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class="vector-toc-list"> <li id="toc-Aristotle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aristotle"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Aristotle</span> </div> </a> <ul id="toc-Aristotle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Medieval_syllogism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Medieval_syllogism"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Medieval syllogism</span> </div> </a> <ul id="toc-Medieval_syllogism-sublist" class="vector-toc-list"> <li id="toc-Boethius" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Boethius"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Boethius</span> </div> </a> <ul id="toc-Boethius-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Peter_Abelard" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Peter_Abelard"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.2</span> <span>Peter Abelard</span> </div> </a> <ul id="toc-Peter_Abelard-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Jean_Buridan" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Jean_Buridan"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.3</span> <span>Jean Buridan</span> </div> </a> <ul id="toc-Jean_Buridan-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Modern_history" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Modern_history"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Modern history</span> </div> </a> <button aria-controls="toc-Modern_history-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Modern history subsection</span> </button> <ul id="toc-Modern_history-sublist" class="vector-toc-list"> <li id="toc-Boole's_acceptance_of_Aristotle" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Boole's_acceptance_of_Aristotle"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Boole's acceptance of Aristotle</span> </div> </a> <ul id="toc-Boole's_acceptance_of_Aristotle-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Basic_structure" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Basic_structure"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Basic structure</span> </div> </a> <button aria-controls="toc-Basic_structure-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 Basic structure subsection</span> </button> <ul id="toc-Basic_structure-sublist" class="vector-toc-list"> <li id="toc-Polysyllogism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polysyllogism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Polysyllogism</span> </div> </a> <ul id="toc-Polysyllogism-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Types" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Types"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Types</span> </div> </a> <button aria-controls="toc-Types-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 Types subsection</span> </button> <ul id="toc-Types-sublist" class="vector-toc-list"> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> <li id="toc-Barbara_(AAA-1)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Barbara_(AAA-1)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Barbara (AAA-1)</span> </div> </a> <ul id="toc-Barbara_(AAA-1)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Celarent_(EAE-1)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Celarent_(EAE-1)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2</span> <span>Celarent (EAE-1)</span> </div> </a> <ul id="toc-Celarent_(EAE-1)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Darii_(AII-1)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Darii_(AII-1)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.3</span> <span>Darii (AII-1)</span> </div> </a> <ul id="toc-Darii_(AII-1)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ferio_(EIO-1)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ferio_(EIO-1)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.4</span> <span>Ferio (EIO-1)</span> </div> </a> <ul id="toc-Ferio_(EIO-1)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Baroco_(AOO-2)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Baroco_(AOO-2)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.5</span> <span>Baroco (AOO-2)</span> </div> </a> <ul id="toc-Baroco_(AOO-2)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bocardo_(OAO-3)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bocardo_(OAO-3)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.6</span> <span>Bocardo (OAO-3)</span> </div> </a> <ul id="toc-Bocardo_(OAO-3)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Barbari_(AAI-1)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Barbari_(AAI-1)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.7</span> <span><i>Barbari (AAI-1)</i></span> </div> </a> <ul id="toc-Barbari_(AAI-1)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Celaront_(EAO-1)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Celaront_(EAO-1)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.8</span> <span><i>Celaront (EAO-1)</i></span> </div> </a> <ul id="toc-Celaront_(EAO-1)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Camestros_(AEO-2)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Camestros_(AEO-2)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.9</span> <span><i>Camestros (AEO-2)</i></span> </div> </a> <ul id="toc-Camestros_(AEO-2)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Felapton_(EAO-3)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Felapton_(EAO-3)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.10</span> <span><i>Felapton (EAO-3)</i></span> </div> </a> <ul id="toc-Felapton_(EAO-3)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Darapti_(AAI-3)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Darapti_(AAI-3)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.11</span> <span><i>Darapti (AAI-3)</i></span> </div> </a> <ul id="toc-Darapti_(AAI-3)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Table_of_all_syllogisms" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Table_of_all_syllogisms"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Table of all syllogisms</span> </div> </a> <ul id="toc-Table_of_all_syllogisms-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Terms_in_syllogism" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Terms_in_syllogism"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Terms in syllogism</span> </div> </a> <ul id="toc-Terms_in_syllogism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Existential_import" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Existential_import"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Existential import</span> </div> </a> <ul id="toc-Existential_import-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Syllogistic_fallacies" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Syllogistic_fallacies"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Syllogistic fallacies</span> </div> </a> <ul id="toc-Syllogistic_fallacies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_types" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Other_types"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Other types</span> </div> </a> <ul id="toc-Other_types-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <button aria-controls="toc-References-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 References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Syllogism</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 63 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-63" 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">63 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Syllogismus" title="Syllogismus – Alemannic" lang="gsw" hreflang="gsw" data-title="Syllogismus" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D9%8A%D8%A7%D8%B3_(%D9%85%D9%86%D8%B7%D9%82)" title="قياس (منطق) – Arabic" lang="ar" hreflang="ar" data-title="قياس (منطق)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sillogizm" title="Sillogizm – Azerbaijani" lang="az" hreflang="az" data-title="Sillogizm" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BB%D0%BE%D0%B3%D0%B8%D0%B7%D1%8A%D0%BC" title="Силогизъм – Bulgarian" lang="bg" hreflang="bg" data-title="Силогизъм" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Sullogismos" title="Sullogismos – Breton" lang="br" hreflang="br" data-title="Sullogismos" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Sil%C2%B7logisme" title="Sil·logisme – Catalan" lang="ca" hreflang="ca" data-title="Sil·logisme" 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/Sylogismus" title="Sylogismus – Czech" lang="cs" hreflang="cs" data-title="Sylogismus" 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/Syllogisme" title="Syllogisme – Danish" lang="da" hreflang="da" data-title="Syllogisme" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://de.wikipedia.org/wiki/Syllogismus" title="Syllogismus – German" lang="de" hreflang="de" data-title="Syllogismus" 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/S%C3%BCllogism" title="Süllogism – Estonian" lang="et" hreflang="et" data-title="Süllogism" 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%A3%CF%85%CE%BB%CE%BB%CE%BF%CE%B3%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Συλλογισμός – Greek" lang="el" hreflang="el" data-title="Συλλογισμός" 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/Silogismo" title="Silogismo – Spanish" lang="es" hreflang="es" data-title="Silogismo" 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/Silogismo" title="Silogismo – Esperanto" lang="eo" hreflang="eo" data-title="Silogismo" 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/Silogismo" title="Silogismo – Basque" lang="eu" hreflang="eu" data-title="Silogismo" 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/%D9%82%DB%8C%D8%A7%D8%B3" title="قیاس – Persian" lang="fa" hreflang="fa" data-title="قیاس" 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/Syllogisme" title="Syllogisme – French" lang="fr" hreflang="fr" data-title="Syllogisme" 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/Siloxismo" title="Siloxismo – Galician" lang="gl" hreflang="gl" data-title="Siloxismo" 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/%EC%82%BC%EB%8B%A8%EB%85%BC%EB%B2%95" title="삼단논법 – Korean" lang="ko" hreflang="ko" data-title="삼단논법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8D%D5%AB%D5%AC%D5%AC%D5%B8%D5%A3%D5%AB%D5%BD%D5%BF%D5%AB%D5%AF%D5%A1" title="Սիլլոգիստիկա – Armenian" lang="hy" hreflang="hy" data-title="Սիլլոգիստիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A8%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AF%E0%A4%B5%E0%A4%BE%E0%A4%95%E0%A5%8D%E0%A4%AF" title="न्यायवाक्य – Hindi" lang="hi" hreflang="hi" data-title="न्यायवाक्य" 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/Silogizam" title="Silogizam – Croatian" lang="hr" hreflang="hr" data-title="Silogizam" 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/Silogismo" title="Silogismo – Ido" lang="io" hreflang="io" data-title="Silogismo" 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/Silogisme" title="Silogisme – Indonesian" lang="id" hreflang="id" data-title="Silogisme" 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-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Syllogismo" title="Syllogismo – Interlingua" lang="ia" hreflang="ia" data-title="Syllogismo" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/R%C3%B6khenda" title="Rökhenda – Icelandic" lang="is" hreflang="is" data-title="Rökhenda" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Sillogismo" title="Sillogismo – Italian" lang="it" hreflang="it" data-title="Sillogismo" 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%A1%D7%99%D7%9C%D7%95%D7%92%D7%99%D7%96%D7%9D" title="סילוגיזם – Hebrew" lang="he" hreflang="he" data-title="סילוגיזם" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9E%D0%B9_%D2%9B%D0%BE%D1%80%D1%8B%D1%82%D1%8B%D0%BD%D0%B4%D1%8B" title="Ой қорытынды – Kazakh" lang="kk" hreflang="kk" data-title="Ой қорытынды" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BB%D0%BB%D0%BE%D0%B3%D0%B8%D0%B7%D0%BC" title="Силлогизм – Kyrgyz" lang="ky" hreflang="ky" data-title="Силлогизм" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Syllogismus" title="Syllogismus – Latin" lang="la" hreflang="la" data-title="Syllogismus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Syllogismus" title="Syllogismus – Luxembourgish" lang="lb" hreflang="lb" data-title="Syllogismus" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Silogizmas" title="Silogizmas – Lithuanian" lang="lt" hreflang="lt" data-title="Silogizmas" 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/Szillogizmus" title="Szillogizmus – Hungarian" lang="hu" hreflang="hu" data-title="Szillogizmus" 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%A1%D0%B8%D0%BB%D0%BE%D0%B3%D0%B8%D0%B7%D0%B0%D0%BC" title="Силогизам – Macedonian" lang="mk" hreflang="mk" data-title="Силогизам" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%B5%E0%A4%BE%E0%A4%95%E0%A5%8D%E0%A4%AF" title="संवाक्य – Marathi" lang="mr" hreflang="mr" data-title="संवाक्य" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Syllogisme" title="Syllogisme – Dutch" lang="nl" hreflang="nl" data-title="Syllogisme" 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/%E4%B8%89%E6%AE%B5%E8%AB%96%E6%B3%95" title="三段論法 – Japanese" lang="ja" hreflang="ja" data-title="三段論法" 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/Syllogisme" title="Syllogisme – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Syllogisme" 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-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Silogisme" title="Silogisme – Novial" lang="nov" hreflang="nov" data-title="Silogisme" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Sillogisme" title="Sillogisme – Occitan" lang="oc" hreflang="oc" data-title="Sillogisme" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Sillogizm" title="Sillogizm – Uzbek" lang="uz" hreflang="uz" data-title="Sillogizm" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Silogism" title="Silogism – Piedmontese" lang="pms" hreflang="pms" data-title="Silogism" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Syllogismus" title="Syllogismus – Low German" lang="nds" hreflang="nds" data-title="Syllogismus" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sylogizm" title="Sylogizm – Polish" lang="pl" hreflang="pl" data-title="Sylogizm" 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/Silogismo" title="Silogismo – Portuguese" lang="pt" hreflang="pt" data-title="Silogismo" 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/Silogism" title="Silogism – Romanian" lang="ro" hreflang="ro" data-title="Silogism" 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%A1%D0%B8%D0%BB%D0%BB%D0%BE%D0%B3%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Силлогистика – Russian" lang="ru" hreflang="ru" data-title="Силлогистика" 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/Silogjizmi" title="Silogjizmi – Albanian" lang="sq" hreflang="sq" data-title="Silogjizmi" 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/Syllogism" title="Syllogism – Simple English" lang="en-simple" hreflang="en-simple" data-title="Syllogism" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Sylogizmus" title="Sylogizmus – Slovak" lang="sk" hreflang="sk" data-title="Sylogizmus" 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/Silogizem" title="Silogizem – Slovenian" lang="sl" hreflang="sl" data-title="Silogizem" 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/%D9%82%DB%8C%D8%A7%D8%B3" title="قیاس – Central Kurdish" lang="ckb" hreflang="ckb" data-title="قیاس" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BB%D0%BE%D0%B3%D0%B8%D0%B7%D0%B0%D0%BC" title="Силогизам – Serbian" lang="sr" hreflang="sr" data-title="Силогизам" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Syllogismi" title="Syllogismi – Finnish" lang="fi" hreflang="fi" data-title="Syllogismi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Syllogism" title="Syllogism – Swedish" lang="sv" hreflang="sv" data-title="Syllogism" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Silohismo" title="Silohismo – Tagalog" lang="tl" hreflang="tl" data-title="Silohismo" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Tas%C4%B1m" title="Tasım – Turkish" lang="tr" hreflang="tr" data-title="Tasım" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%B8%D0%BB%D0%BE%D0%B3%D1%96%D0%B7%D0%BC" title="Силогізм – Ukrainian" lang="uk" hreflang="uk" data-title="Силогізм" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%82%DB%8C%D8%A7%D8%B3_(%D9%85%D9%86%D8%B7%D9%82)" title="قیاس (منطق) – Urdu" lang="ur" hreflang="ur" data-title="قیاس (منطق)" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tam_%C4%91o%E1%BA%A1n_lu%E1%BA%ADn" title="Tam đoạn luận – Vietnamese" lang="vi" hreflang="vi" data-title="Tam đoạn luận" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%9B%B4%E8%A8%80%E4%B8%89%E6%AE%B5%E8%AE%BA" title="直言三段论 – Wu" lang="wuu" hreflang="wuu" data-title="直言三段论" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%AE%9A%E8%A8%80%E4%B8%89%E6%AE%B5%E8%AB%96" title="定言三段論 – Cantonese" lang="yue" hreflang="yue" data-title="定言三段論" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%9B%B4%E8%A8%80%E4%B8%89%E6%AE%B5%E8%AE%BA" title="直言三段论 – Chinese" lang="zh" hreflang="zh" data-title="直言三段论" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q107342#sitelinks-wikipedia" 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class="mbox-text-span">This article <b>is written like a <a href="/wiki/Wikipedia:What_Wikipedia_is_not#Wikipedia_is_not_a_publisher_of_original_thought" title="Wikipedia:What Wikipedia is not">personal reflection, personal essay, or argumentative essay</a></b> that states a Wikipedia editor's personal feelings or presents an original argument about a topic.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Syllogism&action=edit">help improve it</a> by rewriting it in an <a href="/wiki/Wikipedia:Writing_better_articles#Information_style_and_tone" title="Wikipedia:Writing better articles">encyclopedic style</a>.</span> <span class="date-container"><i>(<span class="date">February 2023</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>A <b>syllogism</b> (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: <span lang="grc">συλλογισμός</span>, <i>syllogismos</i>, 'conclusion, inference') is a kind of <a href="/wiki/Argument" title="Argument">logical argument</a> that applies <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">deductive reasoning</a> to arrive at a <a href="/wiki/Logical_consequence" title="Logical consequence">conclusion</a> based on two <a href="/wiki/Proposition" title="Proposition">propositions</a> that are asserted or assumed to be true. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Socrates_Louvre.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Socrates_Louvre.jpg/220px-Socrates_Louvre.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Socrates_Louvre.jpg/330px-Socrates_Louvre.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Socrates_Louvre.jpg/440px-Socrates_Louvre.jpg 2x" data-file-width="1944" data-file-height="2592" /></a><figcaption>"Socrates" at the Louvre</figcaption></figure> <p>In its earliest form (defined by <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> in his 350 BC book <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i>), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> For example, knowing that all men are mortal (major premise), and that <a href="/wiki/Socrates" title="Socrates">Socrates</a> is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: </p> <blockquote><div class="poem"> <p>All men are mortal.<br /> Socrates is a man.<br /> Therefore, Socrates is mortal.<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> </p> </div></blockquote><p>In antiquity, two rival syllogistic theories existed: <a href="/wiki/Term_logic" title="Term logic">Aristotelian syllogism</a> and <a href="/wiki/Stoic_logic" title="Stoic logic">Stoic syllogism</a>.<sup id="cite_ref-:0_3-0" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> From the <a href="/wiki/Middle_Ages" title="Middle Ages">Middle Ages</a> onwards, <i>categorical syllogism</i> and <i>syllogism</i> were usually used interchangeably. This article is concerned only with this historical use. The syllogism was at the core of historical deductive reasoning, whereby facts are determined by combining existing statements, in contrast to <a href="/wiki/Inductive_reasoning" title="Inductive reasoning">inductive reasoning</a>, in which facts are predicted by repeated observations. </p><p>Within some academic contexts, syllogism has been superseded by <a href="/wiki/First-order_logic" title="First-order logic">first-order predicate logic</a> following the work of <a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a>, in particular his <i><a href="/wiki/Begriffsschrift" title="Begriffsschrift">Begriffsschrift</a></i> (<i>Concept Script</i>; 1879). Syllogism, being a method of valid logical reasoning, will always be useful in most circumstances, and for general-audience introductions to logic and clear-thinking.<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><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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_history">Early history</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=1" title="Edit section: Early history"><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/History_of_logic" title="History of logic">History of logic</a></div> <p>In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism.<sup id="cite_ref-:0_3-1" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Aristotle">Aristotle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=2" title="Edit section: Aristotle"><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/Term_logic" title="Term logic">Term logic</a></div> <p><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> defines the syllogism as "a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so."<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> Despite this very general definition, in <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i> Aristotle limits himself to categorical syllogisms that consist of three <a href="/wiki/Categorical_proposition" title="Categorical proposition">categorical propositions</a>, including categorical <a href="/wiki/Modal_logic" title="Modal logic">modal</a> syllogisms.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The use of syllogisms as a tool for understanding can be dated back to the logical reasoning discussions of <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>. Before the mid-12th century, medieval logicians were only familiar with a portion of Aristotle's works, including such titles as <i><a href="/wiki/Categories_(Aristotle)" title="Categories (Aristotle)">Categories</a></i> and <i><a href="/wiki/On_Interpretation" title="On Interpretation">On Interpretation</a></i>, works that contributed heavily to the prevailing Old Logic, or <i><a href="/wiki/Logica_vetus" class="mw-redirect" title="Logica vetus">logica vetus</a></i>. The onset of a New Logic, or <i><a href="/wiki/Logica_nova" title="Logica nova">logica nova</a></i>, arose alongside the reappearance of <i>Prior Analytics</i>, the work in which Aristotle developed his theory of the syllogism. </p><p><i>Prior Analytics</i>, upon rediscovery, was instantly regarded by logicians as "a closed and complete body of doctrine", leaving very little for thinkers of the day to debate, and reorganize. Aristotle's theory on the syllogism for <i><a href="/wiki/Assertoric" title="Assertoric">assertoric</a></i> sentences was considered especially remarkable, with only small systematic changes occurring to the concept over time. This theory of the syllogism would not enter the context of the more comprehensive logic of consequence until logic began to be reworked in general in the mid-14th century by the likes of <a href="/wiki/John_Buridan" class="mw-redirect" title="John Buridan">John Buridan</a>. </p><p>Aristotle's <i>Prior Analytics</i> did not, however, incorporate such a comprehensive theory on the modal syllogism—a syllogism that has at least one <a href="/wiki/Modal_logic" title="Modal logic">modalized</a> premise, that is, a premise containing the modal words <i>necessarily</i>, <i>possibly</i>, or <i>contingently</i>. Aristotle's terminology in this aspect of his theory was deemed vague, and in many cases unclear, even contradicting some of his statements from <i>On Interpretation</i>. His original assertions on this specific component of the theory were left up to a considerable amount of conversation, resulting in a wide array of solutions put forth by commentators of the day. The system for modal syllogisms laid forth by Aristotle would ultimately be deemed unfit for practical use, and would be replaced by new distinctions and new theories altogether. </p> <div class="mw-heading mw-heading3"><h3 id="Medieval_syllogism">Medieval syllogism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=3" title="Edit section: Medieval syllogism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Boethius">Boethius</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=4" title="Edit section: Boethius"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Boethius" title="Boethius">Boethius</a> (c. 475–526) contributed an effort to make the ancient Aristotelian logic more accessible. While his Latin translation of <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i> went primarily unused before the 12th century, his textbooks on the categorical syllogism were central to expanding the syllogistic discussion. Rather than in any additions that he personally made to the field, Boethius' logical legacy lies in his effective transmission of prior theories to later logicians, as well as his clear and primarily accurate presentations of Aristotle's contributions. </p> <div class="mw-heading mw-heading4"><h4 id="Peter_Abelard">Peter Abelard</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=5" title="Edit section: Peter Abelard"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Another of medieval logic's first contributors from the Latin West, <a href="/wiki/Peter_Abelard" title="Peter Abelard">Peter Abelard</a> (1079–1142), gave his own thorough evaluation of the syllogism concept, and accompanying theory in the <i>Dialectica</i>—a discussion of logic based on Boethius' commentaries and monographs. His perspective on syllogisms can be found in other works as well, such as <i>Logica Ingredientibus</i>. With the help of Abelard's distinction between <i><a href="/wiki/De_dicto" class="mw-redirect" title="De dicto">de dicto</a></i> modal sentences and <i><a href="/wiki/De_re" class="mw-redirect" title="De re">de re</a></i> modal sentences, medieval logicians began to shape a more coherent concept of Aristotle's modal syllogism model. </p> <div class="mw-heading mw-heading4"><h4 id="Jean_Buridan">Jean Buridan</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=6" title="Edit section: Jean Buridan"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The French philosopher <a href="/wiki/Jean_Buridan" title="Jean Buridan">Jean Buridan</a> (c. 1300 – 1361), whom some consider the foremost logician of the later Middle Ages, contributed two significant works: <i>Treatise on Consequence</i> and <i>Summulae de Dialectica</i>, in which he discussed the concept of the syllogism, its components and distinctions, and ways to use the tool to expand its logical capability. For 200 years after Buridan's discussions, little was said about syllogistic logic. Historians of logic have assessed that the primary changes in the post-Middle Age era were changes in respect to the public's awareness of original sources, a lessening of appreciation for the logic's sophistication and complexity, and an increase in logical ignorance—so that logicians of the early 20th century came to view the whole system as ridiculous.<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> <div class="mw-heading mw-heading2"><h2 id="Modern_history">Modern history</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=7" title="Edit section: Modern history"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Aristotelian syllogism dominated Western philosophical thought for many centuries. Syllogism itself is about drawing valid conclusions from assumptions (<a href="/wiki/Axiom" title="Axiom">axioms</a>), rather than about verifying the assumptions. However, people over time focused on the logic aspect, forgetting the importance of verifying the assumptions. </p><p>In the 17th century, <a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a> emphasized that experimental verification of axioms must be carried out rigorously, and cannot take syllogism itself as the best way to draw conclusions in nature.<sup id="cite_ref-instauration_9-0" class="reference"><a href="#cite_note-instauration-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Bacon proposed a more inductive approach to the observation of nature, which involves experimentation, and leads to discovering and building on axioms to create a more general conclusion.