{"id":5538,"date":"2023-04-09T12:54:30","date_gmt":"2023-04-09T04:54:30","guid":{"rendered":"http:\/\/tsinghualogic.net\/JRC\/?page_id=5538"},"modified":"2023-06-28T22:37:33","modified_gmt":"2023-06-28T14:37:33","slug":"topological-philosophy-of-science","status":"publish","type":"page","link":"https:\/\/tsinghualogic.net\/JRC\/topological-philosophy-of-science\/","title":{"rendered":"<strong>Topological Philosophy of Science<\/strong>"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"5538\" class=\"elementor elementor-5538\" data-elementor-settings=\"[]\">\n\t\t\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3171522 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3171522\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-81f8093\" data-id=\"81f8093\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bb80708 elementor-widget elementor-widget-heading\" data-id=\"bb80708\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.5.6 - 28-02-2022 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h5 class=\"elementor-heading-title elementor-size-default\">Course Description<\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2df87c58 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2df87c58\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-22543ad4\" data-id=\"22543ad4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6c534c65 elementor-widget elementor-widget-text-editor\" data-id=\"6c534c65\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.5.6 - 28-02-2022 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#818a91;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#818a91;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<!-- wp:heading {\"level\":4} --><!-- \/wp:heading --><!-- wp:paragraph -->\n<div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>Probability and inductive inference seem so closely tied that it is almost impossible to discuss one without the other. This course develops the provocative, alternative view that the underlying structure of the problem of induction and the true path to its epistemic justification are topological rather than probabilistic. Whereas the usual motive for probabilism since Hume is coherence (conclusions \u201cfit together\u201d in an extended logical sense), topology is more intimately connected with reliability and learnability, an alternative foundational perspective in epistemology. The idea is that empirical verifiability, refutability and convergence to the truth are all ultimately topological concepts. That is directly the case when inquiry is literally driven by propositional information about the world under study. Surprisingly, perhaps, it is also true within a broadly frequentist statistical framework for inductive inference.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<ul>\n<li>Lecturer: <a href=\"https:\/\/www.cmu.edu\/dietrich\/philosophy\/people\/faculty\/kevin-kelly.html\"><u>Kevin Kelly<\/u><\/a>\u00a0(Carnegie\u00a0Mellon\u00a0University)<\/li>\n<li>TA: Dong Huanfang (\u8463\u7115\u9632)\u00a0<\/li>\n<li>Time: 9:50-12:15, 26 June \u2013 30 June<\/li>\n<li>Venue: \u4e00\u6559201<\/li>\n<\/ul>\n<!-- \/wp:paragraph -->\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0948602 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0948602\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-00f678e\" data-id=\"00f678e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e5b5f48 elementor-widget elementor-widget-heading\" data-id=\"e5b5f48\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">Schedule<\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c0de12b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c0de12b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-218f751\" data-id=\"218f751\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-73877aa elementor-tabs-view-horizontal elementor-widget elementor-widget-tabs\" data-id=\"73877aa\" data-element_type=\"widget\" data-widget_type=\"tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.5.6 - 28-02-2022 *\/\n.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tabs-wrapper{width:25%;-ms-flex-negative:0;flex-shrink:0}.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tab-desktop-title.elementor-active{border-right-style:none}.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tab-desktop-title.elementor-active:after,.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tab-desktop-title.elementor-active:before{height:999em;width:0;right:0;border-right-style:solid}.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tab-desktop-title.elementor-active:before{top:0;-webkit-transform:translateY(-100%);-ms-transform:translateY(-100%);transform:translateY(-100%)}.