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<li id="toc-Syllogism_in_the_first_figure" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Syllogism_in_the_first_figure"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Syllogism in the first figure</span> </div> </a> <ul id="toc-Syllogism_in_the_first_figure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Syllogism_in_the_second_figure" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Syllogism_in_the_second_figure"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Syllogism in the second figure</span> </div> </a> <ul id="toc-Syllogism_in_the_second_figure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Syllogism_in_the_third_figure" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Syllogism_in_the_third_figure"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Syllogism in the third figure</span> </div> </a> <ul id="toc-Syllogism_in_the_third_figure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Table_of_syllogisms" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Table_of_syllogisms"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Table of syllogisms</span> </div> </a> <ul id="toc-Table_of_syllogisms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Decline_of_term_logic" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Decline_of_term_logic"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Decline of term logic</span> </div> </a> <ul id="toc-Decline_of_term_logic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Revival" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Revival"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Revival</span> </div> </a> <ul id="toc-Revival-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Boole’s_acceptance_of_Aristotle" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Boole’s_acceptance_of_Aristotle"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</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> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">15</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">16</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> 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href="https://de.wikipedia.org/wiki/Begriffslogik" title="Begriffslogik – German" lang="de" hreflang="de" data-title="Begriffslogik" 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/Traditsiooniline_loogika" title="Traditsiooniline loogika – Estonian" lang="et" hreflang="et" data-title="Traditsiooniline loogika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/L%C3%B3gica_de_t%C3%A9rminos" title="Lógica de términos – Spanish" lang="es" hreflang="es" data-title="Lógica de términos" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Logique_traditionnelle" title="Logique traditionnelle – French" lang="fr" hreflang="fr" data-title="Logique traditionnelle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Logika_leksikal" title="Logika leksikal – Indonesian" lang="id" hreflang="id" data-title="Logika leksikal" 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-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Tradicion%C3%A1lis_logika" title="Tradicionális logika – Hungarian" lang="hu" hreflang="hu" data-title="Tradicionális logika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A7%D8%B5%D8%B7%D9%84%D8%A7%D8%AD%D9%8A_%D9%85%D9%86%D8%B7%D9%82" title="اصطلاحي منطق – Pashto" lang="ps" hreflang="ps" data-title="اصطلاحي منطق" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Teoria_nazw" title="Teoria nazw – Polish" lang="pl" hreflang="pl" data-title="Teoria nazw" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Logica_tradi%C8%9Bional%C4%83" title="Logica tradițională – Romanian" lang="ro" hreflang="ro" data-title="Logica tradițională" data-language-autonym="Română" 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searchaux" style="display:none">Approach to logic</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Cleanup_rewrite plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Crystal_Clear_app_kedit.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Crystal_Clear_app_kedit.svg/40px-Crystal_Clear_app_kedit.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Crystal_Clear_app_kedit.svg/60px-Crystal_Clear_app_kedit.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Crystal_Clear_app_kedit.svg/80px-Crystal_Clear_app_kedit.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>may need to be rewritten</b> to comply with Wikipedia's <a href="/wiki/Wikipedia:Manual_of_Style" title="Wikipedia:Manual of Style">quality standards</a>.<span class="hide-when-compact"> <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Term_logic&action=edit">You can help</a>. The <a href="/wiki/Talk:Term_logic" title="Talk:Term logic">talk page</a> may contain suggestions.</span> <span class="date-container"><i>(<span class="date">January 2023</span>)</i></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Logic" title="Logic">logic</a> and <a href="/wiki/Formal_semantics_(natural_language)" title="Formal semantics (natural language)">formal semantics</a>, <b>term logic</b>, also known as <b>traditional logic</b>, <b><a href="/wiki/Syllogism" title="Syllogism">syllogistic logic</a></b> or <b><a href="/wiki/Aristotelianism" title="Aristotelianism">Aristotelian</a> logic</b>, is a loose name for an approach to <a href="/wiki/Formal_logic" class="mw-redirect" title="Formal logic">formal logic</a> that began with <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a> and was developed further in <a href="/wiki/Ancient_history" title="Ancient history">ancient history</a> mostly by his followers, the <a href="/wiki/Peripatetics" class="mw-redirect" title="Peripatetics">Peripatetics</a>. It was revived after the third century CE by <a href="/wiki/Porphyry_(philosopher)" title="Porphyry (philosopher)">Porphyry</a>'s <a href="/wiki/Isagoge" title="Isagoge">Isagoge</a>. </p><p>Term logic revived in <a href="/wiki/Middle_Ages" title="Middle Ages">medieval</a> times, first in <a href="/wiki/Islamic_logic" class="mw-redirect" title="Islamic logic">Islamic logic</a> by <a href="/wiki/Alpharabius" class="mw-redirect" title="Alpharabius">Alpharabius</a> in the tenth century, and later in Christian Europe in the twelfth century with the advent of <a href="/wiki/New_logic" class="mw-redirect" title="New logic">new logic</a>, remaining dominant until the advent of <a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">predicate logic</a> in the late nineteenth century. </p><p>However, even if eclipsed by newer logical systems, term logic still plays a significant role in the study of logic. Rather than radically breaking with term logic, modern logics typically expand it. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Aristotle's_system"><span id="Aristotle.27s_system"></span>Aristotle's system</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=1" title="Edit section: Aristotle's system"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>'s logical work is collected in the six texts that are collectively known as the <i><a href="/wiki/Organon" title="Organon">Organon</a></i>. Two of these texts in particular, namely the <i><a href="/wiki/Prior_Analytics" title="Prior Analytics">Prior Analytics</a></i> and <i><a href="/wiki/De_Interpretatione" class="mw-redirect" title="De Interpretatione">De Interpretatione</a></i>, contain the heart of Aristotle's treatment of judgements and formal <a href="/wiki/Inference" title="Inference">inference</a>, and it is principally this part of Aristotle's works that is about term <a href="/wiki/Logic" title="Logic">logic</a>. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by <a href="/wiki/Jan_Lukasiewicz" class="mw-redirect" title="Jan Lukasiewicz">Jan Lukasiewicz</a> of a revolutionary paradigm.<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> Lukasiewicz's approach was reinvigorated in the early 1970s by <a href="/wiki/John_Corcoran_(logician)" title="John Corcoran (logician)">John Corcoran</a> and <a href="/wiki/Timothy_Smiley" title="Timothy Smiley">Timothy Smiley</a> – which informs modern translations of <i>Prior Analytics</i> by Robin Smith in 1989 and <a href="/wiki/Gisela_Striker" title="Gisela Striker">Gisela Striker</a> in 2009.<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><p>The <i>Prior Analytics</i> represents the first formal study of logic, where logic is understood as the study of arguments. An argument is a series of true or false statements which lead to a true or false conclusion.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In the <i>Prior Analytics</i>, Aristotle identifies valid and invalid forms of arguments called syllogisms. A syllogism is an argument that consists of at least three sentences: at least two <a href="/wiki/Premise" title="Premise">premises</a> and a conclusion. Although Aristotle does not call them "<a href="/wiki/Categories_(Aristotle)" title="Categories (Aristotle)">categorical</a> sentences", tradition does; he deals with them briefly in the <i>Analytics</i> and more extensively in <i><a href="/wiki/De_Interpretatione" class="mw-redirect" title="De Interpretatione">On Interpretation</a></i>.<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> Each proposition (statement that is a thought of the kind expressible by a declarative sentence)<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> of a syllogism is a categorical sentence which has a subject and a predicate connected by a verb. The usual way of connecting the subject and predicate of a categorical sentence as Aristotle does in <i>On Interpretation</i> is by using a linking verb e.g. P is S. However, in the Prior Analytics Aristotle rejects the usual form in favour of three of his inventions: </p> <ul><li>P belongs to S</li> <li>P is predicated of S</li> <li>P is said of S</li></ul> <p>Aristotle does not explain why he introduces these innovative expressions but scholars conjecture that the reason may have been that it facilitates the use of letters instead of terms avoiding the ambiguity that results in Greek when letters are used with the linking verb.<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> In his formulation of syllogistic propositions, instead of the copula ("All/some... are/are not..."), Aristotle uses the expression, "... belongs to/does not belong to all/some..." or "... is said/is not said of all/some..."<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> There are four different types of categorical sentences: universal affirmative (A), universal negative (E), particular affirmative (I) and particular negative (O). </p> <ul><li>A - A belongs to every B</li> <li>E - A belongs to no B</li> <li>I - A belongs to some B</li> <li>O - A does not belong to some B</li></ul> <p>A method of symbolization that originated and was used in the Middle Ages greatly simplifies the study of the Prior Analytics. Following this tradition then, let: </p> <dl><dd>a = belongs to every</dd></dl> <dl><dd>e = belongs to no</dd></dl> <dl><dd>i = belongs to some</dd></dl> <dl><dd>o = does not belong to some</dd></dl> <p>Categorical sentences may then be abbreviated as follows: </p> <dl><dd>AaB = A belongs to every B (Every B is A)</dd></dl> <dl><dd>AeB = A belongs to no B (No B is A)</dd></dl> <dl><dd>AiB = A belongs to some B (Some B is A)</dd></dl> <dl><dd>AoB = A does not belong to some B (Some B is not A)</dd></dl> <p>From the viewpoint of modern logic, only a few types of sentences can be represented in this way.