{"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\u00f2gica 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\/\">Filosofia (1r 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\u00f2gica formal<\/span><\/span><\/div>\n\n\n<h2 class=\"wp-block-heading\">Qu\u00e8 \u00e9s la l\u00f2gica?<\/h2>\n\n\n\n<p>La l\u00f2gica \u00e9s la disciplina filos\u00f2fica que estudia les regles del pensament v\u00e0lid. S&#039;ocupa d&#039;analitzar com raonem, com inferim conclusions a partir de premisses i com podem evitar errors o fal\u00b7l\u00e0cies a les nostres argumentacions.<\/p>\n\n\n\n<p>En termes generals, la l\u00f2gica cerca respondre preguntes com: qu\u00e8 fa que un argument sigui correcte?, com distingim un raonament v\u00e0lid d&#039;un inv\u00e0lid?, quines s\u00f3n les estructures b\u00e0siques del pensament rigor\u00f3s?<\/p>\n\n\n\n<p>Aprendre l\u00f2gica no vol dir memoritzar f\u00f3rmules, sin\u00f3 adquirir eines per pensar amb claredat, identificar sup\u00f2sits, avaluar idees i participar en debats amb arguments s\u00f2lids. En aquesta unitat ens centrarem en la l\u00f2gica formal, que analitza la forma (estructura) dels raonaments, independentment del contingut.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Qu\u00e8 \u00e9s una proposici\u00f3 l\u00f2gica?<\/h2>\n\n\n\n<p>Una proposici\u00f3 l\u00f2gica \u00e9s un enunciat que afirma una cosa que pot ser veritable o falsa. Per exemple, avui plou o 2 + 2 = 4 s\u00f3n proposicions, perqu\u00e8 podem comprovar si s\u00f3n certes o no. En canvi, expressions com \u00abPlou ja!\u00bb o \u00abTant de bo no plogui\u00bb no ho s\u00f3n, perqu\u00e8 no afirmen res que puguem avaluar l\u00f2gicament.<\/p>\n\n\n\n<p>La l\u00f2gica proposicional estudia la forma dels raonaments partint d\u201faquest tipus d\u201fafirmacions. El seu objectiu no \u00e9s determinar si una proposici\u00f3 \u00e9s veritable en un cas concret, sin\u00f3 analitzar si el raonament en conjunt \u00e9s v\u00e0lid.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Connectives l\u00f2giques b\u00e0siques<\/h2>\n\n\n\n<p>Les connectives l\u00f2giques permeten combinar proposicions simples per formar proposicions compostes. Les principals s\u00f3n:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Negaci\u00f3 ( \u00ac )<\/strong>: nega una proposici\u00f3. Si p \u00e9s \u00abPlou\u00bb, aleshores \u00acp \u00e9s \u00abNo plou\u00bb.<\/li>\n\n\n\n<li><strong>Conjunci\u00f3 ( \u2227 )<\/strong>: uneix dues proposicions i afirma que totes dues s\u00f3n verdaderes. \u00abPlou i fa fred\u00bb nom\u00e9s \u00e9s veritable si plou <strong>y<\/strong> fa fred.<\/li>\n\n\n\n<li><strong>Disjunci\u00f3 ( \u2228 )<\/strong>: afirma que almenys una de les dues proposicions \u00e9s veritable. \u00abPlou o fa fred\u00bb \u00e9s veritable si se&#039;n compleix almenys una.<\/li>\n\n\n\n<li><strong>Condicional ( \u2192 )<\/strong>: expressa una relaci\u00f3 d&#039;implicaci\u00f3. \u00abSi plou, em mullo\u00bb (p \u2192 q) nom\u00e9s \u00e9s falsa quan plou (p) i no em mullo (no q).<\/li>\n\n\n\n<li><strong>Bicondicional ( \u2194 )<\/strong>: indica equival\u00e8ncia. \u00abEm mullo si i nom\u00e9s si plou\u00bb implica que les dues proposicions s\u00f3n veritables o les dues falses.<\/li>\n<\/ul>\n\n\n\n<p>Aquestes connectives permeten construir estructures complexes i analitzar com es relacionen entre si diferents afirmacions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Exemples de formalitzaci\u00f3:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Enunciat: \u00abSi estudio, aprovar\u00e9 l&#039;examen.