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class="vector-toc-link" href="#Deductive_arguments"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Deductive arguments</span> </div> </a> <ul id="toc-Deductive_arguments-sublist" class="vector-toc-list"> <li id="toc-Validity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Validity"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Validity</span> </div> </a> <ul id="toc-Validity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Soundness" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Soundness"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Soundness</span> </div> </a> <ul id="toc-Soundness-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Inductive_arguments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Inductive_arguments"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Inductive arguments</span> </div> </a> <ul id="toc-Inductive_arguments-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Defeasible_arguments_and_argumentation_schemes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Defeasible_arguments_and_argumentation_schemes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Defeasible arguments and argumentation schemes</span> </div> </a> <ul id="toc-Defeasible_arguments_and_argumentation_schemes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-By_analogy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#By_analogy"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>By analogy</span> </div> </a> <ul id="toc-By_analogy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_kinds" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_kinds"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Other kinds</span> </div> </a> <button aria-controls="toc-Other_kinds-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 Other kinds subsection</span> </button> <ul id="toc-Other_kinds-sublist" class="vector-toc-list"> <li id="toc-World-disclosing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#World-disclosing"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>World-disclosing</span> </div> </a> <ul id="toc-World-disclosing-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Explanations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Explanations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Explanations</span> </div> </a> <ul id="toc-Explanations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fallacies_and_non-arguments" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fallacies_and_non-arguments"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Fallacies and non-arguments</span> </div> </a> <ul id="toc-Fallacies_and_non-arguments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elliptical_or_ethymematic_arguments" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Elliptical_or_ethymematic_arguments"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Elliptical or ethymematic arguments</span> </div> </a> <ul id="toc-Elliptical_or_ethymematic_arguments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Argument_mining" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Argument_mining"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Argument mining</span> </div> </a> <ul id="toc-Argument_mining-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</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> 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Available in 59 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-59" 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">59 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%AD%D8%AC%D8%A9_(%D9%85%D9%86%D8%B7%D9%82)" title="حجة (منطق) – Arabic" lang="ar" hreflang="ar" data-title="حجة (منطق)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A4%E0%A7%B0%E0%A7%8D%E0%A6%95_(%E0%A6%A4%E0%A7%B0%E0%A7%8D%E0%A6%95%E0%A6%B6%E0%A6%BE%E0%A6%B8%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A7%B0)" title="তৰ্ক (তৰ্কশাস্ত্ৰ) – Assamese" lang="as" hreflang="as" data-title="তৰ্ক (তৰ্কশাস্ত্ৰ)" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Argumentu" title="Argumentu – Asturian" lang="ast" hreflang="ast" data-title="Argumentu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Arqument" title="Arqument – Azerbaijani" lang="az" hreflang="az" data-title="Arqument" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Argument" title="Argument – Catalan" lang="ca" hreflang="ca" data-title="Argument" 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/Argument" title="Argument – Czech" lang="cs" hreflang="cs" data-title="Argument" 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/Argumentation" title="Argumentation – Danish" lang="da" hreflang="da" data-title="Argumentation" 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/Argument" title="Argument – German" lang="de" hreflang="de" data-title="Argument" 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/Arutlus" title="Arutlus – Estonian" lang="et" hreflang="et" data-title="Arutlus" 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%B9%CF%87%CE%B5%CE%AF%CF%81%CE%B7%CE%BC%CE%B1" title="Επιχείρημα – Greek" lang="el" hreflang="el" data-title="Επιχείρημα" 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/Argumento" title="Argumento – Spanish" lang="es" hreflang="es" data-title="Argumento" 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/Argumento_(filozofio)" title="Argumento (filozofio) – Esperanto" lang="eo" hreflang="eo" data-title="Argumento (filozofio)" 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/Argudio" title="Argudio – Basque" lang="eu" hreflang="eu" data-title="Argudio" 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%A8%D8%B1%D9%87%D8%A7%D9%86_(%D9%85%D9%86%D8%B7%D9%82)" title="برهان (منطق) – Persian" lang="fa" hreflang="fa" data-title="برهان (منطق)" 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/Argumentation" title="Argumentation – French" lang="fr" hreflang="fr" data-title="Argumentation" 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/Argumentaci%C3%B3n" title="Argumentación – Galician" lang="gl" hreflang="gl" data-title="Argumentación" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%85%BC%EC%A6%9D" title="논증 – Korean" lang="ko" hreflang="ko" data-title="논증" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A4%E0%A4%B0%E0%A5%8D%E0%A4%95" title="तर्क – Hindi" lang="hi" hreflang="hi" data-title="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/Argument" title="Argument – Croatian" lang="hr" hreflang="hr" data-title="Argument" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Argumento_(retoriko)" title="Argumento (retoriko) – Ido" lang="io" hreflang="io" data-title="Argumento (retoriko)" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Argumentasi" title="Argumentasi – Indonesian" lang="id" hreflang="id" data-title="Argumentasi" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Argomento_(filosofia)" title="Argomento (filosofia) – Italian" lang="it" hreflang="it" data-title="Argomento (filosofia)" 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%98%D7%99%D7%A2%D7%95%D7%9F" title="טיעון – Hebrew" lang="he" hreflang="he" data-title="טיעון" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%A0%E1%83%92%E1%83%A3%E1%83%9B%E1%83%94%E1%83%9C%E1%83%A2%E1%83%98" title="არგუმენტი – Georgian" lang="ka" hreflang="ka" data-title="არგუმენტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%80%D0%B3%D1%83%D0%BC%D0%B5%D0%BD%D1%82" title="Аргумент – Kazakh" lang="kk" hreflang="kk" data-title="Аргумент" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Argumentum" title="Argumentum – Latin" lang="la" hreflang="la" data-title="Argumentum" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Arguments" title="Arguments – Latvian" lang="lv" hreflang="lv" data-title="Arguments" 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/Argumentas_(logika)" title="Argumentas (logika) – Lithuanian" lang="lt" hreflang="lt" data-title="Argumentas (logika)" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/%C3%89rv" title="Érv – Hungarian" lang="hu" hreflang="hu" data-title="Érv" 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%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%BA%D0%B8_%D0%B0%D1%80%D0%B3%D1%83%D0%BC%D0%B5%D0%BD%D1%82" title="Логички аргумент – Macedonian" lang="mk" hreflang="mk" data-title="Логички аргумент" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%90%E1%83%A0%E1%83%92%E1%83%A3%E1%83%9B%E1%83%94%E1%83%9C%E1%83%A2%E1%83%98" title="არგუმენტი – Mingrelian" lang="xmf" hreflang="xmf" data-title="არგუმენტი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hujah" title="Hujah – Malay" lang="ms" hreflang="ms" data-title="Hujah" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Argument_(logica)" title="Argument (logica) – Dutch" lang="nl" hreflang="nl" data-title="Argument (logica)" 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/%E8%AB%96%E8%A8%BC" title="論証 – Japanese" lang="ja" hreflang="ja" data-title="論証" 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/Argumentasjon" title="Argumentasjon – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Argumentasjon" 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-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%D9%86%D8%B7%D9%82_(%D8%A7%D8%B3%D8%AA%D8%AF%D9%84%D8%A7%D9%84)" title="منطق (استدلال) – Pashto" lang="ps" hreflang="ps" data-title="منطق (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/Argument_(retoryka)" title="Argument (retoryka) – Polish" lang="pl" hreflang="pl" data-title="Argument (retoryka)" 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/Argumento" title="Argumento – Portuguese" lang="pt" hreflang="pt" data-title="Argumento" 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/Argument" title="Argument – Romanian" lang="ro" hreflang="ro" data-title="Argument" 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%90%D1%80%D0%B3%D1%83%D0%BC%D0%B5%D0%BD%D1%82_(%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0)" title="Аргумент (логика) – Russian" lang="ru" hreflang="ru" data-title="Аргумент (логика)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Argumenti" title="Argumenti – Albanian" lang="sq" hreflang="sq" data-title="Argumenti" 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/Argument" title="Argument – Simple English" lang="en-simple" hreflang="en-simple" data-title="Argument" 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-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%AF%D9%84%D9%8A%D9%84" title="دليل – Sindhi" lang="sd" hreflang="sd" data-title="دليل" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Argument_(logika)" title="Argument (logika) – Slovak" lang="sk" hreflang="sk" data-title="Argument (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/Argument_(logika)" title="Argument (logika) – Slovenian" lang="sl" hreflang="sl" data-title="Argument (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%A8%DB%95%DA%B5%DA%AF%DB%95_(%D9%84%DB%86%DA%98%DB%8C%DA%A9)" title="بەڵگە (لۆژیک) – Central Kurdish" lang="ckb" hreflang="ckb" data-title="بەڵگە (لۆژیک)" 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/Argument_(logika)" title="Argument (logika) – Serbian" lang="sr" hreflang="sr" data-title="Argument (logika)" 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/Dokaz_(logika)" title="Dokaz (logika) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Dokaz (logika)" 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-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Argum%C3%A9ntasi" title="Arguméntasi – Sundanese" lang="su" hreflang="su" data-title="Arguméntasi" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Argumentti" title="Argumentti – Finnish" lang="fi" hreflang="fi" data-title="Argumentti" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link 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<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">Attempt to persuade or to determine the truth of a conclusion</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">This article is about the subject as it is studied in logic and philosophy. For informal arguments, see <a href="/wiki/Disagreement_(disambiguation)" class="mw-redirect mw-disambig" title="Disagreement (disambiguation)">Disagreement (disambiguation)</a>. For other uses, see <a href="/wiki/Argument_(disambiguation)" class="mw-disambig" title="Argument (disambiguation)">Argument (disambiguation)</a>.