<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="Basics">Basics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=2" title="Edit section: Basics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The fundamental assumption behind the theory is that the <a href="/wiki/Formal_system" title="Formal system">formal</a> model of <a href="/wiki/Propositions" class="mw-redirect" title="Propositions">propositions</a> are composed of two <a href="/wiki/Symbol_(formal)" title="Symbol (formal)">logical symbols</a> called terms – hence the name "two-term theory" or "term logic" – and that the <a href="/wiki/Reasoning" class="mw-redirect" title="Reasoning">reasoning</a> process is in turn built from propositions: </p> <ul><li>The <i>term</i> is a <a href="/wiki/Part_of_speech" title="Part of speech">part of speech</a> representing something, but which is not true or false in its own right, such as "man" or "mortal". As originally conceived, all terms would be drawn from one of ten <i><a href="/wiki/Categories_(Aristotle)" title="Categories (Aristotle)">categories</a></i> enumerated by Aristotle in his <i><a href="/wiki/Organon" title="Organon">Organon</a></i>, classifying all objects and qualities within the domain of logical discourse.</li> <li>The <a href="/wiki/Formal_system" title="Formal system">formal</a> model of <i>proposition</i> consists of two terms, one of which, the "<a href="/wiki/Predicate_(grammar)" title="Predicate (grammar)">predicate</a>", is "affirmed" or "denied" of the other, the "<a href="/wiki/Subject_(grammar)" title="Subject (grammar)">subject</a>", and which is capable of <a href="/wiki/Truth" title="Truth">truth</a> or <a href="/wiki/Deception" title="Deception">falsity</a>.</li> <li>The <i><a href="/wiki/Syllogism" title="Syllogism">syllogism</a></i> is an <a href="/wiki/Inference" title="Inference">inference</a> in which one <a href="/wiki/Proposition" title="Proposition">proposition</a> (the "<a href="/wiki/Consequent" title="Consequent">conclusion</a>") follows of necessity from two other propositions (the "<a href="/wiki/Premise" title="Premise">premises</a>").</li></ul> <p>A proposition may be universal or particular, and it may be affirmative or negative. Traditionally, the four kinds of propositions are: </p> <dl><dd><ul><li>A-type: Universal and affirmative ("All philosophers are mortal")</li> <li>E-type: Universal and negative ("All philosophers are not mortal")</li> <li>I-type: Particular and affirmative ("Some philosophers are mortal")</li> <li>O-type: Particular and negative ("Some philosophers are not mortal")</li></ul></dd></dl> <p>This was called the <i>fourfold scheme</i> of propositions (see <a href="/wiki/Syllogism#Types" title="Syllogism">types of syllogism</a> for an explanation of the letters A, I, E, and O in the traditional square). Aristotle's <i>original</i> <a href="/wiki/Square_of_opposition" title="Square of opposition">square of opposition</a>, however, does not lack <a href="/wiki/Syllogism#Existential_import" title="Syllogism">existential import</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Term">Term</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=3" title="Edit section: Term"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Term_(logic)" title="Term (logic)">term</a> (Greek ὅρος <i>horos</i>) is the basic component of the proposition. The original meaning of the <i>horos</i> (and also of the Latin <i>terminus</i>) is "extreme" or "boundary". The two terms lie on the outside of the proposition, joined by the act of affirmation or denial. </p><p>For early modern <a href="/wiki/Logician" class="mw-redirect" title="Logician">logicians</a> like Arnauld (whose <i><a href="/wiki/Port-Royal_Logic" title="Port-Royal Logic">Port-Royal Logic</a></i> was the best-known text of his day), it is a psychological entity like an "idea" or "<a href="/wiki/Concept" title="Concept">concept</a>". <a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">Mill</a> considers it a word. To assert "all Greeks are men" is not to say that the concept of Greeks is the concept of men, or that word "Greeks" is the word "men". A <a href="/wiki/Proposition" title="Proposition">proposition</a> cannot be built from real things or ideas, but it is not just meaningless words either. </p> <div class="mw-heading mw-heading2"><h2 id="Proposition">Proposition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=4" title="Edit section: Proposition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In term logic, a "proposition" is simply a <i>form of language</i>: a particular kind of <a href="/wiki/Sentence_(linguistics)" title="Sentence (linguistics)">sentence</a>, in which the subject and <a href="/wiki/Predicate_(grammar)" title="Predicate (grammar)">predicate</a> are combined, so as to assert something true or false. It is not a thought, or an <a href="/wiki/Abstract_entity" class="mw-redirect" title="Abstract entity">abstract entity</a>. The word <i>"propositio"</i> is from the Latin, meaning the first premise of a <a href="/wiki/Syllogism" title="Syllogism">syllogism</a>. Aristotle uses the word premise (<i>protasis</i>) as a sentence affirming or denying one thing or another (<i><a href="/wiki/Posterior_Analytics" title="Posterior Analytics">Posterior Analytics</a></i> 1. 1 24a 16), so a <a href="/wiki/Premise" title="Premise">premise</a> is also a form of words. </p><p>However, as in modern philosophical logic, it means that which is asserted by the sentence. Writers before <a href="/wiki/Frege" class="mw-redirect" title="Frege">Frege</a> and <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russell</a>, such as <a href="/wiki/F._H._Bradley" title="F. H. Bradley">Bradley</a>, sometimes spoke of the "judgment" as something distinct from a sentence, but this is not quite the same. As a further confusion the word "sentence" derives from the Latin, meaning an <a href="/wiki/Opinion" title="Opinion">opinion</a> or <a href="/wiki/Judgment" class="mw-redirect" title="Judgment">judgment</a>, and so is equivalent to "<a href="/wiki/Proposition" title="Proposition">proposition</a>". </p><p>The <i><a href="/wiki/Logical_quality" title="Logical quality">logical quality</a></i> of a proposition is whether it is affirmative (the predicate is affirmed of the subject) or negative (the predicate is denied of the subject). Thus <i>every philosopher is mortal</i> is affirmative, since the mortality of philosophers is affirmed universally, whereas <i>no philosopher is mortal</i> is negative by denying such mortality in particular. </p><p>The <i>quantity</i> of a proposition is whether it is universal (the predicate is affirmed or denied of all subjects or of "the whole") or particular (the predicate is affirmed or denied of some subject or a "part" thereof). In case where <a href="/wiki/Existential" class="mw-redirect" title="Existential">existential</a> import is assumed, <a href="/wiki/Quantifier_(linguistics)" class="mw-redirect" title="Quantifier (linguistics)">quantification</a> implies the existence of at least one subject, unless disclaimed. </p> <div class="mw-heading mw-heading2"><h2 id="Singular_terms">Singular terms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=5" title="Edit section: Singular terms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For Aristotle, the distinction between singular<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2022)">citation needed</span></a></i>]</sup> and universal is a fundamental <a href="/wiki/Metaphysical" class="mw-redirect" title="Metaphysical">metaphysical</a> one, and not merely <a href="/wiki/Grammatical" class="mw-redirect" title="Grammatical">grammatical</a>. A singular term for Aristotle is <a href="/wiki/Substance_theory" title="Substance theory">primary substance</a>, which can only be <a href="/wiki/Predicate_(grammar)" title="Predicate (grammar)">predicated</a> of itself: (this) "Callias" or (this) "Socrates" are not predicable of any other thing, thus one does not say <i>every Socrates</i> one says <i>every human</i> (<i>De Int.</i> 7; <i>Meta.</i> D9, 1018a4). It may feature as a grammatical predicate, as in the sentence "the person coming this way is Callias". But it is still a <i>logical</i> subject. </p><p>He contrasts universal (<i>katholou</i>)<sup id="cite_ref-katholouLSJ_9-0" class="reference"><a href="#cite_note-katholouLSJ-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> secondary substance, genera, with primary substance, particular (<i>kath' hekaston</i>)<sup id="cite_ref-katholouLSJ_9-1" class="reference"><a href="#cite_note-katholouLSJ-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><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> specimens. The formal nature of <a href="/wiki/Universal_(metaphysics)" title="Universal (metaphysics)">universals</a>, in so far as they can be generalized "always, or for the most part", is the subject matter of both scientific study and formal logic.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The essential feature of the <a href="/wiki/Syllogism" title="Syllogism">syllogism</a> is that, of the four terms in the two premises, one must occur twice. Thus </p> <dl><dd>All Greeks are <b>men</b></dd> <dd>All <b>men</b> are mortal.</dd></dl> <p>The subject of one premise, must be the predicate of the other, and so it is necessary to eliminate from the logic any terms which cannot function both as subject and predicate, namely singular terms. </p><p>However, in a popular 17th-century version of the syllogism, <a href="/wiki/Port-Royal_Logic" title="Port-Royal Logic">Port-Royal Logic</a>, singular terms were treated as universals:<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>All men are mortals</dd> <dd>All Socrates are men</dd> <dd>All Socrates are mortals</dd></dl> <p>This is clearly awkward, a weakness exploited by Frege in his devastating attack on the system. </p><p>The famous syllogism "Socrates is a man ...", is frequently quoted as though from Aristotle,<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> but in fact, it is nowhere in the <i><a href="/wiki/Organon" title="Organon">Organon</a></i>. <a href="/wiki/Sextus_Empiricus" title="Sextus Empiricus">Sextus Empiricus</a> in his <i>Hyp. Pyrrh</i> (Outlines of Pyrronism) ii. 164 first mentions the related syllogism "Socrates is a human being, Every human being is an animal, Therefore, Socrates is an animal." </p> <div class="mw-heading mw-heading3"><h3 id="The_three_figures">The three figures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=6" title="Edit section: The three figures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Depending on the position of the middle term, Aristotle divides the syllogism into three kinds: syllogism in the first, second, and third figure.<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> If the Middle Term is subject of one premise and predicate of the other, the premises are in the First Figure. If the Middle Term is predicate of both premises, the premises are in the Second Figure. If the Middle Term is subject of both premises, the premises are in the Third Figure.<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><p>Symbolically, the Three Figures may be represented as follows:<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> <table class="wikitable"> <tbody><tr> <th> </th> <th>First figure </th> <th>Second figure </th> <th>Third figure </th></tr> <tr> <td> </td> <td>Predicate — Subject </td> <td>Predicate — Subject </td> <td>Predicate — Subject </td></tr> <tr> <td>Major premise </td> <td>A ------------ B </td> <td>B ------------ A </td> <td>A ------------ B </td></tr> <tr> <td>Minor premise </td> <td>B ------------ C </td> <td>B ------------ C </td> <td>C ------------ B </td></tr> <tr> <td>Conclusion </td> <td>A ********** C </td> <td>A ********** C </td> <td>A ********** C </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="The_fourth_figure">The fourth figure</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=7" title="Edit section: The fourth figure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <blockquote><p>In Aristotelian syllogistic (<i>Prior Analytics</i>, Bk I Caps 4-7), syllogisms are divided into three figures according to the position of the middle term in the two premises. The fourth figure, in which the middle term is the predicate in the major premise and the subject in the minor, was added by Aristotle's pupil <a href="/wiki/Theophrastus" title="Theophrastus">Theophrastus</a> and does not occur in Aristotle's work, although there is evidence that Aristotle knew of fourth-figure syllogisms.