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class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Prediction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Prediction"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Prediction</span> </div> </a> <ul id="toc-Prediction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistical_syllogism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistical_syllogism"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Statistical syllogism</span> </div> </a> <ul id="toc-Statistical_syllogism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Argument_from_analogy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Argument_from_analogy"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Argument from analogy</span> </div> </a> <ul id="toc-Argument_from_analogy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Causal_inference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Causal_inference"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Causal inference</span> </div> </a> <ul id="toc-Causal_inference-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Methods" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Methods</span> </div> </a> <button aria-controls="toc-Methods-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Methods subsection</span> </button> <ul id="toc-Methods-sublist" class="vector-toc-list"> <li id="toc-Enumerative_induction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Enumerative_induction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Enumerative induction</span> </div> </a> <ul id="toc-Enumerative_induction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eliminative_induction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Eliminative_induction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Eliminative induction</span> </div> </a> <ul id="toc-Eliminative_induction-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>History</span> </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Ancient_philosophy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ancient_philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Ancient philosophy</span> </div> </a> <ul id="toc-Ancient_philosophy-sublist" class="vector-toc-list"> <li id="toc-Aristotle_and_the_Peripatetic_School" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Aristotle_and_the_Peripatetic_School"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Aristotle and the Peripatetic School</span> </div> </a> <ul id="toc-Aristotle_and_the_Peripatetic_School-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pyrrhonism" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pyrrhonism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Pyrrhonism</span> </div> </a> <ul id="toc-Pyrrhonism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ancient_medicine" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ancient_medicine"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span>Ancient medicine</span> </div> </a> <ul id="toc-Ancient_medicine-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Early_modern_philosophy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Early_modern_philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Early modern philosophy</span> </div> </a> <ul id="toc-Early_modern_philosophy-sublist" class="vector-toc-list"> <li id="toc-David_Hume" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#David_Hume"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>David Hume</span> </div> </a> <ul id="toc-David_Hume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Immanuel_Kant" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Immanuel_Kant"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>Immanuel Kant</span> </div> </a> <ul id="toc-Immanuel_Kant-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Late_modern_philosophy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Late_modern_philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Late modern philosophy</span> </div> </a> <ul id="toc-Late_modern_philosophy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Contemporary_philosophy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Contemporary_philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Contemporary philosophy</span> </div> </a> <ul id="toc-Contemporary_philosophy-sublist" class="vector-toc-list"> <li id="toc-Bertrand_Russell" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bertrand_Russell"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.1</span> <span>Bertrand Russell</span> </div> </a> <ul id="toc-Bertrand_Russell-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gilbert_Harman" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Gilbert_Harman"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4.2</span> <span>Gilbert Harman</span> </div> </a> <ul id="toc-Gilbert_Harman-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Comparison_with_deductive_reasoning" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Comparison_with_deductive_reasoning"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Comparison with deductive reasoning</span> </div> </a> <ul id="toc-Comparison_with_deductive_reasoning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Problem_of_induction" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Problem_of_induction"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Problem of induction</span> </div> </a> <button aria-controls="toc-Problem_of_induction-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Problem of induction subsection</span> </button> <ul id="toc-Problem_of_induction-sublist" class="vector-toc-list"> <li id="toc-Biases" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Biases"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Biases</span> </div> </a> <ul id="toc-Biases-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bayesian_inference" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bayesian_inference"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Bayesian inference</span> </div> </a> <ul id="toc-Bayesian_inference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Inductive_inference" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Inductive_inference"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Inductive inference</span> </div> </a> <ul id="toc-Inductive_inference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Inductive reasoning</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 64 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-64" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">64 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D9%82%D8%B1%D8%A7%D8%A1_(%D9%85%D9%86%D8%B7%D9%82)" title="استقراء (منطق) – Arabic" lang="ar" hreflang="ar" data-title="استقراء (منطق)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0nduksiya_(m%C9%99ntiqi_n%C9%99tic%C9%99)" title="İnduksiya (məntiqi nəticə) – Azerbaijani" lang="az" hreflang="az" data-title="İnduksiya (məntiqi nəticə)" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0_%D0%B8%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D0%B8%D1%8F" title="Логическа индукция – Bulgarian" lang="bg" hreflang="bg" data-title="Логическа индукция" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Indukcija" title="Indukcija – Bosnian" lang="bs" hreflang="bs" data-title="Indukcija" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Raonament_inductiu" title="Raonament inductiu – Catalan" lang="ca" hreflang="ca" data-title="Raonament inductiu" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Logick%C3%A1_indukce" title="Logická indukce – Czech" lang="cs" hreflang="cs" data-title="Logická indukce" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Induktion_(metode)" title="Induktion (metode) – Danish" lang="da" hreflang="da" data-title="Induktion (metode)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Induktion_(Philosophie)" title="Induktion (Philosophie) – German" lang="de" hreflang="de" data-title="Induktion (Philosophie)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Induktsioon" title="Induktsioon – Estonian" lang="et" hreflang="et" data-title="Induktsioon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%80%CE%B1%CE%B3%CF%89%CE%B3%CE%AE_(%CF%86%CE%B9%CE%BB%CE%BF%CF%83%CE%BF%CF%86%CE%AF%CE%B1)" title="Επαγωγή (φιλοσοφία) – Greek" lang="el" hreflang="el" data-title="Επαγωγή (φιλοσοφία)" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Razonamiento_inductivo" title="Razonamiento inductivo – Spanish" lang="es" hreflang="es" data-title="Razonamiento inductivo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Indukta_logiko" title="Indukta logiko – Esperanto" lang="eo" hreflang="eo" data-title="Indukta logiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Metodo_induktibo" title="Metodo induktibo – Basque" lang="eu" hreflang="eu" data-title="Metodo induktibo" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D9%82%D8%B1%D8%A7" title="استقرا – Persian" lang="fa" hreflang="fa" data-title="استقرا" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Induction_(logique)" title="Induction (logique) – French" lang="fr" hreflang="fr" data-title="Induction (logique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Razoamento_indutivo" title="Razoamento indutivo – Galician" lang="gl" hreflang="gl" data-title="Razoamento indutivo" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/R%C5%A9c%C5%A9ra_rwa_ng%C5%A9ng%C5%A9%C4%A9ro_(inductive_reasoning)" title="Rũcũra rwa ngũngũĩro (inductive reasoning) – Kikuyu" lang="ki" hreflang="ki" data-title="Rũcũra rwa ngũngũĩro (inductive reasoning)" data-language-autonym="Gĩkũyũ" data-language-local-name="Kikuyu" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B7%80%EB%82%A9" title="귀납 – Korean" lang="ko" hreflang="ko" data-title="귀납" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%AF%D5%A1%D5%AE%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Մակածություն – Armenian" lang="hy" hreflang="hy" data-title="Մակածություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%86%E0%A4%97%E0%A4%AE%E0%A4%A8%E0%A4%BE%E0%A4%A4%E0%A5%8D%E0%A4%AE%E0%A4%95_%E0%A4%A4%E0%A4%B0%E0%A5%8D%E0%A4%95" title="आगमनात्मक तर्क – Hindi" lang="hi" hreflang="hi" data-title="आगमनात्मक तर्क" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Indukcija" title="Indukcija – Croatian" lang="hr" hreflang="hr" data-title="Indukcija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Penalaran_induktif" title="Penalaran induktif – Indonesian" lang="id" hreflang="id" data-title="Penalaran induktif" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Tillei%C3%B0sla" title="Tilleiðsla – Icelandic" lang="is" hreflang="is" data-title="Tilleiðsla" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Induzione" title="Induzione – Italian" lang="it" hreflang="it" data-title="Induzione" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%99%D7%A0%D7%93%D7%95%D7%A7%D7%A6%D7%99%D7%94" title="אינדוקציה – Hebrew" lang="he" hreflang="he" data-title="אינדוקציה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D1%82%D1%96_%D0%BF%D0%B0%D0%B9%D1%8B%D0%BC%D0%B4%D0%B0%D1%83" title="Индуктивті пайымдау – Kazakh" lang="kk" hreflang="kk" data-title="Индуктивті пайымдау" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Indukcija_(izzi%C5%86as_metode)" title="Indukcija (izziņas metode) – Latvian" lang="lv" hreflang="lv" data-title="Indukcija (izziņas metode)" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Indukcija_(metodas)" title="Indukcija (metodas) – Lithuanian" lang="lt" hreflang="lt" data-title="Indukcija (metodas)" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Okulambika_ebirowoozo(Inductive_reasoning)" title="Okulambika ebirowoozo(Inductive reasoning) – Ganda" lang="lg" hreflang="lg" data-title="Okulambika ebirowoozo(Inductive reasoning)" data-language-autonym="Luganda" data-language-local-name="Ganda" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Indukt%C3%ADv_%C3%A9rvel%C3%A9s" title="Induktív érvelés – Hungarian" lang="hu" hreflang="hu" data-title="Induktív érvelés" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0)" title="Индукција (логика) – Macedonian" lang="mk" hreflang="mk" data-title="Индукција (логика)" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D0%B8" title="Индукци – Mongolian" lang="mn" hreflang="mn" data-title="Индукци" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Inductie_(filosofie)" title="Inductie (filosofie) – Dutch" lang="nl" hreflang="nl" data-title="Inductie (filosofie)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B8%B0%E7%B4%8D" title="帰納 – Japanese" lang="ja" hreflang="ja" data-title="帰納" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Induksjon_(filosofi)" title="Induksjon (filosofi) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Induksjon (filosofi)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Induksiya_(mantiq)" title="Induksiya (mantiq) – Uzbek" lang="uz" hreflang="uz" data-title="Induksiya (mantiq)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D9%82%D8%B1%D8%A7" title="استقرا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="استقرا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%82%DB%8C%D8%A7%D8%B3%D9%8A_%D8%A7%D8%B3%D8%AA%D8%AF%D9%84%D8%A7%D9%84" title="قیاسي استدلال – Pashto" lang="ps" hreflang="ps" data-title="قیاسي استدلال" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rozumowanie_indukcyjne" title="Rozumowanie indukcyjne – Polish" lang="pl" hreflang="pl" data-title="Rozumowanie indukcyjne" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/M%C3%A9todo_indutivo" title="Método indutivo – Portuguese" lang="pt" hreflang="pt" data-title="Método indutivo" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ra%C8%9Bionament_inductiv" title="Raționament inductiv – Romanian" lang="ro" hreflang="ro" data-title="Raționament inductiv" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D0%B5_%D1%83%D0%BC%D0%BE%D0%B7%D0%B0%D0%BA%D0%BB%D1%8E%D1%87%D0%B5%D0%BD%D0%B8%D0%B5" title="Индуктивное умозаключение – Russian" lang="ru" hreflang="ru" data-title="Индуктивное умозаключение" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Inductive_raisonin" title="Inductive raisonin – Scots" lang="sco" hreflang="sco" data-title="Inductive raisonin" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Induksioni" title="Induksioni – Albanian" lang="sq" hreflang="sq" data-title="Induksioni" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Inductive_reasoning" title="Inductive reasoning – Simple English" lang="en-simple" hreflang="en-simple" data-title="Inductive reasoning" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Indukcia_(logika)" title="Indukcia (logika) – Slovak" lang="sk" hreflang="sk" data-title="Indukcia (logika)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Indukcija_(logika)" title="Indukcija (logika) – Slovenian" lang="sl" hreflang="sl" data-title="Indukcija (logika)" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%8C%D8%B3%D8%AA%DB%8C%D9%82%D8%B1%D8%A7" title="ئیستیقرا – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئیستیقرا" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0)" title="Индукција (логика) – Serbian" lang="sr" hreflang="sr" data-title="Индукција (логика)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Indukcija" title="Indukcija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Indukcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Induktiivinen_p%C3%A4%C3%A4ttely" title="Induktiivinen päättely – Finnish" lang="fi" hreflang="fi" data-title="Induktiivinen päättely" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Induktion_(filosofi)" title="Induktion (filosofi) – Swedish" lang="sv" hreflang="sv" data-title="Induktion (filosofi)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8A%E0%AE%95%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%B5%E0%AE%B4%E0%AE%BF%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AE%95%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%B1%E0%AE%BF%E0%AE%A4%E0%AE%B2%E0%AF%8D" title="தொகுப்புவழிப் பகுத்தறிதல் – Tamil" lang="ta" hreflang="ta" data-title="தொகுப்புவழிப் பகுத்தறிதல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%98%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D0%B8%D1%8F" title="Индукция – Tatar" lang="tt" hreflang="tt" data-title="Индукция" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%83%E0%B8%AB%E0%B9%89%E0%B9%80%E0%B8%AB%E0%B8%95%E0%B8%B8%E0%B8%9C%E0%B8%A5%E0%B9%81%E0%B8%9A%E0%B8%9A%E0%B8%AD%E0%B8%B8%E0%B8%9B%E0%B8%99%E0%B8%B1%E0%B8%A2" title="การให้เหตุผลแบบอุปนัย – Thai" lang="th" hreflang="th" data-title="การให้เหตุผลแบบอุปนัย" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%98%D1%81%D1%82%D0%B8%D2%9B%D1%80%D0%BE%D1%8A" title="Истиқроъ – Tajik" lang="tg" hreflang="tg" data-title="Истиқроъ" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/T%C3%BCmevar%C4%B1m" title="Tümevarım – Turkish" lang="tr" hreflang="tr" data-title="Tümevarım" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Induktiw_logika" title="Induktiw logika – Turkmen" lang="tk" hreflang="tk" data-title="Induktiw logika" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%D0%B4%D1%83%D0%BA%D1%86%D1%96%D1%8F_(%D0%BB%D0%BE%D0%B3%D1%96%D0%BA%D0%B0)" title="Індукція (логіка) – Ukrainian" lang="uk" hreflang="uk" data-title="Індукція (логіка)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D9%82%D8%B1%D8%A7%D8%A6%DB%8C_%D9%85%D9%86%D8%B7%D9%82" title="استقرائی منطق – Urdu" lang="ur" hreflang="ur" data-title="استقرائی منطق" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Suy_lu%E1%BA%ADn_quy_n%E1%BA%A1p" title="Suy luận quy nạp – Vietnamese" lang="vi" hreflang="vi" data-title="Suy luận quy nạp" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BD%92%E7%BA%B3%E6%8E%A8%E7%90%86" title="归纳推理 – Wu" lang="wuu" hreflang="wuu" data-title="归纳推理" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AD%B8%E7%B4%8D" title="歸納 – Cantonese" lang="yue" hreflang="yue" data-title="歸納" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BD%92%E7%BA%B3%E6%8E%A8%E7%90%86" title="归纳推理 – Chinese" lang="zh" hreflang="zh" data-title="归纳推理" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q484511#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Inductive_reasoning" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Method of logical reasoning</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Inductive inference" redirects here. Not to be confused with <a href="/wiki/Mathematical_induction" title="Mathematical induction">mathematical induction</a>, which is actually a form of deductive rather than inductive reasoning.</div> <p class="mw-empty-elt"> </p><p><b>Inductive reasoning</b> is any of various <a href="/wiki/Method_of_reasoning" class="mw-redirect" title="Method of reasoning">methods of reasoning</a> in which broad generalizations or <a href="/wiki/Principle" title="Principle">principles</a> are derived from a body of observations.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Inductive reasoning is in contrast to <a href="/wiki/Deductive_reasoning" title="Deductive reasoning"><i>deductive</i> reasoning</a> (such as <a href="/wiki/Mathematical_induction" title="Mathematical induction">mathematical induction</a>), where the conclusion of a deductive argument is <i>certain</i>, given the premises are correct; in contrast, the truth of the conclusion of an inductive argument is at best <i><a href="/wiki/Probable" class="mw-redirect" title="Probable">probable</a></i>, based upon the evidence given.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=1" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The types of inductive reasoning include generalization, prediction, <a href="/wiki/Statistical_syllogism" title="Statistical syllogism">statistical syllogism</a>, argument from analogy, and causal inference. There are also differences in how their results are regarded. </p> <div class="mw-heading mw-heading3"><h3 id="Inductive_generalization">Inductive generalization</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=2" title="Edit section: Inductive generalization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A generalization (more accurately, an <i>inductive generalization</i>) proceeds from premises about a <a href="/wiki/Sample_(statistics)" class="mw-redirect" title="Sample (statistics)">sample</a> to a conclusion about the <a href="/wiki/Statistical_population" title="Statistical population">population</a>.<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The observation obtained from this sample is projected onto the broader population.<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>The proportion Q of the sample has attribute A.</dd> <dd>Therefore, the proportion Q of the population has attribute A.</dd></dl> <p>For example, if there are 20 balls—either black or white—in an urn: to estimate their respective numbers, a <i>sample</i> of four balls is drawn, three are black and one is white. An inductive generalization may be that there are 15 black and five white balls in the urn. However this is only one of 17 possibilities as to the <i>actual</i> number of each color of balls in the urn (the <i>population)</i> -- there may, of course, have been 19 black and just 1 white ball, or only 3 black balls and 17 white, or any mix in between. The probability of each possible distribution being the actual numbers of black and white balls can be estimated using techniques such as <a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a>, where prior assumptions about the distribution are updated with the observed sample, or <a href="/wiki/Maximum_likelihood_estimation" title="Maximum likelihood estimation">maximum likelihood estimation</a> (MLE), which identifies the distribution most likely given the observed sample. </p><p>How much the premises support the conclusion depends upon the number in the sample group, the number in the population, and the degree to which the sample represents the population (which, for a static population, may be achieved by taking a random sample). The greater the sample size relative to the population and the more closely the sample represents the population, the stronger the generalization is. The <a href="/wiki/Hasty_generalization" class="mw-redirect" title="Hasty generalization">hasty generalization</a> and the <a href="/wiki/Biased_sample" class="mw-redirect" title="Biased sample">biased sample</a> are generalization fallacies. </p> <div class="mw-heading mw-heading4"><h4 id="Statistical_generalization">Statistical generalization</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=3" title="Edit section: Statistical generalization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A statistical generalization is a type of inductive argument in which a conclusion about a population is inferred using a <a href="/wiki/Sample_(statistics)" class="mw-redirect" title="Sample (statistics)">statistically representative sample</a>. For example: </p> <dl><dd>Of a sizeable random sample of voters surveyed, 66% support Measure Z.</dd> <dd>Therefore, approximately 66% of voters support Measure Z.</dd></dl> <p>The measure is highly reliable within a well-defined margin of error provided that the selection process was genuinely random and that the numbers of items in the sample having the properties considered are large. It is readily quantifiable. Compare the preceding argument with the following. "Six of the ten people in my book club are Libertarians. Therefore, about 60% of people are Libertarians." The argument is weak because the sample is non-random and the sample size is very small. </p><p>Statistical generalizations are also called <i>statistical projections</i><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and <i>sample projections</i>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Anecdotal_generalization">Anecdotal generalization</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=4" title="Edit section: Anecdotal generalization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An anecdotal generalization is a type of inductive argument in which a conclusion about a population is inferred using a non-statistical sample.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In other words, the generalization is based on <a href="/wiki/Anecdotal_evidence" title="Anecdotal evidence">anecdotal evidence</a>. For example: </p> <dl><dd>So far, this year his son's Little League team has won 6 of 10 games.</dd> <dd>Therefore, by season's end, they will have won about 60% of the games.