<sup id="cite_ref-instauration_9-1" class="reference"><a href="#cite_note-instauration-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Yet, a full method of drawing conclusions in nature is not the scope of logic or syllogism, and the inductive method was covered in Aristotle's subsequent treatise, the <i><a href="/wiki/Posterior_Analytics" title="Posterior Analytics">Posterior Analytics</a></i>. </p><p>In the 19th century, modifications to syllogism were incorporated to deal with <a href="/wiki/Disjunctive_syllogism" title="Disjunctive syllogism">disjunctive</a> ("A or B") and <a href="/wiki/Conditional_syllogism" class="mw-redirect" title="Conditional syllogism">conditional</a> ("if A then B") statements. <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Immanuel Kant</a> famously claimed, in <i>Logic</i> (1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know. (This work is not necessarily representative of Kant's mature philosophy, which is often regarded as an innovation to logic itself.) Kant's opinion stood unchallenged in the West until 1879, when <a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a> published his <i><a href="/wiki/Begriffsschrift" title="Begriffsschrift">Begriffsschrift</a></i> (<i>Concept Script</i>). This introduced a calculus, a method of representing categorical statements (and statements that are not provided for in syllogism as well) by the use of quantifiers and variables. </p><p>A noteworthy exception is the logic developed in <a href="/wiki/Bernard_Bolzano" title="Bernard Bolzano">Bernard Bolzano</a>'s work <i><a href="/wiki/Bernard_Bolzano#Wissenschaftslehre_(Theory_of_Science)" title="Bernard Bolzano">Wissenschaftslehre</a></i> (<i>Theory of Science</i>, 1837), the principles of which were applied as a direct critique of Kant, in the posthumously published work <i>New Anti-Kant</i> (1850). The work of Bolzano had been largely overlooked until the late 20th century, among other reasons, because of the intellectual environment at the time in <a href="/wiki/Bohemia" title="Bohemia">Bohemia</a>, which was then part of the <a href="/wiki/Austrian_Empire" title="Austrian Empire">Austrian Empire</a>. In the last 20 years, Bolzano's work has resurfaced and become subject of both translation and contemporary study. </p><p>This led to the rapid development of <a href="/wiki/Sentential_logic" class="mw-redirect" title="Sentential logic">sentential logic</a> and first-order <a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">predicate logic</a>, subsuming syllogistic reasoning, which was, therefore, after 2000 years, suddenly considered obsolete by many.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research"><span title="The material near this tag possibly contains original research. (January 2013)">original research?</span></a></i>]</sup> The Aristotelian system is explicated in modern fora of academia primarily in introductory material and historical study. </p><p>One notable exception to this modern relegation is the continued application of Aristotelian logic by officials of the <a href="/wiki/Congregation_for_the_Doctrine_of_the_Faith" class="mw-redirect" title="Congregation for the Doctrine of the Faith">Congregation for the Doctrine of the Faith</a>, and the Apostolic Tribunal of the <a href="/wiki/Roman_Rota" title="Roman Rota">Roman Rota</a>, which still requires that any arguments crafted by Advocates be presented in syllogistic format. </p> <div class="mw-heading mw-heading3"><h3 id="Boole's_acceptance_of_Aristotle"><span id="Boole.27s_acceptance_of_Aristotle"></span>Boole's acceptance of Aristotle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=8" title="Edit section: Boole's acceptance of Aristotle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/George_Boole" title="George Boole">George Boole</a>'s unwavering acceptance of Aristotle's logic is emphasized by the historian of logic <a href="/wiki/John_Corcoran_(logician)" title="John Corcoran (logician)">John Corcoran</a> in an accessible introduction to <i><a href="/wiki/Laws_of_Thought" class="mw-redirect" title="Laws of Thought">Laws of Thought</a></i>.<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><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> Corcoran also wrote a point-by-point comparison of <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i> and <i><a href="/wiki/The_Laws_of_Thought" title="The Laws of Thought">Laws of Thought</a></i>.<sup id="cite_ref-:1_12-0" class="reference"><a href="#cite_note-:1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were "to go under, over, and beyond" Aristotle's logic by:<sup id="cite_ref-:1_12-1" class="reference"><a href="#cite_note-:1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <ol><li>providing it with mathematical foundations involving equations;</li> <li>extending the class of problems it could treat, as solving equations was added to assessing <a href="/wiki/Validity_(logic)" title="Validity (logic)">validity</a>; and</li> <li>expanding the range of applications it could handle, such as expanding propositions of only two terms to those having arbitrarily many.</li></ol> <p>More specifically, Boole agreed with what <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> said; Boole's 'disagreements', if they might be called that, concern what Aristotle did not say. First, in the realm of foundations, Boole reduced Aristotle's four propositional forms to one form, the form of equations, which by itself was a revolutionary idea. Second, in the realm of logic's problems, Boole's addition of equation solving to logic—another revolutionary idea—involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving. Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle." </p> <div class="mw-heading mw-heading2"><h2 id="Basic_structure">Basic structure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=9" title="Edit section: Basic structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A categorical syllogism consists of three parts: </p> <ol><li>Major premise</li> <li>Minor premise</li> <li>Conclusion/Consequent</li></ol> <p>Each part is a <a href="/wiki/Categorical_proposition" title="Categorical proposition">categorical proposition</a>, and each categorical proposition contains two categorical terms.<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> In Aristotle, each of the premises is in the form "All S are P," "Some S are P", "No S are P" or "Some S are not P", where "S" is the subject-term and "P" is the predicate-term: </p> <ul><li>"All S are P," and "No S are P" are termed <a href="/wiki/Universal_proposition" class="mw-redirect" title="Universal proposition"><i>universal</i> propositions</a>;</li> <li>"Some S are P" and "Some S are not P" are termed <a href="/wiki/Particular_proposition" class="mw-redirect" title="Particular proposition"><i>particular</i> propositions</a>.</li></ul> <p>More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the <i>major term</i> (i.e., the <a href="/wiki/Predicate_(grammar)" title="Predicate (grammar)">predicate</a> of the conclusion); in a minor premise, this is the <i>minor term</i> (i.e., the subject of the conclusion). For example: </p> <dl><dd><b>Major premise</b>: All humans are mortal.</dd> <dd><b>Minor premise</b>: All Greeks are humans.</dd> <dd><b>Conclusion/Consequent</b>: All Greeks are mortal.</dd></dl> <p>Each of the three distinct terms represents a category. From the example above, <i>humans</i>, <i>mortal</i>, and <i>Greeks</i>: <i>mortal</i> is the major term, and <i>Greeks</i> the minor term. The premises also have one term in common with each other, which is known as the <i>middle term</i>; in this example, <i>humans</i>. Both of the premises are universal, as is the conclusion. </p> <dl><dd><b>Major premise</b>: All mortals die.</dd> <dd><b>Minor premise</b>: All men are mortals.</dd> <dd><b>Conclusion/Consequent</b>: All men die.</dd></dl> <p>Here, the major term is <i>die</i>, the minor term is <i>men</i>, and the middle term is <i>mortals</i>. Again, both premises are universal, hence so is the conclusion. </p> <div class="mw-heading mw-heading3"><h3 id="Polysyllogism">Polysyllogism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=10" title="Edit section: Polysyllogism"><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/Polysyllogism" title="Polysyllogism">Polysyllogism</a></div> <p>A polysyllogism, or a <b>sorites</b>, is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, one might argue that all lions are big cats, all big cats are predators, and all predators are carnivores. To conclude that therefore all lions are carnivores is to construct a sorites argument. </p> <div class="mw-heading mw-heading2"><h2 id="Types">Types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=11" title="Edit section: Types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Original_research plainlinks metadata ambox ambox-content ambox-Original_research" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>possibly contains <a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">original research</a></b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Syllogism&action=edit">improve it</a> by <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verifying</a> the claims made and adding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Statements consisting only of original research should be removed.</span> <span class="date-container"><i>(<span class="date">July 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Square_of_opposition,_set_diagrams.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Square_of_opposition%2C_set_diagrams.svg/220px-Square_of_opposition%2C_set_diagrams.svg.png" decoding="async" width="220" height="285" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Square_of_opposition%2C_set_diagrams.svg/330px-Square_of_opposition%2C_set_diagrams.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Square_of_opposition%2C_set_diagrams.svg/440px-Square_of_opposition%2C_set_diagrams.svg.png 2x" data-file-width="479" data-file-height="620" /></a><figcaption>Relationships between the four types of propositions in the <a href="/wiki/Square_of_opposition" title="Square of opposition">square of opposition</a><br /><br />(Black areas are empty,<br />red areas are nonempty.)</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_valid_argument_forms" title="List of valid argument forms">List of valid argument forms</a></div> <p>There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form (note: M – Middle, S – subject, P – predicate.): </p> <dl><dd><b>Major premise</b>: All M are P.</dd> <dd><b>Minor premise</b>: All S are M.</dd> <dd><b>Conclusion/Consequent</b>: All S are P.</dd></dl> <p>The premises and conclusion of a syllogism can be any of four types, which are labeled by letters<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> as follows. The meaning of the letters is given by the table: </p> <table class="wikitable"> <tbody><tr> <th>code </th> <th>quantifier </th> <th>subject </th> <th>copula </th> <th>predicate </th> <th>type </th> <th>example </th></tr> <tr> <td>A </td> <td>All </td> <td>S </td> <td>are </td> <td>P </td> <td>universal affirmative </td> <td>All humans are mortal. </td></tr> <tr> <td>E </td> <td>No </td> <td>S </td> <td>are </td> <td>P </td> <td>universal negative </td> <td>No humans are perfect. </td></tr> <tr> <td>I </td> <td>Some </td> <td>S </td> <td>are </td> <td>P </td> <td>particular affirmative </td> <td>Some humans are healthy. </td></tr> <tr> <td>O </td> <td>Some </td> <td>S </td> <td>are <b>not</b> </td> <td>P </td> <td>particular negative </td> <td>Some humans are not old. </td></tr></tbody></table> <p>In <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i>, Aristotle uses mostly the letters A, B, and C (Greek letters <i><a href="/wiki/Alpha" title="Alpha">alpha</a></i>, <i><a href="/wiki/Beta" title="Beta">beta</a></i>, and <i><a href="/wiki/Gamma" title="Gamma">gamma</a></i>) as term place holders, rather than giving concrete examples. It is traditional to use <i>is</i> rather than <i>are</i> as the <a href="/wiki/Copula_(linguistics)" title="Copula (linguistics)">copula</a>, hence <i>All A is B</i> rather than <i>All As are Bs</i>. It is traditional and convenient practice to use a, e, i, o as <a href="/wiki/Infix_notation" title="Infix notation">infix operators</a> so the categorical statements can be written succinctly. The following table shows the longer form, the succinct shorthand, and equivalent expressions in predicate logic: </p> <table class="wikitable"> <tbody><tr> <th>Form </th> <th>Shorthand </th> <th>Predicate logic </th></tr> <tr> <td>All A is B </td> <td>AaB </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x(A(x)\rightarrow B(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi>B</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x(A(x)\rightarrow B(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa548417440e34706f0736faaef676d7d24e955a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.831ex; height:2.843ex;" alt="{\displaystyle \forall x(A(x)\rightarrow B(x))}"></span>  <i>or</i>  <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg \exists x(A(x)\land \neg B(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi mathvariant="normal">¬</mi> <mi>B</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg \exists x(A(x)\land \neg B(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a63441bee7e7a47e438c4cd63384d0ccf065e9f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.9ex; height:2.843ex;" alt="{\displaystyle \neg \exists x(A(x)\land \neg B(x))}"></span> </td></tr> <tr> <td>No A is B </td> <td>AeB </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg \exists x(A(x)\land B(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>B</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg \exists x(A(x)\land B(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0bb40fe694ba4333b83511eecc986bb60f92054" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.349ex; height:2.843ex;" alt="{\displaystyle \neg \exists x(A(x)\land B(x))}"></span>  <i>or</i>  <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x(A(x)\rightarrow \neg B(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi mathvariant="normal">¬</mi> <mi>B</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x(A(x)\rightarrow \neg B(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4899d4797690611f556560a863274550ee0e571" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.381ex; height:2.843ex;" alt="{\displaystyle \forall x(A(x)\rightarrow \neg B(x))}"></span> </td></tr> <tr> <td>Some A is B </td> <td>AiB </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x(A(x)\land B(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>B</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists x(A(x)\land B(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cbf34b07a0377e2619dabe7ffd6ef3e1a1244a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.799ex; height:2.843ex;" alt="{\displaystyle \exists x(A(x)\land B(x))}"></span> </td></tr> <tr> <td>Some A is not B </td> <td>AoB </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x(A(x)\land \neg B(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi mathvariant="normal">¬</mi> <mi>B</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists x(A(x)\land \neg B(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ff90955e097789c5d76d5af52f969ef867d1ca5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.349ex; height:2.843ex;" alt="{\displaystyle \exists x(A(x)\land \neg B(x))}"></span> </td></tr></tbody></table> <p>The convention here is that the letter S is the subject of the conclusion, P is the predicate of the conclusion, and M is the middle term. The major premise links M