strong>Conjunci\u00f3n ( \u2227 )<\/strong>: une dos proposiciones y afirma que ambas son verdaderas. \u00abLlueve y hace fr\u00edo\u00bb solo es verdadera si llueve <strong>y<\/strong> hace fr\u00edo.<\/li>\n\n\n\n<li><strong>Disyunci\u00f3n ( \u2228 )<\/strong>: afirma que al menos una de las dos proposiciones es verdadera. \u00abLlueve o hace fr\u00edo\u00bb es verdadera si se cumple al menos una.<\/li>\n\n\n\n<li><strong>Condicional ( \u2192 )<\/strong>: expresa una relaci\u00f3n de implicaci\u00f3n. \u00abSi llueve, me mojo\u00bb (p \u2192 q) solo es falsa cuando llueve (p) y no me mojo (no q).<\/li>\n\n\n\n<li><strong>Bicondicional ( \u2194 )<\/strong>: indica equivalencia. \u00abMe mojo si y solo si llueve\u00bb implica que ambas proposiciones son verdaderas o ambas falsas.<\/li>\n<\/ul>\n\n\n\n<p>Estas conectivas permiten construir estructuras complejas y analizar c\u00f3mo se relacionan entre s\u00ed distintas afirmaciones.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Ejemplos de formalizaci\u00f3n:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Enunciado: \u00abSi estudio, aprobar\u00e9 el examen.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f3gica: p \u2192 q (donde p = \u00abEstudio\u00bb y q = \u00abApruebo el examen\u00bb)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Enunciado: \u00abJuan es fil\u00f3sofo y escribe libros.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f3gica: p \u2227 q (p = \u00abJuan es fil\u00f3sofo\u00bb, q = \u00abJuan escribe libros\u00bb)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Enunciado: \u00abNo es cierto que Mar\u00eda sea honesta.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f3gica: \u00acp (p = \u00abMar\u00eda es honesta\u00bb)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Enunciado: \u00abO llueve o hace sol.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f3gica: p \u2228 q (p = \u00abLlueve\u00bb, q = \u00abHace sol\u00bb)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Estos ejemplos muestran c\u00f3mo el lenguaje natural puede traducirse a proposiciones l\u00f3gicas, lo cual nos permite analizarlas de manera formal y rigurosa.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Las tablas de verdad<\/h2>\n\n\n\n<p>Las tablas de verdad son herramientas que permiten calcular el valor de verdad de proposiciones compuestas en todos los casos posibles. Se utiliza una tabla para cada combinaci\u00f3n de valores de verdad de las proposiciones simples que la componen.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/lapalabrarazonada.es\/wp-content\/uploads\/2025\/06\/tablas-de-verdad-1024x576.jpg\" alt=\"\" class=\"wp-image-2456\" srcset=\"https:\/\/lapalabrarazonada.es\/wp-content\/uploads\/2025\/06\/tablas-de-verdad-1024x576.jpg 1024w, https:\/\/lapalabrarazonada.es\/wp-content\/uploads\/2025\/06\/tablas-de-verdad-300x169.jpg 300w, https:\/\/lapalabrarazonada.es\/wp-content\/uploads\/2025\/06\/tablas-de-verdad-768x432.jpg 768w, https:\/\/lapalabrarazonada.es\/wp-content\/uploads\/2025\/06\/tablas-de-verdad.jpg 1366w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Leyes y equivalencias l\u00f3gicas<\/h2>\n\n\n\n<p>En l\u00f3gica formal existen ciertas leyes que siempre se cumplen y que permiten transformar proposiciones sin alterar su valor de verdad. Algunas de las m\u00e1s importantes son:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Doble negaci\u00f3n<\/strong>: \u00ac(\u00acp) \u2194 p<\/li>\n\n\n\n<li><strong>Conmutativa<\/strong>:\n<ul class=\"wp-block-list\">\n<li>p \u2227 q \u2194 q \u2227 p<\/li>\n\n\n\n<li>p \u2228 q \u2194 q \u2228 p<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Asociativa<\/strong>:\n<ul class=\"wp-block-list\">\n<li>(p \u2227 q) \u2227 r \u2194 p \u2227 (q \u2227 r)<\/li>\n\n\n\n<li>(p \u2228 q) \u2228 r \u2194 p \u2228 (q \u2228 r)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Distributiva<\/strong>:\n<ul class=\"wp-block-list\">\n<li>p \u2227 (q \u2228 r) \u2194 (p \u2227 q) \u2228 (p \u2227 r)<\/li>\n\n\n\n<li>p \u2228 (q \u2227 r) \u2194 (p \u2228 q) \u2227 (p \u2228 r)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Estas equivalencias se utilizan para simplificar expresiones, transformar argumentos y demostrar su validez de forma m\u00e1s clara.