</div> <p> An <b>argument</b> is a series of <a href="/wiki/Sentence_(linguistics)" title="Sentence (linguistics)">sentences</a>, <a href="/wiki/Statement_(logic)" title="Statement (logic)">statements</a>, or <a href="/wiki/Proposition" title="Proposition">propositions</a> some of which are called <a href="/wiki/Premise" title="Premise">premises</a> and one is the <a href="/wiki/Logical_consequence" title="Logical consequence">conclusion</a>.<sup id="cite_ref-Sinnott-Armstrong_2015_1-0" class="reference"><a href="#cite_note-Sinnott-Armstrong_2015-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The purpose of an argument is to give <a href="/wiki/Reason_(argument)" title="Reason (argument)">reasons</a> for one's conclusion via justification, <a href="/wiki/Explanation" title="Explanation">explanation</a>, and/or <a href="/wiki/Persuasion" title="Persuasion">persuasion</a>. </p><p>Arguments are intended to determine or show the degree of truth or acceptability of another statement called a conclusion.<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><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> The process of crafting or delivering arguments, <b>argumentation</b>, can be studied from three main perspectives: the <a href="/wiki/Logic" title="Logic">logical</a>, the <a href="/wiki/Dialectic" title="Dialectic">dialectical</a> and the <a href="/wiki/Rhetoric" title="Rhetoric">rhetorical</a> perspective.<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><p>In <a href="/wiki/Logic" title="Logic">logic</a>, an argument is usually expressed not in <a href="/wiki/Natural_language" title="Natural language">natural language</a> but in a symbolic <a href="/wiki/Formal_language" title="Formal language">formal language</a>, and it can be defined as any group of <a href="/wiki/Proposition" title="Proposition">propositions</a> of which one is claimed to follow from the others through <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">deductively</a> valid <a href="/wiki/Inference" title="Inference">inferences</a> that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific fields such as <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> and <a href="/wiki/Computer_science" title="Computer science">computer science</a>. Logic is the study of the forms of <a href="/wiki/Reason" title="Reason">reasoning</a> in arguments and the development of standards and criteria to evaluate arguments.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Deductive arguments can be <a href="/wiki/Validity_(logic)" title="Validity (logic)">valid</a>, and the valid ones can be <a href="/wiki/Soundness" title="Soundness">sound</a>: in a valid argument, premises necessitate the conclusion, even if one or more of the premises is false and the conclusion is false; in a sound argument, true premises necessitate a true conclusion. <a href="/wiki/Inductive_argument" class="mw-redirect" title="Inductive argument">Inductive arguments</a>, by contrast, can have different degrees of logical strength: the stronger or more cogent the argument, the greater the probability that the conclusion is true, the weaker the argument, the lesser that probability.<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> The standards for evaluating non-deductive arguments may rest on different or additional criteria than truth—for example, the persuasiveness of so-called "indispensability claims" in <a href="/wiki/Transcendental_arguments" class="mw-redirect" title="Transcendental arguments">transcendental arguments</a>,<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> the quality of hypotheses in <a href="/wiki/Retroduction" class="mw-redirect" title="Retroduction">retroduction</a>, or even the <a href="/wiki/World_disclosure" title="World disclosure">disclosure</a> of new possibilities for thinking and acting.<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> </p><p>In dialectics, and also in a more colloquial sense, an argument can be conceived as a social and verbal means of trying to resolve, or at least contend with, a conflict or difference of opinion that has arisen or exists between two or more parties.<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> For the <a href="/wiki/Rhetoric" title="Rhetoric">rhetorical</a> perspective, the argument is constitutively linked with the context, in particular with the time and place in which the argument is located. From this perspective, the argument is evaluated not just by two parties (as in a dialectical approach) but also by an audience.<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> In both dialectic and rhetoric, arguments are used not through formal but through natural language. Since classical antiquity, philosophers and rhetoricians have developed lists of argument types in which premises and conclusions are connected in informal and defeasible ways.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=1" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Latin root <i>arguere</i> (to make bright, enlighten, make known, prove, etc.) is from <a href="/wiki/Proto-Indo-European" class="mw-redirect" title="Proto-Indo-European">Proto-Indo-European</a> <i>argu-yo-</i>, suffixed form of <i>arg-</i> (to shine; white).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Formal_and_informal">Formal and informal</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=2" title="Edit section: Formal and informal"><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">Further information: <a href="/wiki/Informal_logic" title="Informal logic">Informal logic</a> and <a href="/wiki/Formal_logic" class="mw-redirect" title="Formal logic">Formal logic</a></div> <p>Informal arguments as studied in <i>informal logic</i>, are presented in <a href="/wiki/Ordinary_language" class="mw-redirect" title="Ordinary language">ordinary language</a> and are intended for everyday <a href="/wiki/Discourse" title="Discourse">discourse</a>. Formal arguments are studied in <i>formal logic</i> (historically called <i>symbolic logic</i>, more commonly referred to as <i>mathematical logic</i> today) and are expressed in a <a href="/wiki/Formal_language" title="Formal language">formal language</a>. Informal logic emphasizes the study of <a href="/wiki/Argumentation" class="mw-redirect" title="Argumentation">argumentation</a>; formal logic emphasizes <a href="/wiki/Entailment" class="mw-redirect" title="Entailment">implication</a> and <a href="/wiki/Inference" title="Inference">inference</a>. Informal arguments are sometimes implicit. The rational structure—the relationship of claims, premises, warrants, relations of implication, and conclusion—is not always spelled out and immediately visible and must be made explicit by analysis. </p> <div class="mw-heading mw-heading2"><h2 id="Standard_logical_account_of_argument_types">Standard logical account of argument types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=3" title="Edit section: Standard logical account of argument types"><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>There are several kinds of arguments in logic, the best known of which are "deductive" and "inductive." An argument has one or more premises but only one conclusion. Each premise and the conclusion are <a href="/wiki/Truthbearer" class="mw-redirect" title="Truthbearer">truth bearers</a> or "truth-candidates", each capable of being either true or false (but not both). These truth values bear on the terminology used with arguments. </p> <div class="mw-heading mw-heading3"><h3 id="Deductive_arguments">Deductive arguments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=4" title="Edit section: Deductive arguments"><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/Deductive_argument" class="mw-redirect" title="Deductive argument">Deductive argument</a></div> <p>A <i>deductive argument</i> asserts that the <a href="/wiki/Truth" title="Truth">truth</a> of the conclusion is a <a href="/wiki/Logical_consequence" title="Logical consequence">logical consequence</a> of the premises: if the premises are true, the conclusion must be true. It would be self-contradictory to assert the premises and deny the conclusion because the negation of the conclusion is contradictory to the truth of the premises. Based on the premises, the conclusion follows necessarily (with certainty). Given premises that A=B and B=C, then the conclusion follows necessarily that A=C. Deductive arguments are sometimes referred to as "truth-preserving" arguments. For example, consider the argument that because bats can fly (premise=true), and all flying creatures are birds (premise=false), therefore bats are birds (conclusion=false). If we assume the premises are true, the conclusion follows necessarily, and it is a valid argument. </p> <div class="mw-heading mw-heading4"><h4 id="Validity">Validity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=5" title="Edit section: Validity"><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/Validity_(logic)" title="Validity (logic)">Validity (logic)</a></div> <p>In terms of validity, deductive arguments may be either valid or invalid. An argument is valid, if and only if (iff) it is impossible in all possible worlds for the premises to be true and the conclusion false; validity is about what is possible; it is concerned with how the premises and conclusion relate and what is possible.<sup id="cite_ref-Sinnott-Armstrong_2015_1-1" class="reference"><a href="#cite_note-Sinnott-Armstrong_2015-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> An argument is formally valid <a href="/wiki/If_and_only_if" title="If and only if">if and only if</a> the denial of the conclusion is incompatible with accepting all the premises. </p><p>In formal logic, the validity of an argument depends not on the actual truth or falsity of its premises and conclusion, but on whether the argument has a valid <a href="/wiki/Argument_form" class="mw-redirect" title="Argument form">logical form</a>.<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 2023)">citation needed</span></a></i>]</sup> The validity of an argument is not a guarantee of the truth of its conclusion. A valid argument may have false premises that render it inconclusive: the conclusion of a valid argument with one or more false premises may be true or false. </p><p>Logic seeks to discover the forms that make arguments valid. A form of argument is valid if and only if the conclusion is true under all interpretations of that argument in which the premises are true. Since the validity of an argument depends on its form, an argument can be shown invalid by showing that its form is invalid. This can be done by a counter example of the same form of argument with premises that are true under a given interpretation, but a conclusion that is false under that interpretation. In informal logic this is called a <a href="/wiki/Counter_argument" class="mw-redirect" title="Counter argument">counter argument</a>. </p><p>The form of an argument can be shown by the use of symbols. For each argument form, there is a corresponding statement form, called a <a href="/wiki/Corresponding_conditional_(logic)" class="mw-redirect" title="Corresponding conditional (logic)">corresponding conditional</a>, and an argument form is valid if and only if its corresponding conditional is a <a href="/wiki/Logical_truth" title="Logical truth">logical truth</a>. A statement form which is logically true is also said to be a valid statement form. A statement form is a logical truth if it is true under all <a href="/wiki/Interpretation_(logic)" title="Interpretation (logic)">interpretations</a>. A statement form can be shown to be a logical truth by either (a) showing that it is a <a href="/wiki/Tautology_(logic)" title="Tautology (logic)">tautology</a> or (b) by means of a <a href="/wiki/Proof_procedure" title="Proof procedure">proof procedure</a>. </p><p>The corresponding conditional of a valid argument is a necessary truth (true <i>in all possible worlds</i>) and so the conclusion necessarily follows from the premises, or follows of logical necessity. The conclusion of a valid argument is not necessarily true, it depends on whether the premises are true. If the conclusion, itself, is a necessary truth, it is without regard to the premises. </p><p>Some examples: </p> <ul><li><i>All Greeks are human and all humans are mortal; therefore, all Greeks are mortal.