{"id":9038,"date":"2024-05-15T14:28:02","date_gmt":"2024-05-15T17:28:02","guid":{"rendered":"https:\/\/iiep.economicas.uba.ar\/?p=9038"},"modified":"2025-10-02T12:21:30","modified_gmt":"2025-10-02T15:21:30","slug":"notacion-demostracion-y-heuristica-un-enfoque-desde-la-practica-matematica","status":"publish","type":"post","link":"https:\/\/economicas.uba.ar\/iiep\/notacion-demostracion-y-heuristica-un-enfoque-desde-la-practica-matematica\/","title":{"rendered":"Notaci\u00f3n, demostraci\u00f3n y heur\u00edstica. Un enfoque desde la pr\u00e1ctica matem\u00e1tica."},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"9038\" class=\"elementor elementor-9038\" data-elementor-post-type=\"post\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7545bbc e-flex e-con-boxed e-con e-parent\" data-id=\"7545bbc\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b34acbe elementor-widget elementor-widget-text-editor\" data-id=\"b34acbe\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-12 wd-alignment-left\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div id=\"wd-65fb3ddda7398\" class=\"title-wrapper wd-wpb set-mb-s reset-last-child wd-rs-65fb3ddda7398 wd-title-color-primary wd-title-style-default wd-width-100 text-left wd-underline-colored\"><div class=\"title-subtitle subtitle-color-primary font-default subtitle-style-default wd-font-weight- wd-fontsize-xs\"><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-12 wd-alignment-left\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div id=\"wd-6644ef0d7d021\" class=\"title-wrapper wd-wpb set-mb-s reset-last-child wd-rs-6644ef0d7d021 wd-title-color-primary wd-title-style-default wd-width-100 text-left wd-underline-colored\"><div class=\"title-subtitle subtitle-color-primary font-default subtitle-style-default wd-font-weight- wd-fontsize-xs\">PIP<\/div><div class=\"liner-continer\"><h4 class=\"woodmart-title-container title wd-font-weight- wd-fontsize-l\">Notaci\u00f3n, demostraci\u00f3n y heur\u00edstica. Un enfoque desde la pr\u00e1ctica matem\u00e1tica<\/h4><\/div><div class=\"title-after_title set-cont-mb-s reset-last-child wd-fontsize-xs\">DIRECTOR: Legris, Javier<br \/>CO TITULAR: Visolkolskis, A\u00edda Sandra<\/div><\/div><\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-12 wd-alignment-left\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div id=\"wd-64de67f78cb80\" class=\"title-wrapper wd-wpb set-mb-s reset-last-child wd-rs-64de67f78cb80 wd-title-color-default wd-title-style-default wd-width-90 text-left wd-off-anim wpb_animate_when_almost_visible wpb_wd-zoom-in wd-zoom-in wd-anim-name_wd-zoom-in vc_custom_1692297218849 wd-underline-colored wpb_start_animation animated\"><div class=\"liner-continer\"><h2 class=\"woodmart-title-container title wd-font-weight-300 wd-fontsize-m\"><strong><u>Sobre el proyecto<\/u><\/strong><\/h2><\/div><\/div><div class=\"wpb_text_column wpb_content_element vc_custom_1715793620872\"><div class=\"wpb_wrapper\"><p>El objetivo fundamental del proyecto consiste en analizar las interconexiones entre notaci\u00f3n, demostraci\u00f3n y heur\u00edstica en el conocimiento matem\u00e1tico. Este an\u00e1lisis adopta la perspectiva de la filosof\u00eda de la pr\u00e1ctica matem\u00e1tica, tomando en consideraci\u00f3n casos particulares. El proyecto tiene como gu\u00eda las siguientes hip\u00f3tesis: Las notaciones, en un sentido general del t\u00e9rmino (que incluye tanto diagramas, figuras geom\u00e9trica, ecuaciones algebraicas, grafos, etc.), son determinantes tanto en los procesos de descubrimiento como de demostraci\u00f3n matem\u00e1ticos. (2) El an\u00e1lisis filos\u00f3fico de las demostraciones no se limita a su estructura l\u00f3gica, sino que incluye los procedimientos heur\u00edsticos asociados a su descubrimiento y construcci\u00f3n (hip\u00f3tesis auxiliares, etc.). Las ideas de Charles S. Peirce se cuenta entre los pilares para (y a la vez objeto de estudio en) el desarrollo de la investigaci\u00f3n. De este modo, los siguientes conceptos son herramientas clave en las diferentes etapas del proyecto: razonamiento diagram\u00e1tico, conocimiento simb\u00f3lico, visualizaci\u00f3n, acci\u00f3n, creatividad, demostraci\u00f3n teorem\u00e1tica, abducci\u00f3n, razonamiento teorem\u00e1tico, razonamiento anal\u00f3gico y demostraci\u00f3n formal. Entre los casos a analizar se encuentran los siguientes: el valor explicativo de las construcciones geom\u00e9tricas en Hippocrates de Quios, el teorema de Desargues en geometr\u00eda proyectiva y el intento de Carnap de fundamentar la geometr\u00eda mediante un sistema formal. La distinci\u00f3n, debida a Peirce, entre razonamiento corolarial y teorem\u00e1tico, y la l\u00f3gica de los Gr\u00e1ficos existenciales, tambi\u00e9n de Peirce, son una importante herramienta de an\u00e1lisis para tratar los problemas que aparezcan durante el desarrollo del proyecto. Adicionalmente, el proyecto incluye un estudio del papel desempa\u00f1ado por las notaciones en la aplicaci\u00f3n de la matem\u00e1tica en las ciencias emp\u00edricas, especialmente su papel heur\u00edstico para la formulaci\u00f3n de hip\u00f3tesis. La oposici\u00f3n entre diagramas y lenguaje formal ser\u00e1 discutida. Cabe subrayar el esp\u00edritu interdisciplinario del proyecto, cuyos resultados pueden ser objeto de discusi\u00f3n en la Historia de la Ciencia, la Did\u00e1ctica de la matem\u00e1tica y las ciencias cognitivas. Por \u00faltimo, el proyecto ser\u00e1 el marco para defender, en general, una concepci\u00f3n semi\u00f3tica del conocimiento matem\u00e1tico.