<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></blockquote> <div class="mw-heading mw-heading2"><h2 id="Syllogism_in_the_first_figure">Syllogism in the first figure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=8" title="Edit section: Syllogism in the first figure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <i>Prior Analytics</i> translated by A. J. Jenkins as it appears in volume 8 of the Great Books of the Western World, Aristotle says of the First Figure: "... If A is predicated of all B, and B of all C, A must be predicated of all 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> In the <i>Prior Analytics</i> translated by Robin Smith, Aristotle says of the first figure: "... For if A is predicated of every B and B of every C, it is necessary for A to be predicated of every C."<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> </p><p>Taking <i>a</i> = <i>is predicated of all</i> = <i>is predicated of every</i>, and using the symbolical method used in the Middle Ages, then the first figure is simplified to:<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> <dl><dd>If AaB</dd> <dd></dd> <dd>and BaC</dd> <dd></dd> <dd>then AaC.</dd></dl> <p>Or what amounts to the same thing: </p> <dl><dd>AaB, BaC; therefore AaC</dd></dl> <p>When the four syllogistic propositions, a, e, i, o are placed in the first figure, Aristotle comes up with the following valid forms of deduction for the first figure: </p> <dl><dd>AaB, BaC; therefore, AaC</dd></dl> <dl><dd>AeB, BaC; therefore, AeC</dd></dl> <dl><dd>AaB, BiC; therefore, AiC</dd></dl> <dl><dd>AeB, BiC; therefore, AoC</dd></dl> <p>In the Middle Ages, for <a href="/wiki/Mnemonic" title="Mnemonic">mnemonic</a> reasons they were called "Barbara", "Celarent", "Darii" and "Ferio" respectively.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>The difference between the first figure and the other two figures is that the syllogism of the first figure is complete while that of the second and third is not. This is important in Aristotle's theory of the syllogism for the first figure is axiomatic while the second and third require proof. The proof of the second and third figure always leads back to the first figure.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Syllogism_in_the_second_figure">Syllogism in the second figure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=9" title="Edit section: Syllogism in the second figure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This is what Robin Smith says in English that Aristotle said in Ancient Greek: "... If M belongs to every N but to no X, then neither will N belong to any X. For if M belongs to no X, neither does X belong to any M; but M belonged to every N; therefore, X will belong to no N (for the first figure has again come about)."<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>The above statement can be simplified by using the symbolical method used in the Middle Ages: </p> <dl><dd>If MaN</dd> <dd></dd> <dd>but MeX</dd> <dd></dd> <dd>then NeX.</dd> <dd></dd> <dd>For if MeX</dd> <dd></dd> <dd>then XeM</dd> <dd></dd> <dd>but MaN</dd> <dd></dd> <dd>therefore XeN.</dd></dl> <p>When the four syllogistic propositions, a, e, i, o are placed in the second figure, Aristotle comes up with the following valid forms of deduction for the second figure: </p> <dl><dd>MaN, MeX; therefore NeX</dd></dl> <dl><dd>MeN, MaX; therefore NeX</dd></dl> <dl><dd>MeN, MiX; therefore NoX</dd></dl> <dl><dd>MaN, MoX; therefore NoX</dd></dl> <p>In the Middle Ages, for mnemonic reasons they were called respectively "Camestres", "Cesare", "Festino" and "Baroco".<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Syllogism_in_the_third_figure">Syllogism in the third figure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=10" title="Edit section: Syllogism in the third figure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Aristotle says in the Prior Analytics, "... If one term belongs to all and another to none of the same thing, or if they both belong to all or none of it, I call such figure the third." Referring to universal terms, "... then when both P and R belongs to every S, it results of necessity that P will belong to some R."<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>Simplifying: </p> <dl><dd>If PaS</dd> <dd></dd> <dd>and RaS</dd> <dd></dd> <dd>then PiR.</dd></dl> <p>When the four syllogistic propositions, a, e, i, o are placed in the third figure, Aristotle develops six more valid forms of deduction: </p> <dl><dd>PaS, RaS; therefore PiR</dd></dl> <dl><dd>PeS, RaS; therefore PoR</dd></dl> <dl><dd>PiS, RaS; therefore PiR</dd></dl> <dl><dd>PaS, RiS; therefore PiR</dd></dl> <dl><dd>PoS, RaS; therefore PoR</dd></dl> <dl><dd>PeS, RiS; therefore PoR</dd></dl> <p>In the Middle Ages, for mnemonic reasons, these six forms were called respectively: "Darapti", "Felapton", "Disamis", "Datisi", "Bocardo" and "Ferison".<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Table_of_syllogisms">Table of syllogisms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=11" title="Edit section: Table of syllogisms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <caption>Table of syllogisms<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th>Figure </th> <th>Major premise </th> <th>Minor premise </th> <th>Conclusion </th> <th>Mnemonic name </th></tr> <tr> <th rowspan="4">First Figure </th> <td>AaB </td> <td>BaC </td> <td>AaC </td> <td>Barbara </td></tr> <tr> <td>AeB </td> <td>BaC </td> <td>AeC </td> <td>Celarent </td></tr> <tr> <td>AaB </td> <td>BiC </td> <td>AiC </td> <td>Darii </td></tr> <tr> <td>AeB </td> <td>BiC </td> <td>AoC </td> <td>Ferio </td></tr> <tr> <th rowspan="4">Second Figure </th> <td>MaN </td> <td>MeX </td> <td>NeX </td> <td>Camestres </td></tr> <tr> <td>MeN </td> <td>MaX </td> <td>NeX </td> <td>Cesare </td></tr> <tr> <td>MeN </td> <td>MiX </td> <td>NoX </td> <td>Festino </td></tr> <tr> <td>MaN </td> <td>MoX </td> <td>NoX </td> <td><a href="/wiki/Baroco" title="Baroco">Baroco</a> </td></tr> <tr> <th rowspan="6">Third Figure </th> <td>PaS </td> <td>RaS </td> <td>PiR </td> <td>Darapti </td></tr> <tr> <td>PeS </td> <td>RaS </td> <td>PoR </td> <td>Felapton </td></tr> <tr> <td>PiS </td> <td>RaS </td> <td>PiR </td> <td>Disamis </td></tr> <tr> <td>PaS </td> <td>RiS </td> <td>PiR </td> <td>Datisi </td></tr> <tr> <td>PoS </td> <td>RaS </td> <td>PoR </td> <td>Bocardo </td></tr> <tr> <td>PeS </td> <td>RiS </td> <td>PoR </td> <td>Ferison </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Decline_of_term_logic">Decline of term logic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=12" title="Edit section: Decline of term logic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Term logic began to decline in <a href="/wiki/Europe" title="Europe">Europe</a> during the <a href="/wiki/Renaissance" title="Renaissance">Renaissance</a>, when logicians like <a href="/wiki/Rodolphus_Agricola" title="Rodolphus Agricola">Rodolphus Agricola</a> Phrisius (1444–1485) and <a href="/wiki/Petrus_Ramus" title="Petrus Ramus">Ramus</a> (1515–1572) began to promote place logics. The logical tradition called <a href="/wiki/Port-Royal_Logic" title="Port-Royal Logic">Port-Royal Logic</a>, or sometimes "traditional logic", saw propositions as combinations of ideas rather than of terms, but otherwise followed many of the conventions of term logic. It remained influential, especially in England, until the 19th century. <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a> created a distinctive <a href="/wiki/Logical_calculus" class="mw-redirect" title="Logical calculus">logical calculus</a>, but nearly all of his work on <a href="/wiki/Logic" title="Logic">logic</a> remained unpublished and unremarked until <a href="/wiki/Louis_Couturat" title="Louis Couturat">Louis Couturat</a> went through the Leibniz <i><a href="/wiki/Nachlass" title="Nachlass">Nachlass</a></i> around 1900, publishing his pioneering studies in logic. </p><p>19th-century attempts to algebraize logic, such as the work of <a href="/wiki/George_Boole" title="George Boole">Boole</a> (1815–1864) and <a href="/wiki/John_Venn" title="John Venn">Venn</a> (1834–1923), typically yielded systems highly influenced by the term-logic tradition. The first <a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">predicate logic</a> was that of <a href="/wiki/Frege" class="mw-redirect" title="Frege">Frege</a>'s landmark <i><a href="/wiki/Begriffsschrift" title="Begriffsschrift">Begriffsschrift</a></i> (1879), little read before 1950, in part because of its eccentric notation. Modern <a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">predicate logic</a> as we know it began in the 1880s with the writings of <a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a>, who influenced <a href="/wiki/Peano" class="mw-redirect" title="Peano">Peano</a> (1858–1932) and even more, <a href="/wiki/Ernst_Schr%C3%B6der_(mathematician)" title="Ernst Schröder (mathematician)">Ernst Schröder</a> (1841–1902). It reached fruition in the hands of <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> and <a href="/wiki/A._N._Whitehead" class="mw-redirect" title="A. N. Whitehead">A. N. Whitehead</a>, whose <i><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i> (1910–13) made use of a variant of Peano's predicate logic. </p><p>Term logic also survived to some extent in traditional <a href="/wiki/Roman_Catholic" class="mw-redirect" title="Roman Catholic">Roman Catholic</a> education, especially in <a href="/wiki/Seminary" title="Seminary">seminaries</a>. Medieval Catholic <a href="/wiki/Theology" title="Theology">theology</a>, especially the writings of <a href="/wiki/Thomas_Aquinas" title="Thomas Aquinas">Thomas Aquinas</a>, had a powerfully <a href="/wiki/Aristotle" title="Aristotle">Aristotelean</a> cast, and thus term logic became a part of Catholic theological reasoning. For example, Joyce's <i>Principles of Logic</i> (1908; 3rd edition 1949), written for use in Catholic seminaries, made no mention of <a href="/wiki/Frege" class="mw-redirect" title="Frege">Frege</a> or of <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a>.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (August 2023)">page needed</span></a></i>]</sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="Quotation needed from source to verify. (August 2023)">need quotation to verify</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Revival">Revival</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=13" title="Edit section: Revival"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some philosophers have complained that predicate logic: </p> <ul><li>Is unnatural in a sense, in that its syntax does not follow the syntax of the sentences that figure in our everyday reasoning. It is, as <a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Quine</a> acknowledged, "<a href="/wiki/Procrustean" class="mw-redirect" title="Procrustean">Procrustean</a>," employing an <a href="/wiki/Artificial_language" title="Artificial language">artificial language</a> of <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">function</a> and <a href="/wiki/Logical_argument" class="mw-redirect" title="Logical argument">argument</a>, <a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">quantifier</a>, and <a href="/wiki/Bound_variable" class="mw-redirect" title="Bound variable">bound variable</a>.