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tab-desktop-title.elementor-active:after{top:100%}.elementor-widget-tabs.elementor-tabs-view-horizontal .elementor-tab-desktop-title{display:table-cell}.elementor-widget-tabs.elementor-tabs-view-horizontal .elementor-tab-desktop-title.elementor-active{border-bottom-style:none}.elementor-widget-tabs.elementor-tabs-view-horizontal .elementor-tab-desktop-title.elementor-active:after,.elementor-widget-tabs.elementor-tabs-view-horizontal .elementor-tab-desktop-title.elementor-active:before{bottom:0;height:0;width:999em;border-bottom-style:solid}.elementor-widget-tabs.elementor-tabs-view-horizontal .elementor-tab-desktop-title.elementor-active:before{right:100%}.elementor-widget-tabs.elementor-tabs-view-horizontal .elementor-tab-desktop-title.elementor-active:after{left:100%}.elementor-widget-tabs .elementor-tab-content,.elementor-widget-tabs .elementor-tab-title,.elementor-widget-tabs .elementor-tab-title:after,.elementor-widget-tabs .elementor-tab-title:before,.elementor-widget-tabs .elementor-tabs-content-wrapper{border:1px #d4d4d4}.elementor-widget-tabs .elementor-tabs{text-align:left}.elementor-widget-tabs .elementor-tabs-wrapper{overflow:hidden}.elementor-widget-tabs .elementor-tab-title{cursor:pointer;outline:var(--focus-outline,none)}.elementor-widget-tabs .elementor-tab-desktop-title{position:relative;padding:20px 25px;font-weight:700;line-height:1;border:solid transparent}.elementor-widget-tabs .elementor-tab-desktop-title.elementor-active{border-color:#d4d4d4}.elementor-widget-tabs .elementor-tab-desktop-title.elementor-active:after,.elementor-widget-tabs .elementor-tab-desktop-title.elementor-active:before{display:block;content:\"\";position:absolute}.elementor-widget-tabs .elementor-tab-mobile-title{padding:10px;cursor:pointer}.elementor-widget-tabs .elementor-tab-content{padding:20px;display:none}@media (max-width:767px){.elementor-tabs .elementor-tab-content,.elementor-tabs .elementor-tab-title{border-style:solid solid none}.elementor-tabs .elementor-tabs-wrapper{display:none}.elementor-tabs .elementor-tabs-content-wrapper{border-bottom-style:solid}.elementor-tabs .elementor-tab-content{padding:10px}}@media (min-width:768px){.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tabs{display:-webkit-box;display:-ms-flexbox;display:flex}.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tabs-wrapper{-webkit-box-orient:vertical;-webkit-box-direction:normal;-ms-flex-direction:column;flex-direction:column}.elementor-widget-tabs.elementor-tabs-view-vertical .elementor-tabs-content-wrapper{-webkit-box-flex:1;-ms-flex-positive:1;flex-grow:1;border-style:solid solid solid none}.elementor-widget-tabs.elementor-tabs-view-horizontal .elementor-tab-content{border-style:none solid solid}.elementor-widget-tabs.elementor-tabs-alignment-center .elementor-tabs-wrapper,.elementor-widget-tabs.elementor-tabs-alignment-end .elementor-tabs-wrapper,.elementor-widget-tabs.elementor-tabs-alignment-stretch .elementor-tabs-wrapper{display:-webkit-box;display:-ms-flexbox;display:flex}.elementor-widget-tabs.elementor-tabs-alignment-center .elementor-tabs-wrapper{-webkit-box-pack:center;-ms-flex-pack:center;justify-content:center}.elementor-widget-tabs.elementor-tabs-alignment-end .elementor-tabs-wrapper{-webkit-box-pack:end;-ms-flex-pack:end;justify-content:flex-end}.elementor-widget-tabs.elementor-tabs-alignment-stretch.elementor-tabs-view-horizontal .elementor-tab-title{width:100%}.elementor-widget-tabs.elementor-tabs-alignment-stretch.elementor-tabs-view-vertical .elementor-tab-title{height:100%}.elementor-tabs .elementor-tab-mobile-title{display:none}}<\/style>\t\t<div class=\"elementor-tabs\">\n\t\t\t<div class=\"elementor-tabs-wrapper\" role=\"tablist\" >\n\t\t\t\t\t\t\t\t\t<div id=\"elementor-tab-title-1211\" class=\"elementor-tab-title elementor-tab-desktop-title\" aria-selected=\"true\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"elementor-tab-content-1211\" aria-expanded=\"false\">Day 1: Introduction<\/div>\n\t\t\t\t\t\t\t\t\t<div id=\"elementor-tab-title-1212\" class=\"elementor-tab-title elementor-tab-desktop-title\" aria-selected=\"false\" data-tab=\"2\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1212\" aria-expanded=\"false\">Day 2: Empirical Topology<\/div>\n\t\t\t\t\t\t\t\t\t<div id=\"elementor-tab-title-1213\" class=\"elementor-tab-title elementor-tab-desktop-title\" aria-selected=\"false\" data-tab=\"3\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1213\" aria-expanded=\"false\">Day 3: Learning<\/div>\n\t\t\t\t\t\t\t\t\t<div id=\"elementor-tab-title-1214\" class=\"elementor-tab-title elementor-tab-desktop-title\" aria-selected=\"false\" data-tab=\"4\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1214\" aria-expanded=\"false\">Day 4: Realism and Anti-realism<\/div>\n\t\t\t\t\t\t\t\t\t<div id=\"elementor-tab-title-1215\" class=\"elementor-tab-title