</dd></dl> <p>This inference is less reliable (and thus more likely to commit the fallacy of hasty generalization) than a statistical generalization, first, because the sample events are non-random, and second because it is not reducible to a mathematical expression. Statistically speaking, there is simply no way to know, measure and calculate the circumstances affecting performance that will occur in the future. On a philosophical level, the argument relies on the presupposition that the operation of future events will mirror the past. In other words, it takes for granted a uniformity of nature, an unproven principle that cannot be derived from the empirical data itself. Arguments that tacitly presuppose this uniformity are sometimes called <i>Humean</i> after the philosopher who was first to subject them to philosophical scrutiny.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Prediction">Prediction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=5" title="Edit section: Prediction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An inductive prediction draws a conclusion about a future, current, or past instance from a sample of other instances. Like an inductive generalization, an inductive prediction relies on a data set consisting of specific instances of a phenomenon. But rather than conclude with a general statement, the inductive prediction concludes with a specific statement about the <a href="/wiki/Probability" title="Probability">probability</a> that a single instance will (or will not) have an attribute shared (or not shared) by the other instances.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>Proportion Q of observed members of group G have had attribute A.</dd> <dd>Therefore, there is a probability corresponding to Q that other members of group G will have attribute A when next observed.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Statistical_syllogism">Statistical syllogism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=6" title="Edit section: Statistical syllogism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Statistical_syllogism" title="Statistical syllogism">Statistical syllogism</a></div> <p>A statistical <a href="/wiki/Syllogism" title="Syllogism">syllogism</a> proceeds from a generalization about a group to a conclusion about an individual. </p> <dl><dd>Proportion Q of the known instances of population P has attribute A.</dd> <dd>Individual I is another member of P.</dd> <dd>Therefore, there is a probability corresponding to Q that I has A.</dd></dl> <p>For example: </p> <dl><dd>90% of graduates from Excelsior Preparatory school go on to university.</dd> <dd>Bob is a graduate of Excelsior Preparatory school.</dd> <dd>Therefore, Bob will probably go on to university.</dd></dl> <p>This is a <i>statistical syllogism</i>.<sup id="cite_ref-Logic_11-0" class="reference"><a href="#cite_note-Logic-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Even though one cannot be sure Bob will attend university, the exact probability of this outcome is fully assured (given no further information). Two <i><a href="/wiki/Dicto_simpliciter" class="mw-redirect" title="Dicto simpliciter">dicto simpliciter</a></i> fallacies can occur in statistical syllogisms: "<a href="/wiki/Accident_(fallacy)" title="Accident (fallacy)">accident</a>" and "<a href="/wiki/Converse_accident" title="Converse accident">converse accident</a>". </p> <div class="mw-heading mw-heading3"><h3 id="Argument_from_analogy">Argument from analogy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=7" title="Edit section: Argument from analogy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Argument_from_analogy" title="Argument from analogy">Argument from analogy</a></div> <p>The process of analogical inference involves noting the shared properties of two or more things and from this basis inferring that they also share some further property:<sup id="cite_ref-Baronett_12-0" class="reference"><a href="#cite_note-Baronett-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>P and Q are similar with respect to properties a, b, and c.</dd> <dd>Object P has been observed to have further property x.</dd> <dd>Therefore, Q probably has property x also.</dd></dl> <p>Analogical reasoning is very frequent in <a href="/wiki/Common_sense" title="Common sense">common sense</a>, <a href="/wiki/Science" title="Science">science</a>, <a href="/wiki/Philosophy" title="Philosophy">philosophy</a>, <a href="/wiki/Law" title="Law">law</a>, and the <a href="/wiki/Humanities" title="Humanities">humanities</a>, but sometimes it is accepted only as an auxiliary method. A refined approach is <a href="/wiki/Case-based_reasoning" title="Case-based reasoning">case-based reasoning</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>Mineral A and Mineral B are both igneous rocks often containing veins of quartz and are most commonly found in South America in areas of ancient volcanic activity.</dd> <dd>Mineral A is also a soft stone suitable for carving into jewelry.</dd> <dd>Therefore, mineral B is probably a soft stone suitable for carving into jewelry.</dd></dl> <p>This is <i>analogical induction</i>, according to which things alike in certain ways are more prone to be alike in other ways. This form of induction was explored in detail by philosopher John Stuart Mill in his <i>System of Logic</i>, where he states, "[t]here can be no doubt that every resemblance [not known to be irrelevant] affords some degree of probability, beyond what would otherwise exist, in favor of the conclusion."<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> See <a href="/wiki/Mill%27s_Methods" class="mw-redirect" title="Mill's Methods">Mill's Methods</a>. </p><p>Some thinkers contend that analogical induction is a subcategory of inductive generalization because it assumes a pre-established uniformity governing events.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (June 2020)">citation needed</span></a></i>]</sup> Analogical induction requires an auxiliary examination of the <i>relevancy</i> of the characteristics cited as common to the pair. In the preceding example, if a premise were added stating that both stones were mentioned in the records of early Spanish explorers, this common attribute is extraneous to the stones and does not contribute to their probable affinity. </p><p>A pitfall of analogy is that features can be <a href="/wiki/Cherry-picked" class="mw-redirect" title="Cherry-picked">cherry-picked</a>: while objects may show striking similarities, two things juxtaposed may respectively possess other characteristics not identified in the analogy that are characteristics sharply <i>dis</i>similar. Thus, analogy can mislead if not all relevant comparisons are made. </p> <div class="mw-heading mw-heading3"><h3 id="Causal_inference">Causal inference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=8" title="Edit section: Causal inference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Causal_reasoning" title="Causal reasoning">Causal reasoning</a></div> <p>A causal inference draws a conclusion about a possible or probable causal connection based on the conditions of the occurrence of an effect. Premises about the correlation of two things can indicate a causal relationship between them, but additional factors must be confirmed to establish the exact form of the causal relationship.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2022)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Methods">Methods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=9" title="Edit section: Methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The two principal methods used to reach inductive generalizations are <i>enumerative induction</i> and <i>eliminative induction.</i><sup id="cite_ref-dan_15-0" class="reference"><a href="#cite_note-dan-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-jm_16-0" class="reference"><a href="#cite_note-jm-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Enumerative_induction">Enumerative induction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=10" title="Edit section: Enumerative induction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Enumerative induction is an inductive method in which a generalization is constructed based on the <i>number</i> of instances that support it. The more supporting instances, the stronger the conclusion.<sup id="cite_ref-dan_15-1" class="reference"><a href="#cite_note-dan-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-jm_16-1" class="reference"><a href="#cite_note-jm-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>The most basic form of enumerative induction reasons from particular instances to all instances and is thus an unrestricted generalization.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> If one observes 100 swans, and all 100 were white, one might infer a probable universal <a href="/wiki/Categorical_proposition" title="Categorical proposition">categorical proposition</a> of the form <i>All swans are white</i>. As this <a href="/wiki/Argument_form" class="mw-redirect" title="Argument form">reasoning form</a>'s premises, even if true, do not entail the conclusion's truth, this is a form of inductive inference. The conclusion might be true, and might be thought probably true, yet it can be false. Questions regarding the justification and form of enumerative inductions have been central in <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>, as enumerative induction has a pivotal role in the traditional model of the <a href="/wiki/Scientific_method" title="Scientific method">scientific method</a>. </p> <dl><dd>All life forms so far discovered are composed of cells.</dd> <dd>Therefore, all life forms are composed of cells.</dd></dl> <p>This is <i>enumerative induction</i>, also known as <i>simple induction</i> or <i>simple predictive induction</i>. It is a subcategory of inductive generalization. In everyday practice, this is perhaps the most common form of induction. For the preceding argument, the conclusion is tempting but makes a prediction well in excess of the evidence. First, it assumes that life forms observed until now can tell us how future cases will be: an appeal to uniformity. Second, the conclusion <i>All</i> is a bold assertion. A single contrary instance foils the argument. And last, quantifying the level of probability in any mathematical form is problematic.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> By what standard do we measure our Earthly sample of known life against all (possible) life? Suppose we do discover some new organism—such as some microorganism floating in the mesosphere or an asteroid—and it is cellular. Does the addition of this corroborating evidence oblige us to raise our probability assessment for the subject proposition? It is generally deemed reasonable to answer this question "yes", and for a good many this "yes" is not only reasonable but incontrovertible. So then just <i>how much</i> should this new data change our probability assessment? Here, consensus melts away, and in its place arises a question about whether we can talk of probability coherently at all with or without numerical quantification. </p> <dl><dd>All life forms so far discovered have been composed of cells.</dd> <dd>Therefore, the <i>next</i> life form discovered will be composed of cells.</dd></dl> <p>This is enumerative induction in its <i>weak form</i>. It truncates "all" to a mere single instance and, by making a far weaker claim, considerably strengthens the probability of its conclusion. Otherwise, it has the same shortcomings as the strong form: its sample population is non-random, and quantification methods are elusive. </p> <div class="mw-heading mw-heading3"><h3 id="Eliminative_induction">Eliminative induction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=11" title="Edit section: Eliminative induction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Eliminative_induction" class="mw-redirect" title="Eliminative induction">Eliminative induction</a>, also called variative induction, is an inductive method first put forth by <a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a>;<sup id="cite_ref-:2_19-0" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> in it a generalization is constructed based on the <i>variety</i> of instances that support it. Unlike enumerative induction, eliminative induction reasons based on the various kinds of instances that support a conclusion, rather than the number of instances that support it. As the variety of instances increases, the more possible conclusions based on those instances can be identified as incompatible and eliminated. This, in turn, increases the strength of any conclusion that remains consistent with the various instances. In this context, confidence is the function of how many instances have been identified as incompatible and eliminated. This confidence is expressed as the Baconian probability i|n (read as "i out of n") where n reasons for finding a claim incompatible has been identified and i of these have been eliminated by evidence or argument.<sup id="cite_ref-:2_19-1" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>There are three ways of attacking an argument; these ways - known as defeaters in <a href="/wiki/Defeasible_reasoning" title="Defeasible reasoning">defeasible reasoning</a> literature - are : rebutting, undermining, and undercutting. Rebutting defeats by offering a counter-example, undermining defeats by questioning the validity of the evidence, and undercutting defeats by pointing out conditions where a conclusion is not true when the inference is. By identifying defeaters and proving them wrong is how this approach builds confidence. <sup id="cite_ref-:2_19-2" class="reference"><a href="#cite_note-:2-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>This type of induction may use different methodologies such as quasi-experimentation, which tests and, where possible, eliminates rival hypotheses.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Different evidential tests may also be employed to eliminate possibilities that are entertained.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>Eliminative induction is crucial to the scientific method and is used to eliminate hypotheses that are inconsistent with observations and experiments.<sup id="cite_ref-dan_15-2" class="reference"><a href="#cite_note-dan-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-jm_16-2" class="reference"><a href="#cite_note-jm-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> It focuses on possible causes instead of observed actual instances of causal connections.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b>. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Inductive_reasoning&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">June 2020</span>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=12" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ancient_philosophy">Ancient philosophy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=13" title="Edit section: Ancient philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a move from particular to universal, <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> in the 300s BCE used the Greek word <i>epagogé</i>, which <a href="/wiki/Cicero" title="Cicero">Cicero</a> translated into the Latin word <i>inductio</i>.<sup id="cite_ref-Gattei_23-0" class="reference"><a href="#cite_note-Gattei-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Aristotle_and_the_Peripatetic_School">Aristotle and the Peripatetic School</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=14" title="Edit section: Aristotle and the Peripatetic School"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Aristotle's <i><a href="/wiki/Posterior_Analytics" title="Posterior Analytics">Posterior Analytics</a></i> covers the methods of inductive proof in natural philosophy and in the social sciences. The first book of <a href="https://en.wikisource.org/wiki/Organon_(Owen)/The_Posterior_Analytics" class="extiw" title="s:Organon (Owen)/The Posterior Analytics">Posterior Analytics</a> describes the nature and science of demonstration and its elements: including definition, division, intuitive reason of first principles, particular and universal demonstration, affirmative and negative demonstration, the difference between science and opinion, etc. </p> <div class="mw-heading mw-heading4"><h4 id="Pyrrhonism">Pyrrhonism</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=15" title="Edit section: Pyrrhonism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ancient <a href="/wiki/Pyrrhonism" title="Pyrrhonism">Pyrrhonists</a> were the first Western philosophers to point out the <a href="/wiki/Problem_of_induction" title="Problem of induction">Problem of induction</a>: that induction cannot, according to them, justify the acceptance of universal statements as true.<sup id="cite_ref-Gattei_23-1" class="reference"><a href="#cite_note-Gattei-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Ancient_medicine">Ancient medicine</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=16" title="Edit section: Ancient medicine"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Empiric_school" title="Empiric school">Empiric school</a> of ancient Greek medicine employed <i><a href="/wiki/Epilogism" title="Epilogism">epilogism</a></i> as a method of inference. 'Epilogism' is a theory-free method that looks at history through the accumulation of facts without major generalization and with consideration of the consequences of making causal claims.<sup id="cite_ref-:1_24-0" class="reference"><a href="#cite_note-:1-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Epilogism is an inference which moves entirely within the domain of visible and evident things, it tries not to invoke <a href="/wiki/Unobservable" title="Unobservable">unobservables</a>. </p><p>The <a href="/wiki/Dogmatic_school" title="Dogmatic school">Dogmatic school</a> of ancient Greek medicine employed <i>analogismos</i> as a method of inference.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> This method used analogy to reason from what was observed to unobservable forces. </p> <div class="mw-heading mw-heading3"><h3 id="Early_modern_philosophy">Early modern philosophy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=17" title="Edit section: Early modern philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1620, <a href="/wiki/Early_modern_philosophy" title="Early modern philosophy">early modern philosopher</a> <a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a> repudiated the value of mere experience and enumerative induction alone. <a href="/wiki/Baconian_method" title="Baconian method">His method</a> of <a href="/wiki/Inductivism" title="Inductivism">inductivism</a> required that minute and many-varied observations that uncovered the natural world's structure and causal relations needed to be coupled with enumerative induction in order to have knowledge beyond the present scope of experience. Inductivism therefore required enumerative induction as a component. </p> <div class="mw-heading mw-heading4"><h4 id="David_Hume">David Hume</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=18" title="Edit section: David Hume"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The empiricist <a href="/wiki/David_Hume" title="David Hume">David Hume</a>'s 1740 stance found enumerative induction to have no rational, let alone logical, basis; instead, induction was the product of instinct rather than reason, a custom of the mind and an everyday requirement to live. While observations, such as the motion of the sun, could be coupled with the principle of the <a href="/wiki/Uniformitarianism" title="Uniformitarianism">uniformity of nature</a> to produce conclusions that seemed to be certain, the <a href="/wiki/Problem_of_induction" title="Problem of induction">problem of induction</a> arose from the fact that the uniformity of nature was not a logically valid principle, therefore it could not be defended as deductively rational, but also could not be defended as inductively rational by appealing to the fact that the uniformity of nature has accurately described the past and therefore, will likely accurately describe the future because that is an inductive argument and therefore circular since induction is what needs to be justified. </p><p>Since Hume first wrote about the dilemma between the invalidity of deductive arguments and the circularity of inductive arguments in support of the uniformity of nature, this supposed dichotomy between merely two modes of inference, deduction and induction, has been contested with the discovery of a third mode of inference known as abduction, or <a href="/wiki/Abductive_reasoning" title="Abductive reasoning">abductive reasoning</a>, which was first formulated and advanced by <a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a>, in 1886, where he referred to it as "reasoning by hypothesis."<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Inference to the best explanation is often, yet arguably, treated as synonymous to abduction as it was first identified by Gilbert Harman in 1965 where he referred to it as "abductive reasoning," yet his definition of abduction slightly differs from Pierce's definition.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Regardless, if abduction is in fact a third mode of inference rationally independent from the other two, then either the uniformity of nature can be rationally justified through abduction, or Hume's dilemma is more of a trilemma. Hume was also skeptical of the application of enumerative induction and reason to reach certainty about unobservables and especially the inference of causality from the fact that modifying an aspect of a relationship prevents or produces a particular outcome. </p> <div class="mw-heading mw-heading4"><h4 id="Immanuel_Kant">Immanuel Kant</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=19" title="Edit section: Immanuel Kant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Awakened from "dogmatic slumber" by a German translation of Hume's work, <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Kant</a> sought to explain the possibility of <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a>. In 1781, Kant's <i><a href="/wiki/Critique_of_Pure_Reason" title="Critique of Pure Reason">Critique of Pure Reason</a></i> introduced <i><a href="/wiki/Rationalism" title="Rationalism">rationalism</a></i> as a path toward knowledge distinct from <i><a href="/wiki/Empiricism" title="Empiricism">empiricism</a></i>. Kant sorted statements into two types. <a href="/wiki/Analytic-synthetic_distinction" class="mw-redirect" title="Analytic-synthetic distinction">Analytic</a> statements are true by virtue of the <a href="/wiki/Syntax" title="Syntax">arrangement</a> of their terms and <a href="/wiki/Semantics" title="Semantics">meanings</a>, thus analytic statements are <a href="/wiki/Tautology_(logic)" title="Tautology (logic)">tautologies</a>, merely logical truths, true by <a href="/wiki/Logical_truth" title="Logical truth">necessity</a>. Whereas <a href="/wiki/Analytic-synthetic_distinction" class="mw-redirect" title="Analytic-synthetic distinction">synthetic</a> statements hold meanings to refer to states of facts, <a href="/wiki/Contingency_(philosophy)" title="Contingency (philosophy)">contingencies</a>. Against both rationalist philosophers like <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a> and <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a> as well as against empiricist philosophers like <a href="/wiki/John_Locke" title="John Locke">Locke</a> and <a href="/wiki/David_Hume" title="David Hume">Hume</a>, Kant's <i><a href="/wiki/Critique_of_Pure_Reason" title="Critique of Pure Reason">Critique of Pure Reason</a></i> is a sustained argument that in order to have knowledge we need both a contribution of our mind (concepts) as well as a contribution of our senses (intuitions). Knowledge proper is for Kant thus restricted to what we can possibly perceive (<i><a href="/wiki/Phenomena" class="mw-redirect" title="Phenomena">phenomena</a></i>), whereas objects of mere thought ("<a href="/wiki/Thing-in-itself" title="Thing-in-itself">things in themselves</a>") are in principle unknowable due to the impossibility of ever perceiving them. </p><p>Reasoning that the mind must contain its own categories for organizing <a href="/wiki/Sense_data" title="Sense data">sense data</a>, making experience of objects in <i>space</i> and <i>time (<a href="/wiki/Phenomena" class="mw-redirect" title="Phenomena">phenomena</a>)</i> possible, Kant concluded that the <a href="/wiki/Uniformitarianism" title="Uniformitarianism">uniformity of nature</a> was an <i>a priori</i> truth.