</li> <li>Suffers from theoretical problems, probably the most serious being <a href="/wiki/Empty_name" title="Empty name">empty names</a> and identity statements.</li></ul> <p>Even academic philosophers entirely in the mainstream, such as <a href="/wiki/Gareth_Evans_(philosopher)" title="Gareth Evans (philosopher)">Gareth Evans</a>, have written as follows: </p> <dl><dd>"I come to <a href="/wiki/Semantic" class="mw-redirect" title="Semantic">semantic</a> investigations with a preference for <i>homophonic</i> theories; theories which try to take serious account of the syntactic and semantic devices which actually exist in the language ...I would prefer [such] a theory ... over a theory which is only able to deal with [sentences of the form "all A's are B's"] by "discovering" hidden <a href="/wiki/Logical_constants" class="mw-redirect" title="Logical constants">logical constants</a> ... The objection would not be that such [Fregean] truth conditions are not correct, but that, in a sense which we would all dearly love to have more exactly explained, the syntactic shape of the sentence is treated as so much misleading surface structure" (Evans 1977)</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Boole’s_acceptance_of_Aristotle"><span id="Boole.E2.80.99s_acceptance_of_Aristotle"></span>Boole’s acceptance of Aristotle</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=14" title="Edit section: Boole’s acceptance of Aristotle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Alexander_-_Commentaria_in_Analytica_priora_Aristotelis,_1549_-_4725692.tif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Alexander_-_Commentaria_in_Analytica_priora_Aristotelis%2C_1549_-_4725692.tif/lossy-page1-220px-Alexander_-_Commentaria_in_Analytica_priora_Aristotelis%2C_1549_-_4725692.tif.jpg" decoding="async" width="220" height="316" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Alexander_-_Commentaria_in_Analytica_priora_Aristotelis%2C_1549_-_4725692.tif/lossy-page1-330px-Alexander_-_Commentaria_in_Analytica_priora_Aristotelis%2C_1549_-_4725692.tif.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Alexander_-_Commentaria_in_Analytica_priora_Aristotelis%2C_1549_-_4725692.tif/lossy-page1-440px-Alexander_-_Commentaria_in_Analytica_priora_Aristotelis%2C_1549_-_4725692.tif.jpg 2x" data-file-width="3322" data-file-height="4772" /></a><figcaption><i>Commentaria in Analytica priora Aristotelis</i>, 1549</figcaption></figure> <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>Laws of Thought</i><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Corcoran also wrote a point-by-point comparison of <i>Prior Analytics</i> and <i>Laws of Thought</i>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<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: </p> <ol><li>providing it with mathematical foundations involving equations;</li> <li>extending the class of problems it could treat– from assessing validity to solving equations; and</li> <li>expanding the range of applications it could handle– e.g. from propositions having 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 the four propositional forms of <a href="/wiki/Aristotle%27s_logic" class="mw-redirect" title="Aristotle's logic">Aristotle's logic</a> to formulas in the form of equations– by itself 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="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Converse_(logic)" title="Converse (logic)">Converse (logic)</a></li> <li><a href="/wiki/Obversion" title="Obversion">Obversion</a></li> <li><a href="/wiki/Port-Royal_Logic" title="Port-Royal Logic">Port-Royal Logic</a></li> <li><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional calculus</a></li> <li><a href="/wiki/Stoic_logic" title="Stoic logic">Stoic logic</a></li> <li><a href="/wiki/Syntax%E2%80%93semantics_interface" title="Syntax–semantics interface">Syntax–semantics interface</a></li> <li><a href="/wiki/Traditional_grammar" title="Traditional grammar">Traditional grammar</a></li> <li><a href="/wiki/Transposition_(logic)" class="mw-redirect" title="Transposition (logic)">Transposition (logic)</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=16" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 25em;"> <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">Degnan, M. 1994. Recent Work in Aristotle's Logic. Philosophical Books 35.2 (April, 1994): 81-89.</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">*Review of "Aristotle, Prior Analytics: Book I, Gisela Striker (translation and commentary), Oxford UP, 2009, 268pp., $39.95 (pbk), <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-925041-7" title="Special:BookSources/978-0-19-925041-7">978-0-19-925041-7</a>." in the <i>Notre Dame Philosophical Reviews</i>, <a rel="nofollow" class="external text" href="http://ndpr.nd.edu/review.cfm?id=18787">2010.02.02</a>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNoltRohatyn1988" class="citation book cs1">Nolt, John; Rohatyn, Dennis (1988). <i>Logic: Schaum's outline of theory and problems</i>. McGraw Hill. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-053628-7" title="Special:BookSources/0-07-053628-7"><bdi>0-07-053628-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Logic%3A+Schaum%27s+outline+of+theory+and+problems&rft.pages=1&rft.pub=McGraw+Hill&rft.date=1988&rft.isbn=0-07-053628-7&rft.aulast=Nolt&rft.aufirst=John&rft.au=Rohatyn%2C+Dennis&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobin_Smith" class="citation book cs1">Robin Smith. <i>Aristotle: Prior Analytics</i>. p. XVII.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aristotle%3A+Prior+Analytics&rft.pages=XVII&rft.au=Robin+Smith&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_Nolt/Dennis_Rohatyn" class="citation book cs1">John Nolt/Dennis Rohatyn. <i>Logic: Schaum's Outline of Theory and Problems</i>. pp. 274–275.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Logic%3A+Schaum%27s+Outline+of+Theory+and+Problems&rft.pages=274-275&rft.au=John+Nolt%2FDennis+Rohatyn&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnagnostopoulos2009" class="citation book cs1">Anagnostopoulos, Georgios (2009). <i>A Companion to Aristotle</i>. Wiley-Blackwell. p. 33. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4051-2223-8" title="Special:BookSources/978-1-4051-2223-8"><bdi>978-1-4051-2223-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Companion+to+Aristotle&rft.pages=33&rft.pub=Wiley-Blackwell&rft.date=2009&rft.isbn=978-1-4051-2223-8&rft.aulast=Anagnostopoulos&rft.aufirst=Georgios&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPatzig1969" class="citation book cs1">Patzig, Günther (1969). <i>Aristotle's theory of the syllogism</i>. Springer. p. 49. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-277-0030-8" title="Special:BookSources/978-90-277-0030-8"><bdi>978-90-277-0030-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aristotle%27s+theory+of+the+syllogism&rft.pages=49&rft.pub=Springer&rft.date=1969&rft.isbn=978-90-277-0030-8&rft.aulast=Patzig&rft.aufirst=G%C3%BCnther&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></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 class="citation book cs1"><i>The Cambridge Companion to Aristotle</i>. pp. 34–35.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Aristotle&rft.pages=34-35&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-katholouLSJ-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-katholouLSJ_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-katholouLSJ_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0057:entry=kaqo/lou"><span title="Ancient Greek (to 1453)-language text"><span lang="grc">καθόλου</span></span></a>. <a href="/wiki/Henry_Liddell" title="Henry Liddell">Liddell, Henry George</a>; <a href="/wiki/Robert_Scott_(philologist)" title="Robert Scott (philologist)">Scott, Robert</a>; <i><a href="/wiki/A_Greek%E2%80%93English_Lexicon" title="A Greek–English Lexicon">A Greek–English Lexicon</a></i> at the <a href="/wiki/Perseus_Project" class="mw-redirect" title="Perseus Project">Perseus Project</a>.</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 rel="nofollow" class="external text" href="https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0057:entry=e(/kastos"><span title="Ancient Greek (to 1453)-language text"><span lang="grc">καθ' ἕκαστον</span></span></a> in <a href="/wiki/Henry_Liddell" title="Henry Liddell">Liddell</a> and <a href="/wiki/Robert_Scott_(philologist)" title="Robert Scott (philologist)">Scott</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">They are mentioned briefly in the <i>De Interpretatione</i>. Afterwards, in the chapters of the <i>Prior Analytics</i> where Aristotle methodically sets out his theory of the syllogism, they are entirely ignored.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Arnauld, Antoine and Nicole, Pierre; (1662) <i>La logique, ou l'art de penser</i>. Part 2, chapter 3</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">For example: Kapp, <i>Greek Foundations of Traditional Logic</i>, New York 1942, p. 17, Copleston <i><a href="/wiki/A_History_of_Philosophy_(Copleston)" title="A History of Philosophy (Copleston)">A History of Philosophy</a></i> Vol. I., p. 277, <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russell</a>, <i>A History of Western Philosophy</i> London 1946 p. 218.</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>The Cambridge Companion to Aristotle</i>. p. 35. <q>At the foundation of Aristotle's syllogistic is a theory of a specific class of arguments: arguments having as premises exactly two categorical sentences with one term in common.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Aristotle&rft.pages=35&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></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 id="CITEREFRobin_Smith" class="citation book cs1">Robin Smith. <i>Aristotle: Prior Analytics</i>. p. XVIII.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aristotle%3A+Prior+Analytics&rft.pages=XVIII&rft.au=Robin+Smith&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" 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 id="CITEREFHenrik_Legerlund" class="citation book cs1">Henrik Legerlund. <i>Modal Syllogistics in the Middle Ages</i>. p. 4.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modal+Syllogistics+in+the+Middle+Ages&rft.pages=4&rft.au=Henrik+Legerlund&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRussellBlackwell1983" class="citation book cs1">Russell, Bertrand; Blackwell, Kenneth (1983). <i>Cambridge essays, 1888-99</i>. Routledge. p. 411. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-04-920067-8" title="Special:BookSources/978-0-04-920067-8"><bdi>978-0-04-920067-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cambridge+essays%2C+1888-99&rft.pages=411&rft.pub=Routledge&rft.date=1983&rft.isbn=978-0-04-920067-8&rft.aulast=Russell&rft.aufirst=Bertrand&rft.au=Blackwell%2C+Kenneth&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>Great Books of the Western World</i>. Vol. 8. p. 40.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Great+Books+of+the+Western+World&rft.pages=40&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobin_Smith" class="citation book cs1">Robin Smith. <i>Aristotle: </i>Prior Analytics<i><span></span></i>. p. 4.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aristotle%3A+Prior+Analytics&rft.pages=4&rft.au=Robin+Smith&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>The Cambridge Companion to Aristotle</i>. p. 41.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Aristotle&rft.pages=41&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>The Cambridge Companion to Aristotle</i>. p. 41.