elementor-tab-desktop-title\" aria-selected=\"false\" data-tab=\"5\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1215\" aria-expanded=\"false\">Day 5: Chance<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t<div class=\"elementor-tabs-content-wrapper\" role=\"tablist\" aria-orientation=\"vertical\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-tab-title elementor-tab-mobile-title\" aria-selected=\"true\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"elementor-tab-content-1211\" aria-expanded=\"false\">Day 1: Introduction<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1211\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"tabpanel\" aria-labelledby=\"elementor-tab-title-1211\" tabindex=\"0\" hidden=\"false\"><div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>1. Some Philosophy of Science<\/p>\n<p style=\"padding-left: 40px;\">1.1. Coherentism and Reliabilism<\/p>\n<p style=\"padding-left: 40px;\">1.2. Contextualism<\/p>\n<p style=\"padding-left: 80px;\">i. Information<\/p>\n<p style=\"padding-left: 80px;\">ii. Question<\/p>\n<p style=\"padding-left: 80px;\">iii. Similarity<\/p>\n<p style=\"padding-left: 40px;\">1.3. Optimalism<\/p>\n<p style=\"padding-left: 40px;\">1.4. Verifiability and Hume&#8217;s Problem of Induction<\/p>\n<p>2. Why Topology?<\/p>\n<p>3. Worlds and Propositions<\/p>\n<p style=\"padding-left: 40px;\">3.1. Distribution and DeMorgan Laws b. Duality<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page\" title=\"Page 2\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>4. Propositional Structures<\/p>\n<p style=\"padding-left: 40px;\">4.1. Homeomorphism<\/p>\n<p style=\"padding-left: 40px;\">4.2. Types of Propositional Structures<\/p>\n<p style=\"padding-left: 40px;\">4.3. Operations on Propositional Structures<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-tab-title elementor-tab-mobile-title\" aria-selected=\"false\" data-tab=\"2\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1212\" aria-expanded=\"false\">Day 2: Empirical Topology<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1212\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"tabpanel\" aria-labelledby=\"elementor-tab-title-1212\" tabindex=\"0\" hidden=\"hidden\"><div class=\"page\" title=\"Page 2\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<ol>\n<li>\n<p>Sequential Outcomes<\/p>\n<\/li>\n<li>\n<p>Empirical Context<\/p>\n<\/li>\n<li>\n<p>Topological Operators<\/p>\n<ol>\n<li>\n<p>Interior = \u201cwill be verified\u201d<\/p>\n<\/li>\n<li>\n<p>Exterior = \u201cwill be refuted\u201d<\/p>\n<\/li>\n<li>\n<p>Closure = \u201cwill never be refuted\u201d<\/p>\n<\/li>\n<li>\n<p>Boundary = \u201cwill never be decided\u201d<\/p>\n<\/li>\n<li>\n<p>Frontier = \u201cfalse but will never be refuted\u201d<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<p>Hume\u2019s Problem of Induction<\/p>\n<\/li>\n<li>\n<p>Popper&#8217;s Problem of Metaphysics<\/p>\n<\/li>\n<li>\n<p>Topological Complexity<\/p>\n<ol>\n<li>\n<p>Open = \u201cverifiable\u201d<\/p>\n<\/li>\n<li>\n<p>Closed = \u201crefutable\u201d<\/p>\n<\/li>\n<li>\n<p>Clopen = \u201cdecidable\u201d<\/p>\n<\/li>\n<li>\n<p>Locally Closed = \u201cis a model\u201d<\/p>\n<\/li>\n<li>\n<p>Sigma-constructible = \u201cis a paradigm\u201d<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<p>More Examples<\/p>\n<ol>\n<li>\n<p>Asynchronous Outcomes<\/p>\n<\/li>\n<li>\n<p>The Sleeping Scientist<\/p>\n<\/li>\n<li>\n<p>Continuous Variables<\/p>\n<\/li>\n<li>\n<p>Laws<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-tab-title elementor-tab-mobile-title\" aria-selected=\"false\" data-tab=\"3\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1213\" aria-expanded=\"false\">Day 3: Learning<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1213\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"tabpanel\" aria-labelledby=\"elementor-tab-title-1213\" tabindex=\"0\" hidden=\"hidden\"><div class=\"page\" title=\"Page 2\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<ol>\n<li>\n<p>Methods<\/p>\n<\/li>\n<li>\n<p>Concepts of Learning<\/p>\n<\/li>\n<li>\n<p>Topological Characterizations of Learnability<\/p>\n<\/li>\n<li>\n<p>Examples<\/p>\n<\/li>\n<li>\n<p>The Negative Induction from the History of Science<\/p>\n<\/li>\n<li>\n<p>Ockham&#8217;s Razor<\/p>\n<\/li>\n<\/ol>\n<p style=\"padding-left: 40px;\">6.1. Empirical Simplicity<\/p>\n<p style=\"padding-left: 40px;\">6.2. Ockham Methods<\/p>\n<p style=\"padding-left: 40px;\">6.3. Justification<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-tab-title elementor-tab-mobile-title\" aria-selected=\"false\" data-tab=\"4\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1214\" aria-expanded=\"false\">Day 4: Realism and