<sup id="cite_ref-Salmon_28-0" class="reference"><a href="#cite_note-Salmon-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> A class of synthetic statements that was not <a href="/wiki/Contingency_(philosophy)" title="Contingency (philosophy)">contingent</a> but true by necessity, was then <a href="/wiki/Synthetic_a_priori" class="mw-redirect" title="Synthetic a priori">synthetic <i>a priori</i></a>. Kant thus saved both <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a> and <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a>. On the basis of the argument that what goes beyond our knowledge is "nothing to us,"<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> he discarded <a href="/wiki/Scientific_realism" title="Scientific realism">scientific realism</a>. Kant's position that knowledge comes about by a cooperation of perception and our capacity to think (<a href="/wiki/Transcendental_idealism" title="Transcendental idealism">transcendental idealism</a>) gave birth to the movement of <a href="/wiki/German_idealism" title="German idealism">German idealism</a>. <a href="/wiki/Georg_Friedrich_Wilhelm_Hegel" class="mw-redirect" title="Georg Friedrich Wilhelm Hegel">Hegel</a>'s <a href="/wiki/Absolute_idealism" title="Absolute idealism">absolute idealism</a> subsequently flourished across continental Europe and England. </p> <div class="mw-heading mw-heading3"><h3 id="Late_modern_philosophy">Late modern philosophy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=20" title="Edit section: Late modern philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Positivism" title="Positivism">Positivism</a>, developed by <a href="/wiki/Claude_Henri_de_Rouvroy,_comte_de_Saint-Simon" class="mw-redirect" title="Claude Henri de Rouvroy, comte de Saint-Simon">Henri de Saint-Simon</a> and promulgated in the 1830s by his former student <a href="/wiki/Auguste_Comte" title="Auguste Comte">Auguste Comte</a>, was the first <a href="/wiki/Late_modern_philosophy" class="mw-redirect" title="Late modern philosophy">late modern</a> <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>. In the aftermath of the <a href="/wiki/French_Revolution" title="French Revolution">French Revolution</a>, fearing society's ruin, Comte opposed <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a>. Human knowledge had evolved from religion to metaphysics to science, said Comte, which had flowed from <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> to <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> to <a href="/wiki/Physics" title="Physics">physics</a> to <a href="/wiki/Chemistry" title="Chemistry">chemistry</a> to <a href="/wiki/Biology" title="Biology">biology</a> to <a href="/wiki/Sociology" title="Sociology">sociology</a>—in that order—describing increasingly intricate domains. All of society's knowledge had become scientific, with questions of <a href="/wiki/Theology" title="Theology">theology</a> and of <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a> being unanswerable. Comte found enumerative induction reliable as a consequence of its grounding in available experience. He asserted the use of science, rather than metaphysical truth, as the correct method for the improvement of human society. </p><p>According to Comte, <a href="/wiki/Scientific_method" title="Scientific method">scientific method</a> frames predictions, confirms them, and states laws—positive statements—irrefutable by <a href="/wiki/Theology" title="Theology">theology</a> or by <a href="/wiki/Metaphysics" title="Metaphysics">metaphysics</a>. Regarding experience as justifying enumerative induction by demonstrating the <a href="/wiki/Uniformitarianism" title="Uniformitarianism">uniformity of nature</a>,<sup id="cite_ref-Salmon_28-1" class="reference"><a href="#cite_note-Salmon-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> the British philosopher <a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">John Stuart Mill</a> welcomed Comte's positivism, but thought <a href="/wiki/Scientific_laws" class="mw-redirect" title="Scientific laws">scientific laws</a> susceptible to recall or revision and Mill also withheld from Comte's <a href="/wiki/Religion_of_Humanity" title="Religion of Humanity">Religion of Humanity</a>. Comte was confident in treating <a href="/wiki/Scientific_law" title="Scientific law">scientific law</a> as an <a href="/wiki/Foundationalism" title="Foundationalism">irrefutable foundation for all knowledge</a>, and believed that churches, honouring eminent scientists, ought to focus public mindset on <i><a href="/wiki/Altruism" title="Altruism">altruism</a></i>—a term Comte coined—to apply science for humankind's social welfare via <a href="/wiki/Sociology" title="Sociology">sociology</a>, Comte's leading science. </p><p>During the 1830s and 1840s, while Comte and Mill were the leading philosophers of science, <a href="/wiki/William_Whewell" title="William Whewell">William Whewell</a> found enumerative induction not nearly as convincing, and, despite the dominance of inductivism, formulated "superinduction".<sup id="cite_ref-Toretti-p220_30-0" class="reference"><a href="#cite_note-Toretti-p220-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Whewell argued that "the peculiar import of the term <i>Induction</i>" should be recognised: "there is some Conception <i>superinduced</i> upon the facts", that is, "the Invention of a new Conception in every inductive inference". The creation of Conceptions is easily overlooked and prior to Whewell was rarely recognised.<sup id="cite_ref-Toretti-p220_30-1" class="reference"><a href="#cite_note-Toretti-p220-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Whewell explained: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>"Although we bind together facts by superinducing upon them a new Conception, this Conception, once introduced and applied, is looked upon as inseparably connected with the facts, and necessarily implied in them. Having once had the phenomena bound together in their minds in virtue of the Conception, men can no longer easily restore them back to detached and incoherent condition in which they were before they were thus combined."<sup id="cite_ref-Toretti-p220_30-2" class="reference"><a href="#cite_note-Toretti-p220-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>These "superinduced" explanations may well be flawed, but their accuracy is suggested when they exhibit what Whewell termed <i><a href="/wiki/Consilience" title="Consilience">consilience</a></i>—that is, simultaneously predicting the inductive generalizations in multiple areas—a feat that, according to Whewell, can establish their truth. Perhaps to accommodate the prevailing view of science as inductivist method, Whewell devoted several chapters to "methods of induction" and sometimes used the phrase "logic of induction", despite the fact that induction lacks rules and cannot be trained.<sup id="cite_ref-Toretti-p220_30-3" class="reference"><a href="#cite_note-Toretti-p220-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>In the 1870s, the originator of <a href="/wiki/Pragmatism" title="Pragmatism">pragmatism</a>, <a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">C S Peirce</a> performed vast investigations that clarified the basis of <a href="/wiki/Deductive_inference" class="mw-redirect" title="Deductive inference">deductive inference</a> as a mathematical proof (as, independently, did <a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a>). Peirce recognized induction but always insisted on a third type of inference that Peirce variously termed <i><a href="/wiki/Abductive_reasoning" title="Abductive reasoning">abduction</a></i> or <i>retroduction</i> or <i>hypothesis</i> or <i>presumption</i>.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Later philosophers termed Peirce's abduction, etc., <i><a href="/wiki/Inference_to_the_Best_Explanation" class="mw-redirect" title="Inference to the Best Explanation">Inference to the Best Explanation</a></i> (IBE).<sup id="cite_ref-Poston_32-0" class="reference"><a href="#cite_note-Poston-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Contemporary_philosophy">Contemporary philosophy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=21" title="Edit section: Contemporary philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Bertrand_Russell">Bertrand Russell</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=22" title="Edit section: Bertrand Russell"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Having highlighted Hume's <a href="/wiki/Problem_of_induction" title="Problem of induction">problem of induction</a>, <a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">John Maynard Keynes</a> posed <i>logical probability</i> as its answer, or as near a solution as he could arrive at.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> found Keynes's <i><a href="/wiki/A_Treatise_on_Probability" title="A Treatise on Probability">Treatise on Probability</a></i> the best examination of induction, and believed that if read with <a href="/wiki/Jean_Nicod" title="Jean Nicod">Jean Nicod</a>'s <i>Le Probleme logique de l'induction</i> as well as <a href="/wiki/R._B._Braithwaite" title="R. B. Braithwaite">R B Braithwaite</a>'s review of Keynes's work in the October 1925 issue of <i>Mind</i>, that would cover "most of what is known about induction", although the "subject is technical and difficult, involving a good deal of mathematics".<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Two decades later, <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russell</a> followed Keynes in regarding enumerative induction as an "independent logical principle".<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Russell1945_37-0" class="reference"><a href="#cite_note-Russell1945-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Russell found: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>"Hume's skepticism rests entirely upon his rejection of the principle of induction. The principle of induction, as applied to causation, says that, if <i>A</i> has been found very often accompanied or followed by <i>B</i>, then it is probable that on the next occasion on which <i>A</i> is observed, it will be accompanied or followed by <i>B</i>. If the principle is to be adequate, a sufficient number of instances must make the probability not far short of certainty. If this principle, or any other from which it can be deduced, is true, then the casual inferences which Hume rejects are valid, not indeed as giving certainty, but as giving a sufficient probability for practical purposes. If this principle is not true, every attempt to arrive at general scientific laws from particular observations is fallacious, and Hume's skepticism is inescapable for an empiricist. The principle itself cannot, of course, without circularity, be inferred from observed uniformities, since it is required to justify any such inference. It must, therefore, be, or be deduced from, an independent principle not based on experience. To this extent, Hume has proved that pure empiricism is not a sufficient basis for science. But if this one principle is admitted, everything else can proceed in accordance with the theory that all our knowledge is based on experience. It must be granted that this is a serious departure from pure empiricism, and that those who are not empiricists may ask why, if one departure is allowed, others are forbidden. These, however, are not questions directly raised by Hume's arguments. What these arguments prove—and I do not think the proof can be controverted—is that induction is an independent logical principle, incapable of being inferred either from experience or from other logical principles, and that without this principle, science is impossible."<sup id="cite_ref-Russell1945_37-1" class="reference"><a href="#cite_note-Russell1945-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup></p></blockquote> <div class="mw-heading mw-heading4"><h4 id="Gilbert_Harman">Gilbert Harman</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=23" title="Edit section: Gilbert Harman"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a 1965 paper, <a href="/wiki/Gilbert_Harman" title="Gilbert Harman">Gilbert Harman</a> explained that enumerative induction is not an autonomous phenomenon, but is simply a disguised consequence of Inference to the Best Explanation (IBE).<sup id="cite_ref-Poston_32-1" class="reference"><a href="#cite_note-Poston-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> IBE is otherwise synonymous with <a href="/wiki/C_S_Peirce" class="mw-redirect" title="C S Peirce">C S Peirce</a>'s <i><a href="/wiki/Abductive_reasoning" title="Abductive reasoning">abduction</a></i>.<sup id="cite_ref-Poston_32-2" class="reference"><a href="#cite_note-Poston-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Many philosophers of science espousing <a href="/wiki/Scientific_realism" title="Scientific realism">scientific realism</a> have maintained that IBE is the way that scientists develop approximately true scientific theories about nature.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Comparison_with_deductive_reasoning">Comparison with deductive reasoning</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=24" title="Edit section: Comparison with deductive reasoning"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Argument_terminology_used_in_logic_(en).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Argument_terminology_used_in_logic_%28en%29.svg/400px-Argument_terminology_used_in_logic_%28en%29.svg.png" decoding="async" width="400" height="283" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Argument_terminology_used_in_logic_%28en%29.svg/600px-Argument_terminology_used_in_logic_%28en%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Argument_terminology_used_in_logic_%28en%29.svg/800px-Argument_terminology_used_in_logic_%28en%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a><figcaption>Argument terminology</figcaption></figure> <p>Inductive reasoning is a form of argument that—in contrast to deductive reasoning—allows for the possibility that a conclusion can be false, even if all of the <a href="/wiki/Premise" title="Premise">premises</a> are true.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> This difference between deductive and inductive reasoning is reflected in the terminology used to describe deductive and inductive arguments. In deductive reasoning, an argument is "<a href="/wiki/Validity_(logic)" title="Validity (logic)">valid</a>" when, assuming the argument's premises are true, the conclusion <i>must be</i> true. If the argument is valid and the premises <i>are</i> true, then the argument is <a href="/wiki/Soundness" title="Soundness">"sound"</a>. In contrast, in inductive reasoning, an argument's premises can never guarantee that the conclusion <i>must be</i> true. Instead, an argument is "strong" when, assuming the argument's premises are true, the conclusion is <i>probably</i> true. If the argument is strong and the premises are thought to be true, then the argument is said to be "cogent".<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Less formally, the conclusion of an inductive argument may be called "probable", "plausible", "likely", "reasonable", or "justified", but never "certain" or "necessary". Logic affords no bridge from the probable to the certain. </p><p>The futility of attaining certainty through some critical mass of probability can be illustrated with a coin-toss exercise. Suppose someone tests whether a coin is either a fair one or two-headed. They flip the coin ten times, and ten times it comes up heads. At this point, there is a strong reason to believe it is two-headed. After all, the chance of ten heads in a row is .000976: less than one in one thousand. Then, after 100 flips, every toss has come up heads. Now there is "virtual" certainty that the coin is two-headed, and one can regard it as "true" that the coin is probably two-headed. Still, one can neither logically nor empirically rule out that the next toss will produce tails. No matter how many times in a row it comes up heads, this remains the case. If one programmed a machine to flip a coin over and over continuously, at some point the result would be a string of 100 heads. In the fullness of time, all combinations will appear. </p><p>As for the slim prospect of getting ten out of ten heads from a fair coin—the outcome that made the coin appear biased—many may be surprised to learn that the chance of any sequence of heads or tails is equally unlikely (e.g., H-H-T-T-H-T-H-H-H-T) and yet it occurs in <i>every</i> trial of ten tosses. That means <i>all</i> results for ten tosses have the same probability as getting ten out of ten heads, which is 0.000976. If one records the heads-tails sequences, for whatever result, that exact sequence had a chance of 0.000976. </p><p>An argument is deductive when the conclusion is necessary given the premises. That is, the conclusion must be true if the premises are true. For example, after getting 10 heads in a row one might deduce that the coin had met some statistical criterion to be regarded as probably two-sided, a conclusion that would not be falsified even if the next toss yielded tails. </p><p>If a deductive conclusion follows duly from its premises, then it is valid; otherwise, it is invalid (that an argument is invalid is not to say its conclusions are false; it may have a true conclusion, just not on account of the premises). An examination of the following examples will show that the relationship between premises and conclusion is such that the truth of the conclusion is already implicit in the premises. Bachelors are unmarried because we <i>say</i> they are; we have defined them so. Socrates is mortal because we have included him in a set of beings that are mortal. The conclusion for a valid deductive argument is already contained in the premises since its truth is strictly a matter of logical relations. It cannot say more than its premises. Inductive premises, on the other hand, draw their substance from fact and evidence, and the conclusion accordingly makes a factual claim or prediction. Its reliability varies proportionally with the evidence. Induction wants to reveal something <i>new</i> about the world. One could say that induction wants to say <i>more</i> than is contained in the premises. </p><p>To better see the difference between inductive and deductive arguments, consider that it would not make sense to say: "all rectangles so far examined have four right angles, so the next one I see will have four right angles." This would treat logical relations as something factual and discoverable, and thus variable and uncertain. Likewise, speaking deductively we may permissibly say. "All unicorns can fly; I have a unicorn named Charlie; thus Charlie can fly." This deductive argument is valid because the logical relations hold; we are not interested in their factual soundness. </p><p>The conclusions of inductive reasoning are inherently <a href="/wiki/Uncertainty" title="Uncertainty">uncertain</a>. It only deals with the extent to which, given the premises, the conclusion is "credible" according to some theory of evidence. Examples include a <a href="/wiki/Many-valued_logic" title="Many-valued logic">many-valued logic</a>, <a href="/wiki/Dempster%E2%80%93Shafer_theory" title="Dempster–Shafer theory">Dempster–Shafer theory</a>, or <a href="/wiki/Probability" title="Probability">probability theory</a> with rules for inference such as <a href="/wiki/Bayes%27_theorem" title="Bayes' theorem">Bayes' rule</a>. Unlike deductive reasoning, it does not rely on universals holding over a <a href="/wiki/Closed_world_assumption" class="mw-redirect" title="Closed world assumption">closed domain of discourse</a> to draw conclusions, so it can be applicable even in cases of <a href="/wiki/Open_world_assumption" class="mw-redirect" title="Open world assumption">epistemic uncertainty</a> (technical issues with this may arise however; for example, the <a href="/wiki/Axioms_of_probability#Second_axiom" class="mw-redirect" title="Axioms of probability">second axiom of probability</a> is a closed-world assumption).<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p><p>Another crucial difference between these two types of argument is that deductive certainty is impossible in non-axiomatic or empirical systems such as <a href="/wiki/Reality" title="Reality">reality</a>, leaving inductive reasoning as the primary route to (probabilistic) knowledge of such systems.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p><p>Given that "if <i>A</i> is true then that would cause <i>B</i>, <i>C</i>, and <i>D</i> to be true", an example of deduction would be "<i>A</i> is true therefore we can deduce that <i>B</i>, <i>C</i>, and <i>D</i> are true". An example of induction would be "<i>B</i>, <i>C</i>, and <i>D</i> are observed to be true therefore <i>A</i> might be true". <i>A</i> is a <a href="/wiki/Causality" title="Causality">reasonable</a> explanation for <i>B</i>, <i>C</i>, and <i>D</i> being true. </p><p>For example: </p> <dl><dd>A large enough asteroid impact would create a very large crater and cause a severe <a href="/wiki/Impact_winter" title="Impact winter">impact winter</a> that could drive the non-avian dinosaurs to extinction.</dd> <dd>We observe that there is a <a href="/wiki/Chicxulub_crater" title="Chicxulub crater">very large crater</a> in the Gulf of Mexico dating to very near the time of the extinction of the non-avian dinosaurs.</dd> <dd>Therefore, it is possible that this impact could explain why the non-avian dinosaurs became extinct.</dd></dl> <p>Note, however, that the asteroid explanation for the mass extinction is not necessarily correct. Other events with the potential to affect global climate also coincide with the <a href="/wiki/Cretaceous%E2%80%93Paleogene_extinction_event" title="Cretaceous–Paleogene extinction event">extinction of the non-avian dinosaurs</a>. For example, the release of <a href="/wiki/Volcanic_gas" title="Volcanic gas">volcanic gases</a> (particularly <a href="/wiki/Sulfur_dioxide" title="Sulfur dioxide">sulfur dioxide</a>) during the formation of the <a href="/wiki/Deccan_Traps" title="Deccan Traps">Deccan Traps</a> in <a href="/wiki/India" title="India">India</a>. </p><p>Another example of an inductive argument: </p> <dl><dd>All biological life forms that we know of depend on liquid water to exist.</dd> <dd>Therefore, if we discover a new biological life form, it will probably depend on liquid water to exist.</dd></dl> <p>This argument could have been made every time a new biological life form was found, and would have had a correct conclusion every time; however, it is still possible that in the future a biological life form not requiring liquid water could be discovered. As a result, the argument may be stated as: </p> <dl><dd>All biological life forms that we know of depend on liquid water to exist.</dd> <dd>Therefore, all biological life probably depends on liquid water to exist.</dd></dl> <p>A classical example of an "incorrect" statistical syllogism was presented by John Vickers: </p> <dl><dd>All of the swans we have seen are white.</dd> <dd>Therefore, we "know" that all swans are white.</dd></dl> <p>The conclusion fails because the population of swans then known was not actually representative of all swans. A more reasonable conclusion would be: in line with applicable conventions, we might reasonably <a href="/wiki/Expectation_(epistemic)" class="mw-redirect" title="Expectation (epistemic)">expect</a> all swans in England to be white, at least in the short-term. </p><p>Succinctly put: deduction is about <i>certainty/necessity</i>; induction is about <i>probability</i>.<sup id="cite_ref-Logic_11-1" class="reference"><a href="#cite_note-Logic-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Any single assertion will answer to one of these two criteria. Another approach to the analysis of reasoning is that of <a href="/wiki/Modal_logic" title="Modal logic">modal logic</a>, which deals with the distinction between the necessary and the <i>possible</i> in a way not concerned with probabilities among things deemed possible. </p><p>The philosophical definition of inductive reasoning is more nuanced than a simple progression from particular/individual instances to broader generalizations. Rather, the premises of an inductive <a href="/wiki/Logical_argument" class="mw-redirect" title="Logical argument">logical argument</a> indicate some degree of support (inductive probability) for the conclusion but do not <a href="/wiki/Entailment" class="mw-redirect" title="Entailment">entail</a> it; that is, they suggest truth but do not ensure it. In this manner, there is the possibility of moving from general statements to individual instances (for example, statistical syllogisms). </p><p>Note that the definition of <i>inductive</i> reasoning described here differs from <a href="/wiki/Mathematical_induction" title="Mathematical induction">mathematical induction</a>, which, in fact, is a form of <i>deductive</i> reasoning. Mathematical induction is used to provide strict proofs of the properties of recursively defined sets.