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Ejercicios y ejemplos comentados<\/h2>\n\n\n\n<p><strong>Ejercicio 1: Identifica las proposiciones<\/strong><br>Enunciado: \u00abSi Pedro estudia y duerme bien, aprobar\u00e1 el examen.\u00bb<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>p: Pedro estudia<\/li>\n\n\n\n<li>q: Pedro duerme bien<\/li>\n\n\n\n<li>r: Pedro aprueba el examen<\/li>\n\n\n\n<li>Forma l\u00f3gica: (p \u2227 q) \u2192 r<\/li>\n<\/ul>\n\n\n\n<p><strong>Ejercicio 2: Construye la tabla de verdad de la disyunci\u00f3n exclusiva<\/strong><br>Enunciado: \u00abO bien llueve, o bien hace sol, pero no ambas.\u00bb Forma l\u00f3gica: (p \u2228 q) \u2227 \u00ac(p \u2227 q)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>p<\/td><td>q<\/td><td>p \u2228 q<\/td><td>p \u2227 q<\/td><td>\u00ac(p \u2227 q)<\/td><td>(p \u2228 q) \u2227 \u00ac(p \u2227 q)<\/td><\/tr><tr><td>V<\/td><td>V<\/td><td>V<\/td><td>V<\/td><td>F<\/td><td>F<\/td><\/tr><tr><td>V<\/td><td>F<\/td><td>V<\/td><td>F<\/td><td>V<\/td><td>V<\/td><\/tr><tr><td>F<\/td><td>V<\/td><td>V<\/td><td>F<\/td><td>V<\/td><td>V<\/td><\/tr><tr><td>F<\/td><td>F<\/td><td>F<\/td><td>F<\/td><td>V<\/td><td>F<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Ejercicio 3: Aplica leyes l\u00f3gicas<\/strong><br>Simplifica la expresi\u00f3n: \u00ac(p \u2228 \u00acp)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aplicamos la ley del tercero excluido: p \u2228 \u00acp \u2194 V<\/li>\n\n\n\n<li>Entonces: \u00ac(V) \u2194 F<\/li>\n\n\n\n<li>Resultado final: F (contradicci\u00f3n)<\/li>\n<\/ul>\n\n\n\n<p>Estos ejercicios te permitir\u00e1n practicar la l\u00f3gica formal de forma progresiva y aplicar el pensamiento riguroso a situaciones concretas que luego te ser\u00e1n \u00fatiles en el an\u00e1lisis de discursos y razonamientos filos\u00f3ficos.<\/p>","protected":false},"excerpt":{"rendered":"<p>\u00bfQu\u00e9 es la l\u00f3gica? La l\u00f3gica es la disciplina filos\u00f3fica que estudia las reglas del pensamiento v\u00e1lido. Se ocupa de analizar c\u00f3mo razonamos, c\u00f3mo inferimos conclusiones a partir de premisas y c\u00f3mo podemos evitar errores o falacias en nuestras argumentaciones. En t\u00e9rminos generales, la l\u00f3gica busca responder a preguntas como: \u00bfqu\u00e9 hace que un argumento [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":2466,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"iawp_total_views":81,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[469],"tags":[468],"class_list":["post-2455","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sa5","tag-contenidos-sa5"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>La l\u00f3gica formal - La Palabra Razonada<\/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:\/\/lapalabrarazonada.es\/ca\/la-logica-formal\/\" \/>\n<meta property=\"og:locale\" content=\"ca_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"La l\u00f3gica formal - La Palabra Razonada\" \/>\n<meta property=\"og:description\" content=\"\u00bfQu\u00e9 es la l\u00f3gica? 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La l\u00f3gica es la disciplina filos\u00f3fica que estudia las reglas del pensamiento v\u00e1lido. Se ocupa de analizar c\u00f3mo razonamos, c\u00f3mo inferimos conclusiones a partir de premisas y c\u00f3mo podemos evitar errores o falacias en nuestras argumentaciones. 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