with P and the minor premise links M with S. However, the middle term can be either the subject or the predicate of each premise where it appears. The differing positions of the major, minor, and middle terms gives rise to another classification of syllogisms known as the <i>figure</i>. Given that in each case the conclusion is S-P, the four figures are: </p> <table class="wikitable"> <tbody><tr> <td> </td> <th>Figure 1 </th> <th>Figure 2 </th> <th>Figure 3 </th> <th>Figure 4 </th></tr> <tr> <th>Major premise </th> <td>M–P </td> <td>P–M </td> <td>M–P </td> <td>P–M </td></tr> <tr> <th>Minor premise </th> <td>S–M </td> <td>S–M </td> <td>M–S </td> <td>M–S </td></tr></tbody></table> <p>(Note, however, that, following Aristotle's treatment of the figures, some logicians—e.g., <a href="/wiki/Peter_Abelard" title="Peter Abelard">Peter Abelard</a> and <a href="/wiki/Jean_Buridan" title="Jean Buridan">Jean Buridan</a>—reject the fourth figure as a figure distinct from the first.) </p><p>Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure". </p><p>The vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not <a href="/wiki/Logical_consequence" title="Logical consequence">follow logically</a> from the premises). The table below shows the valid forms. Even some of these are sometimes considered to commit the <a href="/wiki/Existential_fallacy" title="Existential fallacy">existential fallacy</a>, meaning they are invalid if they mention an empty category. These controversial patterns are marked in <i>italics</i>. All but four of the patterns in italics (felapton, darapti, fesapo and bamalip) are weakened moods, i.e. it is possible to draw a stronger conclusion from the premises. </p> <table class="wikitable"> <tbody><tr> <th>Figure 1 </th> <th>Figure 2 </th> <th>Figure 3 </th> <th>Figure 4 </th></tr> <tr> <td>B<b>a</b>rb<b>a</b>r<b>a</b> </td> <td>C<b>e</b>s<b>a</b>r<b>e</b> </td> <td>D<b>a</b>t<b>i</b>s<b>i</b> </td> <td>C<b>a</b>l<b>e</b>m<b>e</b>s </td></tr> <tr> <td>C<b>e</b>l<b>a</b>r<b>e</b>nt </td> <td>C<b>a</b>m<b>e</b>str<b>e</b>s </td> <td>D<b>i</b>s<b>a</b>m<b>i</b>s </td> <td>D<b>i</b>m<b>a</b>t<b>i</b>s </td></tr> <tr> <td>D<b>a</b>r<b>ii</b> </td> <td>F<b>e</b>st<b>i</b>n<b>o</b> </td> <td>F<b>e</b>r<b>i</b>s<b>o</b>n </td> <td>Fr<b>e</b>s<b>i</b>s<b>o</b>n </td></tr> <tr> <td>F<b>e</b>r<b>io</b> </td> <td>B<b>a</b>r<b>o</b>c<b>o</b> </td> <td>B<b>o</b>c<b>a</b>rd<b>o</b> </td> <td><i>C<b>a</b>l<b>e</b>m<b>o</b>s</i> </td></tr> <tr> <td><i>B<b>a</b>rb<b>a</b>r<b>i</b></i> </td> <td><i>C<b>e</b>s<b>a</b>r<b>o</b></i> </td> <td><i>F<b>e</b>l<b>a</b>pt<b>o</b>n</i> </td> <td><i>F<b>e</b>s<b>a</b>p<b>o</b></i> </td></tr> <tr> <td><i>C<b>e</b>l<b>a</b>r<b>o</b>nt</i> </td> <td><i>C<b>a</b>m<b>e</b>str<b>o</b>s</i> </td> <td><i>D<b>a</b>r<b>a</b>pt<b>i</b></i> </td> <td><i>B<b>a</b>m<b>a</b>l<b>i</b>p</i> </td></tr></tbody></table> <p>The letters A, E, I, and O have been used since the <a href="/wiki/Scholasticism" title="Scholasticism">medieval Schools</a> to form <a href="/wiki/Mnemonic" title="Mnemonic">mnemonic</a> names for the forms as follows: 'Barbara' stands for AAA, 'Celarent' for EAE, etc. </p><p>Next to each premise and conclusion is a shorthand description of the sentence. So in AAI-3, the premise "All squares are rectangles" becomes "MaP"; the symbols mean that the first term ("square") is the middle term, the second term ("rectangle") is the predicate of the conclusion, and the relationship between the two terms is labeled "a" (All M are P). </p><p>The following table shows all syllogisms that are essentially different. The similar syllogisms share the same premises, just written in a different way. For example "Some pets are kittens" (SiM in <a href="#Darii_(AII-1)">Darii</a>) could also be written as "Some kittens are pets" (MiS in Datisi). </p><p>In the Venn diagrams, the black areas indicate no elements, and the red areas indicate at least one element. In the predicate logic expressions, a horizontal bar over an expression means to negate ("logical not") the result of that expression. </p><p>It is also possible to use <a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">graphs</a> (consisting of vertices and edges) to evaluate syllogisms.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=12" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Barbara_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Modus_Barbara_%28Euler%29.svg/215px-Modus_Barbara_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Modus_Barbara_%28Euler%29.svg/323px-Modus_Barbara_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Modus_Barbara_%28Euler%29.svg/430px-Modus_Barbara_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Barbara.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modus_Barbara.svg/185px-Modus_Barbara.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modus_Barbara.svg/278px-Modus_Barbara.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modus_Barbara.svg/370px-Modus_Barbara.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><style data-mw-deduplicate="TemplateStyles:r1239334494">@media screen{html.skin-theme-clientpref-night .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}}</style><span class="tmp-color" style="color:#dd0000">M: men</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: Greeks</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: mortal</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Barbara_(AAA-1)"><span id="Barbara_.28AAA-1.29"></span>Barbara (AAA-1)<span class="anchor" id="Modus_Barbara"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=13" title="Edit section: Barbara (AAA-1)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>   All men are mortal. (MaP)</dd> <dd>   All Greeks are men. (SaM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> All Greeks are mortal. (SaP)</dd></dl> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Celarent_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Modus_Celarent_%28Euler%29.svg/215px-Modus_Celarent_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Modus_Celarent_%28Euler%29.svg/323px-Modus_Celarent_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Modus_Celarent_%28Euler%29.svg/430px-Modus_Celarent_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Celarent.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Modus_Celarent.svg/185px-Modus_Celarent.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Modus_Celarent.svg/278px-Modus_Celarent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Modus_Celarent.svg/370px-Modus_Celarent.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: reptile</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: snake</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: fur</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Celarent_(EAE-1)"><span id="Celarent_.28EAE-1.29"></span>Celarent (EAE-1)<span class="anchor" id="Modus_Celarent"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=14" title="Edit section: Celarent (EAE-1)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Similar: Cesare (EAE-2) </p> <dl><dd>   No reptile has fur. (MeP)</dd> <dd>   All snakes are reptiles. (SaM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> No snake has fur. (SeP)</dd></dl> <div style="clear:both;" class=""></div> <p><span class="anchor" id="Modus_Camestres"></span> </p> <table class="collapsible collapsed" style="width: 100%; border: 1px solid #aaaaaa;"> <tbody><tr> <th bgcolor="#ccccff">Camestres (AEE-2) </th></tr> <tr> <td> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Camestres_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Modus_Camestres_%28Euler%29.svg/215px-Modus_Camestres_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Modus_Camestres_%28Euler%29.svg/323px-Modus_Camestres_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Modus_Camestres_%28Euler%29.svg/430px-Modus_Camestres_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Camestres.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Modus_Camestres.svg/185px-Modus_Camestres.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Modus_Camestres.svg/278px-Modus_Camestres.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Modus_Camestres.svg/370px-Modus_Camestres.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: reptile</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: fur</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: snake</span></span> </td></tr></tbody></table> <p>Camestres is essentially like Celarent with S and P exchanged.<br /> Similar: Calemes (AEE-4) </p> <dl><dd>   All snakes are reptiles. (PaM)</dd> <dd>   No fur bearing animal is a reptile. (SeM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> No fur bearing animal is a snake. (SeP)</dd></dl> </td></tr></tbody></table> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Darii_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Modus_Darii_%28Euler%29.svg/215px-Modus_Darii_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Modus_Darii_%28Euler%29.svg/323px-Modus_Darii_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Modus_Darii_%28Euler%29.svg/430px-Modus_Darii_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Darii.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Modus_Darii.svg/185px-Modus_Darii.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Modus_Darii.svg/278px-Modus_Darii.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Modus_Darii.svg/370px-Modus_Darii.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: rabbit</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: pet</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: fur</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Darii_(AII-1)"><span id="Darii_.28AII-1.29"></span>Darii (AII-1)<span class="anchor" id="Modus_Darii"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=15" title="Edit section: Darii (AII-1)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Similar: Datisi (AII-3) </p> <dl><dd>   All rabbits have fur. (MaP)</dd> <dd>   Some pets are rabbits. (SiM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some pets have fur. (SiP)</dd></dl> <div style="clear:both;" class=""></div> <p><span class="anchor" id="Modus_Disamis"></span> </p> <table class="collapsible collapsed" style="width: 100%; border: 1px solid #aaaaaa;"> <tbody><tr> <th bgcolor="#ccccff">Disamis (IAI-3) </th></tr> <tr> <td> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Disamis_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Modus_Disamis_%28Euler%29.svg/215px-Modus_Disamis_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Modus_Disamis_%28Euler%29.svg/323px-Modus_Disamis_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Modus_Disamis_%28Euler%29.svg/430px-Modus_Disamis_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Disamis.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Modus_Disamis.svg/185px-Modus_Disamis.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Modus_Disamis.svg/278px-Modus_Disamis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Modus_Disamis.svg/370px-Modus_Disamis.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: rabbit</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: fur</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: pet</span></span> </td></tr></tbody></table> <p>Disamis is essentially like Darii with S and P exchanged.<br /> Similar: Dimatis (IAI-4) </p> <dl><dd>   Some rabbits are pets. (MiP)</dd> <dd>   All rabbits have fur. (MaP)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some fur bearing animals are pets. (SiP)</dd></dl> </td></tr></tbody></table> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Ferio_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Modus_Ferio_%28Euler%29.svg/215px-Modus_Ferio_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Modus_Ferio_%28Euler%29.svg/323px-Modus_Ferio_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Modus_Ferio_%28Euler%29.svg/430px-Modus_Ferio_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Ferio.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Ferio.svg/185px-Modus_Ferio.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Ferio.svg/278px-Modus_Ferio.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Ferio.svg/370px-Modus_Ferio.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: homework</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: reading</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: fun</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Ferio_(EIO-1)"><span id="Ferio_.28EIO-1.29"></span>Ferio (EIO-1)<span class="anchor" id="Modus_Ferio"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=16" title="Edit section: Ferio (EIO-1)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4) </p> <dl><dd>   No homework is fun. (MeP)</dd> <dd>   Some reading is homework. (SiM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some reading is not fun. (SoP)</dd></dl> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Baroco_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Baroco_%28Euler%29.svg/215px-Modus_Baroco_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Baroco_%28Euler%29.svg/323px-Modus_Baroco_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Baroco_%28Euler%29.svg/430px-Modus_Baroco_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Baroco.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Modus_Baroco.svg/185px-Modus_Baroco.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Modus_Baroco.svg/278px-Modus_Baroco.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Modus_Baroco.svg/370px-Modus_Baroco.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: mammal</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: pet</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: cat</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Baroco_(AOO-2)"><span id="Baroco_.28AOO-2.29"></span>Baroco (AOO-2)<span class="anchor" id="Modus_Baroco"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=17" title="Edit section: Baroco (AOO-2)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>   All cats are mammals. (PaM)</dd> <dd>   Some pets are not mammals. (SoM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some pets are not cats. (SoP)</dd></dl> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Bocardo_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Modus_Bocardo_%28Euler%29.svg/215px-Modus_Bocardo_%28Euler%29.svg.png" decoding="async" width="215" height="196" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Modus_Bocardo_%28Euler%29.svg/323px-Modus_Bocardo_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Modus_Bocardo_%28Euler%29.svg/430px-Modus_Bocardo_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="546" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Bocardo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Modus_Bocardo.svg/185px-Modus_Bocardo.svg.png" decoding="async" width="185" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Modus_Bocardo.svg/278px-Modus_Bocardo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Modus_Bocardo.svg/370px-Modus_Bocardo.svg.png 2x" data-file-width="718" data-file-height="934" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: cat</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: mammal</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: pet</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Bocardo_(OAO-3)"><span id="Bocardo_.28OAO-3.29"></span>Bocardo (OAO-3)<span class="anchor" id="Modus_Bocardo"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=18" title="Edit section: Bocardo (OAO-3)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>   Some cats are not pets. (MoP)</dd> <dd>   All cats are mammals. (MaS)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some mammals are not pets. (SoP)</dd></dl> <div style="clear:both;" class=""></div> <hr /> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Barbari_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Modus_Barbari_%28Euler%29.svg/215px-Modus_Barbari_%28Euler%29.svg.png" decoding="async" width="215" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Modus_Barbari_%28Euler%29.svg/323px-Modus_Barbari_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Modus_Barbari_%28Euler%29.svg/430px-Modus_Barbari_%28Euler%29.svg.png 2x" data-file-width="599" data-file-height="600" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Barbari.