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> The deductive nature of mathematical induction derives from its basis in a non-finite number of cases, in contrast with the finite number of cases involved in an enumerative induction procedure like <a href="/wiki/Proof_by_exhaustion" title="Proof by exhaustion">proof by exhaustion</a>. Both mathematical induction and proof by exhaustion are examples of <a href="/wiki/Complete_induction" class="mw-redirect" title="Complete induction">complete induction</a>. Complete induction is a masked type of deductive reasoning. </p> <div class="mw-heading mw-heading2"><h2 id="Problem_of_induction">Problem of induction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=25" title="Edit section: Problem of induction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Problem_of_induction" title="Problem of induction">Problem of induction</a></div> <p>Although philosophers at least as far back as the <a href="/wiki/Pyrrhonism" title="Pyrrhonism">Pyrrhonist</a> philosopher <a href="/wiki/Sextus_Empiricus" title="Sextus Empiricus">Sextus Empiricus</a> have pointed out the unsoundness of inductive reasoning,<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> the classic philosophical critique of the <a href="/wiki/Problem_of_induction" title="Problem of induction">problem of induction</a> was given by the Scottish philosopher <a href="/wiki/David_Hume" title="David Hume">David Hume</a>.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Although the use of inductive reasoning demonstrates considerable success, the justification for its application has been questionable. Recognizing this, Hume highlighted the fact that our mind often draws conclusions from relatively limited experiences that appear correct but which are actually far from certain. In deduction, the truth value of the conclusion is based on the truth of the premise. In induction, however, the dependence of the conclusion on the premise is always uncertain. For example, let us assume that all ravens are black. The fact that there are numerous black ravens supports the assumption. Our assumption, however, becomes invalid once it is discovered that there are white ravens. Therefore, the general rule "all ravens are black" is not the kind of statement that can ever be certain. Hume further argued that it is impossible to justify inductive reasoning: this is because it cannot be justified deductively, so our only option is to justify it inductively. Since this argument is circular, with the help of <a href="/wiki/Hume%27s_fork" title="Hume's fork">Hume's fork</a> he concluded that our use of induction is not logically justifiable .<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p><p>Hume nevertheless stated that even if induction were proved unreliable, we would still have to rely on it. So instead of a position of <a href="/wiki/Philosophical_skepticism" title="Philosophical skepticism">severe skepticism</a>, Hume advocated a <a href="/wiki/Scientific_skepticism" title="Scientific skepticism">practical skepticism</a> based on <a href="/wiki/Common_sense" title="Common sense">common sense</a>, where the inevitability of induction is accepted.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> illustrated Hume's skepticism in a story about a chicken who, fed every morning without fail and following the laws of induction, concluded that this feeding would always continue, until his throat was eventually cut by the farmer.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p><p>In 1963, <a href="/wiki/Karl_Popper" title="Karl Popper">Karl Popper</a> wrote, "Induction, <i>i.e.</i> inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure."<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gillies_50-0" class="reference"><a href="#cite_note-Gillies-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> Popper's 1972 book <i>Objective Knowledge</i>—whose first chapter is devoted to the problem of induction—opens, "I think I have solved a major philosophical problem: the <a href="/wiki/Problem_of_induction" title="Problem of induction">problem of induction</a>".<sup id="cite_ref-Gillies_50-1" class="reference"><a href="#cite_note-Gillies-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> In Popper's schema, enumerative induction is "a kind of optical illusion" cast by the steps of conjecture and refutation during a <i>problem shift</i>.<sup id="cite_ref-Gillies_50-2" class="reference"><a href="#cite_note-Gillies-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> An imaginative leap, the <i>tentative solution</i> is improvised, lacking inductive rules to guide it.<sup id="cite_ref-Gillies_50-3" class="reference"><a href="#cite_note-Gillies-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> The resulting, unrestricted generalization is deductive, an entailed consequence of all explanatory considerations.<sup id="cite_ref-Gillies_50-4" class="reference"><a href="#cite_note-Gillies-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> Controversy continued, however, with Popper's putative solution not generally accepted.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Donald_A._Gillies" title="Donald A. Gillies">Donald A. Gillies</a> argues that <a href="/wiki/Rule_of_inference" title="Rule of inference">rules of inferences</a> related to inductive reasoning are overwhelmingly absent from science, and describes most scientific inferences as "involv[ing] conjectures thought up by human ingenuity and creativity, and by no means inferred in any mechanical fashion, or according to precisely specified rules."<sup id="cite_ref-Gillies-p111_52-0" class="reference"><a href="#cite_note-Gillies-p111-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Gillies also provides a rare counterexample "in the machine learning programs of <a href="/wiki/Artificial_Intelligence" class="mw-redirect" title="Artificial Intelligence">AI</a>."<sup id="cite_ref-Gillies-p111_52-1" class="reference"><a href="#cite_note-Gillies-p111-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Biases">Biases</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=26" title="Edit section: Biases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Inductive reasoning is also known as hypothesis construction because any conclusions made are based on current knowledge and predictions.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2012)">citation needed</span></a></i>]</sup> As with deductive arguments, biases can distort the proper application of inductive argument, thereby preventing the reasoner from forming the most <a href="/wiki/Logical_consequence" title="Logical consequence">logical conclusion</a> based on the clues. Examples of these biases include the <a href="/wiki/Availability_heuristic" title="Availability heuristic">availability heuristic</a>, <a href="/wiki/Confirmation_bias" title="Confirmation bias">confirmation bias</a>, and the <a href="/wiki/Gambler%27s_fallacy" title="Gambler's fallacy">predictable-world bias</a>. </p><p>The availability heuristic is regarded as causing the reasoner to depend primarily upon information that is readily available. People have a tendency to rely on information that is easily accessible in the world around them. For example, in surveys, when people are asked to estimate the percentage of people who died from various causes, most respondents choose the causes that have been most prevalent in the media such as terrorism, murders, and airplane accidents, rather than causes such as disease and traffic accidents, which have been technically "less accessible" to the individual since they are not emphasized as heavily in the world around them. </p><p>Confirmation bias is based on the natural tendency to confirm rather than deny a hypothesis. Research has demonstrated that people are inclined to seek solutions to problems that are more consistent with known hypotheses rather than attempt to refute those hypotheses. Often, in experiments, subjects will ask questions that seek answers that fit established hypotheses, thus confirming these hypotheses. For example, if it is hypothesized that Sally is a sociable individual, subjects will naturally seek to confirm the premise by asking questions that would produce answers confirming that Sally is, in fact, a sociable individual. </p><p>The predictable-world bias revolves around the inclination to perceive order where it has not been proved to exist, either at all or at a particular level of abstraction. Gambling, for example, is one of the most popular examples of predictable-world bias. Gamblers often begin to think that they see simple and obvious patterns in the outcomes and therefore believe that they are able to predict outcomes based on what they have witnessed. In reality, however, the outcomes of these games are difficult to predict and highly complex in nature. In general, people tend to seek some type of simplistic order to explain or justify their beliefs and experiences, and it is often difficult for them to realise that their perceptions of order may be entirely different from the truth.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Bayesian_inference">Bayesian inference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=27" title="Edit section: Bayesian inference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As a logic of induction rather than a theory of belief, <a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a> does not determine which beliefs are <i>a priori</i> rational, but rather determines how we should rationally change the beliefs we have when presented with evidence. We begin by considering an exhaustive list of possibilities, a definite probabilistic characterisation of each of them (in terms of likelihoods) and precise <a href="/wiki/Prior_probability" title="Prior probability">prior probabilities</a> for them (e.g. based on logic or induction from previous experience) and, when faced with evidence, we adjust the strength of our belief in the given hypotheses in a precise manner using <a href="/wiki/Conditional_probability" title="Conditional probability">Bayesian logic</a> to yield candidate 'a posteriori probabilities', taking no account of the extent to which the new evidence may happen to give us specific reasons to doubt our assumptions. Otherwise it is advisable to review and repeat as necessary the consideration of possibilities and their characterisation until, perhaps, a stable situation is reached.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Inductive_inference">Inductive inference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=28" title="Edit section: Inductive inference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Around 1960, <a href="/wiki/Ray_Solomonoff" title="Ray Solomonoff">Ray Solomonoff</a> founded the theory of universal <a href="/wiki/Solomonoff%27s_theory_of_inductive_inference" title="Solomonoff's theory of inductive inference">inductive inference</a>, a theory of prediction based on observations, for example, predicting the next symbol based upon a given series of symbols. This is a formal inductive framework that combines <a href="/wiki/Algorithmic_information_theory" title="Algorithmic information theory">algorithmic information theory</a> with the Bayesian framework. Universal inductive inference is based on solid philosophical foundations and 'seems to be an inadequate tool for dealing with any reasonably complex or real-world environment',<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> and can be considered as a mathematically formalized <a href="/wiki/Occam%27s_razor" title="Occam's razor">Occam's razor</a>. Fundamental ingredients of the theory are the concepts of <a href="/wiki/Algorithmic_probability" title="Algorithmic probability">algorithmic probability</a> and <a href="/wiki/Kolmogorov_complexity" title="Kolmogorov complexity">Kolmogorov complexity</a>. </p><p>Inductive inference typically considers hypothesis classes with a countable size. A recent advance<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> established a sufficient and necessary condition for inductive inference: a finite error bound is guaranteed if and only if the hypothesis class is a countable union of online learnable classes. Notably, this condition allows the hypothesis class to have an uncountable size while remaining learnable within this framework. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=29" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output 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title="Recursive Bayesian estimation">Recursive Bayesian estimation</a></li> <li><a href="/wiki/Statistical_inference" title="Statistical inference">Statistical inference</a></li> <li><a href="/wiki/Stephen_Toulmin" title="Stephen Toulmin">Stephen Toulmin</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=30" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a 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Retrieved <span class="nowrap">7 March</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mundanopedia&rft.atitle=Deductive%2C+Inductive+Reasoning%3A+Definition%2C+Differences%2C+Examples&rft.date=2022-01-10&rft_id=https%3A%2F%2Fmundanopedia.com%2Feconomics%2Fmicroeconomics%2Fdeductive-and-inductive-reasoning-methods%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Assessment Strategies for Science: Grades 6–8</i>. 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Upper Saddle River, NJ: Pearson Education. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-238034-8" title="Special:BookSources/978-0-13-238034-8"><bdi>978-0-13-238034-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essentials+of+Logic&rft.place=Upper+Saddle+River%2C+NJ&rft.edition=Second&rft.pub=Pearson+Education&rft.date=2006&rft.isbn=978-0-13-238034-8&rft.aulast=Copi&rft.aufirst=I.M.&rft.au=Cohen%2C+C.&rft.au=Flage%2C+D.E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRussell1948" class="citation book cs1"><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russell, Bertrand</a> (1948). <i>Human Knowledge: Its Scope and Limits</i>. 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Boston, MA: Cengage Learning. p. 283. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-133-93464-6" title="Special:BookSources/978-1-133-93464-6"><bdi>978-1-133-93464-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Practical+Study+of+Argument%2C+Enhanced+Seventh+Edition&rft.place=Boston%2C+MA&rft.pages=283&rft.pub=Cengage+Learning&rft.date=2013&rft.isbn=978-1-133-93464-6&rft.aulast=Govier&rft.aufirst=Trudy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Schaum's Outlines, Logic, Second Edition. John Nolt, Dennis Rohatyn, Archille Varzi. McGraw-Hill, 1998. p. 223</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Schaum's Outlines, Logic, p. 230</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohnsonJohnsonNessFarenga2005" class="citation book cs1">Johnson, Dale D.; Johnson, Bonnie; Ness, Daniel; Farenga, Stephen J. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cMOPtcgQfT8C"><i>Trivializing Teacher Education: The Accreditation Squeeze</i></a>. Rowman & Littlefield. pp. <span class="nowrap">182–</span>83. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780742535367" title="Special:BookSources/9780742535367"><bdi>9780742535367</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Trivializing+Teacher+Education%3A+The+Accreditation+Squeeze&rft.pages=%3Cspan+class%3D%22nowrap%22%3E182-%3C%2Fspan%3E83&rft.pub=Rowman+%26+Littlefield&rft.date=2005&rft.isbn=9780742535367&rft.aulast=Johnson&rft.aufirst=Dale+D.&rft.au=Johnson%2C+Bonnie&rft.au=Ness%2C+Daniel&rft.au=Farenga%2C+Stephen+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DcMOPtcgQfT8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Introduction to Logic. Gensler p. 280</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRomeyn2004" class="citation journal cs1">Romeyn, J. W. (2004). <a rel="nofollow" class="external text" href="https://pure.rug.nl/ws/files/2720641/romeijn_-_hypotheses_and_predictions.pdf">"Hypotheses and Inductive Predictions: Including Examples on Crash Data"</a> <span class="cs1-format">(PDF)</span>. <i>Synthese</i>. <b>141</b> (3): <span class="nowrap">333–</span>64. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FB%3ASYNT.0000044993.82886.9e">10.1023/B:SYNT.0000044993.82886.9e</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/20118486">20118486</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121862013">121862013</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201024141846/https://pure.rug.nl/ws/files/2720641/romeijn_-_hypotheses_and_predictions.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 24 October 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">22 August</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Synthese&rft.atitle=Hypotheses+and+Inductive+Predictions%3A+Including+Examples+on+Crash+Data&rft.volume=141&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E333-%3C%2Fspan%3E64&rft.date=2004&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121862013%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F20118486%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1023%2FB%3ASYNT.0000044993.82886.9e&rft.aulast=Romeyn&rft.aufirst=J.+W.&rft_id=https%3A%2F%2Fpure.rug.nl%2Fws%2Ffiles%2F2720641%2Fromeijn_-_hypotheses_and_predictions.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-Logic-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Logic_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Logic_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Introduction to Logic. Harry J. Gensler, Rutledge, 2002. p. 268</span> </li> <li id="cite_note-Baronett-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Baronett_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaronett2008" class="citation book cs1">Baronett, Stan (2008). <i>Logic</i>. Upper Saddle River, NJ: Pearson Prentice Hall. pp. <span class="nowrap">321–</span>25.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Logic&rft.place=Upper+Saddle+River%2C+NJ&rft.pages=%3Cspan+class%3D%22nowrap%22%3E321-%3C%2Fspan%3E25&rft.pub=Pearson+Prentice+Hall&rft.date=2008&rft.aulast=Baronett&rft.aufirst=Stan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">For more information on inferences by analogy, see <a rel="nofollow" class="external text" href="http://www.cs.hut.fi/Opinnot/T-93.850/2005/Papers/juthe2005-analogy.pdf">Juthe, 2005</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090306070520/http://www.cs.hut.fi/Opinnot/T-93.850/2005/Papers/juthe2005-analogy.pdf">Archived</a> 6 March 2009 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">A System of Logic. Mill 1843/1930. p. 333</span> </li> <li id="cite_note-dan-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-dan_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-dan_15-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-dan_15-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHunter1998" class="citation journal cs1">Hunter, Dan (September 1998). "No Wilderness of Single Instances: Inductive Inference in Law". <i>Journal of Legal Education</i>. <b>48</b> (3): <span class="nowrap">370–</span>72.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Legal+Education&rft.atitle=No+Wilderness+of+Single+Instances%3A+Inductive+Inference+in+Law&rft.volume=48&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E370-%3C%2Fspan%3E72&rft.date=1998-09&rft.aulast=Hunter&rft.aufirst=Dan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-jm-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-jm_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-jm_16-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-jm_16-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ.M.2012" class="citation book cs1">J.M., Bochenski (2012). Caws, Peter (ed.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fnqhBQAAQBAJ"><i>The Methods of Contemporary Thought</i></a>. Springer Science & Business Media. pp. <span class="nowrap">108–</span>09. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9401035781" title="Special:BookSources/978-9401035781"><bdi>978-9401035781</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">5 June</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Methods+of+Contemporary+Thought&rft.pages=%3Cspan+class%3D%22nowrap%22%3E108-%3C%2Fspan%3E09&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012&rft.isbn=978-9401035781&rft.aulast=J.M.&rft.aufirst=Bochenski&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DfnqhBQAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChurchill1990" class="citation book cs1">Churchill, Robert Paul (1990). <i>Logic: An Introduction</i> (2nd ed.). New York: St. Martin's Press. p. 355. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-312-02353-9" title="Special:BookSources/978-0-312-02353-9"><bdi>978-0-312-02353-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/21216829">21216829</a>. <q>In a typical enumerative induction, the premises list the individuals observed to have a common property, and the conclusion claims that all individuals of the same population have that property.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Logic%3A+An+Introduction&rft.place=New+York&rft.pages=355&rft.edition=2nd&rft.pub=St.+Martin%27s+Press&rft.date=1990&rft_id=info%3Aoclcnum%2F21216829&rft.isbn=978-0-312-02353-9&rft.aulast=Churchill&rft.aufirst=Robert+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Schaum's Outlines, Logic, pp. 243–35</span> </li> <li id="cite_note-:2-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_19-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:2_19-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoodenoughWeinstockKlein2013" class="citation book cs1">Goodenough, John B.; Weinstock, Charles B.; Klein, Ari Z. (2013). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/6606668">"Eliminative induction: A basis for arguing system confidence"</a>. <i>2013 35th International Conference on Software Engineering (ICSE)</i>. pp. <span class="nowrap">1161–</span>1164. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FICSE.2013.6606668">10.1109/ICSE.2013.6606668</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4673-3076-3" title="Special:BookSources/978-1-4673-3076-3"><bdi>978-1-4673-3076-3</bdi></a> – via IEEE.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Eliminative+induction%3A+A+basis+for+arguing+system+confidence&rft.btitle=2013+35th+International+Conference+on+Software+Engineering+%28ICSE%29&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1161-%3C%2Fspan%3E1164&rft.date=2013&rft_id=info%3Adoi%2F10.1109%2FICSE.2013.6606668&rft.isbn=978-1-4673-3076-3&rft.aulast=Goodenough&rft.aufirst=John+B.&rft.au=Weinstock%2C+Charles+B.&rft.au=Klein%2C+Ari+Z.&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F6606668&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoppeDunn2001" class="citation book cs1">Hoppe, Rob; Dunn, William N. (2001). <i>Knowledge, Power, and Participation in Environmental Policy Analysis</i>. Transaction Publishers. p. 419. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4128-2721-8" title="Special:BookSources/978-1-4128-2721-8"><bdi>978-1-4128-2721-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Knowledge%2C+Power%2C+and+Participation+in+Environmental+Policy+Analysis&rft.pages=419&rft.pub=Transaction+Publishers&rft.date=2001&rft.isbn=978-1-4128-2721-8&rft.aulast=Hoppe&rft.aufirst=Rob&rft.au=Dunn%2C+William+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchum2001" class="citation book cs1">Schum, David A. (2001). <i>The Evidential Foundations of Probabilistic Reasoning</i>. Evanston, Illinois: Northwestern University Press. p. 32. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8101-1821-1" title="Special:BookSources/0-8101-1821-1"><bdi>0-8101-1821-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Evidential+Foundations+of+Probabilistic+Reasoning&rft.place=Evanston%2C+Illinois&rft.pages=32&rft.pub=Northwestern+University+Press&rft.date=2001&rft.isbn=0-8101-1821-1&rft.aulast=Schum&rft.aufirst=David+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHodgeHodgeRadick2003" class="citation book cs1">Hodge, Jonathan; Hodge, Michael Jonathan Sessions; Radick, Gregory (2003). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/cambridgecompani00hodg_248"><i>The Cambridge Companion to Darwin</i></a></span>. Cambridge: Cambridge University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/cambridgecompani00hodg_248/page/n189">174</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-77197-8" title="Special:BookSources/0-521-77197-8"><bdi>0-521-77197-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Darwin&rft.place=Cambridge&rft.pages=174&rft.pub=Cambridge+University+Press&rft.date=2003&rft.isbn=0-521-77197-8&rft.aulast=Hodge&rft.aufirst=Jonathan&rft.au=Hodge%2C+Michael+Jonathan+Sessions&rft.au=Radick%2C+Gregory&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcambridgecompani00hodg_248&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-Gattei-23"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gattei_23-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gattei_23-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Stefano Gattei, <i>Karl Popper's Philosophy of Science: Rationality without Foundations</i> (New York: <a href="/wiki/Routledge" title="Routledge">Routledge</a>, 2009), ch. 2 "Science and philosophy", <a rel="nofollow" class="external text" href="https://books.google.com/books?id=oPPu1JvMBFoC&pg=PA28#v=twopage">pp. 28–30</a>.</span> </li> <li id="cite_note-:1-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-:1_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaleb2010" class="citation book cs1">Taleb, Nassim Nicholas (2010). <i>The Black Swan: Second Edition: The Impact of the Highly Improbable Fragility</i>. New York: Random House Publishing Group. pp. 199, 302, 383. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0812973815" title="Special:BookSources/978-0812973815"><bdi>978-0812973815</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Black+Swan%3A+Second+Edition%3A+The+Impact+of+the+Highly+Improbable+Fragility&rft.place=New+York&rft.pages=199%2C+302%2C+383&rft.pub=Random+House+Publishing+Group&rft.date=2010&rft.isbn=978-0812973815&rft.aulast=Taleb&rft.aufirst=Nassim+Nicholas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><a href="/wiki/Galen" title="Galen">Galen</a> <i>On Medical Experience</i>, 24.</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlutynski2011" class="citation journal cs1">Plutynski, Anya (2011). <a rel="nofollow" class="external text" href="https://philpapers.org/rec/PLUFPO">"Four Problems of Abduction: A Brief History"</a>. <i>HOPOS: The Journal of the International Society for the History of Philosophy of Science</i>. <b>1</b> (2): <span class="nowrap">227–</span>248. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F660746">10.1086/660746</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15332806">15332806</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230411064730/https://philpapers.org/rec/PLUFPO">Archived</a> from the original on 11 April 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">16 April</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=HOPOS%3A+The+Journal+of+the+International+Society+for+the+History+of+Philosophy+of+Science&rft.atitle=Four+Problems+of+Abduction%3A+A+Brief+History&rft.volume=1&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E227-%3C%2Fspan%3E248&rft.date=2011&rft_id=info%3Adoi%2F10.1086%2F660746&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15332806%23id-name%3DS2CID&rft.aulast=Plutynski&rft.aufirst=Anya&rft_id=https%3A%2F%2Fphilpapers.org%2Frec%2FPLUFPO&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcauliffe2015" class="citation journal cs1">Mcauliffe, William H. B. (2015). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/10.2979/trancharpeirsoc.51.3.300">"How did Abduction Get Confused with Inference to the Best Explanation?"</a>. <i>Transactions of the Charles S. Peirce Society</i>. <b>51</b> (3): <span class="nowrap">300–</span>319. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2979%2Ftrancharpeirsoc.51.3.300">10.2979/trancharpeirsoc.51.3.300</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0009-1774">0009-1774</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/10.2979/trancharpeirsoc.51.3.300">10.2979/trancharpeirsoc.51.3.300</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:43255826">43255826</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220416041215/https://www.jstor.org/stable/10.2979/trancharpeirsoc.51.3.300">Archived</a> from the original on 16 April 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">16 April</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+Charles+S.+Peirce+Society&rft.atitle=How+did+Abduction+Get+Confused+with+Inference+to+the+Best+Explanation%3F&rft.volume=51&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E300-%3C%2Fspan%3E319&rft.date=2015&rft.issn=0009-1774&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A43255826%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F10.2979%2Ftrancharpeirsoc.51.3.300%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2979%2Ftrancharpeirsoc.51.3.300&rft.aulast=Mcauliffe&rft.aufirst=William+H.+B.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F10.2979%2Ftrancharpeirsoc.51.3.300&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-Salmon-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-Salmon_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Salmon_28-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Wesley C Salmon, <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/210401">"The uniformity of Nature"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180818182105/https://www.jstor.org/stable/210401">Archived</a> 18 August 2018 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>Philosophy and Phenomenological Research</i>, 1953 Sep;<b>14</b>(1):39–48, [39].</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Cf. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKant1787" class="citation book cs1">Kant, Immanuel (1787). <i>Critique of Pure Reason</i>. pp. B132.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Critique+of+Pure+Reason&rft.pages=B132&rft.date=1787&rft.aulast=Kant&rft.aufirst=Immanuel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-Toretti-p220-30"><span class="mw-cite-backlink">^ <a href="#cite_ref-Toretti-p220_30-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Toretti-p220_30-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Toretti-p220_30-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Toretti-p220_30-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">Roberto Torretti, <i>The Philosophy of Physics</i> (Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 1999), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA219">219–21</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192130/https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA219">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a><a rel="nofollow" class="external text" href="https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA216">[216]</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192129/https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA216">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text">Roberto Torretti, <i>The Philosophy of Physics</i> (Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 1999), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA226">pp. 226</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192128/https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA226">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA228">228–29</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192127/https://books.google.com/books?id=vg_wxiLRvvYC&pg=PA228">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-Poston-32"><span class="mw-cite-backlink">^ <a href="#cite_ref-Poston_32-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Poston_32-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Poston_32-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Ted Poston <a rel="nofollow" class="external text" href="http://www.iep.utm.edu/found-ep">"Foundationalism"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190926003413/http://www.iep.utm.edu/found-ep">Archived</a> 26 September 2019 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, § b "Theories of proper inference", §§ iii "Liberal inductivism", <i><a href="/wiki/Internet_Encyclopedia_of_Philosophy" title="Internet Encyclopedia of Philosophy">Internet Encyclopedia of Philosophy</a></i>, 10 Jun 2010 (last updated): "Strict inductivism is motivated by the thought that we have some kind of inferential knowledge of the world that cannot be accommodated by deductive inference from epistemically <a href="/wiki/Basic_belief" title="Basic belief">basic beliefs</a>. A fairly recent debate has arisen over the merits of strict inductivism. Some philosophers have argued that there are other forms of nondeductive inference that do not fit the model of enumerative induction. <a href="/wiki/C.S._Peirce" class="mw-redirect" title="C.S. Peirce">C.S. Peirce</a> describes a form of inference called '<a href="/wiki/Abductive_reasoning" title="Abductive reasoning">abduction</a>' or '<a href="/wiki/Inference_to_the_best_explanation" class="mw-redirect" title="Inference to the best explanation">inference to the best explanation</a>'. This form of inference appeals to explanatory considerations to justify belief. One infers, for example, that two students copied answers from a third because this is the best explanation of the available data—they each make the same mistakes and the two sat in view of the third. Alternatively, in a more theoretical context, one infers that there are very small unobservable <a href="/wiki/Molecules" class="mw-redirect" title="Molecules">particles</a> because this is the best explanation of <a href="/wiki/Brownian_motion" title="Brownian motion">Brownian motion</a>. Let us call 'liberal inductivism' any view that accepts the legitimacy of a form of inference to the best explanation that is distinct from enumerative induction. For a defense of liberal inductivism, see <a href="/wiki/Gilbert_Harman" title="Gilbert Harman">Gilbert Harman</a>'s classic (1965) paper. Harman defends a strong version of liberal inductivism according to which enumerative induction is just a disguised form of <a href="/wiki/Inference_to_the_best_explanation" class="mw-redirect" title="Inference to the best explanation">inference to the best explanation</a>".</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text">David Andrews, <i>Keynes and the British Humanist Tradition: The Moral Purpose of the Market</i> (New York: <a href="/wiki/Routledge" title="Routledge">Routledge</a>, 2010), pp. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=1VsYOwRsOVUC&pg=PA63">63–65</a>.</span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRussell1927" class="citation book cs1">Russell, Bertrand (1927). <i>An Outline of Philosophy</i>. London and New York: Allen and Unwin.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Outline+of+Philosophy&rft.place=London+and+New+York&rft.pub=Allen+and+Unwin&rft.date=1927&rft.aulast=Russell&rft.aufirst=Bertrand&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span> reprinted in Bertrand Russell, <i>The Basic Writings of Bertrand Russell</i> (New York: <a href="/wiki/Routledge" title="Routledge">Routledge</a>, 2009), "The validity of inference"], pp. 157–64, quote on <a rel="nofollow" class="external text" href="https://books.google.com/books?id=jqun5YJGt-wC&pg=PA159">p. 159</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192130/https://books.google.com/books?id=jqun5YJGt-wC&pg=PA159">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><a href="#CITEREFRussell1948">Russell 1948</a>, pp. 396–450.</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text">Gregory Landini, <i>Russell</i> (New York: Routledge, 2011), p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Simvmwn2m2gC&pg=PA230">230</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192127/https://books.google.com/books?id=Simvmwn2m2gC&pg=PA230">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-Russell1945-37"><span class="mw-cite-backlink">^ <a href="#cite_ref-Russell1945_37-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Russell1945_37-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Bertrand Russell, <i>A History of Western Philosophy</i> (London: George Allen and Unwin, 1945 / New York: Simon and Schuster, 1945), pp. 673–74.</span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text">Stathis Psillos, <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2956303">"On Van Fraassen's critique of abductive reasoning"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180818183602/https://www.jstor.org/stable/2956303">Archived</a> 18 August 2018 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, <i>Philosophical Quarterly</i>, 1996 Jan;<b>46</b>(182):31–47, [31].</span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text">John Vickers. <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/induction-problem/">The Problem of Induction</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140407014814/http://plato.stanford.edu/entries/induction-problem/">Archived</a> 7 April 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. The Stanford Encyclopedia of Philosophy.</span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHerms" class="citation web cs1">Herms, D. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090319202920/http://www.dartmouth.edu/~bio125/logic.Giere.pdf">"Logical Basis of Hypothesis Testing in Scientific Research"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.dartmouth.edu/~bio125/logic.Giere.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 19 March 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">24 July</span> 2005</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Logical+Basis+of+Hypothesis+Testing+in+Scientific+Research&rft.aulast=Herms&rft.aufirst=D.&rft_id=http%3A%2F%2Fwww.dartmouth.edu%2F~bio125%2Flogic.Giere.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKosko1990" class="citation journal cs1">Kosko, Bart (1990). "Fuzziness vs. Probability". <i>International Journal of General Systems</i>. <b>17</b> (1): <span class="nowrap">211–</span>40. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F03081079008935108">10.1080/03081079008935108</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+General+Systems&rft.atitle=Fuzziness+vs.+Probability&rft.volume=17&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E211-%3C%2Fspan%3E40&rft.date=1990&rft_id=info%3Adoi%2F10.1080%2F03081079008935108&rft.aulast=Kosko&rft.aufirst=Bart&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/kant-reason/#TheReaReaCogRolLim">"Kant's Account of Reason"</a>. <i>Stanford Encyclopedia of Philosophy : Kant's account of reason</i>. Metaphysics Research Lab, Stanford University. 2018. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151208082150/http://plato.stanford.edu/entries/kant-reason/#TheReaReaCogRolLim">Archived</a> from the original on 8 December 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">27 November</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Kant%27s+Account+of+Reason&rft.btitle=Stanford+Encyclopedia+of+Philosophy+%3A+Kant%27s+account+of+reason&rft.pub=Metaphysics+Research+Lab%2C+Stanford+University&rft.date=2018&rft_id=http%3A%2F%2Fplato.stanford.edu%2Fentries%2Fkant-reason%2F%23TheReaReaCogRolLim&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChowdhry2015" class="citation book cs1">Chowdhry, K.R. (2015). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=MmVwBgAAQBAJ&q=%22mathematical+induction%22+deduction&pg=PA26"><i>Fundamentals of Discrete Mathematical Structures</i></a> (3rd ed.). PHI Learning Pvt. Ltd. p. 26. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-8120350748" title="Special:BookSources/978-8120350748"><bdi>978-8120350748</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 December</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Discrete+Mathematical+Structures&rft.pages=26&rft.edition=3rd&rft.pub=PHI+Learning+Pvt.+Ltd.&rft.date=2015&rft.isbn=978-8120350748&rft.aulast=Chowdhry&rft.aufirst=K.R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DMmVwBgAAQBAJ%26q%3D%2522mathematical%2Binduction%2522%2Bdeduction%26pg%3DPA26&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text">Sextus Empiricus, <i>Outlines of Pyrrhonism</i>. Trans. <a href="/wiki/Robert_Gregg_Bury" title="Robert Gregg Bury">R.G. Bury</a>, Harvard University Press, Cambridge, Massachusetts, 1933, p. 283.</span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_Hume1910" class="citation book cs1"><a href="/wiki/David_Hume" title="David Hume">David Hume</a> (1910) [1748]. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071231182807/http://18th.eserver.org/hume-enquiry.html#4"><i>An Enquiry concerning Human Understanding</i></a>. P.F. Collier & Son. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-825060-9" title="Special:BookSources/978-0-19-825060-9"><bdi>978-0-19-825060-9</bdi></a>. Archived from <a rel="nofollow" class="external text" href="http://18th.eserver.org/hume-enquiry.html#4">the original</a> on 31 December 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">27 December</span> 2007</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Enquiry+concerning+Human+Understanding&rft.pub=P.F.+Collier+%26+Son&rft.date=1910&rft.isbn=978-0-19-825060-9&rft.au=David+Hume&rft_id=http%3A%2F%2F18th.eserver.org%2Fhume-enquiry.html%234&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text">Vickers, John. <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/induction-problem/#2HumIndJus">"The Problem of Induction"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140407014814/http://plato.stanford.edu/entries/induction-problem/#2HumIndJus">Archived</a> 7 April 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (Section 2). <i>Stanford Encyclopedia of Philosophy</i>. 21 June 2010</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text">Vickers, John. <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/induction-problem/#IndJus">"The Problem of Induction"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140407014814/http://plato.stanford.edu/entries/induction-problem/#IndJus">Archived</a> 7 April 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (Section 2.1). <i>Stanford Encyclopedia of Philosophy</i>. 21 June 2010.</span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRussel1997" class="citation book cs1">Russel, Bertrand (1997). <i>The Problems of Philosophy</i>. Oxford: Oxford University Press. p. 66. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0195115529" title="Special:BookSources/978-0195115529"><bdi>978-0195115529</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Problems+of+Philosophy&rft.place=Oxford&rft.pages=66&rft.pub=Oxford+University+Press&rft.date=1997&rft.isbn=978-0195115529&rft.aulast=Russel&rft.aufirst=Bertrand&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPopperMiller1983" class="citation journal cs1">Popper, Karl R.; Miller, David W. (1983). "A proof of the impossibility of inductive probability". <i><a href="/wiki/Nature_(journal)" title="Nature (journal)">Nature</a></i>. <b>302</b> (5910): <span class="nowrap">687–</span>88. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1983Natur.302..687P">1983Natur.302..687P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F302687a0">10.1038/302687a0</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4317588">4317588</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=A+proof+of+the+impossibility+of+inductive+probability&rft.volume=302&rft.issue=5910&rft.pages=%3Cspan+class%3D%22nowrap%22%3E687-%3C%2Fspan%3E88&rft.date=1983&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4317588%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F302687a0&rft_id=info%3Abibcode%2F1983Natur.302..687P&rft.aulast=Popper&rft.aufirst=Karl+R.&rft.au=Miller%2C+David+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-Gillies-50"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gillies_50-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gillies_50-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Gillies_50-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Gillies_50-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Gillies_50-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text">Donald Gillies, "Problem-solving and the problem of induction", in <i>Rethinking Popper</i> (Dordrecht: <a href="/wiki/Springer_(publisher)" class="mw-redirect" title="Springer (publisher)">Springer</a>, 2009), Zuzana Parusniková & Robert S Cohen, eds, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=R3aywtFIKKsC&pg=PA103#v=twopage">pp. 103–05</a>.</span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text">Ch 5 "The controversy around inductive logic" in <a href="/wiki/Richard_Mattessich" title="Richard Mattessich">Richard Mattessich</a>, ed, <i>Instrumental Reasoning and Systems Methodology: An Epistemology of the Applied and Social Sciences</i> (Dordrecht: <a href="/wiki/D._Reidel" title="D. Reidel">D. Reidel Publishing</a>, 1978), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=i8kmptHdx3MC&pg=PA141#v=twopage">pp. 141–43</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192130/https://books.google.com/books?id=i8kmptHdx3MC&pg=PA141#v=twopage">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-Gillies-p111-52"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gillies-p111_52-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gillies-p111_52-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Donald Gillies, "Problem-solving and the problem of induction", in <i>Rethinking Popper</i> (Dordrecht: <a href="/wiki/Springer_(publisher)" class="mw-redirect" title="Springer (publisher)">Springer</a>, 2009), Zuzana Parusniková & Robert S Cohen, eds, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=R3aywtFIKKsC&pg=PA111">p. 111</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220509192129/https://books.google.com/books?id=R3aywtFIKKsC&pg=PA111">Archived</a> 9 May 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>: "I argued earlier that there are some exceptions to Popper's claim that rules of inductive inference do not exist. However, these exceptions are relatively rare. They occur, for example, in the machine learning programs of <a href="/wiki/Artificial_Intelligence" class="mw-redirect" title="Artificial Intelligence">AI</a>. For the vast bulk of human science both past and present, rules of inductive inference do not exist. For such science, Popper's model of conjectures which are freely invented and then tested out seems to be more accurate than any model based on inductive inferences. Admittedly, there is talk nowadays in the context of science carried out by humans of 'inference to the best explanation' or 'abductive inference', but such so-called inferences are not at all inferences based on precisely formulated rules like the deductive rules of inference. Those who talk of 'inference to the best explanation' or 'abductive inference', for example, never formulate any precise rules according to which these so-called inferences take place. In reality, the 'inferences' which they describe in their examples involve conjectures thought up by human ingenuity and creativity, and by no means inferred in any mechanical fashion, or according to precisely specified rules".</span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGray2011" class="citation book cs1">Gray, Peter (2011). <i>Psychology</i> (Sixth ed.). New York: Worth. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4292-1947-1" title="Special:BookSources/978-1-4292-1947-1"><bdi>978-1-4292-1947-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Psychology&rft.place=New+York&rft.edition=Sixth&rft.pub=Worth&rft.date=2011&rft.isbn=978-1-4292-1947-1&rft.aulast=Gray&rft.aufirst=Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGood1983" class="citation book cs1">Good, Irving J. (1983). <i>Good Thinking: The Foundations of Probability and Its Applications</i> (Dover, New York, 2009 replication ed.). Minneapolis: University of Minneapolis Press. pp. <span class="nowrap">ix–</span>xvii, 18, 27, 29, <span class="nowrap">36–</span>38, <span class="nowrap">123–</span>127.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Good+Thinking%3A+The+Foundations+of+Probability+and+Its+Applications&rft.place=Minneapolis&rft.pages=%3Cspan+class%3D%22nowrap%22%3Eix-%3C%2Fspan%3Exvii%2C+18%2C+27%2C+29%2C+%3Cspan+class%3D%22nowrap%22%3E36-%3C%2Fspan%3E38%2C+%3Cspan+class%3D%22nowrap%22%3E123-%3C%2Fspan%3E127&rft.edition=Dover%2C+New+York%2C+2009+replication&rft.pub=University+of+Minneapolis+Press&rft.date=1983&rft.aulast=Good&rft.aufirst=Irving+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRathmannerHutter2011" class="citation journal cs1">Rathmanner, Samuel; <a href="/wiki/Marcus_Hutter" title="Marcus Hutter">Hutter, Marcus</a> (2011). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe13061076">"A Philosophical Treatise of Universal Induction"</a>. <i>Entropy</i>. <b>13</b> (6): <span class="nowrap">1076–</span>136. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1105.5721">1105.5721</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011Entrp..13.1076R">2011Entrp..13.1076R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fe13061076">10.3390/e13061076</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:2499910">2499910</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Entropy&rft.atitle=A+Philosophical+Treatise+of+Universal+Induction&rft.volume=13&rft.issue=6&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1076-%3C%2Fspan%3E136&rft.date=2011&rft_id=info%3Aarxiv%2F1105.5721&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A2499910%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.3390%2Fe13061076&rft_id=info%3Abibcode%2F2011Entrp..13.1076R&rft.aulast=Rathmanner&rft.aufirst=Samuel&rft.au=Hutter%2C+Marcus&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Fe13061076&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLu2024" class="citation journal cs1">Lu, Z. (2024). <a rel="nofollow" class="external text" href="https://openreview.net/pdf?id=2aGcshccuV">"When is Inductive Inference Possible?"</a>. <i>NeurIPS 2024</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=NeurIPS+2024&rft.atitle=When+is+Inductive+Inference+Possible%3F&rft.date=2024&rft.aulast=Lu&rft.aufirst=Z.&rft_id=https%3A%2F%2Fopenreview.net%2Fpdf%3Fid%3D2aGcshccuV&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=31" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHerms" class="citation web cs1">Herms, D. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090319202920/http://www.dartmouth.edu/~bio125/logic.Giere.pdf">"Logical Basis of Hypothesis Testing in Scientific Research"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.dartmouth.edu/~bio125/logic.Giere.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 19 March 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">24 July</span> 2005</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Logical+Basis+of+Hypothesis+Testing+in+Scientific+Research&rft.aulast=Herms&rft.aufirst=D.&rft_id=http%3A%2F%2Fwww.dartmouth.edu%2F~bio125%2Flogic.Giere.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKemerling2001" class="citation web cs1">Kemerling, G. (27 October 2001). <a rel="nofollow" class="external text" href="http://www.philosophypages.com/lg/e14.htm">"Causal Reasoning"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Causal+Reasoning&rft.date=2001-10-27&rft.aulast=Kemerling&rft.aufirst=G.&rft_id=http%3A%2F%2Fwww.philosophypages.com%2Flg%2Fe14.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHollandHolyoakNisbettThagard1989" class="citation book cs1">Holland, J.H.; Holyoak, K.J.; Nisbett, R.E.; Thagard, P.R. (1989). <i>Induction: Processes of Inference, Learning, and Discovery</i>. Cambridge, MA: <a href="/wiki/MIT_Press" title="MIT Press">MIT Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-58096-0" title="Special:BookSources/978-0-262-58096-0"><bdi>978-0-262-58096-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Induction%3A+Processes+of+Inference%2C+Learning%2C+and+Discovery&rft.place=Cambridge%2C+MA&rft.pub=MIT+Press&rft.date=1989&rft.isbn=978-0-262-58096-0&rft.aulast=Holland&rft.aufirst=J.H.&rft.au=Holyoak%2C+K.J.&rft.au=Nisbett%2C+R.E.&rft.au=Thagard%2C+P.R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHolyoakMorrison2005" class="citation book cs1">Holyoak, K.; Morrison, R. (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=znbkHaC8QeMC"><i>The Cambridge Handbook of Thinking and Reasoning</i></a>. New York: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-82417-0" title="Special:BookSources/978-0-521-82417-0"><bdi>978-0-521-82417-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Handbook+of+Thinking+and+Reasoning&rft.place=New+York&rft.pub=Cambridge+University+Press&rft.date=2005&rft.isbn=978-0-521-82417-0&rft.aulast=Holyoak&rft.aufirst=K.&rft.au=Morrison%2C+R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DznbkHaC8QeMC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Inductive_reasoning&action=edit&section=32" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wiktionary-logo-en-v2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/inductive_reasoning" class="extiw" title="wiktionary:inductive reasoning">inductive reasoning</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikisource-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/38px-Wikisource-logo.svg.png" decoding="async" width="38" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/57px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/76px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></span></div> <div class="side-box-text plainlist"><a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has the text of a 1920 <i><a href="/wiki/Encyclopedia_Americana" title="Encyclopedia Americana">Encyclopedia Americana</a></i> article about <i><b><a href="https://en.wikisource.org/wiki/The_Encyclopedia_Americana_(1920)/Induction_(logic)" class="extiw" title="s:The Encyclopedia Americana (1920)/Induction (logic)">Inductive reasoning</a></b></i>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="http://www.iep.utm.edu/conf-ind">"Confirmation and Induction"</a>. <i><a href="/wiki/Internet_Encyclopedia_of_Philosophy" title="Internet Encyclopedia of Philosophy">Internet Encyclopedia of Philosophy</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Confirmation+and+Induction&rft.btitle=Internet+Encyclopedia+of+Philosophy&rft_id=http%3A%2F%2Fwww.iep.utm.edu%2Fconf-ind&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZalta" class="citation encyclopaedia cs1"><a href="/wiki/Edward_N._Zalta" title="Edward N. Zalta">Zalta, Edward N.</a> (ed.). <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/logic-inductive/">"Inductive Logic"</a>. <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Inductive+Logic&rft.btitle=Stanford+Encyclopedia+of+Philosophy&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Flogic-inductive%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://philpapers.org/browse/induction">Inductive reasoning</a> at <a href="/wiki/PhilPapers" title="PhilPapers">PhilPapers</a></li> <li><a rel="nofollow" class="external text" href="https://www.inphoproject.org/taxonomy/2256">Inductive reasoning</a> at the <a href="/wiki/Indiana_Philosophy_Ontology_Project" class="mw-redirect" title="Indiana Philosophy Ontology Project">Indiana Philosophy Ontology Project</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070927003210/http://www.uncg.edu/phi/phi115/induc4.htm"><i>Four Varieties of Inductive Argument</i></a> from the Department of Philosophy, <a href="/wiki/University_of_North_Carolina_at_Greensboro" title="University of North Carolina at Greensboro">University of North Carolina at Greensboro</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170808171702/http://faculty.ucmerced.edu/sites/default/files/eheit/files/heit2000.pdf">"Properties of Inductive Reasoning"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://faculty.ucmerced.edu/sites/default/files/eheit/files/heit2000.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 8 August 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">16 July</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Properties+of+Inductive+Reasoning&rft_id=http%3A%2F%2Ffaculty.ucmerced.edu%2Fsites%2Fdefault%2Ffiles%2Feheit%2Ffiles%2Fheit2000.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInductive+reasoning" class="Z3988"></span> <span style="font-size:85%;">(166 <a href="/wiki/Kibibyte" class="mw-redirect" title="Kibibyte">KiB</a>)</span>, a psychological review by Evan Heit of the <a href="/wiki/University_of_California,_Merced" title="University of California, Merced">University of California, Merced</a>.</li> <li><a rel="nofollow" class="external text" href="http://dudespaper.com/the-mind-limber.html"><i>The Mind, Limber</i></a> An article which employs the film <a href="/wiki/The_Big_Lebowski" title="The Big Lebowski">The Big Lebowski</a> to explain the value of inductive reasoning.</li> <li><a rel="nofollow" class="external text" href="https://archive.today/20140726215957/http://www.academia.edu/4154895/Some_Remarks_on_the_Pragmatic_Problem_of_Induction.html">The Pragmatic Problem of Induction</a>, by Thomas Bullemore</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output 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hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abductive_reasoning" title="Abductive reasoning">Abductive reasoning</a></li> <li><a href="/wiki/Deductive_reasoning" title="Deductive reasoning">Deductive reasoning</a></li> <li><a class="mw-selflink selflink">Inductive reasoning</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Logic463" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Logic" title="Template:Logic"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Logic" title="Template talk:Logic"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Logic" title="Special:EditPage/Template:Logic"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Logic463" style="font-size:114%;margin:0 4em"><a href="/wiki/Logic" title="Logic">Logic</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Outline_of_logic" title="Outline of logic">Outline</a></li> <li><a href="/wiki/History_of_logic" title="History of logic">History</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Major fields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Computer science</a></li> <li><a href="/wiki/Formal_semantics_(natural_language)" title="Formal semantics (natural language)">Formal semantics (natural language)</a></li> <li><a href="/wiki/Inference" title="Inference">Inference</a></li> <li><a href="/wiki/Philosophy_of_logic" title="Philosophy of logic">Philosophy of logic</a></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Proof</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li> <li><a href="/wiki/Syntax_(logic)" title="Syntax (logic)">Syntax</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Logics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_logic" title="Classical logic">Classical</a></li> <li><a href="/wiki/Informal_logic" title="Informal logic">Informal</a> <ul><li><a href="/wiki/Critical_thinking" title="Critical thinking">Critical thinking</a></li> <li><a href="/wiki/Reason" title="Reason">Reason</a></li></ul></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical</a></li> <li><a href="/wiki/Non-classical_logic" title="Non-classical logic">Non-classical</a></li> <li><a href="/wiki/Philosophical_logic" title="Philosophical logic">Philosophical</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Argumentation_theory" title="Argumentation theory">Argumentation</a></li> <li><a href="/wiki/Metalogic" title="Metalogic">Metalogic</a></li> <li><a href="/wiki/Metamathematics" title="Metamathematics">Metamathematics</a></li> <li><a href="/wiki/Set_theory" title="Set theory">Set</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Foundations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abductive_reasoning" title="Abductive reasoning">Abduction</a></li> <li><a href="/wiki/Analytic%E2%80%93synthetic_distinction" title="Analytic–synthetic distinction">Analytic and synthetic propositions</a></li> <li><a href="/wiki/Antecedent_(logic)" title="Antecedent (logic)">Antecedent</a></li> <li><a href="/wiki/Consequent" title="Consequent">Consequent</a></li> <li><a href="/wiki/Contradiction" title="Contradiction">Contradiction</a> <ul><li><a href="/wiki/Paradox" title="Paradox">Paradox</a></li> <li><a href="/wiki/Antinomy" title="Antinomy">Antinomy</a></li></ul></li> <li><a href="/wiki/Deductive_reasoning" title="Deductive reasoning">Deduction</a></li> <li><a href="/wiki/Deductive_closure" title="Deductive closure">Deductive closure</a></li> <li><a href="/wiki/Definition" title="Definition">Definition</a></li> <li><a href="/wiki/Description" title="Description">Description</a></li> <li><a href="/wiki/Logical_consequence" title="Logical consequence">Entailment</a> <ul><li><a href="/wiki/Entailment_(linguistics)" title="Entailment (linguistics)">Linguistic</a></li></ul></li> <li><a href="/wiki/Logical_form" title="Logical form">Form</a></li> <li><a class="mw-selflink selflink">Induction</a></li> <li><a href="/wiki/Logical_truth" title="Logical truth">Logical truth</a></li> <li><a href="/wiki/Name" title="Name">Name</a></li> <li><a href="/wiki/Necessity_and_sufficiency" title="Necessity and sufficiency">Necessity and sufficiency</a></li> <li><a href="/wiki/Premise" title="Premise">Premise</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Reference" title="Reference">Reference</a></li> <li><a href="/wiki/Statement_(logic)" title="Statement (logic)">Statement</a></li> <li><a href="/wiki/Substitution_(logic)" title="Substitution (logic)">Substitution</a></li> <li><a href="/wiki/Truth" title="Truth">Truth</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity (logic)">Validity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Index_of_logic_articles" title="Index of logic articles">Topics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_mathematical_logic_topics" title="List of mathematical logic topics">Mathematical logic</a></li> <li><a href="/wiki/List_of_Boolean_algebra_topics" title="List of Boolean algebra topics">Boolean algebra</a></li> <li><a href="/wiki/List_of_set_theory_topics" title="List of set theory topics">Set theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_logicians" title="List of logicians">Logicians</a></li> <li><a href="/wiki/List_of_rules_of_inference" title="List of rules of inference">Rules of inference</a></li> <li><a href="/wiki/List_of_paradoxes" title="List of paradoxes">Paradoxes</a></li> <li><a href="/wiki/List_of_fallacies" title="List of fallacies">Fallacies</a></li> <li><a href="/wiki/List_of_logic_symbols" title="List of logic symbols">Logic symbols</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span> </span><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></li> <li><a href="/wiki/Category:Logic" title="Category:Logic">Category</a></li> <li><a href="/wiki/Wikipedia:WikiProject_Logic" title="Wikipedia:WikiProject Logic">WikiProject</a> (<a href="/wiki/Wikipedia_talk:WikiProject_Logic" title="Wikipedia talk:WikiProject Logic">talk</a>)</li> <li><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Special:Recentchangeslinked&target=Template:Logic&hidebots=0">changes</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Philosophy_of_science439" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Philosophy_of_science" title="Template:Philosophy of science"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Philosophy_of_science" title="Template talk:Philosophy of science"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Philosophy_of_science" title="Special:EditPage/Template:Philosophy of science"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Philosophy_of_science439" style="font-size:114%;margin:0 4em"><a href="/wiki/Philosophy_of_science" title="Philosophy of science">Philosophy of science</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Philosophical_analysis" title="Philosophical analysis">Analysis</a></li> <li><a href="/wiki/Analytic%E2%80%93synthetic_distinction" title="Analytic–synthetic distinction">Analytic–synthetic distinction</a></li> <li><a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori"><i>A priori</i> and <i>a posteriori</i></a></li> <li><a href="/wiki/Causality" title="Causality">Causality</a> <ul><li><a href="/wiki/Mill%27s_Methods" class="mw-redirect" title="Mill's Methods">Mill's Methods</a></li></ul></li> <li><a href="/wiki/Commensurability_(philosophy_of_science)" title="Commensurability (philosophy of science)">Commensurability</a></li> <li><a href="/wiki/Consilience" title="Consilience">Consilience</a></li> <li><a href="/wiki/Construct_(philosophy)" title="Construct (philosophy)">Construct</a></li> <li><a href="/wiki/Correlation" title="Correlation">Correlation</a> <ul><li><a href="/wiki/Correlation_function" title="Correlation function">function</a></li></ul></li> <li><a href="/wiki/Creative_synthesis" title="Creative synthesis">Creative synthesis</a></li> <li><a href="/wiki/Demarcation_problem" title="Demarcation problem">Demarcation problem</a></li> <li><a href="/wiki/Empirical_evidence" title="Empirical evidence">Empirical evidence</a></li> <li><a href="/wiki/Experiment" title="Experiment">Experiment</a> <ul><li><a href="/wiki/Design_of_experiments" title="Design of experiments">design</a></li></ul></li> <li><a href="/wiki/Explanatory_power" title="Explanatory power">Explanatory power</a></li> <li><a href="/wiki/Fact" title="Fact">Fact</a></li> <li><a href="/wiki/Falsifiability" title="Falsifiability">Falsifiability</a></li> <li><a href="/wiki/Feminist_method" title="Feminist method">Feminist method</a></li> <li><a href="/wiki/Functional_contextualism" title="Functional contextualism">Functional contextualism</a></li> <li><a href="/wiki/Hypothesis" title="Hypothesis">Hypothesis</a> <ul><li><a href="/wiki/Alternative_hypothesis" title="Alternative hypothesis">alternative</a></li> <li><a href="/wiki/Null_hypothesis" title="Null hypothesis">null</a></li></ul></li> <li><i><a href="/wiki/Ignoramus_et_ignorabimus" title="Ignoramus et ignorabimus">Ignoramus et ignorabimus</a></i></li> <li><a class="mw-selflink selflink">Inductive reasoning</a></li> <li><a href="/wiki/Intertheoretic_reduction" title="Intertheoretic reduction">Intertheoretic reduction</a></li> <li><a href="/wiki/Inquiry" title="Inquiry">Inquiry</a></li> <li><a href="/wiki/Nature_(philosophy)" title="Nature (philosophy)">Nature</a></li> <li><a href="/wiki/Objectivity_(philosophy)" class="mw-redirect" title="Objectivity (philosophy)">Objectivity</a></li> <li><a href="/wiki/Observation" title="Observation">Observation</a></li> <li><a href="/wiki/Paradigm" title="Paradigm">Paradigm</a></li> <li><a href="/wiki/Problem_of_induction" title="Problem of induction">Problem of induction</a></li> <li><a href="/wiki/Scientific_evidence" title="Scientific evidence">Scientific evidence</a> <ul><li><a href="/wiki/Evidence-based_practice" title="Evidence-based practice">Evidence-based practice</a></li></ul></li> <li><a href="/wiki/Scientific_law" title="Scientific law">Scientific law</a></li> <li><a href="/wiki/Scientific_method" title="Scientific method">Scientific method</a></li> <li><a href="/wiki/Scientific_pluralism" title="Scientific pluralism">Scientific pluralism</a></li> <li><a href="/wiki/Scientific_Revolution" title="Scientific Revolution">Scientific Revolution</a></li> <li><a href="/wiki/Testability" title="Testability">Testability</a></li> <li><a href="/wiki/Theory" title="Theory">Theory</a> <ul><li><a href="/wiki/Theory_choice" title="Theory choice">choice</a></li> <li><a href="/wiki/Theory-ladenness" title="Theory-ladenness">ladenness</a></li> <li><a href="/wiki/Scientific_theory" title="Scientific theory">scientific</a></li></ul></li> <li><a href="/wiki/Underdetermination" title="Underdetermination">Underdetermination</a></li> <li><a href="/wiki/Unity_of_science" title="Unity of science">Unity of science</a></li> <li><a href="/wiki/Variable_and_attribute_(research)" title="Variable and attribute (research)">Variable</a> <ul><li><a href="/wiki/Control_variable" title="Control variable">control</a></li> <li><a href="/wiki/Dependent_and_independent_variables" title="Dependent and independent variables">dependent and independent</a></li></ul></li> <li><a href="/wiki/Index_of_philosophy_of_science_articles" title="Index of philosophy of science articles">more...</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coherentism" title="Coherentism">Coherentism</a></li> <li><a href="/wiki/Confirmation_holism" title="Confirmation holism">Confirmation holism</a></li> <li><a href="/wiki/Constructive_empiricism" title="Constructive empiricism">Constructive empiricism</a></li> <li><a href="/wiki/Constructive_realism" title="Constructive realism">Constructive realism</a></li> <li><a href="/wiki/Constructivist_epistemology" class="mw-redirect" title="Constructivist epistemology">Constructivist epistemology</a></li> <li><a href="/wiki/Contextualism" title="Contextualism">Contextualism</a></li> <li><a href="/wiki/Conventionalism" title="Conventionalism">Conventionalism</a></li> <li><a href="/wiki/Deductive-nomological_model" title="Deductive-nomological model">Deductive-nomological model</a></li> <li><a href="/wiki/Epistemological_anarchism" class="mw-redirect" title="Epistemological anarchism">Epistemological anarchism</a></li> <li><a href="/wiki/Evolutionism" title="Evolutionism">Evolutionism</a></li> <li><a href="/wiki/Fallibilism" title="Fallibilism">Fallibilism</a></li> <li><a href="/wiki/Foundationalism" title="Foundationalism">Foundationalism</a></li> <li><a href="/wiki/Hypothetico-deductive_model" title="Hypothetico-deductive model">Hypothetico-deductive model</a></li> <li><a href="/wiki/Inductionism" title="Inductionism">Inductionism</a></li> <li><a href="/wiki/Instrumentalism" title="Instrumentalism">Instrumentalism</a></li> <li><a href="/wiki/Model-dependent_realism" title="Model-dependent realism">Model-dependent realism</a></li> <li><a href="/wiki/Naturalism_(philosophy)" title="Naturalism (philosophy)">Naturalism</a></li> <li><a href="/wiki/Physicalism" title="Physicalism">Physicalism</a></li> <li><a href="/wiki/Positivism" title="Positivism">Positivism</a> / <a href="/wiki/Reductionism" title="Reductionism">Reductionism</a> / <a href="/wiki/Determinism" title="Determinism">Determinism</a></li> <li><a href="/wiki/Pragmatism" title="Pragmatism">Pragmatism</a></li> <li><a href="/wiki/Rationalism" title="Rationalism">Rationalism</a> / <a href="/wiki/Empiricism" title="Empiricism">Empiricism</a></li> <li><a href="/wiki/Received_view_of_theories" title="Received view of theories">Received view</a> / <a href="/wiki/Semantic_view_of_theories" title="Semantic view of theories">Semantic view of theories</a></li> <li><a href="/wiki/Scientific_essentialism" title="Scientific essentialism">Scientific essentialism</a></li> <li><a href="/wiki/Scientific_formalism" title="Scientific formalism">Scientific formalism</a></li> <li><a href="/wiki/Scientific_realism" title="Scientific realism">Scientific realism</a> / <a href="/wiki/Anti-realism" title="Anti-realism">Anti-realism</a></li> <li><a href="/wiki/Scientific_skepticism" title="Scientific skepticism">Scientific skepticism</a></li> <li><a href="/wiki/Scientism" title="Scientism">Scientism</a></li> <li><a href="/wiki/Structuralism_(philosophy_of_science)" title="Structuralism (philosophy of science)">Structuralism</a></li> <li><a href="/wiki/Uniformitarianism" title="Uniformitarianism">Uniformitarianism</a></li> <li><a href="/wiki/Verificationism" title="Verificationism">Verificationism</a></li> <li><a href="/wiki/Vitalism" title="Vitalism">Vitalism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Philosophy of...