</i> : Valid argument; if the premises are true the conclusion must be true.</li> <li><i>Some Greeks are logicians and some logicians are tiresome; therefore, some Greeks are tiresome.</i> Invalid argument: the tiresome logicians might all be Romans (for example).</li> <li><i>Either we are all doomed or we are all saved; we are not all saved; therefore, we are all doomed.</i> Valid argument; the premises entail the conclusion. (This does not mean the conclusion has to be true; it is only true if the premises are true, which they may not be!)</li> <li><i>Some men are hawkers. Some hawkers are rich. Therefore, some men are rich.</i> Invalid argument. This can be more easily seen by giving a counter-example with the same argument form: <ul><li><i>Some people are herbivores. </i>Some herbivores are zebras. Therefore, some people are zebras.<i> Invalid argument, as it is possible that the premises be true and the conclusion false.</i></li></ul></li></ul> <p>In the above second to last case (Some men are hawkers ...), the counter-example follows the same logical form as the previous argument, (Premise 1: "Some <i>X</i> are <i>Y</i>." Premise 2: "Some <i>Y</i> are <i>Z</i>." Conclusion: "Some <i>X</i> are <i>Z</i>.") in order to demonstrate that whatever hawkers may be, they may or may not be rich, in consideration of the premises as such. (See also: <a href="/wiki/Existential_import" class="mw-redirect" title="Existential import">Existential import</a>). </p><p>The forms of argument that render deductions valid are well-established, however some invalid arguments can also be persuasive depending on their construction (<a href="/wiki/Inductive_arguments" class="mw-redirect" title="Inductive arguments">inductive arguments</a>, for example). (See also: <a href="/wiki/Formal_fallacy" title="Formal fallacy">Formal fallacy</a> and <a href="/wiki/Informal_fallacy" title="Informal fallacy">Informal fallacy</a>). </p> <div class="mw-heading mw-heading4"><h4 id="Soundness">Soundness</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=6" title="Edit section: Soundness"><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/Soundness" title="Soundness">Soundness</a></div> <p>An argument is sound when the argument is valid and argument's premise(s) is/are true, therefore the conclusion is true. </p> <div class="mw-heading mw-heading3"><h3 id="Inductive_arguments">Inductive arguments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=7" title="Edit section: Inductive arguments"><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/Inductive_reasoning" title="Inductive reasoning">Inductive reasoning</a></div> <p>An <a href="/wiki/Inductive_argument" class="mw-redirect" title="Inductive argument">inductive argument</a> asserts that the truth of the conclusion is supported by the probability of the premises. For example, given that the <a href="/wiki/Military_budget_of_the_United_States" title="Military budget of the United States">military budget of the United States</a> is the largest in the world (premise=true), then it is probable that it will remain so for the next 10 years (conclusion=true). Arguments that involve predictions are inductive since the future is uncertain. An inductive argument is said to be strong or weak. If the premises of an inductive argument are assumed true, is it probable the conclusion is also true? If yes, the argument is strong. If no, it is weak. A strong argument is said to be cogent if it has all true premises. Otherwise, the argument is uncogent. The military budget argument example is a strong, cogent argument. </p><p>Non-deductive logic is reasoning using arguments in which the premises support the conclusion but do not entail it. Forms of non-deductive logic include the <a href="/wiki/Statistical_syllogism" title="Statistical syllogism">statistical syllogism</a>, which argues from generalizations true for the most part, and <a href="/wiki/Inductive_inference" class="mw-redirect" title="Inductive inference">induction</a>, a form of reasoning that makes generalizations based on individual instances. An inductive argument is said to be <i>cogent</i> if and only if the truth of the argument's premises would render the truth of the conclusion probable (i.e., the argument is <i>strong</i>), and the argument's premises are, in fact, true. Cogency can be considered <a href="/wiki/Inductive_logic" class="mw-redirect" title="Inductive logic">inductive logic</a>'s analogue to <a href="/wiki/Deductive_logic" class="mw-redirect" title="Deductive logic">deductive logic</a>'s "<a href="/wiki/Soundness" title="Soundness">soundness</a>". Despite its name, <a href="/wiki/Mathematical_induction" title="Mathematical induction">mathematical induction</a> is not a form of inductive reasoning. The lack of deductive validity is known as the <a href="/wiki/Problem_of_induction" title="Problem of induction">problem of induction</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Defeasible_arguments_and_argumentation_schemes">Defeasible arguments and argumentation schemes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=8" title="Edit section: Defeasible arguments and argumentation schemes"><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/Argumentation_scheme" title="Argumentation scheme">Argumentation scheme</a></div> <p>In modern argumentation theories, arguments are regarded as defeasible passages from premises to a conclusion. Defeasibility means that when additional information (new evidence or contrary arguments) is provided, the premises may be no longer lead to the conclusion (<a href="/wiki/Non-monotonic_reasoning" class="mw-redirect" title="Non-monotonic reasoning">non-monotonic reasoning</a>). This type of reasoning is referred to as <a href="/wiki/Defeasible_reasoning" title="Defeasible reasoning">defeasible reasoning</a>. For instance we consider the famous Tweety example: </p> <dl><dd><dl><dd>Tweety is a bird.</dd> <dd>Birds generally fly.</dd> <dd>Therefore, Tweety (probably) flies.</dd></dl></dd></dl> <p>This argument is reasonable and the premises support the conclusion unless additional information indicating that the case is an exception comes in. If Tweety is a penguin, the inference is no longer justified by the premise. Defeasible arguments are based on generalizations that hold only in the majority of cases, but are subject to exceptions and defaults. </p><p>In order to represent and assess defeasible reasoning, it is necessary to combine the logical rules (governing the acceptance of a conclusion based on the acceptance of its premises) with rules of material inference, governing how a premise can support a given conclusion (whether it is reasonable or not to draw a specific conclusion from a specific description of a state of affairs). </p><p><a href="/wiki/Argumentation_scheme" title="Argumentation scheme">Argumentation schemes</a> have been developed to describe and assess the acceptability or the <a href="/wiki/Fallacy" title="Fallacy">fallaciousness</a> of defeasible arguments. Argumentation schemes are stereotypical patterns of inference, combining semantic-ontological relations with types of reasoning and logical axioms and representing the abstract structure of the most common types of natural arguments.<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> A typical example is the argument from expert opinion, shown below, which has two premises and a 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> </p> <table class="wikitable"> <caption>Argument from expert opinion </caption> <tbody><tr> <td>Major Premise:</td> <td>Source E is an expert in subject domain S containing proposition A. </td></tr> <tr> <td>Minor Premise:</td> <td>E asserts that proposition A is true (false). </td></tr> <tr> <td>Conclusion:</td> <td>A is true (false). </td></tr></tbody></table> <p>Each scheme may be associated with a set of critical questions, namely criteria for assessing dialectically the reasonableness and acceptability of an argument. The matching critical questions are the standard ways of casting the argument into doubt. </p> <div class="mw-heading mw-heading2"><h2 id="By_analogy">By analogy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=9" title="Edit section: By analogy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Argument by <a href="/wiki/Analogy" title="Analogy">analogy</a> may be thought of as argument from the particular to particular. An argument by analogy may use a particular truth in a premise to argue towards a similar particular truth in the conclusion. For example, if A. Plato was mortal, and B. Socrates was like Plato in other respects, then asserting that C. Socrates was mortal is an example of argument by analogy because the reasoning employed in it proceeds from a particular truth in a premise (Plato was mortal) to a similar particular truth in the conclusion, namely that Socrates was mortal. </p> <div class="mw-heading mw-heading2"><h2 id="Other_kinds">Other kinds</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=10" title="Edit section: Other kinds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Other kinds of arguments may have different or additional standards of validity or justification. For example, philosopher <a href="/wiki/Charles_Taylor_(philosopher)" title="Charles Taylor (philosopher)">Charles Taylor</a> said that so-called <a href="/wiki/Transcendental_arguments" class="mw-redirect" title="Transcendental arguments">transcendental arguments</a> are made up of a "chain of indispensability claims" that attempt to show why something is necessarily true based on its connection to our experience,<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> while <a href="/wiki/Nikolas_Kompridis" title="Nikolas Kompridis">Nikolas Kompridis</a> has suggested that there are two types of "<a href="/wiki/Fallible" class="mw-redirect" title="Fallible">fallible</a>" arguments: one based on truth claims, and the other based on the time-responsive disclosure of possibility (<a href="/wiki/World_disclosure" title="World disclosure">world disclosure</a>).<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Kompridis said that the French philosopher <a href="/wiki/Michel_Foucault" title="Michel Foucault">Michel Foucault</a> was a prominent advocate of this latter form of philosophical argument.<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> </p> <div class="mw-heading mw-heading3"><h3 id="World-disclosing">World-disclosing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=11" title="Edit section: World-disclosing"><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/World_disclosure" title="World disclosure">World disclosure</a></div> <p>World-disclosing arguments are a group of philosophical arguments that according to Nikolas Kompridis employ a <a href="/wiki/World_disclosure" title="World disclosure">disclosive</a> approach, to reveal features of a wider <a href="/wiki/Ontology" title="Ontology">ontological</a> or cultural-linguistic understanding—a "world", in a specifically ontological sense—in order to clarify or transform the background of meaning (<a href="/wiki/Tacit_knowledge" title="Tacit knowledge">tacit knowledge</a>) and what Kompridis has called the "logical space" on which an argument implicitly depends.