Anti-realism<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1214\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"tabpanel\" aria-labelledby=\"elementor-tab-title-1214\" tabindex=\"0\" hidden=\"hidden\"><div class=\"page\" title=\"Page 2\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<ol>\n<li>\n<p>Scientific Contexts<\/p>\n<\/li>\n<li>\n<p>The Golden Triangle<\/p>\n<\/li>\n<li>\n<p>Metaphysical Similarity<\/p>\n<\/li>\n<li>\n<p>Metric Topology and Metrizability<\/p>\n<\/li>\n<li>\n<p>Realism, Empiricism, and Instrumentalism<\/p>\n<\/li>\n<li>\n<p>Underdetermination<\/p>\n<\/li>\n<li>\n<p>Topological Separation Axioms<\/p>\n<\/li>\n<li>\n<p>Theoretical Identifications<\/p>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"page\" title=\"Page 3\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p style=\"padding-left: 80px;\">8.1. Morning and Evening Stars<\/p>\n<p style=\"padding-left: 80px;\">8.2. Light and Electromagnetic Waves<\/p>\n<p style=\"padding-left: 40px;\">9. No-Miracles Arguments<\/p>\n<p style=\"padding-left: 40px;\">10. Ideals and Sigma-ideals<br \/>11. Nowhere Density and Meagerness<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-tab-title elementor-tab-mobile-title\" aria-selected=\"false\" data-tab=\"5\" role=\"tab\" tabindex=\"-1\" aria-controls=\"elementor-tab-content-1215\" aria-expanded=\"false\">Day 5: Chance<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1215\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"tabpanel\" aria-labelledby=\"elementor-tab-title-1215\" tabindex=\"0\" hidden=\"hidden\"><div class=\"page\" title=\"Page 3\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<ol>\n<li>\n<p>Anything Goes<\/p>\n<\/li>\n<li>\n<p>Statistical Coherentism and Reliabilism<\/p>\n<\/li>\n<li>\n<p>Stochastic Contexts<\/p>\n<\/li>\n<\/ol>\n<p style=\"padding-left: 80px;\">3.1. Sigma Fields b. Parameters c. Chances<\/p>\n<p style=\"padding-left: 40px;\">4. Statistical Learning<\/p>\n<p style=\"padding-left: 80px;\">4.1. In Chance<\/p>\n<p style=\"padding-left: 80px;\">4.2. Almost Sure<\/p>\n<p style=\"padding-left: 40px;\">5. The Topology of Statistical Verifiability<\/p>\n<p style=\"padding-left: 40px;\">6. Virtual Information States<\/p>\n<p style=\"padding-left: 40px;\">7. Reduction of Statistical Learnability to Propositional Learnability<\/p>\n<p style=\"padding-left: 40px;\">8. Ockham\u2019s Statistical Razor<\/p>\n<p style=\"padding-left: 40px;\">9. Examples<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-aea05d4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"aea05d4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4fa4c5e\" data-id=\"4fa4c5e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0e0b42c elementor-widget elementor-widget-heading\" data-id=\"0e0b42c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">Lecture Slides<\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d2736ce elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d2736ce\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7465468\" data-id=\"7465468\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0d5f252 elementor-widget elementor-widget-text-editor\" data-id=\"0d5f252\" data-element_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<p>Please find the slides <a href=\"http:\/\/120.48.137.70:8666\/chapter01\">here<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6e3827c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6e3827c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9cb914e\" data-id=\"9cb914e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-534ee66 elementor-widget elementor-widget-heading\" data-id=\"534ee66\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">Recordings<\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-66e332f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"66e332f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-96b3e41\" data-id=\"96b3e41\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-447b1b8 elementor-widget elementor-widget-text-editor\" data-id=\"447b1b8\" data-element_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<p>Please find the recordings <a href=\"https:\/\/cloud.tsinghua.edu.cn\/d\/88bad65ee25a446ea2b8\/\">here<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Course Description Probability and inductive inference  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/5538"}],"collection":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/comments?post=5538"}],"version-history":[{"count":19,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/5538\/revisions"}],"predecessor-version":[{"id":6256,"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/pages\/5538\/revisions\/6256"}],"wp:attachment":[{"href":"https:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/media?parent=5538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}