</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Philosophy_of_biology" title="Philosophy of biology">Biology</a></li> <li><a href="/wiki/Philosophy_of_chemistry" title="Philosophy of chemistry">Chemistry</a></li> <li><a href="/wiki/Philosophy_of_physics" title="Philosophy of physics">Physics</a> <ul><li><a href="/wiki/Philosophy_of_space_and_time" title="Philosophy of space and time">Space and time</a></li></ul></li> <li><a href="/wiki/Philosophy_of_social_science" title="Philosophy of social science">Social science</a> <ul><li><a href="/wiki/Philosophy_of_archaeology" title="Philosophy of archaeology">Archaeology</a></li> <li><a href="/wiki/Philosophy_of_economics" class="mw-redirect" title="Philosophy of economics">Economics‎</a></li> <li><a href="/wiki/Philosophy_of_geography" title="Philosophy of geography">Geography</a></li> <li><a href="/wiki/Philosophy_of_history" title="Philosophy of history">History</a></li> <li><a href="/wiki/Philosophy_of_linguistics" title="Philosophy of linguistics">Linguistics</a></li> <li><a href="/wiki/Philosophy_of_psychology" title="Philosophy of psychology">Psychology</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Criticism_of_science" title="Criticism of science">Criticism of science</a></li> <li><a href="/wiki/Descriptive_research" title="Descriptive research">Descriptive science</a></li> <li><a href="/wiki/Epistemology" title="Epistemology">Epistemology</a></li> <li><a href="/wiki/Exact_sciences" title="Exact sciences">Exact sciences</a></li> <li><a href="/wiki/Faith_and_rationality" title="Faith and rationality">Faith and rationality</a></li> <li><a href="/wiki/Hard_and_soft_science" title="Hard and soft science">Hard and soft science</a></li> <li><a href="/wiki/History_and_philosophy_of_science" title="History and philosophy of science">History and philosophy of science</a></li> <li><a href="/wiki/Non-science" title="Non-science">Non-science</a> <ul><li><a href="/wiki/Pseudoscience" title="Pseudoscience">Pseudoscience</a></li></ul></li> <li><a href="/wiki/Normative_science" title="Normative science">Normative science</a></li> <li><a href="/wiki/Protoscience" title="Protoscience">Protoscience</a></li> <li><a href="/wiki/Questionable_cause" title="Questionable cause">Questionable cause</a></li> <li><a href="/wiki/Relationship_between_religion_and_science" title="Relationship between religion and science">Relationship between religion and science</a></li> <li><a href="/wiki/Rhetoric_of_science" title="Rhetoric of science">Rhetoric of science</a></li> <li><a href="/wiki/Science_studies" title="Science studies">Science studies</a></li> <li><a href="/wiki/Sociology_of_scientific_ignorance" title="Sociology of scientific ignorance">Sociology of scientific ignorance</a></li> <li><a href="/wiki/Sociology_of_scientific_knowledge" title="Sociology of scientific knowledge">Sociology of scientific knowledge</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_philosophers_of_science" title="List of philosophers of science">Philosophers of science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Precursors10" scope="row" class="navbox-group" style="width:7.5em">Precursors</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Roger_Bacon" title="Roger Bacon">Roger Bacon</a></li> <li><a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a></li> <li><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></li> <li><a href="/wiki/David_Hume" title="David Hume">David Hume</a></li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Auguste_Comte" title="Auguste Comte">Auguste Comte</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Pierre Duhem</a></li> <li><a href="/wiki/Rudolf_Steiner" title="Rudolf Steiner">Rudolf Steiner</a></li> <li><a href="/wiki/Karl_Pearson" title="Karl Pearson">Karl Pearson</a></li> <li><a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a></li> <li><a href="/wiki/Wilhelm_Windelband" title="Wilhelm Windelband">Wilhelm Windelband</a></li> <li><a href="/wiki/Alfred_North_Whitehead" title="Alfred North Whitehead">Alfred North Whitehead</a></li> <li><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a></li> <li><a href="/wiki/Otto_Neurath" title="Otto Neurath">Otto Neurath</a></li> <li><a href="/wiki/C._D._Broad" title="C. D. Broad">C. D. Broad</a></li> <li><a href="/wiki/Michael_Polanyi" title="Michael Polanyi">Michael Polanyi</a></li> <li><a href="/wiki/Hans_Reichenbach" title="Hans Reichenbach">Hans Reichenbach</a></li> <li><a href="/wiki/Rudolf_Carnap" title="Rudolf Carnap">Rudolf Carnap</a></li> <li><a href="/wiki/Karl_Popper" title="Karl Popper">Karl Popper</a></li> <li><a href="/wiki/Carl_Gustav_Hempel" title="Carl Gustav Hempel">Carl Gustav Hempel</a></li> <li><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">W. V. O. Quine</a></li> <li><a href="/wiki/Thomas_Kuhn" title="Thomas Kuhn">Thomas Kuhn</a></li> <li><a href="/wiki/Imre_Lakatos" title="Imre Lakatos">Imre Lakatos</a></li> <li><a href="/wiki/Paul_Feyerabend" title="Paul Feyerabend">Paul Feyerabend</a></li> <li><a href="/wiki/Ian_Hacking" title="Ian Hacking">Ian Hacking</a></li> <li><a href="/wiki/Bas_van_Fraassen" title="Bas van Fraassen">Bas van Fraassen</a></li> <li><a href="/wiki/Larry_Laudan" title="Larry Laudan">Larry Laudan</a></li></ul></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <li><a href="/wiki/Category:Philosophy_of_science" title="Category:Philosophy of science">Category</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span> </span><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_kalzium.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/28px-Nuvola_apps_kalzium.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/42px-Nuvola_apps_kalzium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/56px-Nuvola_apps_kalzium.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Science" title="Portal:Science">Science portal</a></li> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Positivism47" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Positivism" title="Template:Positivism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Positivism" title="Template talk:Positivism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Positivism" title="Special:EditPage/Template:Positivism"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Positivism47" style="font-size:114%;margin:0 4em"><a href="/wiki/Positivism" title="Positivism">Positivism</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.0em">Perspectives</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Antihumanism" title="Antihumanism">Antihumanism</a></li> <li><a href="/wiki/Empiricism" title="Empiricism">Empiricism</a></li> <li><a href="/wiki/Rationalism" title="Rationalism">Rationalism</a></li> <li><a href="/wiki/Scientism" title="Scientism">Scientism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Declinations</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Legal_positivism" title="Legal positivism">Legal positivism</a></li> <li><a href="/wiki/Logical_positivism" title="Logical positivism">Logical positivism</a></li> <li><a href="/wiki/Positivist_school_(criminology)" title="Positivist school (criminology)">Positivist school</a></li> <li><a href="/wiki/Postpositivism" title="Postpositivism">Postpositivism</a></li> <li><a href="/wiki/Sociological_positivism" class="mw-redirect" title="Sociological positivism">Sociological positivism</a></li> <li><a href="/wiki/Ernst_Mach" title="Ernst Mach">Machian positivism (empirio-criticism)</a></li> <li><a href="/wiki/Rankean_historical_positivism" class="mw-redirect" title="Rankean historical positivism">Rankean historical positivism</a></li> <li><a href="/wiki/Positivism_in_Poland" class="mw-redirect" title="Positivism in Poland">Polish positivism</a></li> <li><a href="/wiki/Russian_Machism" title="Russian Machism">Russian Machism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Principal concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Consilience" title="Consilience">Consilience</a></li> <li><a href="/wiki/Demarcation_problem" title="Demarcation problem">Demarcation</a></li> <li><a href="/wiki/Evidence" title="Evidence">Evidence</a></li> <li><a class="mw-selflink selflink">Induction</a></li> <li><a href="/wiki/Justification_(epistemology)" title="Justification (epistemology)">Justification</a></li> <li><a href="/wiki/Pseudoscience" title="Pseudoscience">Pseudoscience</a></li> <li><a href="/wiki/Vienna_Circle#Critique_of_metaphysics" title="Vienna Circle">Critique of metaphysics</a></li> <li><a href="/wiki/Unity_of_science" title="Unity of science">Unity of science</a></li> <li><a href="/wiki/Verificationism" title="Verificationism">Verificationism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Antitheses</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Antipositivism" title="Antipositivism">Antipositivism</a></li> <li><a href="/wiki/Confirmation_holism" title="Confirmation holism">Confirmation holism</a></li> <li><a href="/wiki/Critical_theory" title="Critical theory">Critical theory</a></li> <li><a href="/wiki/Falsifiability" title="Falsifiability">Falsifiability</a></li> <li><span title="German-language text"><i lang="de"><a href="/wiki/Geisteswissenschaft" title="Geisteswissenschaft">Geisteswissenschaft</a></i></span></li> <li><a href="/wiki/Hermeneutics" title="Hermeneutics">Hermeneutics</a></li> <li><a href="/wiki/Historicism" title="Historicism">Historicism</a></li> <li><a href="/wiki/Historism" title="Historism">Historism</a></li> <li><a href="/wiki/Human_science" title="Human science">Human science</a></li> <li><a href="/wiki/Humanities" title="Humanities">Humanities</a></li> <li><a href="/wiki/Metaphysics" title="Metaphysics">Metaphysics</a></li> <li><a href="/wiki/Methodological_dualism" title="Methodological dualism">Methodological dualism</a></li> <li><a href="/wiki/Problem_of_induction" title="Problem of induction">Problem of induction</a></li> <li><a href="/wiki/Reflectivism" title="Reflectivism">Reflectivism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Related <a href="/wiki/Paradigm_shift" title="Paradigm shift">paradigm shifts</a><br />in the <a href="/wiki/History_of_science" title="History of science">history of science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">Non-Euclidean geometry</a> (1830s)</li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty principle</a> (1927)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Behavioralism" title="Behavioralism">Behavioralism</a> <ul><li><a href="/wiki/Post-behavioralism" title="Post-behavioralism">Post-behavioralism</a></li></ul></li> <li><a href="/wiki/Critical_rationalism" title="Critical rationalism">Critical rationalism</a></li> <li><a href="/wiki/Criticism_of_science" title="Criticism of science">Criticism of science</a></li> <li><a href="/wiki/Epistemology" title="Epistemology">Epistemology</a> <ul><li><a href="/wiki/Epistemological_anarchism" class="mw-redirect" title="Epistemological anarchism">anarchism</a></li> <li><a href="/wiki/Epistemological_idealism" title="Epistemological idealism">idealism</a></li> <li><a href="/wiki/Epistemological_nihilism" class="mw-redirect" title="Epistemological nihilism">nihilism</a></li> <li><a href="/wiki/Epistemological_pluralism" title="Epistemological pluralism">pluralism</a></li> <li><a href="/wiki/Epistemological_realism" title="Epistemological realism">realism</a></li></ul></li> <li><a href="/wiki/Holism" title="Holism">Holism</a></li> <li><a href="/wiki/Instrumentalism" title="Instrumentalism">Instrumentalism</a></li> <li><a href="/wiki/Modernism" title="Modernism">Modernism</a></li> <li><a href="/wiki/Naturalism_(literature)" title="Naturalism (literature)">Naturalism in literature</a></li> <li><a href="/wiki/Nomothetic_and_idiographic" title="Nomothetic and idiographic">Nomothetic–idiographic distinction</a></li> <li><a href="/wiki/Objectivity_(science)" title="Objectivity (science)">Objectivity in science</a></li> <li><a href="/wiki/Operationalization" title="Operationalization">Operationalism</a></li> <li><a href="/wiki/Phenomenalism" title="Phenomenalism">Phenomenalism</a></li> <li><a href="/wiki/Philosophy_of_science" title="Philosophy of science">Philosophy of science</a> <ul><li><a href="/wiki/Deductive-nomological_model" title="Deductive-nomological model">Deductive-nomological model</a></li> <li><a href="/wiki/Ramsey_sentence" title="Ramsey sentence">Ramsey sentence</a></li> <li><a href="/wiki/Sense_data" title="Sense data">Sense-data theory</a></li></ul></li> <li><a href="/wiki/Qualitative_research" title="Qualitative research">Qualitative research</a></li> <li><a href="/wiki/Relationship_between_religion_and_science" title="Relationship between religion and science">Relationship between religion and science</a></li> <li><a href="/wiki/Sociology" title="Sociology">Sociology</a></li> <li><a href="/wiki/Social_science" title="Social science">Social science</a> <ul><li><a href="/wiki/Philosophy_of_social_science" title="Philosophy of social science">Philosophy</a></li></ul></li> <li><a href="/wiki/Structural_functionalism" title="Structural functionalism">Structural functionalism</a></li> <li><a href="/wiki/Structuralism" title="Structuralism">Structuralism</a></li> <li><a href="/wiki/Structuration_theory" title="Structuration theory">Structuration theory</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Positivist-related_debate47" style="font-size:114%;margin:0 4em">Positivist-related debate</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.0em">Method</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span title="German-language text"><i lang="de"><a href="/wiki/Methodenstreit" title="Methodenstreit">Methodenstreit</a></i></span> (1890s)</li> <li><span title="German-language text"><i lang="de"><a href="/wiki/Werturteilsstreit" title="Werturteilsstreit">Werturteilsstreit</a></i></span> (1909–1959)</li> <li><span title="German-language text"><i lang="de"><a href="/wiki/Positivism_dispute" title="Positivism dispute">Positivismusstreit</a></i></span> (1960s)</li> <li><a href="/wiki/Great_Debates_(international_relations)#Fourth_Great_Debate" title="Great Debates (international relations)">Fourth Great Debate in international relations</a> (1980s)</li> <li><a href="/wiki/Science_wars" title="Science wars">Science wars</a> (1990s)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Contributions</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/The_Course_in_Positive_Philosophy" class="mw-redirect" title="The Course in Positive Philosophy">The Course in Positive Philosophy</a></i> (1830)</li> <li><i><a href="/wiki/A_General_View_of_Positivism" title="A General View of Positivism">A General View of Positivism</a></i> (1848)</li> <li><i><a href="/wiki/Critical_History_of_Philosophy" class="mw-redirect" title="Critical History of Philosophy">Critical History of Philosophy</a></i> (1869)</li> <li><i><a href="/wiki/Idealism_and_Positivism" class="mw-redirect" title="Idealism and Positivism">Idealism and Positivism</a></i> (1879–1884)</li> <li><i><a href="/wiki/The_Analysis_of_Sensations" class="mw-redirect" title="The Analysis of Sensations">The Analysis of Sensations</a></i> (1886)</li> <li><i><a href="/wiki/The_Logic_of_Modern_Physics" title="The Logic of Modern Physics">The Logic of Modern Physics</a></i> (1927)</li> <li><i><a href="/wiki/Language,_Truth,_and_Logic" title="Language, Truth, and Logic">Language, Truth, and Logic</a></i> (1936)</li> <li><i><a href="/wiki/The_Two_Cultures" title="The Two Cultures">The Two Cultures</a></i> (1959)</li> <li><i><a href="/wiki/The_Universe_in_a_Nutshell" title="The Universe in a Nutshell">The Universe in a Nutshell</a></i> (2001)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Proponents</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Richard_Avenarius" title="Richard Avenarius">Richard Avenarius</a></li> <li><a href="/wiki/A._J._Ayer" title="A. J. Ayer">A. J. Ayer</a></li> <li><a href="/wiki/Alexander_Bogdanov" title="Alexander Bogdanov">Alexander Bogdanov</a></li> <li><a href="/wiki/Percy_Williams_Bridgman" title="Percy Williams Bridgman">Percy Williams Bridgman</a></li> <li><a href="/wiki/Auguste_Comte" title="Auguste Comte">Auguste Comte</a></li> <li><a href="/wiki/Eugen_D%C3%BChring" title="Eugen Dühring">Eugen Dühring</a></li> <li><a href="/wiki/%C3%89mile_Durkheim" title="Émile Durkheim">Émile Durkheim</a></li> <li><a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a></li> <li><a href="/wiki/Ernst_Laas" title="Ernst Laas">Ernst Laas</a></li> <li><a href="/wiki/Ernst_Mach" title="Ernst Mach">Ernst Mach</a></li> <li><a href="/wiki/C._P._Snow" title="C. P. Snow">C. P. Snow</a></li> <li><a href="/wiki/Berlin_Circle" title="Berlin Circle">Berlin Circle</a></li> <li><a href="/wiki/Vienna_Circle" title="Vienna Circle">Vienna Circle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Criticism</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Materialism_and_Empirio-criticism" title="Materialism and Empirio-criticism">Materialism and Empirio-criticism</a></i> (1909)</li> <li><i><a href="/wiki/History_and_Class_Consciousness" title="History and Class Consciousness">History and Class Consciousness</a></i> (1923)</li> <li><i><a href="/wiki/The_Logic_of_Scientific_Discovery" title="The Logic of Scientific Discovery">The Logic of Scientific Discovery</a></i> (1934)</li> <li><i><a href="/wiki/The_Poverty_of_Historicism" title="The Poverty of Historicism">The Poverty of Historicism</a></i> (1936)</li> <li><i><a href="/wiki/World_Hypotheses" title="World Hypotheses">World Hypotheses</a></i> (1942)</li> <li><i><a href="/wiki/Two_Dogmas_of_Empiricism" title="Two Dogmas of Empiricism">Two Dogmas of Empiricism</a></i> (1951)</li> <li><i><a href="/wiki/Truth_and_Method" title="Truth and Method">Truth and Method</a></i> (1960)</li> <li><i><a href="/wiki/The_Structure_of_Scientific_Revolutions" title="The Structure of Scientific Revolutions">The Structure of Scientific Revolutions</a></i> (1962)</li> <li><i><a href="/wiki/Conjectures_and_Refutations" class="mw-redirect" title="Conjectures and Refutations">Conjectures and Refutations</a></i> (1963)</li> <li><i><a href="/wiki/One-Dimensional_Man" title="One-Dimensional Man">One-Dimensional Man</a></i> (1964)</li> <li><i><a href="/wiki/Knowledge_and_Human_Interests" title="Knowledge and Human Interests">Knowledge and Human Interests</a></i> (1968)</li> <li><i><a href="/wiki/The_Poverty_of_Theory" class="mw-redirect" title="The Poverty of Theory">The Poverty of Theory</a></i> (1978)</li> <li><i><a href="/wiki/The_Scientific_Image" class="mw-redirect" title="The Scientific Image">The Scientific Image</a></i> (1980)</li> <li><i><a href="/wiki/The_Rhetoric_of_Economics" class="mw-redirect" title="The Rhetoric of Economics">The Rhetoric of Economics</a></i> (1986)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Critics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Theodor_W._Adorno" title="Theodor W. Adorno">Theodor W. Adorno</a></li> <li><a href="/wiki/Gaston_Bachelard" title="Gaston Bachelard">Gaston Bachelard</a></li> <li><a href="/wiki/Mario_Bunge" title="Mario Bunge">Mario Bunge</a></li> <li><a href="/wiki/Wilhelm_Dilthey" title="Wilhelm Dilthey">Wilhelm Dilthey</a></li> <li><a href="/wiki/Paul_Feyerabend" title="Paul Feyerabend">Paul Feyerabend</a></li> <li><a href="/wiki/Hans-Georg_Gadamer" title="Hans-Georg Gadamer">Hans-Georg Gadamer</a></li> <li><a href="/wiki/J%C3%BCrgen_Habermas" title="Jürgen Habermas">Jürgen Habermas</a></li> <li><a href="/wiki/Thomas_Kuhn" title="Thomas Kuhn">Thomas Kuhn</a></li> <li><a href="/wiki/Vladimir_Lenin" title="Vladimir Lenin">Vladimir Lenin</a></li> <li><a href="/wiki/Gy%C3%B6rgy_Luk%C3%A1cs" title="György Lukács">György Lukács</a></li> <li><a href="/wiki/Herbert_Marcuse" title="Herbert Marcuse">Herbert Marcuse</a></li> <li><a href="/wiki/Deirdre_McCloskey" title="Deirdre McCloskey">Deirdre McCloskey</a></li> <li><a href="/wiki/Stephen_Pepper" title="Stephen Pepper">Stephen Pepper</a></li> <li><a href="/wiki/Karl_Popper" title="Karl Popper">Karl Popper</a></li> <li><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Willard Van Orman Quine</a></li> <li><a href="/wiki/E._P._Thompson" title="E. P. Thompson">E. P. Thompson</a></li> <li><a href="/wiki/Bas_van_Fraassen" title="Bas van Fraassen">Bas van Fraassen</a></li> <li><a href="/wiki/Max_Weber" title="Max Weber">Max Weber</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.0em">Concepts in contention</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Knowledge" title="Knowledge">Knowledge</a></li> <li><a href="/wiki/Objectivity_(philosophy)" class="mw-redirect" title="Objectivity (philosophy)">Objectivity</a></li> <li><span title="Ancient Greek (to 1453)-language romanization"><i lang="grc-Latn"><a href="/wiki/Phronesis" title="Phronesis">Phronesis</a></i></span></li> <li><a href="/wiki/Truth" title="Truth">Truth</a></li> <li><span title="German-language text"><i lang="de"><a href="/wiki/Verstehen" title="Verstehen">Verstehen</a></i></span></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/Category:Positivism" title="Category:Positivism">Category</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"></div><div role="navigation" class="navbox" aria-labelledby="Statistics636" style="padding:3px"><table class="nowraplinks hlist mw-collapsible uncollapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Statistics" title="Template:Statistics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Statistics" title="Template talk:Statistics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Statistics" title="Special:EditPage/Template:Statistics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Statistics636" style="font-size:114%;margin:0 4em"><a href="/wiki/Statistics" title="Statistics">Statistics</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Outline_of_statistics" title="Outline of statistics">Outline</a></li> <li><a href="/wiki/List_of_statistics_articles" title="List of statistics articles">Index</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Descriptive_statistics636" style="font-size:114%;margin:0 4em"><a href="/wiki/Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">Continuous data</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Central_tendency" title="Central tendency">Center</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mean" title="Mean">Mean</a> <ul><li><a href="/wiki/Arithmetic_mean" title="Arithmetic mean">Arithmetic</a></li> <li><a href="/wiki/Arithmetic%E2%80%93geometric_mean" title="Arithmetic–geometric mean">Arithmetic-Geometric</a></li> <li><a href="/wiki/Contraharmonic_mean" title="Contraharmonic mean">Contraharmonic</a></li> <li><a href="/wiki/Cubic_mean" title="Cubic mean">Cubic</a></li> <li><a href="/wiki/Generalized_mean" title="Generalized mean">Generalized/power</a></li> <li><a href="/wiki/Geometric_mean" title="Geometric mean">Geometric</a></li> <li><a href="/wiki/Harmonic_mean" title="Harmonic mean">Harmonic</a></li> <li><a href="/wiki/Heronian_mean" title="Heronian mean">Heronian</a></li> <li><a href="/wiki/Heinz_mean" title="Heinz mean">Heinz</a></li> <li><a href="/wiki/Lehmer_mean" title="Lehmer mean">Lehmer</a></li></ul></li> <li><a href="/wiki/Median" title="Median">Median</a></li> <li><a href="/wiki/Mode_(statistics)" title="Mode (statistics)">Mode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_dispersion" title="Statistical dispersion">Dispersion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Average_absolute_deviation" title="Average absolute deviation">Average absolute deviation</a></li> <li><a href="/wiki/Coefficient_of_variation" title="Coefficient of variation">Coefficient of variation</a></li> <li><a href="/wiki/Interquartile_range" title="Interquartile range">Interquartile range</a></li> <li><a href="/wiki/Percentile" title="Percentile">Percentile</a></li> <li><a href="/wiki/Range_(statistics)" title="Range (statistics)">Range</a></li> <li><a href="/wiki/Standard_deviation" title="Standard deviation">Standard deviation</a></li> <li><a href="/wiki/Variance#Sample_variance" title="Variance">Variance</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Shape_of_the_distribution" class="mw-redirect" title="Shape of the distribution">Shape</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Central_limit_theorem" title="Central limit theorem">Central limit theorem</a></li> <li><a href="/wiki/Moment_(mathematics)" title="Moment (mathematics)">Moments</a> <ul><li><a href="/wiki/Kurtosis" title="Kurtosis">Kurtosis</a></li> <li><a href="/wiki/L-moment" title="L-moment">L-moments</a></li> <li><a href="/wiki/Skewness" title="Skewness">Skewness</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Count_data" title="Count data">Count data</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Index_of_dispersion" title="Index of dispersion">Index of dispersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Summary tables</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Frequency_distribution" class="mw-redirect" title="Frequency distribution">Frequency distribution</a></li> <li><a href="/wiki/Grouped_data" title="Grouped data">Grouped data</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Dependence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Pearson_correlation_coefficient" title="Pearson correlation coefficient">Pearson product-moment correlation</a></li> <li><a href="/wiki/Rank_correlation" title="Rank correlation">Rank correlation</a> <ul><li><a href="/wiki/Kendall_rank_correlation_coefficient" title="Kendall rank correlation coefficient">Kendall's τ</a></li> <li><a href="/wiki/Spearman%27s_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's ρ</a></li></ul></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_graphics" title="Statistical graphics">Graphics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bar_chart" title="Bar chart">Bar chart</a></li> <li><a href="/wiki/Biplot" title="Biplot">Biplot</a></li> <li><a href="/wiki/Box_plot" title="Box plot">Box plot</a></li> <li><a href="/wiki/Control_chart" title="Control chart">Control chart</a></li> <li><a href="/wiki/Correlogram" title="Correlogram">Correlogram</a></li> <li><a href="/wiki/Fan_chart_(statistics)" title="Fan chart (statistics)">Fan chart</a></li> <li><a href="/wiki/Forest_plot" title="Forest plot">Forest plot</a></li> <li><a href="/wiki/Histogram" title="Histogram">Histogram</a></li> <li><a href="/wiki/Pie_chart" title="Pie chart">Pie chart</a></li> <li><a href="/wiki/Q%E2%80%93Q_plot" title="Q–Q plot">Q–Q plot</a></li> <li><a href="/wiki/Radar_chart" title="Radar chart">Radar chart</a></li> <li><a href="/wiki/Run_chart" title="Run chart">Run chart</a></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li> <li><a