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Explanations">Explanations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=12" title="Edit section: Explanations"><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/Explanation" title="Explanation">Explanation</a></div> <p>While arguments attempt to show that something was, is, will be, or should be the case, explanations try to show <i>why</i> or <i>how</i> something is or will be. If Fred and Joe address the issue of <i>whether</i> or not Fred's cat has fleas, Joe may state: "Fred, your cat has fleas. Observe, the cat is scratching right now." Joe has made an <i>argument that</i> the cat has fleas. However, if Joe asks Fred, "Why is your cat scratching itself?" the explanation, "... because it has fleas." provides understanding. </p><p>Both the above argument and explanation require knowing the generalities that a) fleas often cause itching, and b) that one often scratches to relieve itching. The difference is in the intent: an argument attempts to settle whether or not some <a href="/wiki/Claim_(logic)" class="mw-redirect" title="Claim (logic)">claim</a> is true, and an explanation attempts to provide understanding of the event. Note, that by subsuming the specific event (of Fred's cat scratching) as an instance of the general rule that "animals scratch themselves when they have fleas", Joe will no longer wonder <i>why</i> Fred's cat is scratching itself. Arguments address problems of belief, explanations address problems of understanding. In the argument above, the statement, "Fred's cat has fleas" is up for debate (i.e. is a claim), but in the explanation, the statement, "Fred's cat has fleas" is assumed to be true (unquestioned at this time) and just needs <i>explaining</i>.<sup id="cite_ref-ReferenceA_19-0" class="reference"><a href="#cite_note-ReferenceA-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Arguments and explanations largely resemble each other in <a href="/wiki/Rhetoric" title="Rhetoric">rhetorical</a> use. This is the cause of much difficulty in <a href="/wiki/Critical_thinking" title="Critical thinking">thinking critically</a> about claims. There are several reasons for this difficulty. </p> <ul><li>People often are not themselves clear on whether they are arguing for or explaining something.</li> <li>The same types of words and phrases are used in presenting explanations and arguments.</li> <li>The terms 'explain' or 'explanation,' et cetera are frequently used in arguments.</li> <li>Explanations are often used within arguments and presented so as to serve <i>as arguments</i>.<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></li> <li>Likewise, "... arguments are essential to the process of justifying the validity of any explanation as there are often multiple explanations for any given phenomenon."<sup id="cite_ref-ReferenceA_19-1" class="reference"><a href="#cite_note-ReferenceA-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li></ul> <p>Explanations and arguments are often studied in the field of <a href="/wiki/Information_systems" class="mw-redirect" title="Information systems">information systems</a> to help explain user acceptance of <a href="/wiki/Knowledge-based_systems" title="Knowledge-based systems">knowledge-based systems</a>. Certain argument types may fit better with personality traits to enhance acceptance by individuals.<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> <div class="mw-heading mw-heading2"><h2 id="Fallacies_and_non-arguments">Fallacies and non-arguments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=13" title="Edit section: Fallacies and non-arguments"><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/Fallacy" title="Fallacy">Fallacy</a></div> <p>Fallacies are types of argument or expressions which are held to be of an invalid form or contain errors in reasoning. </p><p>One type of fallacy occurs when a word frequently used to indicate a conclusion is used as a transition (conjunctive adverb) between independent clauses. In English the words <i>therefore</i>, <i>so</i>, <i>because</i> and <i>hence</i> typically separate the premises from the conclusion of an argument. Thus: <i>Socrates is a man, all men are mortal therefore Socrates is mortal</i> is an argument because the assertion <i>Socrates is mortal</i> follows from the preceding statements. However, <i>I was thirsty and therefore I drank</i> is not an argument, despite its appearance. It is not being claimed that <i>I drank</i> is logically entailed by <i>I was thirsty</i>. The <i>therefore</i> in this sentence indicates <i>for that reason</i> not <i>it follows that</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Elliptical_or_ethymematic_arguments">Elliptical or ethymematic arguments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=14" title="Edit section: Elliptical or ethymematic arguments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Often an argument is invalid or weak because there is a missing premise—the supply of which would make it valid or strong. This is referred to as an elliptical or enthymematic argument (see also <a href="/wiki/Enthymeme#Syllogism_with_an_unstated_premise" title="Enthymeme">Enthymeme § Syllogism with an unstated premise</a>). Speakers and writers will often leave out a necessary premise in their reasoning if it is widely accepted and the writer does not wish to state the blindingly obvious. Example: <i>All metals expand when heated, therefore iron will expand when heated.</i> The missing premise is: <i>Iron is a metal.</i> On the other hand, a seemingly valid argument may be found to lack a premise—a "hidden assumption"—which, if highlighted, can show a fault in reasoning. Example: A witness reasoned: <i>Nobody came out the front door except the milkman; therefore the murderer must have left by the back door.</i> The hidden assumptions are: (1) the milkman was not the murderer and (2) the murderer has left (3) by a door and (4) not by e.g. a window or through <i>an 'ole in 't roof</i> and (5) there are no other doors than the front or back door. </p> <div class="mw-heading mw-heading2"><h2 id="Argument_mining">Argument mining</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=15" title="Edit section: Argument mining"><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_mining" title="Argument mining">Argument mining</a></div> <p>The goal of argument mining is the automatic extraction and identification of argumentative structures from <a href="/wiki/Natural_language" title="Natural language">natural language</a> text with the aid of computer programs.<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> Such argumentative structures include the premise, conclusions, the <a href="/wiki/Argument_scheme" class="mw-redirect" title="Argument scheme">argument scheme</a> and the relationship between the main and subsidiary argument, or the main and counter-argument within discourse.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </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=Argument&action=edit&section=16" 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 .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 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<li><a href="/wiki/Logical_reasoning" title="Logical reasoning">Logical reasoning</a></li> <li><a href="/wiki/Practical_arguments" title="Practical arguments">Practical arguments</a></li> <li><a href="/wiki/Semantic_argument" title="Semantic argument">Semantic argument</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Argument&action=edit&section=17" title="Edit section: Notes"><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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Sinnott-Armstrong_2015-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Sinnott-Armstrong_2015_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Sinnott-Armstrong_2015_1-1"><sup><i><b>b</b></i></sup></a></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 id="CITEREFSinnott-ArmstrongFogelin2015" class="citation book cs1">Sinnott-Armstrong, Walter; Fogelin, Robert J. (2015). <i>Understanding arguments: an introduction to informal logic</i>. Cengage advantage books (9 ed.). Australia; Brazil; Mexico; Singapore; United Kingdom; United States: Cengage Learning. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-285-19736-4" title="Special:BookSources/978-1-285-19736-4"><bdi>978-1-285-19736-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+arguments%3A+an+introduction+to+informal+logic&rft.place=Australia%3B+Brazil%3B+Mexico%3B+Singapore%3B+United+Kingdom%3B+United+States&rft.series=Cengage+advantage+books&rft.edition=9&rft.pub=Cengage+Learning&rft.date=2015&rft.isbn=978-1-285-19736-4&rft.aulast=Sinnott-Armstrong&rft.aufirst=Walter&rft.au=Fogelin%2C+Robert+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgument" 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">Ralph H. Johnson, <i><a rel="nofollow" class="external text" href="https://www.taylorfrancis.com/books/9781135691202">Manifest Rationality: A pragmatic theory of argument</a></i> (New Jersey: Laurence Erlbaum, 2000), 46–49.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">This is called "argument-as-product", distinguished from "argument-as-process" and "argument-as-procedure." Wenzel, J. W. (1987). The rhetorical perspective on argument. In F. H. van Eemeren, R. Grootendorst, J. A. Blair, & C. A. Willard (Eds.), Argumentation. Across the lines of discipline. Proceedings of the conference on argumentation 1986 (pp. 101–109). Dordrecht-Providence: Foris.</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="CITEREFWagemans2021" class="citation cs2">Wagemans, Jean H. M. 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"[Transcendental] arguments consist of a string of what one could call indispensability claims. They move from their starting points to their conclusions by showing that the condition stated in the conclusion is indispensable to the feature identified at the start ... Thus we could spell out Kant's transcendental deduction in the first edition in three stages: experience must have an object, that is, be <i>of</i> something; for this, it must be coherent; and to be coherent it must be shaped by the understanding through the categories."</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="CITEREFKompridis2006" class="citation book cs1">Kompridis, Nikolas (2006). "World Disclosing Arguments?". <i>Critique and Disclosure</i>. 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"User Acceptance of Knowledge-Based System Recommendations: Explanations, Arguments, and Fit" 45th Annual Hawaii International Conference on System Sciences, Hawaii, January 5–8.</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="CITEREFLippiTorroni2016" class="citation journal cs1">Lippi, Marco; Torroni, Paolo (20 April 2016). <a rel="nofollow" class="external text" href="https://dl.acm.org/doi/10.1145/2850417">"Argumentation Mining: State of the Art and Emerging Trends"</a>. <i>ACM Transactions on Internet Technology</i>. <b>16</b> (2): <span class="nowrap">1–</span>25. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F2850417">10.1145/2850417</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/11585%2F523460">11585/523460</a></span>. <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/1533-5399">1533-5399</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:9561587">9561587</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ACM+Transactions+on+Internet+Technology&rft.atitle=Argumentation+Mining%3A+State+of+the+Art+and+Emerging+Trends&rft.volume=16&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E25&rft.date=2016-04-20&rft_id=info%3Ahdl%2F11585%2F523460&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9561587%23id-name%3DS2CID&rft.issn=1533-5399&rft_id=info%3Adoi%2F10.1145%2F2850417&rft.aulast=Lippi&rft.aufirst=Marco&rft.au=Torroni%2C+Paolo&rft_id=https%3A%2F%2Fdl.acm.org%2Fdoi%2F10.1145%2F2850417&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgument" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><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/20210418083659/https://www.i3s.unice.fr/~villata/tutorialIJCAI2016.html">"Argument Mining - IJCAI2016 Tutorial"</a>. <i>www.i3s.unice.fr</i>. Archived from <a rel="nofollow" class="external text" href="https://www.i3s.unice.fr/~villata/tutorialIJCAI2016.html">the original</a> on 18 April 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">9 March</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.i3s.unice.fr&rft.atitle=Argument+Mining+-+IJCAI2016+Tutorial&rft_id=https%3A%2F%2Fwww.i3s.unice.fr%2F~villata%2FtutorialIJCAI2016.