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Aristotle&rft.pages=41&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHenrik_Legerlund" class="citation book cs1">Henrik Legerlund. <i>Modal Syllogistics in the Middle Ages</i>. p. 6.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modal+Syllogistics+in+the+Middle+Ages&rft.pages=6&rft.au=Henrik+Legerlund&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobin_Smith" class="citation book cs1">Robin Smith. <i>Aristotle: Prior Analytics</i>. p. 7.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aristotle%3A+Prior+Analytics&rft.pages=7&rft.au=Robin+Smith&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>The Cambridge Companion to Aristotle</i>. p. 41.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Aristotle&rft.pages=41&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobin_Smith" class="citation book cs1">Robin Smith. <i>Aristotle: Prior Analytics</i>. p. 9.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aristotle%3A+Prior+Analytics&rft.pages=9&rft.au=Robin+Smith&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>The Cambridge Companion to Aristotle</i>. p. 41.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Aristotle&rft.pages=41&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>The Cambridge Companion to Aristotle</i>. p. 41.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cambridge+Companion+to+Aristotle&rft.pages=41&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><a href="/wiki/Frederick_Copleston" title="Frederick Copleston">Copleston</a>'s <i><a href="/wiki/A_History_of_Philosophy_(Copleston)" title="A History of Philosophy (Copleston)">A History of Philosophy</a></i></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><a href="/wiki/George_Boole" title="George Boole">George Boole</a>. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167–169.</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text">John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24 (2003), pp. 261–288.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Term_logic&action=edit&section=17" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Bochenski, I. M., 1951. <i>Ancient Formal Logic</i>. North-Holland.</li> <li><a href="/wiki/Louis_Couturat" title="Louis Couturat">Louis Couturat</a>, 1961 (1901). <i>La Logique de Leibniz</i>. Hildesheim: Georg Olms Verlagsbuchhandlung.</li> <li><a href="/wiki/Gareth_Evans_(philosopher)" title="Gareth Evans (philosopher)">Gareth Evans</a>, 1977, "Pronouns, Quantifiers and Relative Clauses," <i>Canadian Journal of Philosophy</i>.</li> <li><a href="/wiki/Peter_Geach" title="Peter Geach">Peter Geach</a>, 1976. <i>Reason and Argument</i>. University of California Press.</li> <li>Hammond and Scullard, 1992. <i>The Oxford Classical Dictionary</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/0-19-869117-3" title="Special:BookSources/0-19-869117-3">0-19-869117-3</a>.</li> <li>Joyce, George Hayward, 1949 (1908). <i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060227234924/http://uk.geocities.com/frege@btinternet.com/joyce/principlesoflogic.htm">Principles of Logic</a></i>, 3rd ed. Longmans. A manual written for use in Catholic seminaries. Authoritative on traditional logic, with many references to medieval and ancient sources. Contains no hint of modern formal logic. The author lived 1864–1943.</li> <li><a href="/wiki/Jan_%C5%81ukasiewicz" title="Jan Łukasiewicz">Jan Łukasiewicz</a>, 1951. <i>Aristotle's Syllogistic, from the Standpoint of Modern Formal Logic</i>. Oxford Univ. Press.</li> <li><a href="/wiki/William_Calvert_Kneale" class="mw-redirect" title="William Calvert Kneale">William Calvert Kneale</a> and <a href="/wiki/Martha_Kneale" title="Martha Kneale">Martha Kneale</a>, 1962. <i>The Development of Logic</i>. Oxford [England] Clarendon Press. Reviews Aristotelean logic and its influences up to modern times.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPratt-Hartmann2023" class="citation book cs1">Pratt-Hartmann, Ian (2023-03-30). <a rel="nofollow" class="external text" href="https://academic.oup.com/book/46400"><i>Fragments of First-Order Logic</i></a>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-196006-2" title="Special:BookSources/978-0-19-196006-2"><bdi>978-0-19-196006-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fragments+of+First-Order+Logic&rft.pub=Oxford+University+Press&rft.date=2023-03-30&rft.isbn=978-0-19-196006-2&rft.aulast=Pratt-Hartmann&rft.aufirst=Ian&rft_id=https%3A%2F%2Facademic.oup.com%2Fbook%2F46400&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span>. Chapter 2 presents a modern overview, with a bibliography.</li> <li><a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">John Stuart Mill</a>, 1904. <i>A System of Logic</i>, 8th ed. London.</li> <li>Parry and Hacker, 1991. <i>Aristotelian Logic</i>. State University of New York Press.</li> <li><a href="/wiki/Arthur_Prior" title="Arthur Prior">Arthur Prior</a> <dl><dd>1962: <i>Formal Logic</i>, 2nd ed. Oxford Univ. Press. While primarily devoted to modern formal logic, contains much on term and medieval logic.</dd> <dd>1976: <i>The Doctrine of Propositions and Terms</i>. <a href="/wiki/Peter_Geach" title="Peter Geach">Peter Geach</a> and A. J. P. Kenny, eds. London: Duckworth.</dd></dl></li> <li><a href="/wiki/Willard_Quine" class="mw-redirect" title="Willard Quine">Willard Quine</a>, 1986. <i>Philosophy of Logic</i> 2nd ed. Harvard Univ. Press.</li> <li>Rose, Lynn E., 1968. <i>Aristotle's Syllogistic</i>. Springfield: Clarence C. Thomas.</li> <li><a href="/wiki/Frederic_Tamler_Sommers" class="mw-redirect" title="Frederic Tamler Sommers">Sommers, Fred</a> <dl><dd>1970: "The Calculus of Terms," <i>Mind 79</i>: 1-39. Reprinted in Englebretsen, G., ed., 1987. <i>The new syllogistic</i> New York: Peter Lang. <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/0-8204-0448-9" title="Special:BookSources/0-8204-0448-9">0-8204-0448-9</a></dd> <dd>1982: <i>The logic of natural language</i>. Oxford University Press.</dd> <dd>1990: "<a rel="nofollow" class="external text" href="http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ndjfl/1093635336">Predication in the Logic of Terms</a>," <i>Notre Dame Journal of Formal Logic 31</i>: 106–26.</dd> <dd>and Englebretsen, George, 2000: <i>An invitation to formal reasoning. The logic of terms</i>. Aldershot UK: Ashgate. <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/0-7546-1366-6" title="Special:BookSources/0-7546-1366-6">0-7546-1366-6</a>.</dd></dl></li> <li>Szabolcsi Lorne, 2008. <i>Numerical Term Logic</i>. Lewiston: Edwin Mellen Press.</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=Term_logic&action=edit&section=18" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Term_logic" class="extiw" title="commons:Category:Term logic">Term logic</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://philpapers.org/browse/aristotelian-logic">Term logic</a> at <a href="/wiki/PhilPapers" title="PhilPapers">PhilPapers</a></li> <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%3ATerm+logic" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="http://www.iep.utm.edu/aris-log">"Term logic"</a>. <i><a href="/wiki/Internet_Encyclopedia_of_Philosophy" title="Internet Encyclopedia of Philosophy">Internet Encyclopedia of Philosophy</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Term+logic&rft.btitle=Internet+Encyclopedia+of+Philosophy&rft_id=http%3A%2F%2Fwww.iep.utm.edu%2Faris-log&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATerm+logic" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://aristotelianlogic.glashoff.eu">Aristotle's term logic online</a>-This online program provides a platform for experimentation and research on Aristotelian logic.</li> <li>Annotated bibliographies: <dl><dd><a rel="nofollow" class="external text" href="http://www.ontology.co/sommersf.htm">Fred Sommers.</a></dd> <dd><a rel="nofollow" class="external text" href="http://www.ontology.co/biblio/englebretseng.htm">George Englebretsen.</a></dd></dl></li> <li><a href="/wiki/PlanetMath" title="PlanetMath">PlanetMath</a>: <a rel="nofollow" class="external text" href="https://planetmath.org/AristotelianLogic">Aristotelian Logic</a>.</li> <li><a rel="nofollow" class="external text" href="http://thefirstscience.org/syllogistic-machine/">Interactive Syllogistic Machine for Term Logic</a> A web based syllogistic machine for exploring fallacies, figures, terms, and modes of syllogisms.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist 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.navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Formal_semantics" title="Template:Formal semantics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Formal_semantics" title="Template talk:Formal semantics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Formal_semantics" title="Special:EditPage/Template:Formal semantics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Formal_semantics_(natural_language)" style="font-size:114%;margin:0 4em"><a href="/wiki/Formal_semantics_(natural_language)" title="Formal semantics (natural language)">Formal semantics (natural language)</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Central concepts</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/Principle_of_compositionality" title="Principle of compositionality">Compositionality</a></li> <li><a href="/wiki/Denotation" title="Denotation">Denotation</a></li> <li><a href="/wiki/Entailment" class="mw-redirect" title="Entailment">Entailment</a></li> <li><a href="/wiki/Extension_(semantics)" title="Extension (semantics)">Extension</a></li> <li><a href="/wiki/Generalized_quantifier" title="Generalized quantifier">Generalized quantifier</a></li> <li><a href="/wiki/Intension" title="Intension">Intension</a></li> <li><a href="/wiki/Logical_form_(linguistics)" title="Logical form (linguistics)">Logical form</a></li> <li><a href="/wiki/Presupposition" title="Presupposition">Presupposition</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Reference" title="Reference">Reference</a></li> <li><a href="/wiki/Scope_(formal_semantics)" title="Scope (formal semantics)">Scope</a></li> <li><a href="/wiki/Speech_act" title="Speech act">Speech act</a></li> <li><a href="/wiki/Syntax%E2%80%93semantics_interface" title="Syntax–semantics interface">Syntax–semantics interface</a></li> <li><a href="/wiki/Truth-conditional_semantics" title="Truth-conditional semantics">Truth conditions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</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 scope="row" class="navbox-group" style="width:1%">Areas</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/Anaphora_(linguistics)" title="Anaphora (linguistics)">Anaphora</a></li> <li><a href="/wiki/Ambiguity" title="Ambiguity">Ambiguity</a></li> <li><a href="/wiki/Binding_(linguistics)" title="Binding (linguistics)">Binding</a></li> <li><a href="/wiki/Conditional_sentence" title="Conditional sentence">Conditionals</a></li> <li><a href="/wiki/Definiteness" title="Definiteness">Definiteness</a></li> <li><a href="/wiki/Disjunction" class="mw-redirect" title="Disjunction">Disjunction</a></li> <li><a href="/wiki/Evidentiality" title="Evidentiality">Evidentiality</a></li> <li><a href="/wiki/Focus_(linguistics)" title="Focus (linguistics)">Focus</a></li> <li><a href="/wiki/Indexicality" title="Indexicality">Indexicality</a></li> <li><a href="/wiki/Lexical_semantics" title="Lexical semantics">Lexical semantics</a></li> <li><a href="/wiki/Linguistic_modality" class="mw-redirect" title="Linguistic modality">Modality</a></li> <li><a href="/wiki/Negation" title="Negation">Negation</a></li> <li><a href="/wiki/Propositional_attitudes" class="mw-redirect" title="Propositional attitudes">Propositional attitudes</a></li> <li><a