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Modus_Barbari.svg/185px-Modus_Barbari.svg.png" decoding="async" width="185" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Modus_Barbari.svg/278px-Modus_Barbari.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Modus_Barbari.svg/370px-Modus_Barbari.svg.png 2x" data-file-width="718" data-file-height="986" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: man</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: Greek</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: mortal</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Barbari_(AAI-1)"><span id="Barbari_.28AAI-1.29"></span><i>Barbari (AAI-1)</i><span class="anchor" id="Modus_Barbari"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=19" title="Edit section: Barbari (AAI-1)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>   All men are mortal. (MaP)</dd> <dd>   All Greeks are men. (SaM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some Greeks are mortal. (SiP)</dd></dl> <div style="clear:both;" class=""></div> <p><span class="anchor" id="Modus_Bamalip"></span> </p> <table class="collapsible collapsed" style="width: 100%; border: 1px solid #aaaaaa;"> <tbody><tr> <th bgcolor="#ccccff"><i>Bamalip (AAI-4)</i> </th></tr> <tr> <td> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Bamalip_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Modus_Bamalip_%28Euler%29.svg/215px-Modus_Bamalip_%28Euler%29.svg.png" decoding="async" width="215" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Modus_Bamalip_%28Euler%29.svg/323px-Modus_Bamalip_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Modus_Bamalip_%28Euler%29.svg/430px-Modus_Bamalip_%28Euler%29.svg.png 2x" data-file-width="599" data-file-height="600" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Bamalip.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Modus_Bamalip.svg/185px-Modus_Bamalip.svg.png" decoding="async" width="185" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Modus_Bamalip.svg/278px-Modus_Bamalip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Modus_Bamalip.svg/370px-Modus_Bamalip.svg.png 2x" data-file-width="718" data-file-height="986" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: man</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: mortal</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: Greek</span></span> </td></tr></tbody></table> <p><i>Bamalip</i> is exactly like <i>Barbari</i> with S and P exchanged: </p> <dl><dd>   All Greeks are men. (PaM)</dd> <dd>   All men are mortals. (MaS)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some mortals are Greek. (SiP)</dd></dl> </td></tr></tbody></table> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Celaront_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Modus_Celaront_%28Euler%29.svg/215px-Modus_Celaront_%28Euler%29.svg.png" decoding="async" width="215" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Modus_Celaront_%28Euler%29.svg/323px-Modus_Celaront_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Modus_Celaront_%28Euler%29.svg/430px-Modus_Celaront_%28Euler%29.svg.png 2x" data-file-width="599" data-file-height="600" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Celaront.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Celaront.svg/185px-Modus_Celaront.svg.png" decoding="async" width="185" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Celaront.svg/278px-Modus_Celaront.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Celaront.svg/370px-Modus_Celaront.svg.png 2x" data-file-width="718" data-file-height="986" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: reptile</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: snake</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: fur</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Celaront_(EAO-1)"><span id="Celaront_.28EAO-1.29"></span><i>Celaront (EAO-1)</i><span class="anchor" id="Modus_Celaront"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=20" title="Edit section: Celaront (EAO-1)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Similar: <i>Cesaro (EAO-2)</i> </p> <dl><dd>   No reptiles have fur. (MeP)</dd> <dd>   All snakes are reptiles. (SaM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some snakes have no fur. (SoP)</dd></dl> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Camestros_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Modus_Camestros_%28Euler%29.svg/215px-Modus_Camestros_%28Euler%29.svg.png" decoding="async" width="215" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Modus_Camestros_%28Euler%29.svg/323px-Modus_Camestros_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Modus_Camestros_%28Euler%29.svg/430px-Modus_Camestros_%28Euler%29.svg.png 2x" data-file-width="599" data-file-height="600" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Camestros.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Modus_Camestros.svg/185px-Modus_Camestros.svg.png" decoding="async" width="185" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Modus_Camestros.svg/278px-Modus_Camestros.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Modus_Camestros.svg/370px-Modus_Camestros.svg.png 2x" data-file-width="718" data-file-height="986" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: hooves</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: human</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: horse</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Camestros_(AEO-2)"><span id="Camestros_.28AEO-2.29"></span><i>Camestros (AEO-2)</i><span class="anchor" id="Modus_Camestros"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=21" title="Edit section: Camestros (AEO-2)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Similar: <i>Calemos (AEO-4)</i> </p> <dl><dd>   All horses have hooves. (PaM)</dd> <dd>   No humans have hooves. (SeM)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some humans are not horses. (SoP)</dd></dl> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Felapton_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Modus_Felapton_%28Euler%29.svg/215px-Modus_Felapton_%28Euler%29.svg.png" decoding="async" width="215" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Modus_Felapton_%28Euler%29.svg/323px-Modus_Felapton_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Modus_Felapton_%28Euler%29.svg/430px-Modus_Felapton_%28Euler%29.svg.png 2x" data-file-width="598" data-file-height="599" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Felapton.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Modus_Felapton.svg/185px-Modus_Felapton.svg.png" decoding="async" width="185" height="282" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Modus_Felapton.svg/278px-Modus_Felapton.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Modus_Felapton.svg/370px-Modus_Felapton.svg.png 2x" data-file-width="718" data-file-height="1094" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: flower</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: plant</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: animal</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Felapton_(EAO-3)"><span id="Felapton_.28EAO-3.29"></span><i>Felapton (EAO-3)</i><span class="anchor" id="Modus_Felapton"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=22" title="Edit section: Felapton (EAO-3)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Similar: <i>Fesapo (EAO-4)</i> </p> <dl><dd>   No flowers are animals. (MeP)</dd> <dd>   All flowers are plants. (MaS)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some plants are not animals. (SoP)</dd></dl> <div style="clear:both;" class=""></div> <table class="wikitable" style="float: right; text-align: center; margin-top: 10px; margin-bottom: 5px"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/File:Modus_Darapti_(Euler).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Modus_Darapti_%28Euler%29.svg/215px-Modus_Darapti_%28Euler%29.svg.png" decoding="async" width="215" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Modus_Darapti_%28Euler%29.svg/323px-Modus_Darapti_%28Euler%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Modus_Darapti_%28Euler%29.svg/430px-Modus_Darapti_%28Euler%29.svg.png 2x" data-file-width="599" data-file-height="600" /></a></span> </td> <td rowspan="2" style="background-color: white;"><span typeof="mw:File"><a href="/wiki/File:Modus_Darapti.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Darapti.svg/185px-Modus_Darapti.svg.png" decoding="async" width="185" height="282" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Darapti.svg/278px-Modus_Darapti.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Darapti.svg/370px-Modus_Darapti.svg.png 2x" data-file-width="718" data-file-height="1094" /></a></span> </td></tr> <tr> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#dd0000">M: square</span><br /><span class="nowrap"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#00800f">S: rhomb</span>      <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239334494"><span class="tmp-color" style="color:#0000dd">P: rectangle</span></span> </td></tr></tbody></table> <p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="Darapti_(AAI-3)"><span id="Darapti_.28AAI-3.29"></span><i>Darapti (AAI-3)</i><span class="anchor" id="Modus_Darapti"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=23" title="Edit section: Darapti (AAI-3)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>   All <a href="/wiki/Square_(geometry)" class="mw-redirect" title="Square (geometry)">squares</a> are <a href="/wiki/Rectangle" title="Rectangle">rectangles</a>. (MaP)</dd> <dd>   All squares are <a href="/wiki/Rhombus" title="Rhombus">rhombuses</a>. (MaS)</dd> <dd><a href="/wiki/Therefore_sign" title="Therefore sign">∴</a> Some rhombuses are rectangles. (SiP)</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Table_of_all_syllogisms">Table of all syllogisms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=24" title="Edit section: Table of all syllogisms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This table shows all 24 valid syllogisms, represented by <a href="/wiki/Venn_diagram" title="Venn diagram">Venn diagrams</a>. Columns indicate similarity, and are grouped by combinations of premises. Borders correspond to conclusions. Those with an existential assumption are dashed. </p> <table class="wikitable" style="background: #FFF;width:98%; text-align:center; vertical-align:middle;"> <tbody><tr> <th style="background: #AAA;">figure </th> <th colspan="2" style="border-left:2px solid #999;">A ∧ A </th> <th colspan="4" style="border-left:2px solid #999;">A ∧ E </th> <th colspan="2" style="border-left:2px solid #999;">A ∧ I </th> <th colspan="2" style="border-left:2px solid #999;">A ∧ O </th> <th style="border-left:2px solid #999;">E ∧ I </th></tr> <tr> <th style="background: #AAA;">1 </th> <td style="outline-offset:-5px;outline:2px solid #8F8;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Barbara.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modus_Barbara.svg/80px-Modus_Barbara.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modus_Barbara.svg/120px-Modus_Barbara.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/Modus_Barbara.svg/160px-Modus_Barbara.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Barbara</figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px dashed #88F;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Barbari.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Modus_Barbari.svg/76px-Modus_Barbari.svg.png" decoding="async" width="76" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Modus_Barbari.svg/114px-Modus_Barbari.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Modus_Barbari.svg/152px-Modus_Barbari.svg.png 2x" data-file-width="718" data-file-height="986" /></a><figcaption><i>Barbari</i></figcaption></figure> </td> <td style="border-left:2px solid #999;"> </td> <td> </td> <td style="outline-offset:-5px;outline:2px solid #F88;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Celarent.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Modus_Celarent.svg/80px-Modus_Celarent.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Modus_Celarent.svg/120px-Modus_Celarent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Modus_Celarent.svg/160px-Modus_Celarent.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Celarent</figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px dashed #FC4;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Celaront.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Celaront.svg/76px-Modus_Celaront.svg.png" decoding="async" width="76" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Celaront.svg/114px-Modus_Celaront.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Celaront.svg/152px-Modus_Celaront.svg.png 2x" data-file-width="718" data-file-height="986" /></a><figcaption><i>Celaront</i></figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px solid #88F; border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Darii.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Modus_Darii.svg/80px-Modus_Darii.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Modus_Darii.svg/120px-Modus_Darii.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Modus_Darii.svg/160px-Modus_Darii.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Darii</figcaption></figure> </td> <td> </td> <td style="border-left:2px solid #999;"> </td> <td> </td> <td style="outline-offset:-5px;outline:2px solid #FC4;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Ferio.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Ferio.svg/80px-Modus_Ferio.