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgument" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://acl2016tutorial.arg.tech/">"NLP Approaches to Computational Argumentation – ACL 2016, Berlin"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">9 March</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=NLP+Approaches+to+Computational+Argumentation+%E2%80%93+ACL+2016%2C+Berlin&rft_id=http%3A%2F%2Facl2016tutorial.arg.tech%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgument" class="Z3988"></span></span> </li> </ol></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=Argument&action=edit&section=18" title="Edit section: References"><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="Shaw1922" class="citation book cs1">Shaw, Warren Choate (1922). <a rel="nofollow" class="external text" href="https://archive.org/details/artdebate00shawgoog"><i>The Art of Debate</i></a>. Allyn and Bacon. p. <a rel="nofollow" class="external text" href="https://archive.org/details/artdebate00shawgoog/page/n92">74</a>. <q>argument by analogy.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Art+of+Debate&rft.pages=74&rft.pub=Allyn+and+Bacon&rft.date=1922&rft.aulast=Shaw&rft.aufirst=Warren+Choate&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fartdebate00shawgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgument" class="Z3988"></span></li> <li><a href="/wiki/Robert_Audi" title="Robert Audi">Robert Audi</a>, <i>Epistemology</i>, Routledge, 1998. Particularly relevant is Chapter 6, which explores the relationship between knowledge, inference and argument.</li> <li>J. L. Austin <i><a href="/wiki/How_to_Do_Things_With_Words" class="mw-redirect" title="How to Do Things With Words">How to Do Things With Words</a></i>, Oxford University Press, 1976.</li> <li>H. P. Grice, <i>Logic and Conversation</i> in <i>The Logic of Grammar</i>, Dickenson, 1975.</li> <li><a href="/wiki/Vincent_F._Hendricks" title="Vincent F. Hendricks">Vincent F. Hendricks</a>, <i>Thought 2 Talk: A Crash Course in Reflection and Expression</i>, New York: Automatic Press / VIP, 2005, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/87-991013-7-8" title="Special:BookSources/87-991013-7-8">87-991013-7-8</a></li> <li>R. A. DeMillo, R. J. Lipton and A. J. Perlis, <i><a rel="nofollow" class="external text" href="https://www.ics.uci.edu/~pattis/misc/socialproofs.pdf">Social Processes and Proofs of Theorems and Programs</a></i>, Communications of the ACM, Vol. 22, No. 5, 1979. A classic article on the social process of acceptance of proofs in mathematics.</li> <li><a href="/wiki/Yu._Manin" class="mw-redirect" title="Yu. Manin">Yu. Manin</a>, <i>A Course in Mathematical Logic</i>, Springer Verlag, 1977. A mathematical view of logic. This book is different from most books on mathematical logic in that it emphasizes the mathematics of logic, as opposed to the formal structure of logic.</li> <li><a href="/wiki/Cha%C3%AFm_Perelman" title="Chaïm Perelman">Ch. Perelman</a> and L. Olbrechts-Tyteca, <i>The New Rhetoric</i>, Notre Dame, 1970. This classic was originally published in French in 1958.</li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a>, <i>Science and Hypothesis</i>, Dover Publications, 1952</li> <li>Frans van Eemeren and <a href="/wiki/Rob_Grootendorst" title="Rob Grootendorst">Rob Grootendorst</a>, <i>Speech Acts in Argumentative Discussions</i>, Foris Publications, 1984.</li> <li><a href="/wiki/K._R._Popper" class="mw-redirect" title="K. R. Popper">K. R. Popper</a> <i>Objective Knowledge; An Evolutionary Approach</i>, Oxford: Clarendon Press, 1972.</li> <li><a href="/wiki/L._S._Stebbing" class="mw-redirect" title="L. S. Stebbing">L. S. Stebbing</a>, <i>A Modern Introduction to Logic</i>, Methuen and Co., 1948. An account of logic that covers the classic topics of logic and argument while carefully considering modern developments in logic.</li> <li><a href="/wiki/Douglas_N._Walton" title="Douglas N. Walton">Douglas N. Walton</a>, <i>Informal Logic: A Handbook for Critical Argumentation</i>, Cambridge, 1998.</li> <li>Walton, Douglas; Christopher Reed; Fabrizio Macagno, <i>Argumentation Schemes</i>, New York: Cambridge University Press, 2008.</li> <li>Carlos Chesñevar, Ana Maguitman and <a href="/wiki/Ronald_Loui" title="Ronald Loui">Ronald Loui</a>, <i>Logical Models of Argument</i>, ACM Computing Surveys, vol. 32, num. 4, pp. 337–383, 2000.</li> <li><a href="/wiki/T._Edward_Damer" title="T. Edward Damer">T. Edward Damer</a>. <i><a href="/wiki/Attacking_Faulty_Reasoning" title="Attacking Faulty Reasoning">Attacking Faulty Reasoning</a></i>, 5th Edition, Wadsworth, 2005. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-534-60516-8" title="Special:BookSources/0-534-60516-8">0-534-60516-8</a></li> <li>Charles Arthur Willard, A Theory of Argumentation. 1989.</li> <li>Charles Arthur Willard, <a rel="nofollow" class="external text" href="https://philpapers.org/rec/WILAAT-22">Argumentation and the Social Grounds of Knowledge</a>. 1982.</li></ul> <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=Argument&action=edit&section=19" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Salmon, Wesley C. <i>Logic</i>. New Jersey: Prentice-Hall (1963). Library of Congress Catalog Card no. 63–10528.</li> <li>Aristotle, <i>Prior and Posterior Analytics</i>. Ed. and trans. John Warrington. London: Dent (1964)</li> <li>Mates, Benson. <i>Elementary Logic</i>. New York: OUP (1972). Library of Congress Catalog Card no. 74–166004.</li> <li>Mendelson, Elliot. <i>Introduction to Mathematical Logic</i>. New York: Van Nostran Reinholds Company (1964).</li> <li>Frege, Gottlob. <i>The Foundations of Arithmetic</i>. Evanston, IL: Northwestern University Press (1980).</li> <li><a href="/wiki/Brian_Martin_(social_scientist)" title="Brian Martin (social scientist)">Martin, Brian</a>. <i><a rel="nofollow" class="external text" href="http://www.bmartin.cc/pubs/14cm/14cm.pdf">The Controversy Manual</a></i> (Sparsnäs, Sweden: Irene Publishing, 2014).</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=Argument&action=edit&section=20" 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:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Arguments" class="extiw" title="commons:Category:Arguments">Arguments</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://philpapers.org/browse/argument">Argument</a> at <a href="/wiki/PhilPapers" title="PhilPapers">PhilPapers</a></li> <li><a rel="nofollow" class="external text" href="https://www.inphoproject.org/idea/1437">Argument</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><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDutilh_Novaes" class="citation encyclopaedia cs1"><a href="/wiki/Catarina_Dutilh_Novaes" title="Catarina Dutilh Novaes">Dutilh Novaes, Catarina</a>. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/argument/">"Argument and Argumentation"</a>. In <a href="/wiki/Edward_N._Zalta" title="Edward N. Zalta">Zalta, Edward N.</a> (ed.). <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=Argument+and+Argumentation&rft.btitle=Stanford+Encyclopedia+of+Philosophy&rft.aulast=Dutilh+Novaes&rft.aufirst=Catarina&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fargument%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArgument" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcKeon" class="citation encyclopaedia cs1">McKeon, Matthew. <a rel="nofollow" class="external text" href="http://www.iep.utm.edu/argument">"Argument"</a>. <i><a href="/wiki/Internet_Encyclopedia_of_Philosophy" title="Internet Encyclopedia of Philosophy">Internet Encyclopedia of Philosophy</a></i>.</cite><span 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aria-labelledby="Common_fallacies_(list)222" 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"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Fallacies" title="Template:Fallacies"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Fallacies" title="Template talk:Fallacies"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Fallacies" title="Special:EditPage/Template:Fallacies"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Common_fallacies_(list)222" style="font-size:114%;margin:0 4em">Common <a href="/wiki/Fallacy" title="Fallacy">fallacies</a> (<a href="/wiki/List_of_fallacies" title="List of fallacies">list</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Formal_fallacy" title="Formal fallacy">Formal</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 scope="row" class="navbox-group" style="width:1%">In <a href="/wiki/Propositional_calculus" title="Propositional calculus">propositional logic</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/Affirming_a_disjunct" title="Affirming a disjunct">Affirming a disjunct</a></li> <li><a href="/wiki/Affirming_the_consequent" title="Affirming the consequent">Affirming the consequent</a></li> <li><a href="/wiki/Denying_the_antecedent" title="Denying the antecedent">Denying the antecedent</a></li> <li><a href="/wiki/Argument_from_fallacy" title="Argument from fallacy">Argument from fallacy</a></li> <li><a href="/wiki/Masked-man_fallacy" title="Masked-man fallacy">Masked man</a></li> <li><a href="/wiki/Mathematical_fallacy" title="Mathematical fallacy">Mathematical fallacy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">In <a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">quantificational logic</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/Existential_fallacy" title="Existential fallacy">Existential</a></li> <li><a href="/wiki/Affirming_the_consequent" title="Affirming the consequent">Illicit conversion</a></li> <li><a href="/wiki/Proof_by_example" title="Proof by example">Proof by example</a></li> <li><a href="/wiki/Quantifier_shift" title="Quantifier shift">Quantifier shift</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Syllogistic_fallacy" class="mw-redirect" title="Syllogistic fallacy">Syllogistic fallacy</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/Affirmative_conclusion_from_a_negative_premise" title="Affirmative conclusion from a negative premise">Affirmative conclusion from a negative premise</a></li> <li><a href="/wiki/Negative_conclusion_from_affirmative_premises" title="Negative conclusion from affirmative premises">Negative conclusion from affirmative premises</a></li> <li><a href="/wiki/Fallacy_of_exclusive_premises" title="Fallacy of exclusive premises">Exclusive premises</a></li> <li><a href="/wiki/Existential_fallacy" title="Existential fallacy">Existential</a></li> <li><a href="/wiki/Modal_scope_fallacy" class="mw-redirect" title="Modal scope fallacy">Necessity</a></li> <li><a href="/wiki/Fallacy_of_four_terms" title="Fallacy of four terms">Four terms</a></li> <li><a href="/wiki/Illicit_major" title="Illicit major">Illicit major</a></li> <li><a href="/wiki/Illicit_minor" title="Illicit minor">Illicit minor</a></li> <li><a href="/wiki/Fallacy_of_the_undistributed_middle" title="Fallacy of the undistributed middle">Undistributed middle</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Informal_fallacy" title="Informal fallacy">Informal</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 scope="row" class="navbox-group" style="width:1%">Equivocation</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/Equivocation" title="Equivocation">Equivocation</a></li> <li><a href="/wiki/False_equivalence" title="False equivalence">False equivalence</a></li> <li><a href="/wiki/False_attribution" title="False attribution">False attribution</a></li> <li><a href="/wiki/Quoting_out_of_context" title="Quoting out of context">Quoting out of context</a></li> <li><a href="/wiki/Loki%27s_Wager" class="mw-redirect" title="Loki's Wager">Loki's Wager</a></li> <li><a href="/wiki/No_true_Scotsman" title="No true Scotsman">No true Scotsman</a></li> <li><a href="/wiki/Reification_(fallacy)" title="Reification (fallacy)">Reification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Question-begging</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/Circular_reasoning" title="Circular reasoning">Circular reasoning</a> / <a href="/wiki/Begging_the_question" title="Begging the question">Begging the question</a></li> <li><a href="/wiki/Loaded_language" title="Loaded language">Loaded language</a> <ul><li><a href="/wiki/Leading_question" title="Leading question">Leading question</a></li></ul></li> <li><a href="/wiki/Double-barreled_question" title="Double-barreled question">Compound question</a> / <a href="/wiki/Loaded_question" title="Loaded question">Loaded question</a> / <a href="/wiki/Complex_question" title="Complex question">Complex question</a></li> <li><a href="/wiki/No_true_Scotsman" title="No true Scotsman">No true Scotsman</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Correlative-based_fallacies" title="Correlative-based fallacies">Correlative-based</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/False_dilemma" title="False dilemma">False dilemma</a> <ul><li><a href="/wiki/Nirvana_fallacy" title="Nirvana fallacy">Perfect solution</a></li></ul></li> <li><a href="/wiki/Denying_the_correlative" title="Denying the correlative">Denying the correlative</a></li> <li><a href="/wiki/Suppressed_correlative" title="Suppressed correlative">Suppressed correlative</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Fallacies_of_illicit_transference" title="Fallacies of illicit transference">Illicit transference</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/Fallacy_of_composition" title="Fallacy of composition">Composition</a></li> <li><a href="/wiki/Fallacy_of_division" title="Fallacy of division">Division</a></li> <li><a href="/wiki/Ecological_fallacy" title="Ecological fallacy">Ecological</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><i><a href="/wiki/Secundum_quid" title="Secundum quid">Secundum quid</a></i></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/Accident_(fallacy)" title="Accident (fallacy)">Accident</a></li> <li><a href="/wiki/Converse_accident" title="Converse accident">Converse accident</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Faulty_generalization" title="Faulty generalization">Faulty generalization</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/Anecdotal_evidence" title="Anecdotal evidence">Anecdotal evidence</a></li> <li><a href="/wiki/Sampling_bias" title="Sampling bias">Sampling bias</a> <ul><li><a href="/wiki/Cherry_picking" title="Cherry picking">Cherry picking</a></li> <li><a href="/wiki/McNamara_fallacy" title="McNamara fallacy">McNamara</a></li></ul></li> <li><a href="/wiki/Base_rate_fallacy" title="Base rate fallacy">Base rate</a> / <a href="/wiki/Conjunction_fallacy" title="Conjunction fallacy">Conjunction</a></li> <li><a href="/wiki/Double_counting_(fallacy)" title="Double counting (fallacy)">Double counting</a></li> <li><a href="/wiki/Argument_from_analogy" title="Argument from analogy">False analogy</a></li> <li><a href="/wiki/Slothful_induction" title="Slothful induction">Slothful induction</a></li> <li><a href="/wiki/Overwhelming_exception" title="Overwhelming exception">Overwhelming exception</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ambiguity" title="Ambiguity">Ambiguity</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/Fallacy_of_accent" title="Fallacy of accent">Accent</a></li> <li><a href="/wiki/False_precision" title="False precision">False precision</a></li> <li><a href="/wiki/Moving_the_goalposts" title="Moving the goalposts">Moving the goalposts</a></li> <li><a href="/wiki/Quoting_out_of_context" title="Quoting out of context">Quoting out of context</a></li> <li><a href="/wiki/Slippery_slope" title="Slippery slope">Slippery slope</a></li> <li><a href="/wiki/Sorites_paradox" title="Sorites paradox">Sorites paradox</a></li> <li><a href="/wiki/Syntactic_ambiguity" title="Syntactic ambiguity">Syntactic ambiguity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Questionable_cause" title="Questionable cause">Questionable cause</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/Animistic_fallacy" title="Animistic fallacy">Animistic</a> <ul><li><a href="/wiki/Furtive_fallacy" title="Furtive fallacy">Furtive</a></li></ul></li> <li>Correlation implies causation <ul><li><i><a href="/wiki/Correlation_does_not_imply_causation" title="Correlation does not imply causation">Cum hoc</a></i></li> <li><i><a href="/wiki/Post_hoc_ergo_propter_hoc" title="Post hoc ergo propter hoc">Post hoc</a></i></li></ul></li> <li><a href="/wiki/Gambler%27s_fallacy" title="Gambler's fallacy">Gambler's</a> <ul><li><a href="/wiki/Inverse_gambler%27s_fallacy" title="Inverse gambler's fallacy">Inverse</a></li></ul></li> <li><a href="/wiki/Regression_fallacy" title="Regression fallacy">Regression</a></li> <li><a href="/wiki/Fallacy_of_the_single_cause" title="Fallacy of the single cause">Single cause</a></li> <li><a href="/wiki/Slippery_slope" title="Slippery slope">Slippery slope</a></li> <li><a href="/wiki/Texas_sharpshooter_fallacy" title="Texas sharpshooter fallacy">Texas sharpshooter</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Appeals</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/Appeal_to_the_law" title="Appeal to the law">Law/Legality</a></li> <li><a href="/wiki/Appeal_to_the_stone" title="Appeal to the stone">Stone</a> / <a href="/wiki/Proof_by_assertion" title="Proof by assertion">Proof by assertion</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Appeal_to_consequences" title="Appeal to consequences">Consequences</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><i><a href="/wiki/Argumentum_ad_baculum" title="Argumentum ad baculum">Argumentum ad baculum</a></i></li> <li><a href="/wiki/Wishful_thinking" title="Wishful thinking">Wishful thinking</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Appeal_to_emotion" title="Appeal to emotion">Emotion</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/Think_of_the_children" title="Think of the children">Children</a></li> <li><a href="/wiki/Appeal_to_fear" title="Appeal to fear">Fear</a></li> <li><a href="/wiki/Appeal_to_flattery" title="Appeal to flattery">Flattery</a></li> <li><a href="/wiki/Appeal_to_novelty" title="Appeal to novelty">Novelty</a></li> <li><a href="/wiki/Appeal_to_pity" title="Appeal to pity">Pity</a></li> <li><a href="/wiki/Appeal_to_ridicule" title="Appeal to ridicule">Ridicule</a></li> <li><a href="/wiki/In-group_favoritism" title="In-group favoritism">In-group favoritism</a></li> <li><a href="/wiki/Invented_here" title="Invented here">Invented here</a> / <a href="/wiki/Not_invented_here" title="Not invented here">Not invented here</a></li> <li><a href="/wiki/Island_mentality" title="Island mentality">Island mentality</a></li> <li><a href="/wiki/Appeal_to_loyalty" title="Appeal to loyalty">Loyalty</a></li> <li><a href="/wiki/Parade_of_horribles" title="Parade of horribles">Parade of horribles</a></li> <li><a href="/wiki/Appeal_to_spite" class="mw-redirect" title="Appeal to spite">Spite</a></li> <li><a href="/wiki/Flag-waving" title="Flag-waving">Stirring symbols</a></li> <li><a href="/wiki/Wisdom_of_repugnance" title="Wisdom of repugnance">Wisdom of repugnance</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Genetic_fallacy" title="Genetic fallacy">Genetic fallacy</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="Ad_hominem18" scope="row" class="navbox-group" style="width:1%"><i><a href="/wiki/Ad_hominem" title="Ad hominem">Ad hominem</a></i></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/Appeal_to_motive" title="Appeal to motive">Appeal to motive</a></li> <li><a href="/wiki/Association_fallacy" title="Association fallacy">Association</a> <ul><li><i><a href="/wiki/Reductio_ad_Hitlerum" title="Reductio ad Hitlerum">Reductio ad Hitlerum</a></i> <ul><li><a href="/wiki/Godwin%27s_law" title="Godwin's law">Godwin's law</a></li></ul></li> <li><i><a href="/wiki/Red-baiting" title="Red-baiting">Reductio ad Stalinum</a></i></li></ul></li> <li><a href="/wiki/Bulverism" title="Bulverism">Bulverism</a></li> <li><a href="/wiki/Poisoning_the_well" title="Poisoning the well">Poisoning the well</a></li> <li><a href="/wiki/Tone_policing" title="Tone policing">Tone</a></li> <li><i><a href="/wiki/Tu_quoque" title="Tu quoque">Tu quoque</a></i></li> <li><a href="/wiki/Whataboutism" title="Whataboutism">Whataboutism</a></li></ul> </div></td></tr><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/Argument_from_authority" title="Argument from authority">Authority</a> <ul><li><a href="/wiki/Appeal_to_accomplishment" title="Appeal to accomplishment">Accomplishment</a></li> <li><i><a href="/wiki/Ipse_dixit" title="Ipse dixit">Ipse dixit</a></i></li> <li><a href="/wiki/Argumentum_ad_lazarum" title="Argumentum ad lazarum">Poverty</a> / <a href="/wiki/Argumentum_ad_crumenam" title="Argumentum ad crumenam">Wealth</a></li></ul></li> <li><a href="/wiki/Etymological_fallacy" title="Etymological fallacy">Etymology</a></li> <li><a href="/wiki/Appeal_to_nature" title="Appeal to nature">Nature</a></li> <li><a href="/wiki/Appeal_to_tradition" title="Appeal to tradition">Tradition</a> / <a href="/wiki/Appeal_to_novelty" title="Appeal to novelty">Novelty</a> <ul><li><a href="/wiki/Chronological_snobbery" title="Chronological snobbery">Chronological snobbery</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <a href="/wiki/Fallacy_of_relevance" class="mw-redirect" title="Fallacy of relevance">fallacies<br /> of relevance</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="Arguments13" scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Arguments</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><i><a href="/wiki/Ad_nauseam" title="Ad nauseam">Ad nauseam</a></i> <ul><li><a href="/wiki/Sealioning" title="Sealioning">Sealioning</a></li></ul></li> <li><a href="/wiki/Argument_from_anecdote" title="Argument from anecdote">Argument from anecdote</a></li> <li><a href="/wiki/Argument_from_silence" title="Argument from silence">Argument from silence</a></li> <li><a href="/wiki/Argument_to_moderation" title="Argument to moderation">Argument to moderation</a></li> <li><i><a href="/wiki/Argumentum_ad_populum" title="Argumentum ad populum">Argumentum ad populum</a></i></li></ul> </div></td></tr><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/Clich%C3%A9" title="Cliché">Cliché</a></li> <li><i><a href="/wiki/The_Four_Great_Errors" title="The Four Great Errors">The Four Great Errors</a></i></li> <li><a href="/wiki/I%27m_entitled_to_my_opinion" title="I'm entitled to my opinion">I'm entitled to my opinion</a></li> <li><i><a href="/wiki/Irrelevant_conclusion" title="Irrelevant conclusion">Ignoratio elenchi</a></i></li> <li><a href="/wiki/Invincible_ignorance_fallacy" title="Invincible ignorance fallacy">Invincible ignorance</a></li> <li><a href="/wiki/Moralistic_fallacy" title="Moralistic fallacy">Moralistic</a> / <a href="/wiki/Naturalistic_fallacy" title="Naturalistic fallacy">Naturalistic</a></li> <li><a href="/wiki/Motte-and-bailey_fallacy" title="Motte-and-bailey fallacy">Motte-and-bailey fallacy</a></li> <li><a href="/wiki/Psychologist%27s_fallacy" title="Psychologist's fallacy">Psychologist's fallacy</a></li> <li><a href="/wiki/Rationalization_(psychology)" title="Rationalization (psychology)">Rationalization</a></li> <li><a href="/wiki/Red_herring" title="Red herring">Red herring</a> <ul><li><a href="/wiki/Two_wrongs_make_a_right" class="mw-redirect" title="Two wrongs make a right">Two wrongs make a right</a></li></ul></li> <li><a href="/wiki/Special_pleading" title="Special pleading">Special pleading</a></li> <li><a href="/wiki/Straw_man" title="Straw man">Straw man</a></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> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Fallacies" title="Category:Fallacies">Category</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="Mathematical_logic326" 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:Mathematical_logic" title="Template:Mathematical logic"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Mathematical_logic" title="Template talk:Mathematical