<\/p><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-795d9c06 e-flex e-con-boxed e-con e-parent\" data-id=\"795d9c06\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1a14635e elementor-widget elementor-widget-heading\" data-id=\"1a14635e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Integrantes<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1368754b elementor-widget elementor-widget-ucaddon_post_blocks\" data-id=\"1368754b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"ucaddon_post_blocks.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\n<!-- start Post Blocks -->\n\t\t<link id='font-awesome-css' href='https:\/\/economicas.uba.ar\/iiep\/wp-content\/plugins\/unlimited-elements-for-elementor\/assets_libraries\/font-awesome6\/fontawesome-all.min.css' type='text\/css' rel='stylesheet' >\n\t\t<link id='font-awesome-4-shim-css' href='https:\/\/economicas.uba.ar\/iiep\/wp-content\/plugins\/unlimited-elements-for-elementor\/assets_libraries\/font-awesome6\/fontawesome-v4-shims.min.css' type='text\/css' rel='stylesheet' >\n\n<style>\/* widget: Post Blocks *\/\n\n#uc_post_blocks_elementor_1368754b {\n    display:grid;\n}\n#uc_post_blocks_elementor_1368754b .ue_post_blocks_box\n{\n  overflow:hidden;\n}\n\n#uc_post_blocks_elementor_1368754b .ue_post_blocks_image\n{\n  overflow:hidden;\n}\n#uc_post_blocks_elementor_1368754b .ue_post_blocks_image img\n{\n  object-fit: cover;\n  object-position:center center;\n  width:100%;\n  display:block;\n}\n#uc_post_blocks_elementor_1368754b .ue_post_blocks_link a\n{\n  display:inline-block;\n  text-decoration:none;\n  text-align:center;\n}\n\n #uc_post_blocks_elementor_1368754b .ue_post_blocks_box img\n{\n  transition:0.5s;\n}\n #uc_post_blocks_elementor_1368754b .ue_post_blocks_box:hover img\n{\n  transform:scale(1.1,1.1);\n}\n\n\n\n\n#uc_post_blocks_elementor_1368754b .ue-grid-item-meta-data\n{\n  display:inlin-flex;\n  flex-wrap: wrap;\n}\n\n.ue-grid-item-meta-data\n{\n  font-size:12px;\n}\n\n#uc_post_blocks_elementor_1368754b .ue-grid-item-meta-data-icon\n{\n  line-height:1em;\n}\n\n#uc_post_blocks_elementor_1368754b .ue-grid-item-meta-data-icon svg\n{\n  width:1em;\n  height:1em;\n}\n\n\n.ue-grid-item-category a\n{\n  display:inline-block;\n  font-size:10px;\n  text-transform:uppercase;\n}\n\n<\/style>\n\n<div id=\"uc_post_blocks_elementor_1368754b\" class=\"ue_post_blocks uc-items-wrapper\" >\n    <div class=\"ue_post_blocks_box\">\n    <div class=\"ue_post_blocks_image\">\n    <a href=\"https:\/\/economicas.uba.ar\/iiep\/legris-javier\/\" style=\"display:block;\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/economicas.uba.ar\/iiep\/wp-content\/uploads\/JavierLegris.png\"  src=\"https:\/\/economicas.uba.ar\/iiep\/wp-content\/uploads\/JavierLegris.png\" alt=\"JavierLegris\" width=\"500\" height=\"500\"><\/a>\n  <\/div>\n    <div class=\"ue_post_blocks_content\">\n      \n     \n         \n    <div class=\"ue_post_blocks_title\"><a href=\"https:\/\/economicas.uba.ar\/iiep\/legris-javier\/\">Legris, Javier<\/a><\/div>    \n        \n    \n          <\/div>\n<\/div>\n\n<\/div>\n<!-- end Post Blocks -->\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1de9537 e-flex e-con-boxed e-con e-parent\" data-id=\"1de9537\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3adc180 elementor-widget elementor-widget-heading\" data-id=\"3adc180\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Integrantes externos<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4913d0d elementor-widget elementor-widget-text-editor\" data-id=\"4913d0d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Gavriloff, Ivan; Giovannini, Eduardo; Narv\u00e1ez, Mario; Vali\u00f1o, Valeria; Visokolskis, A\u00edda Sandra<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>PIP Notaci\u00f3n, demostraci\u00f3n y heur\u00edstica. Un enfoque desde la pr\u00e1ctica matem\u00e1tica DIRECTOR: Legris, JavierCO TITULAR: Visolkolskis, A\u00edda Sandra Sobre el proyecto El objetivo fundamental del proyecto consiste en analizar las<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[34],"tags":[],"class_list":["post-9038","post","type-post","status-publish","format-standard","hentry","category-conicet-pip"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Notaci\u00f3n, demostraci\u00f3n y heur\u00edstica. Un enfoque desde la pr\u00e1ctica matem\u00e1tica. - IIEP UBA-CONICET<\/title>\n<meta name=\"description\" content=\"Proyectos IIEP UBA-CONICET, Aplicaci\u00f3n de modelos fuzzy y algoritmos en sistemas inteligentes para estudiar el Bienestar Econ\u00f3mico. 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