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Ferio.svg/120px-Modus_Ferio.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Ferio.svg/160px-Modus_Ferio.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Ferio</figcaption></figure> </td></tr> <tr> <th style="background: #AAA;">2 </th> <td style="border-left:2px solid #999;"> </td> <td> </td> <td style="outline-offset:-5px;outline:2px solid #F88;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Camestres.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Modus_Camestres.svg/80px-Modus_Camestres.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Modus_Camestres.svg/120px-Modus_Camestres.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Modus_Camestres.svg/160px-Modus_Camestres.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Camestres</figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px dashed #FC4;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Camestros.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Modus_Camestros.svg/76px-Modus_Camestros.svg.png" decoding="async" width="76" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Modus_Camestros.svg/114px-Modus_Camestros.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Modus_Camestros.svg/152px-Modus_Camestros.svg.png 2x" data-file-width="718" data-file-height="986" /></a><figcaption><i>Camestros</i></figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px solid #F88;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Cesare.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Modus_Cesare.svg/80px-Modus_Cesare.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Modus_Cesare.svg/120px-Modus_Cesare.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Modus_Cesare.svg/160px-Modus_Cesare.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Cesare</figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px dashed #FC4;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Cesaro.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Modus_Cesaro.svg/80px-Modus_Cesaro.svg.png" decoding="async" width="80" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Modus_Cesaro.svg/120px-Modus_Cesaro.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Modus_Cesaro.svg/160px-Modus_Cesaro.svg.png 2x" data-file-width="718" data-file-height="986" /></a><figcaption><i>Cesaro</i></figcaption></figure> </td> <td style="border-left:2px solid #999;"> </td> <td> </td> <td style="outline-offset:-5px;outline:2px solid #FC4;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Baroco.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Modus_Baroco.svg/80px-Modus_Baroco.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Modus_Baroco.svg/120px-Modus_Baroco.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Modus_Baroco.svg/160px-Modus_Baroco.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Baroco</figcaption></figure> </td> <td> </td> <td style="outline-offset:-5px;outline:2px solid #FC4;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Festino.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Modus_Festino.svg/80px-Modus_Festino.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Modus_Festino.svg/120px-Modus_Festino.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Modus_Festino.svg/160px-Modus_Festino.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Festino</figcaption></figure> </td></tr> <tr> <th style="background: #AAA;">3 </th> <td style="border-left:2px solid #999;"> </td> <td style="outline-offset:-5px;outline:2px dashed #88F;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Darapti.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Darapti.svg/66px-Modus_Darapti.svg.png" decoding="async" width="66" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Darapti.svg/99px-Modus_Darapti.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Modus_Darapti.svg/132px-Modus_Darapti.svg.png 2x" data-file-width="718" data-file-height="1094" /></a><figcaption><i>Darapti</i></figcaption></figure> </td> <td style="border-left:2px solid #999;"> </td> <td> </td> <td> </td> <td style="outline-offset:-5px;outline:2px dashed #FC4;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Felapton.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Modus_Felapton.svg/66px-Modus_Felapton.svg.png" decoding="async" width="66" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Modus_Felapton.svg/99px-Modus_Felapton.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Modus_Felapton.svg/132px-Modus_Felapton.svg.png 2x" data-file-width="718" data-file-height="1094" /></a><figcaption><i>Felapton</i></figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px solid #88F;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Datisi.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Modus_Datisi.svg/80px-Modus_Datisi.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Modus_Datisi.svg/120px-Modus_Datisi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Modus_Datisi.svg/160px-Modus_Datisi.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Datisi</figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px solid #88F;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Disamis.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Modus_Disamis.svg/80px-Modus_Disamis.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Modus_Disamis.svg/120px-Modus_Disamis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Modus_Disamis.svg/160px-Modus_Disamis.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Disamis</figcaption></figure> </td> <td style="border-left:2px solid #999;"> </td> <td style="outline-offset:-5px;outline:2px solid #FC4;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Bocardo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Modus_Bocardo.svg/80px-Modus_Bocardo.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Modus_Bocardo.svg/120px-Modus_Bocardo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Modus_Bocardo.svg/160px-Modus_Bocardo.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Bocardo</figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px solid #FC4;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Ferison.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Modus_Ferison.svg/80px-Modus_Ferison.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Modus_Ferison.svg/120px-Modus_Ferison.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Modus_Ferison.svg/160px-Modus_Ferison.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Ferison</figcaption></figure> </td></tr> <tr> <th style="background: #AAA;">4 </th> <td style="border-left:2px solid #999;"> </td> <td style="outline-offset:-5px;outline:2px dashed #88F;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Bamalip.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Modus_Bamalip.svg/76px-Modus_Bamalip.svg.png" decoding="async" width="76" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Modus_Bamalip.svg/114px-Modus_Bamalip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Modus_Bamalip.svg/152px-Modus_Bamalip.svg.png 2x" data-file-width="718" data-file-height="986" /></a><figcaption><i>Bamalip</i></figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px solid #F88;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Calemes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Modus_Calemes.svg/80px-Modus_Calemes.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Modus_Calemes.svg/120px-Modus_Calemes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Modus_Calemes.svg/160px-Modus_Calemes.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Calemes</figcaption></figure> </td> <td style="outline-offset:-5px;outline:2px dashed #FC4;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Calemos.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Calemos.svg/76px-Modus_Calemos.svg.png" decoding="async" width="76" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Calemos.svg/114px-Modus_Calemos.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Calemos.svg/152px-Modus_Calemos.svg.png 2x" data-file-width="718" data-file-height="986" /></a><figcaption><i>Calemos</i></figcaption></figure> </td> <td> </td> <td style="outline-offset:-5px;outline:2px dashed #FC4;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Fesapo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Modus_Fesapo.svg/66px-Modus_Fesapo.svg.png" decoding="async" width="66" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Modus_Fesapo.svg/99px-Modus_Fesapo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Modus_Fesapo.svg/132px-Modus_Fesapo.svg.png 2x" data-file-width="718" data-file-height="1094" /></a><figcaption><i>Fesapo</i></figcaption></figure> </td> <td style="border-left:2px solid #999;"> </td> <td style="outline-offset:-5px;outline:2px solid #88F;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Dimatis.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Modus_Dimatis.svg/80px-Modus_Dimatis.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Modus_Dimatis.svg/120px-Modus_Dimatis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Modus_Dimatis.svg/160px-Modus_Dimatis.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Dimatis</figcaption></figure> </td> <td style="border-left:2px solid #999;"> </td> <td> </td> <td style="outline-offset:-5px;outline:2px solid #FC4;border-left:2px solid #999;"><figure class="mw-halign-none" typeof="mw:File/Thumb"><a href="/wiki/File:Modus_Fresison.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Fresison.svg/80px-Modus_Fresison.svg.png" decoding="async" width="80" height="104" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Fresison.svg/120px-Modus_Fresison.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Modus_Fresison.svg/160px-Modus_Fresison.svg.png 2x" data-file-width="718" data-file-height="934" /></a><figcaption>Fresison</figcaption></figure> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Terms_in_syllogism">Terms in syllogism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=25" title="Edit section: Terms in syllogism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1248332772"><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible"><b>This section has multiple issues.</b> Please help <b><a href="/wiki/Special:EditPage/Syllogism" title="Special:EditPage/Syllogism">improve it</a></b> or discuss these issues on the <b><a href="/wiki/Talk:Syllogism" title="Talk:Syllogism">talk page</a></b>. <small><i>(<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove these messages</a>)</i></small> <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Original_research plainlinks metadata ambox ambox-content ambox-Original_research" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>possibly contains <a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">original research</a></b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Syllogism&action=edit">improve it</a> by <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verifying</a> the claims made and adding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Statements consisting only of original research should be removed.</span> <span class="date-container"><i>(<span class="date">July 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Syllogism" title="Special:EditPage/Syllogism">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">July 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>With Aristotle, we may distinguish <a href="/wiki/Singular_term" title="Singular term">singular terms</a>, such as <i>Socrates</i>, and general terms, such as <i>Greeks</i>. Aristotle further distinguished types (a) and (b): </p> <div><ol style="list-style-type:lower-alpha"><li>terms that could be the subject of predication; and</li><li>terms that could be predicated of others by the use of the copula ("is a").</li></ol></div> <p>Such a predication is known as a <a href="/wiki/Distributive_(linguistics)" class="mw-redirect" title="Distributive (linguistics)">distributive</a>, as opposed to non-distributive as in <i>Greeks are numerous</i>. It is clear that Aristotle's syllogism works only for distributive predication, since we cannot reason <i>All Greeks are animals, animals are numerous, therefore all Greeks are numerous</i>. In Aristotle's view singular terms were of type (a), and general terms of type (b). Thus, <i>Men</i> can be predicated of <i>Socrates</i> but <i>Socrates</i> cannot be predicated of anything. Therefore, for a term to be interchangeable—to be either in the subject or predicate position of a proposition in a syllogism—the terms must be general terms, or <i>categorical terms</i> as they came to be called. Consequently, the propositions of a syllogism should be categorical propositions (both terms general) and syllogisms that employ only categorical terms came to be called <i>categorical syllogisms</i>. </p><p>It is clear that nothing would prevent a singular term occurring in a syllogism—so long as it was always in the subject position—however, such a syllogism, even if valid, is not a categorical syllogism. An example is <i>Socrates is a man, all men are mortal, therefore Socrates is mortal.</i> Intuitively this is as valid as <i>All Greeks are men, all men are mortal therefore all Greeks are mortals</i>. To argue that its validity can be explained by the theory of syllogism would require that we show that <i>Socrates is a man</i> is the equivalent of a categorical proposition. It can be argued <i>Socrates is a man</i> is equivalent to <i>All that are identical to Socrates are men</i>, so our non-categorical syllogism can be justified by use of the equivalence above and then citing BARBARA. </p> <div class="mw-heading mw-heading2"><h2 id="Existential_import">Existential import</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=26" title="Edit section: Existential import"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1248332772"><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible"><b>This section has multiple issues.</b> Please help <b><a href="/wiki/Special:EditPage/Syllogism" title="Special:EditPage/Syllogism">improve it</a></b> or discuss these issues on the <b><a href="/wiki/Talk:Syllogism" title="Talk:Syllogism">talk page</a></b>. <small><i>(<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove these messages</a>)</i></small> <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Original_research plainlinks metadata ambox ambox-content ambox-Original_research" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>possibly contains <a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">original research</a></b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Syllogism&action=edit">improve it</a> by <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verifying</a> the claims made and adding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Statements consisting only of original research should be removed.