logic"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Mathematical_logic" title="Special:EditPage/Template:Mathematical logic"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Mathematical_logic326" style="font-size:114%;margin:0 4em"><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical logic</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axiom" title="Axiom">Axiom</a> <ul><li><a href="/wiki/List_of_axioms" title="List of axioms">list</a></li></ul></li> <li><a href="/wiki/Cardinality" title="Cardinality">Cardinality</a></li> <li><a href="/wiki/First-order_logic" title="First-order logic">First-order logic</a></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Formal proof</a></li> <li><a href="/wiki/Formal_semantics_(logic)" class="mw-redirect" title="Formal semantics (logic)">Formal semantics</a></li> <li><a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">Foundations of mathematics</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Lemma_(mathematics)" title="Lemma (mathematics)">Lemma</a></li> <li><a href="/wiki/Logical_consequence" title="Logical consequence">Logical consequence</a></li> <li><a href="/wiki/Structure_(mathematical_logic)" title="Structure (mathematical logic)">Model</a></li> <li><a href="/wiki/Theorem" title="Theorem">Theorem</a></li> <li><a href="/wiki/Theory_(mathematical_logic)" title="Theory (mathematical logic)">Theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorems (<a href="/wiki/Category:Theorems_in_the_foundations_of_mathematics" title="Category:Theorems in the foundations of mathematics">list</a>)<br /> and <a href="/wiki/Paradoxes_of_set_theory" title="Paradoxes of set theory">paradoxes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/G%C3%B6del%27s_completeness_theorem" title="Gödel's completeness theorem">Gödel's completeness</a> and <a href="/wiki/G%C3%B6del%27s_incompleteness_theorems" title="Gödel's incompleteness theorems">incompleteness theorems</a></li> <li><a href="/wiki/Tarski%27s_undefinability_theorem" title="Tarski's undefinability theorem">Tarski's undefinability</a></li> <li><a href="/wiki/Banach%E2%80%93Tarski_paradox" title="Banach–Tarski paradox">Banach–Tarski paradox</a></li> <li>Cantor's <a href="/wiki/Cantor%27s_theorem" title="Cantor's theorem">theorem,</a> <a href="/wiki/Cantor%27s_paradox" title="Cantor's paradox">paradox</a> and <a href="/wiki/Cantor%27s_diagonal_argument" title="Cantor's diagonal argument">diagonal argument</a></li> <li><a href="/wiki/Compactness_theorem" title="Compactness theorem">Compactness</a></li> <li><a href="/wiki/Halting_problem" title="Halting problem">Halting problem</a></li> <li><a href="/wiki/Lindstr%C3%B6m%27s_theorem" title="Lindström's theorem">Lindström's</a></li> <li><a href="/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem" title="Löwenheim–Skolem theorem">Löwenheim–Skolem</a></li> <li><a href="/wiki/Russell%27s_paradox" title="Russell's paradox">Russell's paradox</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Logic" title="Logic">Logics</a></th><td class="navbox-list-with-group 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 id="Traditional95" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Term_logic" title="Term logic">Traditional</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/Classical_logic" title="Classical logic">Classical logic</a></li> <li><a href="/wiki/Logical_truth" title="Logical truth">Logical truth</a></li> <li><a href="/wiki/Tautology_(logic)" title="Tautology (logic)">Tautology</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Inference" title="Inference">Inference</a></li> <li><a href="/wiki/Logical_equivalence" title="Logical equivalence">Logical equivalence</a></li> <li><a href="/wiki/Consistency" title="Consistency">Consistency</a> <ul><li><a href="/wiki/Equiconsistency" title="Equiconsistency">Equiconsistency</a></li></ul></li> <li><a class="mw-selflink selflink">Argument</a></li> <li><a href="/wiki/Soundness" title="Soundness">Soundness</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity (logic)">Validity</a></li> <li><a href="/wiki/Syllogism" title="Syllogism">Syllogism</a></li> <li><a href="/wiki/Square_of_opposition" title="Square of opposition">Square of opposition</a></li> <li><a href="/wiki/Venn_diagram" title="Venn diagram">Venn diagram</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional</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/Boolean_algebra" title="Boolean algebra">Boolean algebra</a></li> <li><a href="/wiki/Boolean_function" title="Boolean function">Boolean functions</a></li> <li><a href="/wiki/Logical_connective" title="Logical connective">Logical connectives</a></li> <li><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional calculus</a></li> <li><a href="/wiki/Propositional_formula" title="Propositional formula">Propositional formula</a></li> <li><a href="/wiki/Truth_table" title="Truth table">Truth tables</a></li> <li><a href="/wiki/Many-valued_logic" title="Many-valued logic">Many-valued logic</a> <ul><li><a href="/wiki/Three-valued_logic" title="Three-valued logic">3</a></li> <li><a href="/wiki/Finite-valued_logic" title="Finite-valued logic">finite</a></li> <li><a href="/wiki/Infinite-valued_logic" title="Infinite-valued logic">∞</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">Predicate</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/First-order_logic" title="First-order logic">First-order</a> <ul><li><a href="/wiki/List_of_first-order_theories" title="List of first-order theories"><span style="font-size:85%;">list</span></a></li></ul></li> <li><a href="/wiki/Second-order_logic" title="Second-order logic">Second-order</a> <ul><li><a href="/wiki/Monadic_second-order_logic" title="Monadic second-order logic">Monadic</a></li></ul></li> <li><a href="/wiki/Higher-order_logic" title="Higher-order logic">Higher-order</a></li> <li><a href="/wiki/Fixed-point_logic" title="Fixed-point logic">Fixed-point</a></li> <li><a href="/wiki/Free_logic" title="Free logic">Free</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantifiers</a></li> <li><a href="/wiki/Predicate_(mathematical_logic)" title="Predicate (mathematical logic)">Predicate</a></li> <li><a href="/wiki/Monadic_predicate_calculus" title="Monadic predicate calculus">Monadic predicate calculus</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Set_theory" title="Set theory">Set theory</a></th><td class="navbox-list-with-group 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><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Set</a> <ul><li><a href="/wiki/Hereditary_set" title="Hereditary set">hereditary</a></li></ul></li> <li><a href="/wiki/Class_(set_theory)" title="Class (set theory)">Class</a></li> <li>(<a href="/wiki/Urelement" title="Urelement">Ur-</a>)<a href="/wiki/Element_(mathematics)" title="Element (mathematics)">Element</a></li> <li><a href="/wiki/Ordinal_number" title="Ordinal number">Ordinal number</a></li> <li><a href="/wiki/Extensionality" title="Extensionality">Extensionality</a></li> <li><a href="/wiki/Forcing_(mathematics)" title="Forcing (mathematics)">Forcing</a></li> <li><a href="/wiki/Relation_(mathematics)" title="Relation (mathematics)">Relation</a> <ul><li><a href="/wiki/Equivalence_relation" title="Equivalence relation">equivalence</a></li> <li><a href="/wiki/Partition_of_a_set" title="Partition of a set">partition</a></li></ul></li> <li>Set operations: <ul><li><a href="/wiki/Intersection_(set_theory)" title="Intersection (set theory)">intersection</a></li> <li><a href="/wiki/Union_(set_theory)" title="Union (set theory)">union</a></li> <li><a href="/wiki/Complement_(set_theory)" title="Complement (set theory)">complement</a></li> <li><a href="/wiki/Cartesian_product" title="Cartesian product">Cartesian product</a></li> <li><a href="/wiki/Power_set" title="Power set">power set</a></li> <li><a href="/wiki/List_of_set_identities_and_relations" title="List of set identities and relations">identities</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">sets</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/Countable_set" title="Countable set">Countable</a></li> <li><a href="/wiki/Uncountable_set" title="Uncountable set">Uncountable</a></li> <li><a href="/wiki/Empty_set" title="Empty set">Empty</a></li> <li><a href="/wiki/Inhabited_set" title="Inhabited set">Inhabited</a></li> <li><a href="/wiki/Singleton_(mathematics)" title="Singleton (mathematics)">Singleton</a></li> <li><a href="/wiki/Finite_set" title="Finite set">Finite</a></li> <li><a href="/wiki/Infinite_set" title="Infinite set">Infinite</a></li> <li><a href="/wiki/Transitive_set" title="Transitive set">Transitive</a></li> <li><a href="/wiki/Ultrafilter_(set_theory)" class="mw-redirect" title="Ultrafilter (set theory)">Ultrafilter</a></li> <li><a href="/wiki/Recursive_set" class="mw-redirect" title="Recursive set">Recursive</a></li> <li><a href="/wiki/Fuzzy_set" title="Fuzzy set">Fuzzy</a></li> <li><a href="/wiki/Universal_set" title="Universal set">Universal</a></li> <li><a href="/wiki/Universe_(mathematics)" title="Universe (mathematics)">Universe</a> <ul><li><a href="/wiki/Constructible_universe" title="Constructible universe">constructible</a></li> <li><a href="/wiki/Grothendieck_universe" title="Grothendieck universe">Grothendieck</a></li> <li><a href="/wiki/Von_Neumann_universe" title="Von Neumann universe">Von Neumann</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_(mathematics)" title="Map (mathematics)">Maps</a> and <a href="/wiki/Cardinality" title="Cardinality">cardinality</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/Function_(mathematics)" title="Function (mathematics)">Function</a>/<a href="/wiki/Map_(mathematics)" title="Map (mathematics)">Map</a> <ul><li><a href="/wiki/Domain_of_a_function" title="Domain of a function">domain</a></li> <li><a href="/wiki/Codomain" title="Codomain">codomain</a></li> <li><a href="/wiki/Image_(mathematics)" title="Image (mathematics)">image</a></li></ul></li> <li><a href="/wiki/Injective_function" title="Injective function">In</a>/<a href="/wiki/Surjective_function" title="Surjective function">Sur</a>/<a href="/wiki/Bijection" title="Bijection">Bi</a>-jection</li> <li><a href="/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem" title="Schröder–Bernstein theorem">Schröder–Bernstein theorem</a></li> <li><a href="/wiki/Isomorphism" title="Isomorphism">Isomorphism</a></li> <li><a href="/wiki/G%C3%B6del_numbering" title="Gödel numbering">Gödel numbering</a></li> <li><a href="/wiki/Enumeration" title="Enumeration">Enumeration</a></li> <li><a href="/wiki/Large_cardinal" title="Large cardinal">Large cardinal</a> <ul><li><a href="/wiki/Inaccessible_cardinal" title="Inaccessible cardinal">inaccessible</a></li></ul></li> <li><a href="/wiki/Aleph_number" title="Aleph number">Aleph number</a></li> <li><a href="/wiki/Operation_(mathematics)" title="Operation (mathematics)">Operation</a> <ul><li><a href="/wiki/Binary_operation" title="Binary operation">binary</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Set 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/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Zermelo–Fraenkel</a> <ul><li><a href="/wiki/Axiom_of_choice" title="Axiom of choice">axiom of choice</a></li> <li><a href="/wiki/Continuum_hypothesis" title="Continuum hypothesis">continuum hypothesis</a></li></ul></li> <li><a href="/wiki/General_set_theory" title="General set theory">General</a></li> <li><a href="/wiki/Kripke%E2%80%93Platek_set_theory" title="Kripke–Platek set theory">Kripke–Platek</a></li> <li><a href="/wiki/Morse%E2%80%93Kelley_set_theory" title="Morse–Kelley set theory">Morse–Kelley</a></li> <li><a href="/wiki/Naive_set_theory" title="Naive set theory">Naive</a></li> <li><a href="/wiki/New_Foundations" title="New Foundations">New Foundations</a></li> <li><a href="/wiki/Tarski%E2%80%93Grothendieck_set_theory" title="Tarski–Grothendieck set theory">Tarski–Grothendieck</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory" title="Von Neumann–Bernays–Gödel set theory">Von Neumann–Bernays–Gödel</a></li> <li><a href="/wiki/Ackermann_set_theory" title="Ackermann set theory">Ackermann</a></li> <li><a href="/wiki/Constructive_set_theory" title="Constructive