href="/wiki/Tense%E2%80%93aspect%E2%80%93mood" title="Tense–aspect–mood">Tense–aspect–mood</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantification</a></li> <li><a href="/wiki/Vagueness" title="Vagueness">Vagueness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Phenomena</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/Antecedent-contained_deletion" title="Antecedent-contained deletion">Antecedent-contained deletion</a></li> <li><a href="/wiki/Cataphora" title="Cataphora">Cataphora</a></li> <li><a href="/wiki/Coercion_(linguistics)" title="Coercion (linguistics)">Coercion</a></li> <li><a href="/wiki/Conservativity" title="Conservativity">Conservativity</a></li> <li><a href="/wiki/Counterfactuals" class="mw-redirect" title="Counterfactuals">Counterfactuals</a></li> <li><a href="/wiki/Crossover_effects" title="Crossover effects">Crossover effects</a></li> <li><a href="/wiki/Cumulativity_(linguistics)" title="Cumulativity (linguistics)">Cumulativity</a></li> <li><a href="/wiki/De_dicto_and_de_re" title="De dicto and de re">De dicto and de re</a></li> <li><a href="/wiki/De_se" title="De se">De se</a></li> <li><a href="/wiki/Deontic_modality" title="Deontic modality">Deontic modality</a></li> <li><a href="/wiki/Discourse_relation" title="Discourse relation">Discourse relations</a></li> <li><a href="/wiki/Donkey_anaphora" class="mw-redirect" title="Donkey anaphora">Donkey anaphora</a></li> <li><a href="/wiki/Epistemic_modality" title="Epistemic modality">Epistemic modality</a></li> <li><a href="/wiki/Exhaustivity" title="Exhaustivity">Exhaustivity</a></li> <li><a href="/wiki/Faultless_disagreement" title="Faultless disagreement">Faultless disagreement</a></li> <li><a href="/wiki/Free_choice_inference" title="Free choice inference">Free choice inferences</a></li> <li><a href="/wiki/Givenness" title="Givenness">Givenness</a></li> <li><a href="/wiki/Homogeneity_(linguistics)" class="mw-redirect" title="Homogeneity (linguistics)">Homogeneity (linguistics)</a></li> <li><a href="/wiki/Hurford_disjunction" title="Hurford disjunction">Hurford disjunction</a></li> <li><a href="/wiki/Inalienable_possession" title="Inalienable possession">Inalienable possession</a></li> <li><a href="/wiki/Intersective_modifier" title="Intersective modifier">Intersective modification</a></li> <li><a href="/wiki/Logophoricity" title="Logophoricity">Logophoricity</a></li> <li><a href="/wiki/Mirativity" title="Mirativity">Mirativity</a></li> <li><a href="/wiki/Modal_subordination" title="Modal subordination">Modal subordination</a></li> <li><a href="/wiki/Opaque_context" title="Opaque context">Opaque contexts</a></li> <li><a href="/wiki/Performative_utterance" title="Performative utterance">Performatives</a></li> <li><a href="/wiki/Polarity_item" title="Polarity item">Polarity items</a></li> <li><a href="/wiki/Privative_adjective" title="Privative adjective">Privative adjectives</a></li> <li><a href="/wiki/Quantificational_variability_effect" title="Quantificational variability effect">Quantificational variability effect</a></li> <li><a href="/wiki/Responsive_predicate" title="Responsive predicate">Responsive predicate</a></li> <li><a href="/wiki/Rising_declarative" title="Rising declarative">Rising declaratives</a></li> <li><a href="/wiki/Scalar_implicature" title="Scalar implicature">Scalar implicature</a></li> <li><a href="/wiki/Sloppy_identity" title="Sloppy identity">Sloppy identity</a></li> <li><a href="/wiki/Subsective_modifier" title="Subsective modifier">Subsective modification</a></li> <li><a href="/wiki/Subtrigging" title="Subtrigging">Subtrigging</a></li> <li><a href="/wiki/Telicity" title="Telicity">Telicity</a></li> <li><a href="/wiki/Temperature_paradox" title="Temperature paradox">Temperature paradox</a></li> <li><a href="/wiki/Veridicality" title="Veridicality">Veridicality</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formalism</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 scope="row" class="navbox-group" style="width:1%">Formal systems</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/Alternative_semantics" title="Alternative semantics">Alternative semantics</a></li> <li><a href="/wiki/Categorial_grammar" title="Categorial grammar">Categorial grammar</a></li> <li><a href="/wiki/Combinatory_categorial_grammar" title="Combinatory categorial grammar">Combinatory categorial grammar</a></li> <li><a href="/wiki/Discourse_representation_theory" title="Discourse representation theory">Discourse representation theory (DRT)</a></li> <li><a href="/wiki/Dynamic_semantics" title="Dynamic semantics">Dynamic semantics</a></li> <li><a href="/wiki/Generative_grammar" title="Generative grammar">Generative grammar</a></li> <li><a href="/wiki/Glue_semantics" title="Glue semantics">Glue semantics</a></li> <li><a href="/wiki/Inquisitive_semantics" title="Inquisitive semantics">Inquisitive semantics</a></li> <li><a href="/wiki/Intensional_logic" title="Intensional logic">Intensional logic</a></li> <li><a href="/wiki/Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li> <li><a href="/wiki/Mereology" title="Mereology">Mereology</a></li> <li><a href="/wiki/Montague_grammar" title="Montague grammar">Montague grammar</a></li> <li><a href="/wiki/Segmented_discourse_representation_theory" class="mw-redirect" title="Segmented discourse representation theory">Segmented discourse representation theory (SDRT)</a></li> <li><a href="/wiki/Situation_semantics" title="Situation semantics">Situation semantics</a></li> <li><a href="/wiki/Supervaluationism" title="Supervaluationism">Supervaluationism</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li> <li><a href="/wiki/Type_theory_with_records" title="Type theory with records">TTR</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autonomy_of_syntax" title="Autonomy of syntax">Autonomy of syntax</a></li> <li><a href="/wiki/Context_set" class="mw-redirect" title="Context set">Context set</a></li> <li><a href="/wiki/Continuation" title="Continuation">Continuation</a></li> <li><a href="/wiki/Conversational_scoreboard" title="Conversational scoreboard">Conversational scoreboard</a></li> <li><a href="/wiki/Downward_entailing" title="Downward entailing">Downward entailing</a></li> <li><a href="/wiki/Existential_closure" title="Existential closure">Existential closure</a></li> <li><a href="/wiki/Function_application" title="Function application">Function application</a></li> <li><a href="/wiki/Meaning_postulate" title="Meaning postulate">Meaning postulate</a></li> <li><a href="/wiki/Monad_(functional_programming)" title="Monad (functional programming)">Monads</a></li> <li><a href="/wiki/Plural_quantification" title="Plural quantification">Plural quantification</a></li> <li><a href="/wiki/Possible_world" title="Possible world">Possible world</a></li> <li><a href="/wiki/Quantifier_raising" class="mw-redirect" title="Quantifier raising">Quantifier raising</a></li> <li><a href="/wiki/Quantization_(linguistics)" title="Quantization (linguistics)">Quantization</a></li> <li><a href="/wiki/Question_under_discussion" title="Question under discussion">Question under discussion</a></li> <li><a href="/wiki/Semantic_parsing" title="Semantic parsing">Semantic parsing</a></li> <li><a href="/wiki/Squiggle_operator" title="Squiggle operator">Squiggle operator</a></li> <li><a href="/wiki/Strawson_entailment" title="Strawson entailment">Strawson entailment</a></li> <li><a href="/wiki/Strict_conditional" title="Strict conditional">Strict conditional</a></li> <li><a href="/wiki/Type_shifter" title="Type shifter">Type shifter</a></li> <li><a href="/wiki/Universal_grinder" title="Universal grinder">Universal grinder</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</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/Cognitive_semantics" title="Cognitive semantics">Cognitive semantics</a></li> <li><a href="/wiki/Computational_semantics" title="Computational semantics">Computational semantics</a></li> <li><a href="/wiki/Distributional_semantics" title="Distributional semantics">Distributional semantics</a></li> <li><a href="/wiki/Formal_grammar" title="Formal grammar">Formal grammar</a></li> <li><a href="/wiki/Inferentialism" class="mw-redirect" title="Inferentialism">Inferentialism</a></li> <li><a href="/wiki/Logic_translation" title="Logic translation">Logic translation</a></li> <li><a href="/wiki/Linguistics_wars" title="Linguistics wars">Linguistics wars</a></li> <li><a href="/wiki/Philosophy_of_language" title="Philosophy of language">Philosophy of language</a></li> <li><a href="/wiki/Pragmatics" title="Pragmatics">Pragmatics</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</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="Aristotelianism" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Aristotelianism" title="Template:Aristotelianism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Aristotelianism" title="Template talk:Aristotelianism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Aristotelianism" title="Special:EditPage/Template:Aristotelianism"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Aristotelianism" style="font-size:114%;margin:0 4em"><a href="/wiki/Aristotelianism" title="Aristotelianism">Aristotelianism</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Overview</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/Aristotle" title="Aristotle">Aristotle</a></li> <li><a class="mw-selflink selflink">Logic</a></li> <li><a href="/wiki/Lyceum_(classical)" title="Lyceum (classical)">Lyceum</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Ideas and interests</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/Active_intellect" title="Active intellect">Active intellect</a></li> <li><i><a href="/wiki/Antiperistasis" title="Antiperistasis">Antiperistasis</a></i></li> <li><i><a href="/wiki/Arete" title="Arete">Arete</a></i></li> <li><a href="/wiki/Category_of_being" class="mw-redirect" title="Category of being">Category of being</a></li> <li><i><a href="/wiki/Catharsis" title="Catharsis">Catharsis</a></i></li> <li><a href="/wiki/Correspondence_theory_of_truth" title="Correspondence theory of truth">Correspondence theory of truth</a></li> <li><a href="/wiki/Essence" title="Essence">Essence</a>–<a href="/wiki/Accident_(philosophy)" title="Accident (philosophy)">accident</a></li> <li><i><a href="/wiki/Eudaimonia" title="Eudaimonia">Eudaimonia</a></i></li> <li><a href="/wiki/Four_causes" title="Four causes">Four causes</a></li> <li><a href="/wiki/Problem_of_future_contingents" title="Problem of future contingents">Future contingents</a></li> <li><a href="/wiki/Genus%E2%80%93differentia_definition" title="Genus–differentia definition">Genus–differentia</a></li> <li><i><a href="/wiki/Hexis" title="Hexis">Hexis</a></i></li> <li><a href="/wiki/Hylomorphism" title="Hylomorphism">Hylomorphism</a></li> <li><i><a href="/wiki/Lexis_(Aristotle)" title="Lexis (Aristotle)">Lexis</a></i></li> <li><a href="/wiki/Magnanimity" title="Magnanimity">Magnanimity</a></li> <li><i><a href="/wiki/Mimesis#Aristotle" title="Mimesis">Mimesis</a></i></li> <li><i><a href="/wiki/Minima_naturalia" title="Minima naturalia">Minima naturalia</a></i></li> <li><a href="/wiki/Moderate_realism" title="Moderate realism">Moderate realism</a></li> <li><a href="/wiki/Mythos_(Aristotle)" title="Mythos (Aristotle)">Mythos</a></li> <li><i><a href="/wiki/Philia" title="Philia">Philia</a></i></li> <li><a href="/wiki/Horror_vacui_(physics)" title="Horror vacui (physics)">Horror vacui (physics)</a></li> <li><a href="/wiki/Rational_animal" title="Rational animal">Rational animal</a></li> <li><i><a href="/wiki/Phronesis" title="Phronesis">Phronesis</a></i></li> <li><a href="/wiki/Potentiality_and_actuality" title="Potentiality and actuality">Potentiality and actuality</a></li> <li><a href="/wiki/Substance_theory" title="Substance theory">Substance theory</a> (<i><a