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f2gica: p \u2192 q (on p = \u00abEstudi\u00bb iq = \u00abAprovo l&#039;examen\u00bb)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Enunciat: \u00abJuan \u00e9s fil\u00f2sof i escriu llibres.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f2gica: p \u2227 q (p = \u00abJuan \u00e9s fil\u00f2sof\u00bb, q = \u00abJuan escriu llibres\u00bb)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Enunciat: \u00abNo \u00e9s cert que Maria sigui honesta.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f2gica: \u00acp (p = \u00abMaria \u00e9s honesta\u00bb)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Enunciat: \u00abO plou o fa sol.\u00bb\n<ul class=\"wp-block-list\">\n<li>Forma l\u00f2gica: p \u2228 q (p = \u00abPlou\u00bb, q = \u00abFa sol\u00bb)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Aquests exemples mostren com el llenguatge natural es pot traduir a proposicions l\u00f2giques, cosa que ens permet analitzar-les de manera formal i rigorosa.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Les taules de veritat<\/h2>\n\n\n\n<p>Les taules de veritat s\u00f3n eines que permeten calcular el valor de veritat de proposicions compostes en tots els casos possibles. Es fa servir una taula per a cada combinaci\u00f3 de valors de veritat de les proposicions 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\">Lleis i equival\u00e8ncies l\u00f2giques<\/h2>\n\n\n\n<p>En l\u00f2gica formal hi ha certes lleis que sempre es compleixen i que permeten transformar proposicions sense alterar-ne el valor de veritat. Algunes de les m\u00e9s importants s\u00f3n:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Doble negaci\u00f3<\/strong>: \u00ac(\u00acp) \u2194 p<\/li>\n\n\n\n<li><strong>Commutativa<\/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>Associativa<\/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>Aquestes equival\u00e8ncies es fan servir per simplificar expressions, transformar arguments i demostrar-ne la validesa de forma m\u00e9s clara.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Exercicis i exemples comentats<\/h2>\n\n\n\n<p><strong>Exercici 1: Identifica les proposicions<\/strong><br>Enunciat: Si Pedro estudia i dorm b\u00e9, aprovar\u00e0 l&#039;examen.\u00ab<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>p: Pedro estudia<\/li>\n\n\n\n<li>q: Pere dorm b\u00e9<\/li>\n\n\n\n<li>r: Pedro aprova l&#039;examen<\/li>\n\n\n\n<li>Forma l\u00f2gica: (p \u2227 q) \u2192 r<\/li>\n<\/ul>\n\n\n\n<p><strong>Exercici 2: Construeix la taula de veritat de la disjunci\u00f3 exclusiva<\/strong><br>Enunciat: \u00abO b\u00e9 plou, o b\u00e9 fa sol, per\u00f2 no totes dues.\u00bb Forma l\u00f2gica: (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>Exercici 3: Aplica lleis l\u00f2giques<\/strong><br>Simplifica l&#039;expressi\u00f3: \u00ac(p \u2228 \u00acp)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Apliquem la llei del tercer excl\u00f2s: p \u2228 \u00acp \u2194 V<\/li>\n\n\n\n<li>Aleshores: \u00ac(V) \u2194 F<\/li>\n\n\n\n<li>Resultat final: F (contradicci\u00f3)<\/li>\n<\/ul>\n\n\n\n<p>Aquests exercicis us permetran practicar la l\u00f2gica formal de forma progressiva i aplicar el pensament rigor\u00f3s a situacions concretes que despr\u00e9s us seran \u00fatils en l&#039;an\u00e0lisi de discursos i raonaments filos\u00f2fics.<\/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":88,"_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? 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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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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