set theory">Constructive</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Formal_system" title="Formal system">Formal systems</a> (<a href="/wiki/List_of_formal_systems" title="List of formal systems"><span style="font-size:85%;">list</span></a>),<br /><a href="/wiki/Formal_language" title="Formal language">language</a> and <a href="/wiki/Syntax_(logic)" title="Syntax (logic)">syntax</a></th><td class="navbox-list-with-group 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><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alphabet_(formal_languages)" title="Alphabet (formal languages)">Alphabet</a></li> <li><a href="/wiki/Arity" title="Arity">Arity</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata</a></li> <li><a href="/wiki/Axiom_schema" title="Axiom schema">Axiom schema</a></li> <li><a href="/wiki/Expression_(mathematics)" title="Expression (mathematics)">Expression</a> <ul><li><a href="/wiki/Ground_expression" title="Ground expression">ground</a></li></ul></li> <li><a href="/wiki/Extension_by_new_constant_and_function_names" title="Extension by new constant and function names">Extension</a> <ul><li><a href="/wiki/Extension_by_definitions" title="Extension by definitions">by definition</a></li> <li><a href="/wiki/Conservative_extension" title="Conservative extension">conservative</a></li></ul></li> <li><a href="/wiki/Finitary_relation" title="Finitary relation">Relation</a></li> <li><a href="/wiki/Formation_rule" title="Formation rule">Formation rule</a></li> <li><a href="/wiki/Formal_grammar" title="Formal grammar">Grammar</a></li> <li><a href="/wiki/Well-formed_formula" title="Well-formed formula">Formula</a> <ul><li><a href="/wiki/Atomic_formula" title="Atomic formula">atomic</a></li> <li><a href="/wiki/Sentence_(mathematical_logic)" title="Sentence (mathematical logic)">closed</a></li> <li><a href="/wiki/Ground_formula" class="mw-redirect" title="Ground formula">ground</a></li> <li><a href="/wiki/Open_formula" title="Open formula">open</a></li></ul></li> <li><a href="/wiki/Free_variables_and_bound_variables" title="Free variables and bound variables">Free/bound variable</a></li> <li><a href="/wiki/Formal_language" title="Formal language">Language</a></li> <li><a href="/wiki/Metalanguage" title="Metalanguage">Metalanguage</a></li> <li><a href="/wiki/Logical_connective" title="Logical connective">Logical connective</a> <ul><li><a href="/wiki/Negation" title="Negation">¬</a></li> <li><a href="/wiki/Logical_disjunction" title="Logical disjunction">∨</a></li> <li><a href="/wiki/Logical_conjunction" title="Logical conjunction">∧</a></li> <li><a href="/wiki/Material_conditional" title="Material conditional">→</a></li> <li><a href="/wiki/Logical_biconditional" title="Logical biconditional">↔</a></li> <li><a href="/wiki/Logical_equality" title="Logical equality">=</a></li></ul></li> <li><a href="/wiki/Predicate_(mathematical_logic)" title="Predicate (mathematical logic)">Predicate</a> <ul><li><a href="/wiki/Functional_predicate" title="Functional predicate">functional</a></li> <li><a href="/wiki/Predicate_variable" title="Predicate variable">variable</a></li> <li><a href="/wiki/Propositional_variable" title="Propositional variable">propositional variable</a></li></ul></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Proof</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantifier</a> <ul><li><a href="/wiki/Existential_quantification" title="Existential quantification">∃</a></li> <li><a href="/wiki/Uniqueness_quantification" title="Uniqueness quantification">!</a></li> <li><a href="/wiki/Universal_quantification" title="Universal quantification">∀</a></li> <li><a href="/wiki/Quantifier_rank" title="Quantifier rank">rank</a></li></ul></li> <li><a href="/wiki/Sentence_(mathematical_logic)" title="Sentence (mathematical logic)">Sentence</a> <ul><li><a href="/wiki/Atomic_sentence" title="Atomic sentence">atomic</a></li> <li><a href="/wiki/Spectrum_of_a_sentence" title="Spectrum of a sentence">spectrum</a></li></ul></li> <li><a href="/wiki/Signature_(logic)" title="Signature (logic)">Signature</a></li> <li><a href="/wiki/String_(formal_languages)" class="mw-redirect" title="String (formal languages)">String</a></li> <li><a href="/wiki/Substitution_(logic)" title="Substitution (logic)">Substitution</a></li> <li><a href="/wiki/Symbol_(formal)" title="Symbol (formal)">Symbol</a> <ul><li><a href="/wiki/Uninterpreted_function" title="Uninterpreted function">function</a></li> <li><a href="/wiki/Logical_constant" title="Logical constant">logical/constant</a></li> <li><a href="/wiki/Non-logical_symbol" title="Non-logical symbol">non-logical</a></li> <li><a href="/wiki/Variable_(mathematics)" title="Variable (mathematics)">variable</a></li></ul></li> <li><a href="/wiki/Term_(logic)" title="Term (logic)">Term</a></li> <li><a href="/wiki/Theory_(mathematical_logic)" title="Theory (mathematical logic)">Theory</a> <ul><li><a href="/wiki/List_of_mathematical_theories" title="List of mathematical theories"><span style="font-size:85%;">list</span></a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="nowrap">Example <a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic<br />systems</a> <span style="font-size:85%;">(<a href="/wiki/List_of_first-order_theories" title="List of first-order theories">list</a>)</span></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>of <a href="/wiki/True_arithmetic" title="True arithmetic">arithmetic</a>: <ul><li><a href="/wiki/Peano_axioms" title="Peano axioms">Peano</a></li> <li><a href="/wiki/Second-order_arithmetic" title="Second-order arithmetic">second-order</a></li> <li><a href="/wiki/Elementary_function_arithmetic" title="Elementary function arithmetic">elementary function</a></li> <li><a href="/wiki/Primitive_recursive_arithmetic" title="Primitive recursive arithmetic">primitive recursive</a></li> <li><a href="/wiki/Robinson_arithmetic" title="Robinson arithmetic">Robinson</a></li> <li><a href="/wiki/Skolem_arithmetic" title="Skolem arithmetic">Skolem</a></li></ul></li> <li>of the <a href="/wiki/Construction_of_the_real_numbers" title="Construction of the real numbers">real numbers</a> <ul><li><a href="/wiki/Tarski%27s_axiomatization_of_the_reals" title="Tarski's axiomatization of the reals">Tarski's axiomatization</a></li></ul></li> <li>of <a href="/wiki/Axiomatization_of_Boolean_algebras" class="mw-redirect" title="Axiomatization of Boolean algebras">Boolean algebras</a> <ul><li><a href="/wiki/Boolean_algebras_canonically_defined" title="Boolean algebras canonically defined">canonical</a></li> <li><a href="/wiki/Minimal_axioms_for_Boolean_algebra" title="Minimal axioms for Boolean algebra">minimal axioms</a></li></ul></li> <li>of <a href="/wiki/Foundations_of_geometry" title="Foundations of geometry">geometry</a>: <ul><li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean</a>: <ul><li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i></a></li> <li><a href="/wiki/Hilbert%27s_axioms" title="Hilbert's axioms">Hilbert's</a></li> <li><a href="/wiki/Tarski%27s_axioms" title="Tarski's axioms">Tarski's</a></li></ul></li> <li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean</a></li></ul></li></ul> <ul><li><i><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proof_theory" title="Proof theory">Proof theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Formal_proof" title="Formal proof">Formal proof</a></li> <li><a href="/wiki/Natural_deduction" title="Natural deduction">Natural deduction</a></li> <li><a href="/wiki/Logical_consequence" title="Logical consequence">Logical consequence</a></li> <li><a href="/wiki/Rule_of_inference" title="Rule of inference">Rule of inference</a></li> <li><a href="/wiki/Sequent_calculus" title="Sequent calculus">Sequent calculus</a></li> <li><a href="/wiki/Theorem" title="Theorem">Theorem</a></li> <li><a href="/wiki/Formal_system" title="Formal system">Systems</a> <ul><li><a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic</a></li> <li><a href="/wiki/Deductive_system" class="mw-redirect" title="Deductive system">deductive</a></li> <li><a href="/wiki/Hilbert_system" title="Hilbert system">Hilbert</a> <ul><li><a href="/wiki/List_of_Hilbert_systems" class="mw-redirect" title="List of Hilbert systems">list</a></li></ul></li></ul></li> <li><a href="/wiki/Complete_theory" title="Complete theory">Complete theory</a></li> <li><a href="/wiki/Independence_(mathematical_logic)" title="Independence (mathematical logic)">Independence</a> (<a href="/wiki/List_of_statements_independent_of_ZFC" title="List of statements independent of ZFC">from ZFC</a>)</li> <li><a href="/wiki/Proof_of_impossibility" title="Proof of impossibility">Proof of impossibility</a></li> <li><a href="/wiki/Ordinal_analysis" title="Ordinal analysis">Ordinal analysis</a></li> <li><a href="/wiki/Reverse_mathematics" title="Reverse mathematics">Reverse mathematics</a></li> <li><a href="/wiki/Self-verifying_theories" title="Self-verifying theories">Self-verifying theories</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Model_theory" title="Model theory">Model theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Interpretation_(logic)" title="Interpretation (logic)">Interpretation</a> <ul><li><a href="/wiki/Interpretation_function" class="mw-redirect" title="Interpretation function">function</a></li> <li><a href="/wiki/Interpretation_(model_theory)" title="Interpretation (model theory)">of models</a></li></ul></li> <li><a href="/wiki/Structure_(mathematical_logic)" title="Structure (mathematical logic)">Model</a> <ul><li><a href="/wiki/Elementary_equivalence" title="Elementary equivalence">equivalence</a></li> <li><a href="/wiki/Finite_model_theory" title="Finite model theory">finite</a></li> <li><a href="/wiki/Saturated_model" title="Saturated model">saturated</a></li> <li><a href="/wiki/Spectrum_of_a_theory" title="Spectrum of a theory">spectrum</a></li> <li><a href="/wiki/Substructure_(mathematics)" title="Substructure (mathematics)">submodel</a></li></ul></li> <li><a href="/wiki/Non-standard_model" title="Non-standard model">Non-standard model</a> <ul><li><a href="/wiki/Non-standard_model_of_arithmetic" title="Non-standard model of arithmetic">of arithmetic</a></li></ul></li> <li><a href="/wiki/Diagram_(mathematical_logic)" title="Diagram (mathematical logic)">Diagram</a> <ul><li><a href="/wiki/Elementary_diagram" title="Elementary diagram">elementary</a></li></ul></li> <li><a href="/wiki/Categorical_theory" title="Categorical theory">Categorical theory</a></li> <li><a href="/wiki/Model_complete_theory" title="Model complete theory">Model complete theory</a></li> <li><a href="/wiki/Satisfiability" title="Satisfiability">Satisfiability</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li> <li><a href="/wiki/Strength_(mathematical_logic)" title="Strength (mathematical logic)">Strength</a></li> <li><a href="/wiki/Theories_of_truth" class="mw-redirect" title="Theories of truth">Theories of truth</a> <ul><li><a href="/wiki/Semantic_theory_of_truth" title="Semantic theory of truth">semantic</a></li> <li><a href="/wiki/Tarski%27s_theory_of_truth" class="mw-redirect" title="Tarski's theory of truth">Tarski's</a></li> <li><a href="/wiki/Kripke%27s_theory_of_truth" class="mw-redirect" title="Kripke's theory of truth">Kripke's</a></li></ul></li> <li><a href="/wiki/T-schema" title="T-schema">T-schema</a></li> <li><a href="/wiki/Transfer_principle" title="Transfer principle">Transfer principle</a></li> <li><a href="/wiki/Truth_predicate" title="Truth predicate">Truth predicate</a></li> <li><a href="/wiki/Truth_value" title="Truth value">Truth value</a></li> <li><a href="/wiki/Type_(model_theory)" title="Type (model theory)">Type</a></li> <li><a href="/wiki/Ultraproduct" title="Ultraproduct">Ultraproduct</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%"><a href="/wiki/Computability_theory" title="Computability theory">Computability theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Church_encoding" title="Church encoding">Church encoding</a></li> <li><a href="/wiki/Church%E2%80%93Turing_thesis" title="Church–Turing 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