href="/wiki/Stem-and-leaf_display" title="Stem-and-leaf display">Stem-and-leaf display</a></li> <li><a href="/wiki/Violin_plot" title="Violin plot">Violin plot</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_collection636" style="font-size:114%;margin:0 4em"><a href="/wiki/Data_collection" title="Data collection">Data collection</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Design_of_experiments" title="Design of experiments">Study design</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Effect_size" title="Effect size">Effect size</a></li> <li><a href="/wiki/Missing_data" title="Missing data">Missing data</a></li> <li><a href="/wiki/Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a></li> <li><a href="/wiki/Statistical_population" title="Statistical population">Population</a></li> <li><a href="/wiki/Replication_(statistics)" title="Replication (statistics)">Replication</a></li> <li><a href="/wiki/Sample_size_determination" title="Sample size determination">Sample size determination</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">Statistical power</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survey_methodology" title="Survey methodology">Survey methodology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">Sampling</a> <ul><li><a href="/wiki/Cluster_sampling" title="Cluster sampling">Cluster</a></li> <li><a href="/wiki/Stratified_sampling" title="Stratified sampling">Stratified</a></li></ul></li> <li><a href="/wiki/Opinion_poll" title="Opinion poll">Opinion poll</a></li> <li><a href="/wiki/Questionnaire" title="Questionnaire">Questionnaire</a></li> <li><a href="/wiki/Standard_error" title="Standard error">Standard error</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Experiment" title="Experiment">Controlled experiments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></li> <li><a href="/wiki/Factorial_experiment" title="Factorial experiment">Factorial experiment</a></li> <li><a href="/wiki/Interaction_(statistics)" title="Interaction (statistics)">Interaction</a></li> <li><a href="/wiki/Random_assignment" title="Random assignment">Random assignment</a></li> <li><a href="/wiki/Randomized_controlled_trial" title="Randomized controlled trial">Randomized controlled trial</a></li> <li><a href="/wiki/Randomized_experiment" title="Randomized experiment">Randomized experiment</a></li> <li><a href="/wiki/Scientific_control" title="Scientific control">Scientific control</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Adaptive designs</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a></li> <li><a href="/wiki/Stochastic_approximation" title="Stochastic approximation">Stochastic approximation</a></li> <li><a href="/wiki/Up-and-Down_Designs" class="mw-redirect" title="Up-and-Down Designs">Up-and-down designs</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Observational_study" title="Observational study">Observational studies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohort_study" title="Cohort study">Cohort study</a></li> <li><a href="/wiki/Cross-sectional_study" title="Cross-sectional study">Cross-sectional study</a></li> <li><a href="/wiki/Natural_experiment" title="Natural experiment">Natural experiment</a></li> <li><a href="/wiki/Quasi-experiment" title="Quasi-experiment">Quasi-experiment</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistical_inference636" style="font-size:114%;margin:0 4em"><a href="/wiki/Statistical_inference" title="Statistical inference">Statistical inference</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_theory" title="Statistical theory">Statistical theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Population_(statistics)" class="mw-redirect" title="Population (statistics)">Population</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Probability_distribution" title="Probability distribution">Probability distribution</a></li> <li><a href="/wiki/Sampling_distribution" title="Sampling distribution">Sampling distribution</a> <ul><li><a href="/wiki/Order_statistic" title="Order statistic">Order statistic</a></li></ul></li> <li><a href="/wiki/Empirical_distribution_function" title="Empirical distribution function">Empirical distribution</a> <ul><li><a href="/wiki/Density_estimation" title="Density estimation">Density estimation</a></li></ul></li> <li><a href="/wiki/Statistical_model" title="Statistical model">Statistical model</a> <ul><li><a href="/wiki/Model_specification" class="mw-redirect" title="Model specification">Model specification</a></li> <li><a href="/wiki/Lp_space" title="Lp space">L<sup><i>p</i></sup> space</a></li></ul></li> <li><a href="/wiki/Statistical_parameter" title="Statistical parameter">Parameter</a> <ul><li><a href="/wiki/Location_parameter" title="Location parameter">location</a></li> <li><a href="/wiki/Scale_parameter" title="Scale parameter">scale</a></li> <li><a href="/wiki/Shape_parameter" title="Shape parameter">shape</a></li></ul></li> <li><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric family</a> <ul><li><a href="/wiki/Likelihood_function" title="Likelihood function">Likelihood</a> <a href="/wiki/Monotone_likelihood_ratio" title="Monotone likelihood ratio"><span style="font-size:85%;">(monotone)</span></a></li> <li><a href="/wiki/Location%E2%80%93scale_family" title="Location–scale family">Location–scale family</a></li> <li><a href="/wiki/Exponential_family" title="Exponential family">Exponential family</a></li></ul></li> <li><a href="/wiki/Completeness_(statistics)" title="Completeness (statistics)">Completeness</a></li> <li><a href="/wiki/Sufficient_statistic" title="Sufficient statistic">Sufficiency</a></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Statistical functional</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/U-statistic" title="U-statistic">U</a></li> <li><a href="/wiki/V-statistic" title="V-statistic">V</a></li></ul></li> <li><a href="/wiki/Optimal_decision" title="Optimal decision">Optimal decision</a> <ul><li><a href="/wiki/Loss_function" title="Loss function">loss function</a></li></ul></li> <li><a href="/wiki/Efficiency_(statistics)" title="Efficiency (statistics)">Efficiency</a></li> <li><a href="/wiki/Statistical_distance" title="Statistical distance">Statistical distance</a> <ul><li><a href="/wiki/Divergence_(statistics)" title="Divergence (statistics)">divergence</a></li></ul></li> <li><a href="/wiki/Asymptotic_theory_(statistics)" title="Asymptotic theory (statistics)">Asymptotics</a></li> <li><a href="/wiki/Robust_statistics" title="Robust statistics">Robustness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Frequentist_inference" title="Frequentist inference">Frequentist inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Point_estimation" title="Point estimation">Point estimation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Estimating_equations" title="Estimating equations">Estimating equations</a> <ul><li><a href="/wiki/Maximum_likelihood" class="mw-redirect" title="Maximum likelihood">Maximum likelihood</a></li> <li><a href="/wiki/Method_of_moments_(statistics)" title="Method of moments (statistics)">Method of moments</a></li> <li><a href="/wiki/M-estimator" title="M-estimator">M-estimator</a></li> <li><a href="/wiki/Minimum_distance_estimation" class="mw-redirect" title="Minimum distance estimation">Minimum distance</a></li></ul></li> <li><a href="/wiki/Bias_of_an_estimator" title="Bias of an estimator">Unbiased estimators</a> <ul><li><a href="/wiki/Minimum-variance_unbiased_estimator" title="Minimum-variance unbiased estimator">Mean-unbiased minimum-variance</a> <ul><li><a href="/wiki/Rao%E2%80%93Blackwell_theorem" title="Rao–Blackwell theorem">Rao–Blackwellization</a></li> <li><a href="/wiki/Lehmann%E2%80%93Scheff%C3%A9_theorem" title="Lehmann–Scheffé theorem">Lehmann–Scheffé theorem</a></li></ul></li> <li><a href="/wiki/Median-unbiased_estimator" class="mw-redirect" title="Median-unbiased estimator">Median unbiased</a></li></ul></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Plug-in</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Interval_estimation" title="Interval estimation">Interval estimation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Confidence_interval" title="Confidence interval">Confidence interval</a></li> <li><a href="/wiki/Pivotal_quantity" title="Pivotal quantity">Pivot</a></li> <li><a href="/wiki/Likelihood_interval" class="mw-redirect" title="Likelihood interval">Likelihood interval</a></li> <li><a href="/wiki/Prediction_interval" title="Prediction interval">Prediction interval</a></li> <li><a href="/wiki/Tolerance_interval" title="Tolerance interval">Tolerance interval</a></li> <li><a href="/wiki/Resampling_(statistics)" title="Resampling (statistics)">Resampling</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/Jackknife_resampling" title="Jackknife resampling">Jackknife</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Testing hypotheses</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/One-_and_two-tailed_tests" title="One- and two-tailed tests">1- & 2-tails</a></li> <li><a href="/wiki/Power_(statistics)" title="Power (statistics)">Power</a> <ul><li><a href="/wiki/Uniformly_most_powerful_test" title="Uniformly most powerful test">Uniformly most powerful test</a></li></ul></li> <li><a href="/wiki/Permutation_test" title="Permutation test">Permutation test</a> <ul><li><a href="/wiki/Randomization_test" class="mw-redirect" title="Randomization test">Randomization test</a></li></ul></li> <li><a href="/wiki/Multiple_comparisons" class="mw-redirect" title="Multiple comparisons">Multiple comparisons</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio</a></li> <li><a href="/wiki/Score_test" title="Score test">Score/Lagrange multiplier</a></li> <li><a href="/wiki/Wald_test" title="Wald test">Wald</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/List_of_statistical_tests" title="List of statistical tests">Specific tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Z-test" title="Z-test"><i>Z</i>-test <span style="font-size:85%;">(normal)</span></a></li> <li><a href="/wiki/Student%27s_t-test" title="Student's t-test">Student's <i>t</i>-test</a></li> <li><a href="/wiki/F-test" title="F-test"><i>F</i>-test</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Goodness_of_fit" title="Goodness of fit">Goodness of fit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chi-squared_test" title="Chi-squared test">Chi-squared</a></li> <li><a href="/wiki/G-test" title="G-test"><i>G</i>-test</a></li> <li><a href="/wiki/Kolmogorov%E2%80%93Smirnov_test" title="Kolmogorov–Smirnov test">Kolmogorov–Smirnov</a></li> <li><a href="/wiki/Anderson%E2%80%93Darling_test" title="Anderson–Darling test">Anderson–Darling</a></li> <li><a href="/wiki/Lilliefors_test" title="Lilliefors test">Lilliefors</a></li> <li><a href="/wiki/Jarque%E2%80%93Bera_test" title="Jarque–Bera test">Jarque–Bera</a></li> <li><a href="/wiki/Shapiro%E2%80%93Wilk_test" title="Shapiro–Wilk test">Normality <span style="font-size:85%;">(Shapiro–Wilk)</span></a></li> <li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio test</a></li> <li><a href="/wiki/Model_selection" title="Model selection">Model selection</a> <ul><li><a href="/wiki/Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross validation</a></li> <li><a href="/wiki/Akaike_information_criterion" title="Akaike information criterion">AIC</a></li> <li><a href="/wiki/Bayesian_information_criterion" title="Bayesian information criterion">BIC</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Rank_statistics" class="mw-redirect" title="Rank statistics">Rank statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sign_test" title="Sign test">Sign</a> <ul><li><a href="/wiki/Sample_median" class="mw-redirect" title="Sample median">Sample median</a></li></ul></li> <li><a href="/wiki/Wilcoxon_signed-rank_test" title="Wilcoxon signed-rank test">Signed rank <span style="font-size:85%;">(Wilcoxon)</span></a> <ul><li><a href="/wiki/Hodges%E2%80%93Lehmann_estimator" title="Hodges–Lehmann estimator">Hodges–Lehmann estimator</a></li></ul></li> <li><a href="/wiki/Mann%E2%80%93Whitney_U_test" title="Mann–Whitney U test">Rank sum <span style="font-size:85%;">(Mann–Whitney)</span></a></li> <li><a href="/wiki/Nonparametric_statistics" title="Nonparametric statistics">Nonparametric</a> <a href="/wiki/Analysis_of_variance" title="Analysis of variance">anova</a> <ul><li><a href="/wiki/Kruskal%E2%80%93Wallis_test" title="Kruskal–Wallis test">1-way <span style="font-size:85%;">(Kruskal–Wallis)</span></a></li> <li><a href="/wiki/Friedman_test" title="Friedman test">2-way <span style="font-size:85%;">(Friedman)</span></a></li> <li><a href="/wiki/Jonckheere%27s_trend_test" title="Jonckheere's trend test">Ordered alternative <span style="font-size:85%;">(Jonckheere–Terpstra)</span></a></li></ul></li> <li><a href="/wiki/Van_der_Waerden_test" title="Van der Waerden test">Van der Waerden test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bayesian_probability" title="Bayesian probability">Bayesian probability</a> <ul><li><a href="/wiki/Prior_probability" title="Prior probability">prior</a></li> <li><a href="/wiki/Posterior_probability" title="Posterior probability">posterior</a></li></ul></li> <li><a href="/wiki/Credible_interval" title="Credible interval">Credible interval</a></li> <li><a href="/wiki/Bayes_factor" title="Bayes factor">Bayes factor</a></li> <li><a href="/wiki/Bayes_estimator" title="Bayes estimator">Bayesian estimator</a> <ul><li><a href="/wiki/Maximum_a_posteriori_estimation" title="Maximum a posteriori estimation">Maximum posterior estimator</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="CorrelationRegression_analysis636" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></li><li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment</a></li> <li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Confounding" title="Confounding">Confounding variable</a></li> <li><a href="/wiki/Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Errors_and_residuals" title="Errors and residuals">Errors and residuals</a></li> <li><a href="/wiki/Regression_validation" title="Regression validation">Regression validation</a></li> <li><a href="/wiki/Mixed_model" title="Mixed model">Mixed effects models</a></li> <li><a href="/wiki/Simultaneous_equations_model" title="Simultaneous equations model">Simultaneous equations models</a></li> <li><a href="/wiki/Multivariate_adaptive_regression_splines" class="mw-redirect" title="Multivariate adaptive regression splines">Multivariate adaptive regression splines (MARS)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Linear_regression" title="Linear regression">Linear regression</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Simple_linear_regression" title="Simple linear regression">Simple linear regression</a></li> <li><a href="/wiki/Ordinary_least_squares" title="Ordinary least squares">Ordinary least squares</a></li> <li><a href="/wiki/General_linear_model" title="General linear model">General linear model</a></li> <li><a href="/wiki/Bayesian_linear_regression" title="Bayesian linear regression">Bayesian regression</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Non-standard predictors</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonlinear_regression" title="Nonlinear regression">Nonlinear regression</a></li> <li><a href="/wiki/Nonparametric_regression" title="Nonparametric regression">Nonparametric</a></li> <li><a href="/wiki/Semiparametric_regression" title="Semiparametric regression">Semiparametric</a></li> <li><a href="/wiki/Isotonic_regression" title="Isotonic regression">Isotonic</a></li> <li><a href="/wiki/Robust_regression" title="Robust regression">Robust</a></li> <li><a href="/wiki/Homoscedasticity_and_heteroscedasticity" title="Homoscedasticity and heteroscedasticity">Homoscedasticity and Heteroscedasticity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Generalized_linear_model" title="Generalized linear model">Generalized linear model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Exponential_family" title="Exponential family">Exponential families</a></li> <li><a href="/wiki/Logistic_regression" title="Logistic regression">Logistic <span style="font-size:85%;">(Bernoulli)</span></a> / <a href="/wiki/Binomial_regression" title="Binomial regression">Binomial</a> / <a href="/wiki/Poisson_regression" title="Poisson regression">Poisson regressions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Partition_of_sums_of_squares" title="Partition of sums of squares">Partition of variance</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analysis_of_variance" title="Analysis of variance">Analysis of variance (ANOVA, anova)</a></li> <li><a href="/wiki/Analysis_of_covariance" title="Analysis of covariance">Analysis of covariance</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Multivariate ANOVA</a></li> <li><a href="/wiki/Degrees_of_freedom_(statistics)" title="Degrees of freedom (statistics)">Degrees of freedom</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Categorical_/_Multivariate_/_Time-series_/_Survival_analysis636" style="font-size:114%;margin:0 4em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a> / <a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a> / <a href="/wiki/Time_series" title="Time series">Time-series</a> / <a href="/wiki/Survival_analysis" title="Survival analysis">Survival analysis</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohen%27s_kappa" title="Cohen's kappa">Cohen's kappa</a></li> <li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Graphical_model" title="Graphical model">Graphical model</a></li> <li><a href="/wiki/Poisson_regression" title="Poisson regression">Log-linear model</a></li> <li><a href="/wiki/McNemar%27s_test" title="McNemar's test">McNemar's test</a></li> <li><a href="/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics" title="Cochran–Mantel–Haenszel statistics">Cochran–Mantel–Haenszel statistics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_linear_model" title="General linear model">Regression</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Manova</a></li> <li><a href="/wiki/Principal_component_analysis" title="Principal component analysis">Principal components</a></li> <li><a href="/wiki/Canonical_correlation" title="Canonical correlation">Canonical correlation</a></li> <li><a href="/wiki/Linear_discriminant_analysis" title="Linear discriminant analysis">Discriminant analysis</a></li> <li><a href="/wiki/Cluster_analysis" title="Cluster analysis">Cluster analysis</a></li> <li><a href="/wiki/Statistical_classification" title="Statistical classification">Classification</a></li> <li><a href="/wiki/Structural_equation_modeling" title="Structural equation modeling">Structural equation model</a> <ul><li><a href="/wiki/Factor_analysis" title="Factor analysis">Factor analysis</a></li></ul></li> <li><a href="/wiki/Multivariate_distribution" class="mw-redirect" title="Multivariate distribution">Multivariate distributions</a> <ul><li><a href="/wiki/Elliptical_distribution" title="Elliptical distribution">Elliptical distributions</a> <ul><li><a href="/wiki/Multivariate_normal_distribution" title="Multivariate normal distribution">Normal</a></li></ul></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Time_series" title="Time series">Time-series</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Decomposition_of_time_series" title="Decomposition of time series">Decomposition</a></li> <li><a href="/wiki/Trend_estimation" class="mw-redirect" title="Trend estimation">Trend</a></li> <li><a href="/wiki/Stationary_process" title="Stationary process">Stationarity</a></li> <li><a href="/wiki/Seasonal_adjustment" title="Seasonal adjustment">Seasonal adjustment</a></li> <li><a href="/wiki/Exponential_smoothing" title="Exponential smoothing">Exponential smoothing</a></li> <li><a href="/wiki/Cointegration" title="Cointegration">Cointegration</a></li> <li><a href="/wiki/Structural_break" title="Structural break">Structural break</a></li> <li><a href="/wiki/Granger_causality" title="Granger causality">Granger causality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Specific tests</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dickey%E2%80%93Fuller_test" title="Dickey–Fuller test">Dickey–Fuller</a></li> <li><a href="/wiki/Johansen_test" title="Johansen test">Johansen</a></li> <li><a href="/wiki/Ljung%E2%80%93Box_test" title="Ljung–Box test">Q-statistic <span style="font-size:85%;">(Ljung–Box)</span></a></li> <li><a href="/wiki/Durbin%E2%80%93Watson_statistic" title="Durbin–Watson statistic">Durbin–Watson</a></li> <li><a href="/wiki/Breusch%E2%80%93Godfrey_test" title="Breusch–Godfrey test">Breusch–Godfrey</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Time_domain" title="Time domain">Time domain</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autocorrelation" title="Autocorrelation">Autocorrelation (ACF)</a> <ul><li><a href="/wiki/Partial_autocorrelation_function" title="Partial autocorrelation function">partial (PACF)</a></li></ul></li> <li><a href="/wiki/Cross-correlation" title="Cross-correlation">Cross-correlation (XCF)</a></li> <li><a href="/wiki/Autoregressive%E2%80%93moving-average_model" class="mw-redirect" title="Autoregressive–moving-average model">ARMA model</a></li> <li><a href="/wiki/Box%E2%80%93Jenkins_method" title="Box–Jenkins method">ARIMA model <span style="font-size:85%;">(Box–Jenkins)</span></a></li> <li><a href="/wiki/Autoregressive_conditional_heteroskedasticity" title="Autoregressive conditional heteroskedasticity">Autoregressive conditional heteroskedasticity (ARCH)</a></li> <li><a href="/wiki/Vector_autoregression" title="Vector autoregression">Vector autoregression (VAR)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Frequency_domain" title="Frequency domain">Frequency domain</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Spectral_density_estimation" title="Spectral density estimation">Spectral density estimation</a></li> <li><a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li> <li><a href="/wiki/Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li> <li><a href="/wiki/Wavelet" title="Wavelet">Wavelet</a></li> <li><a href="/wiki/Whittle_likelihood" title="Whittle likelihood">Whittle likelihood</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survival_analysis" title="Survival analysis">Survival</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Survival_function" title="Survival function">Survival function</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kaplan%E2%80%93Meier_estimator" title="Kaplan–Meier estimator">Kaplan–Meier estimator (product limit)</a></li> <li><a href="/wiki/Proportional_hazards_model" title="Proportional hazards model">Proportional hazards models</a></li> <li><a href="/wiki/Accelerated_failure_time_model" title="Accelerated failure time model">Accelerated failure time (AFT) model</a></li> <li><a href="/wiki/First-hitting-time_model" title="First-hitting-time model">First hitting time</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Failure_rate" title="Failure rate">Hazard function</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nelson%E2%80%93Aalen_estimator" title="Nelson–Aalen estimator">Nelson–Aalen estimator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Test</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Log-rank_test" class="mw-redirect" title="Log-rank test">Log-rank test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Applications636" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_fields_of_application_of_statistics" title="List of fields of application of statistics">Applications</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Biostatistics" title="Biostatistics">Biostatistics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bioinformatics" title="Bioinformatics">Bioinformatics</a></li> <li><a href="/wiki/Clinical_trial" title="Clinical trial">Clinical trials</a> / <a href="/wiki/Clinical_study_design" title="Clinical study design">studies</a></li> <li><a href="/wiki/Epidemiology" title="Epidemiology">Epidemiology</a></li> <li><a href="/wiki/Medical_statistics" title="Medical statistics">Medical statistics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Engineering_statistics" title="Engineering statistics">Engineering statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chemometrics" title="Chemometrics">Chemometrics</a></li> <li><a href="/wiki/Methods_engineering" title="Methods engineering">Methods engineering</a></li> <li><a href="/wiki/Probabilistic_design" title="Probabilistic design">Probabilistic design</a></li> <li><a href="/wiki/Statistical_process_control" title="Statistical process control">Process</a> / <a 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