</span> <span class="date-container"><i>(<span class="date">July 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Syllogism" title="Special:EditPage/Syllogism">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">July 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>If a statement includes a term such that the statement is false if the term has no instances, then the statement is said to have <i>existential import</i> with respect to that term. It is ambiguous whether or not a universal statement of the form <i>All A is B</i> is to be considered as true, false, or even meaningless if there are no As. If it is considered as false in such cases, then the statement <i>All A is B</i> has existential import with respect to A. </p><p>It is claimed Aristotle's logic system does not cover cases where there are no instances. Aristotle's goal was to develop a logic for science. He relegates fictions, such as mermaids and unicorns, to the realms of poetry and literature. In his mind, they exist outside the ambit of science, which is why he leaves no room for such non-existent entities in his logic. This is a thoughtful choice, not an inadvertent omission. Technically, Aristotelian science is a search for definitions, where a definition is "a phrase signifying a thing's essence." Because non-existent entities cannot be anything, they do not, in Aristotle's mind, possess an essence. This is why he leaves no place for fictional entities like goat-stags (or unicorns).<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> </p><p>However, many logic systems developed since <i>do</i> consider the case where there may be no instances. Medieval logicians were aware of the problem of existential import and maintained that negative propositions do not carry existential import, and that positive propositions with subjects that do not <a href="/wiki/Supposition_theory" title="Supposition theory">supposit</a> are false. </p><p>The following problems arise: </p> <div><ol style="list-style-type:lower-alpha"><li>In natural language and normal use, which statements of the forms, All A is B, No A is B, Some A is B, and Some A is not B, have existential import and with respect to which terms?</li><li>In the four forms of categorical statements used in syllogism, which statements of the form AaB, AeB, AiB and AoB have existential import and with respect to which terms?</li><li>What existential imports must the forms AaB, AeB, AiB and AoB have for the square of opposition to be valid?</li><li>What existential imports must the forms AaB, AeB, AiB and AoB have to preserve the validity of the traditionally valid forms of syllogisms?</li><li>Are the existential imports required to satisfy (d) above such that the normal uses in natural languages of the forms All A is B, No A is B, Some A is B and Some A is not B are intuitively and fairly reflected by the categorical statements of forms AaB, AeB, AiB and AoB?</li></ol></div> <p>For example, if it is accepted that AiB is false if there are no As and AaB entails AiB, then AiB has existential import with respect to A, and so does AaB. Further, if it is accepted that AiB entails BiA, then AiB and AaB have existential import with respect to B as well. Similarly, if AoB is false if there are no As, and AeB entails AoB, and AeB entails BeA (which in turn entails BoA) then both AeB and AoB have existential import with respect to both A and B. It follows immediately that all universal categorical statements have existential import with respect to both terms. If AaB and AeB is a fair representation of the use of statements in normal natural language of All A is B and No A is B respectively, then the following example consequences arise: </p> <dl><dd>"All flying horses are mythical" is false if there are no flying horses.</dd> <dd>If "No men are fire-eating rabbits" is true, then "There are fire-eating rabbits" is true; and so on.</dd></dl> <p>If it is ruled that no universal statement has existential import then the square of opposition fails in several respects (e.g. AaB does not entail AiB) and a number of syllogisms are no longer valid (e.g. BaC, AaB->AiC). </p><p>These problems and paradoxes arise in both natural language statements and statements in syllogism form because of ambiguity, in particular ambiguity with respect to All. If "Fred claims all his books were Pulitzer Prize winners", is Fred claiming that he wrote any books? If not, then is what he claims true? Suppose Jane says none of her friends are poor; is that true if she has no friends? </p><p>The first-order predicate calculus avoids such ambiguity by using formulae that carry no existential import with respect to universal statements. Existential claims must be explicitly stated. Thus, natural language statements—of the forms <i>All A is B, No A is B</i>, <i>Some A is B</i>, and <i>Some A is not B</i>—can be represented in first order predicate calculus in which any existential import with respect to terms A and/or B is either explicit or not made at all. Consequently, the four forms <i>AaB, AeB, AiB</i>, and <i>AoB</i> can be represented in first order predicate in every combination of existential import—so it can establish which construal, if any, preserves the square of opposition and the validity of the traditionally valid syllogism. Strawson claims such a construal is possible, but the results are such that, in his view, the answer to question (e) above is <i>no</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Syllogistic_fallacies">Syllogistic fallacies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=27" title="Edit section: Syllogistic fallacies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>People often make mistakes when reasoning syllogistically.<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><p>For instance, from the premises some A are B, some B are C, people tend to come to a definitive conclusion that therefore some A are C.<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><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> However, this does not follow according to the rules of classical logic. For instance, while some cats (A) are black things (B), and some black things (B) are televisions (C), it does not follow from the parameters that some cats (A) are televisions (C). This is because in the structure of the syllogism invoked (i.e. III-1) the middle term is not distributed in either the major premise or in the minor premise, a pattern called the "<a href="/wiki/Fallacy_of_the_undistributed_middle" title="Fallacy of the undistributed middle">fallacy of the undistributed middle</a>". Because of this, it can be hard to follow formal logic, and a closer eye is needed in order to ensure that an argument is, in fact, valid.<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> </p><p>Determining the validity of a syllogism involves determining the <a href="/wiki/Distribution_of_terms" class="mw-redirect" title="Distribution of terms">distribution</a> of each term in each statement, meaning whether all members of that term are accounted for. </p><p>In simple syllogistic patterns, the fallacies of invalid patterns are: </p> <ul><li><a href="/wiki/Fallacy_of_the_undistributed_middle" title="Fallacy of the undistributed middle">Undistributed middle</a>: Neither of the premises accounts for all members of the middle term, which consequently fails to link the major and minor term.</li> <li><a href="/wiki/Illicit_major" title="Illicit major">Illicit treatment of the major term</a>: The conclusion implicates all members of the major term (P – meaning the proposition is negative); however, the major premise does not account for them all (i.e., P is either an affirmative predicate or a particular subject there).</li> <li><a href="/wiki/Illicit_minor" title="Illicit minor">Illicit treatment of the minor term</a>: Same as above, but for the minor term (S – meaning the proposition is universal) and minor premise (where S is either a particular subject or an affirmative predicate).</li> <li><a href="/wiki/Fallacy_of_exclusive_premises" title="Fallacy of exclusive premises">Exclusive premises</a>: Both premises are negative, meaning no link is established between the major and minor terms.</li> <li><a href="/wiki/Affirmative_conclusion_from_a_negative_premise" title="Affirmative conclusion from a negative premise">Affirmative conclusion from a negative premise</a>: If either premise is negative, the conclusion must also be.</li> <li><a href="/wiki/Negative_conclusion_from_affirmative_premises" title="Negative conclusion from affirmative premises">Negative conclusion from affirmative premises</a>: If both premises are affirmative, the conclusion must also be.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Other_types">Other types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=28" title="Edit section: Other types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Disjunctive_syllogism" title="Disjunctive syllogism">Disjunctive syllogism</a></li> <li><a href="/wiki/Hypothetical_syllogism" title="Hypothetical syllogism">Hypothetical syllogism</a></li> <li><a href="/wiki/Legal_syllogism" title="Legal syllogism">Legal syllogism</a></li> <li><a href="/wiki/Polysyllogism" title="Polysyllogism">Polysyllogism</a></li> <li><a href="/wiki/Prosleptic_syllogism" title="Prosleptic syllogism">Prosleptic syllogism</a></li> <li><a href="/wiki/Quasi-syllogism" title="Quasi-syllogism">Quasi-syllogism</a></li> <li><a href="/wiki/Statistical_syllogism" title="Statistical syllogism">Statistical syllogism</a></li></ul> <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=Syllogism&action=edit&section=29" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1259569809">.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 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.reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFLundberg2018" class="citation book cs1">Lundberg, Christian (2018). <i>The Essential Guide to Rhetoric</i>. Bedford/St.Martin's. p. 38.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Essential+Guide+to+Rhetoric&rft.pages=38&rft.pub=Bedford%2FSt.Martin%27s&rft.date=2018&rft.aulast=Lundberg&rft.aufirst=Christian&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" 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">John Stuart Mill, <i>A System of Logic, Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation</i>, 3rd ed., vol. 1, chap. 2 (London: John W. Parker, 1851), 190.</span> </li> <li id="cite_note-:0-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Michael_Frede" title="Michael Frede">Frede, Michael</a>. 1975. "Stoic vs. Peripatetic Syllogistic." <i>Archive for the History of Philosophy</i> 56:99–124.</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">Hurley, Patrick J. 2011. <i>A Concise Introduction to Logic</i>. Cengage Learning. <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/9780840034175" title="Special:BookSources/9780840034175">9780840034175</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Zegarelli, Mark. 2010. <i>Logic for Dummies</i>. John Wiley & Sons. <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/9781118053072" title="Special:BookSources/9781118053072">9781118053072</a>.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>, <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i>, 24b18–20</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="/wiki/Susanne_Bobzien" title="Susanne Bobzien">Bobzien, Susanne</a>. [2006] 2020. "<a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/logic-ancient/">Ancient Logic</a>." <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>. § <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/logic-ancient/#Ari">Aristotle</a>.</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="CITEREFLagerlund2004" class="citation encyclopaedia cs1">Lagerlund, Henrik (2 February 2004). <a rel="nofollow" class="external text" href="http://plato.stanford.edu/archives/win2012/entries/medieval-syllogism/">"Medieval Theories of the Syllogism"</a>. <i>The Stanford Encyclopedia of Philosophy</i>. Edward N. Zalta<span class="reference-accessdate">. Retrieved <span class="nowrap">17 February</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Medieval+Theories+of+the+Syllogism&rft.btitle=The+Stanford+Encyclopedia+of+Philosophy&rft.pub=Edward+N.+Zalta&rft.date=2004-02-02&rft.aulast=Lagerlund&rft.aufirst=Henrik&rft_id=http%3A%2F%2Fplato.stanford.edu%2Farchives%2Fwin2012%2Fentries%2Fmedieval-syllogism%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" class="Z3988"></span></span> </li> <li id="cite_note-instauration-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-instauration_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-instauration_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Francis_Bacon" title="Francis Bacon">Bacon, Francis</a>. [1620] 2001. <i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20190413000330/http://www.constitution.org/bacon/instauration.htm">The Great Instauration</a></i>. – via <i><a href="/wiki/The_Constitution_Society" title="The Constitution Society">Constitution Society</a></i>. Archived from the <a rel="nofollow" class="external text" href="http://www.constitution.org/bacon/instauration.htm">original</a> on 13 April 2019.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><a href="/wiki/George_Boole" title="George Boole">Boole, George</a>. [1854] 2003. <i><a href="/wiki/The_Laws_of_Thought" title="The Laws of Thought">The Laws of Thought</a></i>, with an introduction by J. Corcoran. Buffalo: <a href="/wiki/Prometheus_Books" title="Prometheus Books">Prometheus Books</a>.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">van Evra, James. 2004. "'The Laws of Thought' by George Boole" (review). <i><a href="/wiki/Philosophy_in_Review" title="Philosophy in Review">Philosophy in Review</a></i> 24:167–69.</span> </li> <li id="cite_note-:1-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/John_Corcoran_(logician)" title="John Corcoran (logician)">Corcoran, John</a>. 2003. "Aristotle's 'Prior Analytics' and Boole's 'Laws of Thought'." <i>History and Philosophy of Logic</i> 24:261–88.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.philosophypages.com/dy/c.htm#capro">"Philosophical Dictionary: Caird-Catharsis"</a>. Philosophypages.com. 2002-08-08<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-12-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Philosophical+Dictionary%3A+Caird-Catharsis&rft.pub=Philosophypages.com&rft.date=2002-08-08&rft_id=http%3A%2F%2Fwww.philosophypages.com%2Fdy%2Fc.htm%23capro&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">According to <a href="/wiki/Copi" title="Copi">Copi</a>, p. 127: 'The letter names are presumed to come from the Latin words "<i><b>A</b></i>ff<i><b>I</b></i>rmo" and "n<i><b>E</b></i>g<i><b>O</b></i>," which mean "I affirm" and "I deny," respectively; the first capitalized letter of each word is for universal, the second for particular'</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</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://www.youtube.com/watch?v=MXRwmOpgqLw">"Syllogisms Made Easy"</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211211/MXRwmOpgqLw">Archived</a> from the original on 2021-12-11 – via www.youtube.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Syllogisms+Made+Easy&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DMXRwmOpgqLw&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</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/20170204235013/http://www.iep.utm.edu/aris-log/">"Groarke, Louis F., "Aristotle: Logic", section 7. (Existential Assumptions), Internet Encyclopedia of Philosophy"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.iep.utm.edu/aris-log/">the original</a> on 2017-02-04<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-03-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Groarke%2C+Louis+F.%2C+%22Aristotle%3A+Logic%22%2C+section+7.+%28Existential+Assumptions%29%2C+Internet+Encyclopedia+of+Philosophy&rft_id=http%3A%2F%2Fwww.iep.utm.edu%2Faris-log%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">See, e.g., Evans, J. St. B. T (1989). <i>Bias in human reasoning</i>. London: LEA.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Khemlani, S., and P. N. Johnson-Laird. 2012. "Theories of the syllogism: A meta-analysis." <i><a href="/wiki/Psychological_Bulletin" title="Psychological Bulletin">Psychological Bulletin</a></i> 138:427–57.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">Chater, N., and M. Oaksford. 1999. "The Probability Heuristics Model of Syllogistic Reasoning." <i><a href="/wiki/Cognitive_Psychology_(journal)" title="Cognitive Psychology (journal)">Cognitive Psychology</a></i> 38:191–258.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLundberg2018" class="citation book cs1">Lundberg, Christian (2018). <i>The Essential Guide to Rhetoric</i>. Bedford/St. Martin's. p. 39.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Essential+Guide+to+Rhetoric&rft.pages=39&rft.pub=Bedford%2FSt.+Martin%27s&rft.date=2018&rft.aulast=Lundberg&rft.aufirst=Christian&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syllogism&action=edit&section=31" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>, [c. 350 BCE] 1989. <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i>, translated by R. Smith. Hackett. <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/0-87220-064-7" title="Special:BookSources/0-87220-064-7">0-87220-064-7</a></li> <li><a href="/wiki/Simon_Blackburn" title="Simon Blackburn">Blackburn, Simon</a>. [1994] 1996. "Syllogism." In <a href="/wiki/The_Oxford_Dictionary_of_Philosophy" title="The Oxford Dictionary of Philosophy"><i>The</i> <i>Oxford Dictionary of Philosophy</i></a>. Oxford University Press. <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/0-19-283134-8" title="Special:BookSources/0-19-283134-8">0-19-283134-8</a>.</li> <li>Broadie, Alexander. 1993. <i>Introduction to Medieval Logic</i>. Oxford University Press. <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/0-19-824026-0" title="Special:BookSources/0-19-824026-0">0-19-824026-0</a>.</li> <li><a href="/wiki/Irving_Copi" title="Irving Copi">Copi, Irving</a>. 1969. <i>Introduction to Logic</i> (3rd ed.). Macmillan Company.</li> <li><a href="/wiki/John_Corcoran_(logician)" title="John Corcoran (logician)">Corcoran, John</a>. 1972. "Completeness of an ancient logic." <i><a href="/wiki/Journal_of_Symbolic_Logic" title="Journal of Symbolic Logic">Journal of Symbolic Logic</a></i> 37:696–702.</li> <li>— 1994. "The founding of logic: Modern interpretations of Aristotle's logic." <i><a href="/wiki/Ancient_Philosophy_(journal)" title="Ancient Philosophy (journal)">Ancient Philosophy</a></i> 14:9–24.</li> <li>Corcoran, John, and Hassan Masoud. 2015. "Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions." <i>History and Philosophy of Logic</i> 36(1):39–61.</li> <li>Englebretsen, George. 1987. <i>The New Syllogistic</i>. Bern: <a href="/wiki/Peter_Lang_(publisher)" title="Peter Lang (publisher)">Peter Lang</a>.</li> <li><a href="/wiki/Charles_Leonard_Hamblin" title="Charles Leonard Hamblin">Hamblin, Charles Leonard</a>. 1970. <i>Fallacies</i>. London: <a href="/wiki/Methuen_Publishing" title="Methuen Publishing">Methuen</a>. <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/0-416-70070-5" title="Special:BookSources/0-416-70070-5">0-416-70070-5</a>. <ul><li><a href="/wiki/Cf." title="Cf.">Cf.</a> on validity of syllogisms: "A simple set of rules of validity was finally produced in the later Middle Ages, based on the concept of Distribution."</li></ul></li> <li><a href="/wiki/Jan_%C5%81ukasiewicz" title="Jan Łukasiewicz">Łukasiewicz, Jan</a>. [1957] 1987. <i>Aristotle's Syllogistic from the Standpoint of Modern Formal Logic</i>. New York: Garland Publishers. <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/0-8240-6924-2" title="Special:BookSources/0-8240-6924-2">0-8240-6924-2</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/15015545">15015545</a>.</li> <li>Malink, Marko. 2013. <i>Aristotle's Modal Syllogistic</i>. Cambridge, MA: <a href="/wiki/Harvard_University_Press" title="Harvard University Press">Harvard University Press</a>.</li> <li>Patzig, Günter. 1968. <i>Aristotle's theory of the syllogism: a logico-philological study of Book A of the Prior Analytics</i>. Dordrecht: Reidel.</li> <li>Rescher, Nicholas. 1966. <i>Galen and the Syllogism</i>. University of Pittsburgh Press. <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/978-0822983958" title="Special:BookSources/978-0822983958">978-0822983958</a>.</li> <li><a href="/wiki/Timothy_Smiley" title="Timothy Smiley">Smiley, Timothy</a>. 1973. "What is a syllogism?" <i><a href="/wiki/Journal_of_Philosophical_Logic" title="Journal of Philosophical Logic">Journal of Philosophical Logic</a></i> 2:136–54.</li> <li>Smith, Robin. 1986. "Immediate propositions and Aristotle's proof theory." <i>Ancient Philosophy</i> 6:47–68.</li> <li>Thom, Paul. 1981. "The Syllogism." <i><a href="/wiki/Philosophia_(journal)" title="Philosophia (journal)">Philosophia</a></i>. München. <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/3-88405-002-8" title="Special:BookSources/3-88405-002-8">3-88405-002-8</a>.</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=Syllogism&action=edit&section=32" title="Edit section: External links"><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="CITEREFSmith" class="citation encyclopaedia cs1">Smith, Robin. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/aristotle-logic/">"Aristotle's Logic"</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=Aristotle%27s+Logic&rft.btitle=Stanford+Encyclopedia+of+Philosophy&rft.aulast=Smith&rft.aufirst=Robin&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Faristotle-logic%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" class="Z3988"></span></li> <li>Koutsoukou-Argyraki, Angeliki. <a rel="nofollow" class="external text" href="https://www.isa-afp.org/entries/Aristotles_Assertoric_Syllogistic.html">Aristotle's Assertoric Syllogistic (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLagerlund" class="citation encyclopaedia cs1">Lagerlund, Henrik. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/medieval-syllogism/">"Medieval Theories of the Syllogism"</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=Medieval+Theories+of+the+Syllogism&rft.btitle=Stanford+Encyclopedia+of+Philosophy&rft.aulast=Lagerlund&rft.aufirst=Henrik&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fmedieval-syllogism%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASyllogism" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://www.historyoflogic.com/aristotle-syllogism-categorical.htm">Aristotle's Prior Analytics: the Theory of Categorical Syllogism</a> an annotated bibliography on Aristotle's syllogistic</li> <li><a rel="nofollow" class="external text" href="https://books.google.com/books?id=yfUysMS31PIC&dq=syllogisms+huseyin+cakir&pg=PA418">Fuzzy Syllogistic System</a></li> <li><a rel="nofollow" class="external text" href="https://gcris.iyte.edu.tr/handle/11147/6777">Development of Fuzzy Syllogistic Algorithms and Applications Distributed Reasoning Approaches</a></li> <li><a rel="nofollow" class="external text" href="https://www.rigpawiki.org/index.php?title=Logic">Comparison between the Aristotelian Syllogism and the Indian/Tibetan Syllogism</a></li> <li><a rel="nofollow" class="external text" href="https://www.wisdomlib.org/buddhism/book/the-buddhist-philosophy-of-universal-flux/d/doc79648.html">The Buddhist Philosophy of Universal Flux (Chapter XXIII – Members of a Syllogism (avayava))</a></li> <li><a rel="nofollow" class="external text" href="https://www.thefirstscience.org/syllogistic/">Online Syllogistic Machine</a> An interactive syllogistic machine for exploring all the fallacies, figures, terms, and modes of syllogisms.</li></ul> <p><br /> </p> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist 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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:Aristotelian_logic" title="Template:Aristotelian logic"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Aristotelian_logic" title="Template talk:Aristotelian logic"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Aristotelian_logic" title="Special:EditPage/Template:Aristotelian logic"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Aristotelian_logic_(syllogistic)" style="font-size:114%;margin:0 4em"><a href="/wiki/Term_logic" title="Term logic">Aristotelian logic</a> (syllogistic)</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/Square_of_opposition" title="Square of opposition">Square of opposition</a></li> <li><a href="/wiki/Problem_of_multiple_generality" title="Problem of multiple generality">Problem of multiple generality</a></li> <li><a href="/wiki/Dictum_de_omni_et_nullo" title="Dictum de omni et nullo">Dictum de omni et nullo</a></li> <li><a href="/wiki/Syncategorematic_term" title="Syncategorematic term">Syncategorema</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Predicable" title="Predicable">Predicable</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/Definition" title="Definition">Definition</a></li> <li><a href="/wiki/Genus_(philosophy)" title="Genus (philosophy)">Genus</a></li> <li><a href="/wiki/Differentia" title="Differentia">Differentia</a></li> <li><a href="/wiki/Property_(philosophy)" title="Property (philosophy)">Property</a></li> <li><a href="/wiki/Accident_(philosophy)" title="Accident (philosophy)">Accident</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Propositions</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/Apodicticity" title="Apodicticity">Apodictic</a></li> <li><a href="/wiki/Assertoric" title="Assertoric">Assertoric</a></li> <li><a href="/wiki/Categorical_proposition" title="Categorical proposition">Categorical</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Syllogism</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/Enthymeme" title="Enthymeme">Enthymeme</a></li> <li><a href="/wiki/Prosleptic_syllogism" title="Prosleptic syllogism">Prosleptic</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Terms" scope="row" class="navbox-group" style="width:1%">Terms</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/End_term" class="mw-redirect" title="End term">End</a></li> <li><a href="/wiki/Middle_term" class="mw-redirect" title="Middle term">Middle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Forms</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/Baralipton" title="Baralipton">Barbara</a></li> <li><a href="/wiki/Baroco" title="Baroco">Baroco</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</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="Organon" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Organon" title="Organon">Organon</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/Categories_(Aristotle)" title="Categories (Aristotle)">Categories</a></li> <li><a href="/wiki/On_Interpretation" title="On Interpretation">On Interpretation</a></li> <li><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></li> <li><a href="/wiki/Posterior_Analytics" title="Posterior Analytics">Posterior Analytics</a></li> <li><a href="/wiki/Topics_(Aristotle)" title="Topics (Aristotle)">Topics</a></li> <li><a href="/wiki/Sophistical_Refutations" title="Sophistical Refutations">Sophistical Refutations</a></li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/wiki/Isagoge" title="Isagoge">Isagoge</a></li> <li><a href="/wiki/Port-Royal_Logic" title="Port-Royal Logic">Port-Royal Logic</a></li> <li><a href="/wiki/Sum_of_Logic" title="Sum of Logic">Sum of Logic</a></li> <li><a href="/wiki/The_False_Subtlety_of_the_Four_Syllogistic_Figures" title="The False Subtlety of the Four Syllogistic Figures">The False Subtlety of the Four Syllogistic Figures</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_logic" 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_logic" 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="Traditional" 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 href="/wiki/Argument" title="Argument">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 class="mw-selflink selflink">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 thesis">Church–Turing thesis</a></li> <li><a href="/wiki/Computably_enumerable_set" title="Computably enumerable set">Computably enumerable</a></li> <li><a href="/wiki/Computable_function" title="Computable function">Computable function</a></li> <li><a href="/wiki/Computable_set" title="Computable set">Computable set</a></li> <li><a href="/wiki/Decision_problem" title="Decision problem">Decision problem</a> <ul><li><a href="/wiki/Decidability_(logic)" title="Decidability (logic)">decidable</a></li> <li><a href="/wiki/Undecidable_problem" title="Undecidable problem">undecidable</a></li> <li><a href="/wiki/P_(complexity)" title="P (complexity)">P</a></li> <li><a href="/wiki/NP_(complexity)" title="NP (complexity)">NP</a></li> <li><a href="/wiki/P_versus_NP_problem" title="P versus NP problem">P versus NP problem</a></li></ul></li> <li><a href="/wiki/Kolmogorov_complexity" title="Kolmogorov complexity">Kolmogorov complexity</a></li> <li><a href="/wiki/Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li> <li><a href="/wiki/Primitive_recursive_function" title="Primitive recursive function">Primitive recursive function</a></li> <li><a href="/wiki/Recursion" title="Recursion">Recursion</a></li> <li><a href="/wiki/Recursive_set" class="mw-redirect" title="Recursive set">Recursive set</a></li> <li><a href="/wiki/Turing_machine" title="Turing machine">Turing machine</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%">Related</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/Abstract_logic" title="Abstract logic">Abstract logic</a></li> <li><a href="/wiki/Algebraic_logic" title="Algebraic logic">Algebraic logic</a></li> <li><a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">Automated theorem proving</a></li> <li><a href="/wiki/Category_theory" title="Category theory">Category theory</a></li> <li><a href="/wiki/Concrete_category" title="Concrete 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