href="/wiki/Hypokeimenon" title="Hypokeimenon">hypokeimenon</a></i>, <i><a href="/wiki/Ousia" title="Ousia">ousia</a></i>)</li> <li><a href="/wiki/Syllogism" title="Syllogism">Syllogism</a></li> <li><i><a href="/wiki/Telos" title="Telos">Telos</a></i></li> <li><a href="/wiki/Temporal_finitism" title="Temporal finitism">Temporal finitism</a></li> <li><a href="/wiki/Quiddity" title="Quiddity">Quiddity</a></li> <li><a href="/wiki/Haecceity" title="Haecceity">Haecceity</a></li> <li><a href="/wiki/Unmoved_mover" title="Unmoved mover">Unmoved mover</a></li> <li><a href="/wiki/Virtue_ethics" title="Virtue ethics">Virtue ethics</a></li> <li><a href="/wiki/Aristotelian_realist_philosophy_of_mathematics" title="Aristotelian realist philosophy of mathematics">Mathematical realism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Works_of_Aristotle" title="Works of Aristotle">Works</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0;font-style:italic;"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><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><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Aristotelian_physics" title="Aristotelian physics">Physics</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/Physics_(Aristotle)" title="Physics (Aristotle)">Physics</a></li> <li><a href="/wiki/On_the_Heavens" title="On the Heavens">On the Heavens</a></li> <li><a href="/wiki/On_Generation_and_Corruption" title="On Generation and Corruption">On Generation and Corruption</a></li> <li><a href="/wiki/Meteorology_(Aristotle)" title="Meteorology (Aristotle)">Meteorology</a></li> <li><a href="/wiki/On_the_Soul" title="On the Soul">On the Soul</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Aristotle%27s_biology" title="Aristotle's biology">On Animals</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/History_of_Animals" title="History of Animals">History</a></li> <li><a href="/wiki/Parts_of_Animals" title="Parts of Animals">Parts</a></li> <li><a href="/wiki/Movement_of_Animals" title="Movement of Animals">Movement</a></li> <li><a href="/wiki/Progression_of_Animals" title="Progression of Animals">Progression</a></li> <li><a href="/wiki/Generation_of_Animals" title="Generation of Animals">Generation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Metaphysics</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/Metaphysics_(Aristotle)" title="Metaphysics (Aristotle)">Metaphysics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Aristotelian_ethics" title="Aristotelian ethics">Ethics</a> and politics</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/Nicomachean_Ethics" title="Nicomachean Ethics">Nicomachean Ethics</a></li> <li><a href="/wiki/Eudemian_Ethics" title="Eudemian Ethics">Eudemian Ethics</a></li> <li><a href="/wiki/Politics_(Aristotle)" title="Politics (Aristotle)">Politics</a></li> <li><a href="/wiki/Constitution_of_the_Athenians_(Aristotle)" title="Constitution of the Athenians (Aristotle)">Constitution of the Athenians</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Rhetoric and poetics</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/Rhetoric_(Aristotle)" title="Rhetoric (Aristotle)">Rhetoric</a></li> <li><a href="/wiki/Poetics_(Aristotle)" title="Poetics (Aristotle)">Poetics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Parva_Naturalia" title="Parva Naturalia">Parva Naturalia</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/Sense_and_Sensibilia_(Aristotle)" title="Sense and Sensibilia (Aristotle)">Sense and Sensibilia</a></li> <li><a href="/wiki/On_Memory" title="On Memory">On Memory</a></li> <li><a href="/wiki/On_Sleep" title="On Sleep">On Sleep</a></li> <li><a href="/wiki/On_Dreams" title="On Dreams">On Dreams</a></li> <li><a href="/wiki/On_Divination_in_Sleep" title="On Divination in Sleep">On Divination in Sleep</a></li> <li><a href="/wiki/On_Length_and_Shortness_of_Life" title="On Length and Shortness of Life">On Length and Shortness of Life</a></li> <li><a href="/wiki/On_Youth,_Old_Age,_Life_and_Death,_and_Respiration" title="On Youth, Old Age, Life and Death, and Respiration">On Youth, Old Age, Life and Death, and Respiration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lost</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/Protrepticus_(Aristotle)" title="Protrepticus (Aristotle)">Protrepticus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Pseudo-Aristotle" title="Pseudo-Aristotle">Pseudepigrapha</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/On_Breath" title="On Breath">On Breath</a></li> <li><a href="/wiki/On_Colors" title="On Colors">On Colors</a></li> <li><a href="/wiki/On_Plants" title="On Plants">On Plants</a></li> <li><a href="/wiki/On_Indivisible_Lines" title="On Indivisible Lines">On Indivisible Lines</a></li> <li><a href="/wiki/On_Melissus,_Xenophanes,_and_Gorgias" title="On Melissus, Xenophanes, and Gorgias">On Melissus, Xenophanes, and Gorgias</a></li> <li><a href="/wiki/On_the_Universe" title="On the Universe">On the Universe</a></li> <li><a href="/wiki/On_Things_Heard" title="On Things Heard">On Things Heard</a></li> <li><a href="/wiki/Physiognomonics" title="Physiognomonics">Physiognomonics</a></li> <li><a href="/wiki/On_Marvellous_Things_Heard" title="On Marvellous Things Heard">On Marvellous Things Heard</a></li> <li><a href="/wiki/Mechanics_(Aristotle)" title="Mechanics (Aristotle)">Mechanics</a></li> <li><a href="/wiki/Problems_(Aristotle)" title="Problems (Aristotle)">Problems</a></li> <li><a href="/wiki/The_Situations_and_Names_of_Winds" title="The Situations and Names of Winds">The Situations and Names of Winds</a></li> <li><a href="/wiki/On_Virtues_and_Vices" title="On Virtues and Vices">On Virtues and Vices</a></li> <li><a href="/wiki/Economics_(Aristotle)" title="Economics (Aristotle)">Economics</a></li> <li><a href="/wiki/Rhetoric_to_Alexander" title="Rhetoric to Alexander">Rhetoric to Alexander</a></li> <li><a href="/wiki/Magna_Moralia" title="Magna Moralia">Magna Moralia</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Followers</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Peripatetic_school" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Peripatetic_school" title="Peripatetic school">Peripatetic school</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/Aristoxenus" title="Aristoxenus">Aristoxenus</a></li> <li><a href="/wiki/Clearchus_of_Soli" title="Clearchus of Soli">Clearchus of Soli</a></li> <li><a href="/wiki/Dicaearchus" title="Dicaearchus">Dicaearchus</a></li> <li><a href="/wiki/Eudemus_of_Rhodes" title="Eudemus of Rhodes">Eudemus of Rhodes</a></li> <li><a href="/wiki/Theophrastus" title="Theophrastus">Theophrastus</a></li> <li><a href="/wiki/Strato_of_Lampsacus" title="Strato of Lampsacus">Strato of Lampsacus</a></li> <li><a href="/wiki/Lyco_of_Troas" title="Lyco of Troas">Lyco of Troas</a></li> <li><a href="/wiki/Aristo_of_Ceos" title="Aristo of Ceos">Aristo of Ceos</a></li> <li><a href="/wiki/Critolaus" title="Critolaus">Critolaus</a></li> <li><a href="/wiki/Diodorus_of_Tyre" title="Diodorus of Tyre">Diodorus of Tyre</a></li> <li><a href="/wiki/Erymneus" title="Erymneus">Erymneus</a></li> <li><a href="/wiki/Andronicus_of_Rhodes" title="Andronicus of Rhodes">Andronicus of Rhodes</a></li></ul> </div></td></tr></tbody></table><div> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Islamic_Golden_Age" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Islamic_Golden_Age" title="Islamic Golden Age">Islamic Golden Age</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/Al-Kindi" title="Al-Kindi">Al-Kindi</a></li> <li><a href="/wiki/Al-Farabi" title="Al-Farabi">Al-Farabi</a></li> <li><a href="/wiki/Avicenna" title="Avicenna">Avicenna</a> <ul><li><a href="/wiki/Avicennism" title="Avicennism">Avicennism</a></li></ul></li> <li><a href="/wiki/Averroes" title="Averroes">Averroes</a> <ul><li><a href="/wiki/Averroism" title="Averroism">Averroism</a></li></ul></li></ul> </div></td></tr></tbody></table><div> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Jewish" scope="row" class="navbox-group" style="width:1%">Jewish</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/Maimonides" title="Maimonides">Maimonides</a></li></ul> </div></td></tr></tbody></table><div> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Scholasticism" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Scholasticism" title="Scholasticism">Scholasticism</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/Peter_Lombard" title="Peter Lombard">Peter Lombard</a></li> <li><a href="/wiki/Albertus_Magnus" title="Albertus Magnus">Albertus Magnus</a></li> <li><a href="/wiki/Thomas_Aquinas" title="Thomas Aquinas">Thomas Aquinas</a> <ul><li><a href="/wiki/Thomism" title="Thomism">Thomism</a></li></ul></li> <li><a href="/wiki/Duns_Scotus" title="Duns Scotus">Duns Scotus</a> <ul><li><a href="/wiki/Scotism" title="Scotism">Scotism</a></li></ul></li> <li><a href="/wiki/Peter_of_Spain" title="Peter of Spain">Peter of Spain</a></li> <li><a href="/wiki/Jacopo_Zabarella" title="Jacopo Zabarella">Jacopo Zabarella</a></li> <li><a href="/wiki/Pietro_Pomponazzi" title="Pietro Pomponazzi">Pietro Pomponazzi</a></li> <li><a href="/wiki/Cesare_Cremonini_(philosopher)" title="Cesare Cremonini (philosopher)">Cesar Cremonini</a></li></ul> </div></td></tr></tbody></table><div> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Modern" scope="row" class="navbox-group" style="width:1%">Modern</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/John_Henry_Newman" title="John Henry Newman">Newman</a></li> <li><a href="/wiki/Friedrich_Adolf_Trendelenburg" title="Friedrich Adolf Trendelenburg">Trendelenburg</a></li> <li><a href="/wiki/Franz_Brentano" title="Franz Brentano">Brentano</a></li> <li><a href="/wiki/Mortimer_J._Adler" title="Mortimer J. Adler">Adler</a></li> <li><a href="/wiki/Philippa_Foot" title="Philippa Foot">Foot</a></li> <li><a href="/wiki/Alasdair_MacIntyre" title="Alasdair MacIntyre">MacIntyre</a></li> <li><a href="/wiki/Wolfgang_Smith" title="Wolfgang Smith">Smith</a></li> <li><a href="/wiki/Rosalind_Hursthouse" title="Rosalind Hursthouse">Hursthouse</a></li> <li><a href="/wiki/Martha_Nussbaum" title="Martha Nussbaum">Nussbaum</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Transmission_of_the_Greek_Classics" title="Transmission of the Greek Classics">Transmission of the Greek Classics</a></li> <li><a href="/wiki/Plato" title="Plato">Plato</a> <ul><li><a href="/wiki/Platonism" title="Platonism">Platonism</a></li></ul></li> <li><a href="/wiki/Neoplatonism" title="Neoplatonism">Neoplatonism</a></li> <li><a href="/wiki/Commentaries_on_Aristotle" title="Commentaries on Aristotle">Commentaries on Aristotle</a></li> <li><a href="/wiki/Metabasis_paradox" title="Metabasis paradox">Metabasis paradox</a></li> <li><a href="/wiki/Aristotle%27s_views_on_women" title="Aristotle's views on women">Views on women</a></li> <li><a href="/wiki/Aristotle%27s_wheel_paradox" title="Aristotle's wheel paradox">Wheel paradox</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, 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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 class="mw-selflink selflink">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 href="/wiki/Syllogism" title="Syllogism">Syllogism</a></li> <li><a href="/wiki/Square_of_opposition" title="Square of opposition">Square of opposition</a></li> <li><a href="/wiki/Venn_diagram" title="Venn diagram">Venn diagram</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boolean_algebra" title="Boolean algebra">Boolean algebra</a></li> <li><a href="/wiki/Boolean_function" title="Boolean function">Boolean functions</a></li> <li><a href="/wiki/Logical_connective" title="Logical connective">Logical connectives</a></li> <li><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional calculus</a></li> <li><a href="/wiki/Propositional_formula" title="Propositional formula">Propositional formula</a></li> <li><a href="/wiki/Truth_table" title="Truth table">Truth tables</a></li> <li><a href="/wiki/Many-valued_logic" title="Many-valued logic">Many-valued logic</a> <ul><li><a href="/wiki/Three-valued_logic" title="Three-valued logic">3</a></li> <li><a href="/wiki/Finite-valued_logic" title="Finite-valued logic">finite</a></li> <li><a href="/wiki/Infinite-valued_logic" title="Infinite-valued logic">∞</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">Predicate</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/First-order_logic" title="First-order logic">First-order</a> <ul><li><a href="/wiki/List_of_first-order_theories" title="List of first-order theories"><span style="font-size:85%;">list</span></a></li></ul></li> <li><a href="/wiki/Second-order_logic" title="Second-order logic">Second-order</a> <ul><li><a href="/wiki/Monadic_second-order_logic" title="Monadic second-order logic">Monadic</a></li></ul></li> <li><a href="/wiki/Higher-order_logic" title="Higher-order logic">Higher-order</a></li> <li><a href="/wiki/Fixed-point_logic" title="Fixed-point logic">Fixed-point</a></li> <li><a href="/wiki/Free_logic" title="Free logic">Free</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantifiers</a></li> <li><a href="/wiki/Predicate_(mathematical_logic)" title="Predicate (mathematical logic)">Predicate</a></li> <li><a href="/wiki/Monadic_predicate_calculus" title="Monadic predicate calculus">Monadic predicate calculus</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Set_theory" title="Set theory">Set theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Set</a> <ul><li><a href="/wiki/Hereditary_set" title="Hereditary set">hereditary</a></li></ul></li> <li><a href="/wiki/Class_(set_theory)" title="Class (set theory)">Class</a></li> <li>(<a href="/wiki/Urelement" title="Urelement">Ur-</a>)<a href="/wiki/Element_(mathematics)" title="Element (mathematics)">Element</a></li> <li><a href="/wiki/Ordinal_number" title="Ordinal number">Ordinal number</a></li> <li><a href="/wiki/Extensionality" title="Extensionality">Extensionality</a></li> <li><a href="/wiki/Forcing_(mathematics)" title="Forcing (mathematics)">Forcing</a></li> <li><a href="/wiki/Relation_(mathematics)" title="Relation (mathematics)">Relation</a> <ul><li><a href="/wiki/Equivalence_relation" title="Equivalence relation">equivalence</a></li> <li><a href="/wiki/Partition_of_a_set" title="Partition of a set">partition</a></li></ul></li> <li>Set operations: <ul><li><a href="/wiki/Intersection_(set_theory)" title="Intersection (set theory)">intersection</a></li> <li><a href="/wiki/Union_(set_theory)" title="Union (set theory)">union</a></li> <li><a href="/wiki/Complement_(set_theory)" title="Complement (set theory)">complement</a></li> <li><a href="/wiki/Cartesian_product" title="Cartesian product">Cartesian product</a></li> <li><a href="/wiki/Power_set" title="Power set">power set</a></li> <li><a href="/wiki/List_of_set_identities_and_relations" title="List of set identities and relations">identities</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">sets</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Countable_set" title="Countable set">Countable</a></li> <li><a href="/wiki/Uncountable_set" title="Uncountable set">Uncountable</a></li> <li><a href="/wiki/Empty_set" title="Empty set">Empty</a></li> <li><a href="/wiki/Inhabited_set" title="Inhabited set">Inhabited</a></li> <li><a href="/wiki/Singleton_(mathematics)" title="Singleton (mathematics)">Singleton</a></li> <li><a href="/wiki/Finite_set" title="Finite set">Finite</a></li> <li><a href="/wiki/Infinite_set" title="Infinite set">Infinite</a></li> <li><a href="/wiki/Transitive_set" title="Transitive set">Transitive</a></li> <li><a href="/wiki/Ultrafilter_(set_theory)" class="mw-redirect" title="Ultrafilter (set theory)">Ultrafilter</a></li> <li><a href="/wiki/Recursive_set" class="mw-redirect" title="Recursive set">Recursive</a></li> <li><a href="/wiki/Fuzzy_set" title="Fuzzy set">Fuzzy</a></li> <li><a href="/wiki/Universal_set" title="Universal set">Universal</a></li> <li><a href="/wiki/Universe_(mathematics)" title="Universe (mathematics)">Universe</a> <ul><li><a href="/wiki/Constructible_universe" title="Constructible universe">constructible</a></li> <li><a href="/wiki/Grothendieck_universe" title="Grothendieck universe">Grothendieck</a></li> <li><a href="/wiki/Von_Neumann_universe" title="Von Neumann universe">Von Neumann</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_(mathematics)" title="Map (mathematics)">Maps</a> and <a href="/wiki/Cardinality" title="Cardinality">cardinality</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Function_(mathematics)" title="Function (mathematics)">Function</a>/<a href="/wiki/Map_(mathematics)" title="Map (mathematics)">Map</a> <ul><li><a href="/wiki/Domain_of_a_function" title="Domain of a function">domain</a></li> <li><a href="/wiki/Codomain" title="Codomain">codomain</a></li> <li><a href="/wiki/Image_(mathematics)" title="Image (mathematics)">image</a></li></ul></li> <li><a href="/wiki/Injective_function" title="Injective function">In</a>/<a href="/wiki/Surjective_function" title="Surjective function">Sur</a>/<a href="/wiki/Bijection" title="Bijection">Bi</a>-jection</li> <li><a href="/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem" title="Schröder–Bernstein theorem">Schröder–Bernstein theorem</a></li> <li><a href="/wiki/Isomorphism" title="Isomorphism">Isomorphism</a></li> <li><a href="/wiki/G%C3%B6del_numbering" title="Gödel numbering">Gödel numbering</a></li> <li><a href="/wiki/Enumeration" title="Enumeration">Enumeration</a></li> <li><a href="/wiki/Large_cardinal" title="Large cardinal">Large cardinal</a> <ul><li><a href="/wiki/Inaccessible_cardinal" title="Inaccessible cardinal">inaccessible</a></li></ul></li> <li><a href="/wiki/Aleph_number" title="Aleph number">Aleph number</a></li> <li><a href="/wiki/Operation_(mathematics)" title="Operation (mathematics)">Operation</a> <ul><li><a href="/wiki/Binary_operation" title="Binary operation">binary</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Set theories</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Zermelo–Fraenkel</a> <ul><li><a href="/wiki/Axiom_of_choice" title="Axiom of choice">axiom of choice</a></li> <li><a href="/wiki/Continuum_hypothesis" title="Continuum hypothesis">continuum hypothesis</a></li></ul></li> <li><a href="/wiki/General_set_theory" title="General set theory">General</a></li> <li><a href="/wiki/Kripke%E2%80%93Platek_set_theory" title="Kripke–Platek set theory">Kripke–Platek</a></li> <li><a href="/wiki/Morse%E2%80%93Kelley_set_theory" title="Morse–Kelley set theory">Morse–Kelley</a></li> <li><a href="/wiki/Naive_set_theory" title="Naive set theory">Naive</a></li> <li><a href="/wiki/New_Foundations" title="New Foundations">New Foundations</a></li> <li><a href="/wiki/Tarski%E2%80%93Grothendieck_set_theory" title="Tarski–Grothendieck set theory">Tarski–Grothendieck</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory" title="Von Neumann–Bernays–Gödel set theory">Von Neumann–Bernays–Gödel</a></li> <li><a href="/wiki/Ackermann_set_theory" title="Ackermann set theory">Ackermann</a></li> <li><a href="/wiki/Constructive_set_theory" title="Constructive set theory">Constructive</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Formal_system" title="Formal system">Formal systems</a> (<a href="/wiki/List_of_formal_systems" title="List of formal systems"><span style="font-size:85%;">list</span></a>),<br /><a href="/wiki/Formal_language" title="Formal language">language</a> and <a href="/wiki/Syntax_(logic)" title="Syntax (logic)">syntax</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alphabet_(formal_languages)" title="Alphabet (formal languages)">Alphabet</a></li> <li><a href="/wiki/Arity" title="Arity">Arity</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata</a></li> <li><a href="/wiki/Axiom_schema" title="Axiom schema">Axiom schema</a></li> <li><a href="/wiki/Expression_(mathematics)" title="Expression (mathematics)">Expression</a> <ul><li><a href="/wiki/Ground_expression" title="Ground expression">ground</a></li></ul></li> <li><a href="/wiki/Extension_by_new_constant_and_function_names" title="Extension by new constant and function names">Extension</a> <ul><li><a href="/wiki/Extension_by_definitions" title="Extension by definitions">by definition</a></li> <li><a href="/wiki/Conservative_extension" title="Conservative extension">conservative</a></li></ul></li> <li><a href="/wiki/Finitary_relation" title="Finitary relation">Relation</a></li> <li><a href="/wiki/Formation_rule" title="Formation rule">Formation rule</a></li> <li><a href="/wiki/Formal_grammar" title="Formal grammar">Grammar</a></li> <li><a href="/wiki/Well-formed_formula" title="Well-formed formula">Formula</a> <ul><li><a href="/wiki/Atomic_formula" title="Atomic formula">atomic</a></li> <li><a href="/wiki/Sentence_(mathematical_logic)" title="Sentence (mathematical logic)">closed</a></li> <li><a href="/wiki/Ground_formula" class="mw-redirect" title="Ground formula">ground</a></li> <li><a href="/wiki/Open_formula" title="Open formula">open</a></li></ul></li> <li><a href="/wiki/Free_variables_and_bound_variables" title="Free variables and bound variables">Free/bound variable</a></li> <li><a href="/wiki/Formal_language" title="Formal language">Language</a></li> <li><a href="/wiki/Metalanguage" title="Metalanguage">Metalanguage</a></li> <li><a href="/wiki/Logical_connective" title="Logical connective">Logical connective</a> <ul><li><a href="/wiki/Negation" title="Negation">¬</a></li> <li><a href="/wiki/Logical_disjunction" title="Logical disjunction">∨</a></li> <li><a href="/wiki/Logical_conjunction" title="Logical conjunction">∧</a></li> <li><a href="/wiki/Material_conditional" title="Material conditional">→</a></li> <li><a href="/wiki/Logical_biconditional" title="Logical biconditional">↔</a></li> <li><a href="/wiki/Logical_equality" title="Logical equality">=</a></li></ul></li> <li><a href="/wiki/Predicate_(mathematical_logic)" title="Predicate (mathematical logic)">Predicate</a> <ul><li><a href="/wiki/Functional_predicate" title="Functional predicate">functional</a></li> <li><a href="/wiki/Predicate_variable" title="Predicate variable">variable</a></li> <li><a href="/wiki/Propositional_variable" title="Propositional variable">propositional variable</a></li></ul></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Proof</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantifier</a> <ul><li><a href="/wiki/Existential_quantification" title="Existential quantification">∃</a></li> <li><a href="/wiki/Uniqueness_quantification" title="Uniqueness quantification">!</a></li> <li><a href="/wiki/Universal_quantification" title="Universal quantification">∀</a></li> <li><a href="/wiki/Quantifier_rank" title="Quantifier rank">rank</a></li></ul></li> <li><a href="/wiki/Sentence_(mathematical_logic)" title="Sentence (mathematical logic)">Sentence</a> <ul><li><a href="/wiki/Atomic_sentence" title="Atomic sentence">atomic</a></li> <li><a href="/wiki/Spectrum_of_a_sentence" title="Spectrum of a sentence">spectrum</a></li></ul></li> <li><a href="/wiki/Signature_(logic)" title="Signature (logic)">Signature</a></li> <li><a href="/wiki/String_(formal_languages)" class="mw-redirect" title="String (formal languages)">String</a></li> <li><a href="/wiki/Substitution_(logic)" title="Substitution (logic)">Substitution</a></li> <li><a href="/wiki/Symbol_(formal)" title="Symbol (formal)">Symbol</a> <ul><li><a href="/wiki/Uninterpreted_function" title="Uninterpreted function">function</a></li> <li><a href="/wiki/Logical_constant" title="Logical constant">logical/constant</a></li> <li><a href="/wiki/Non-logical_symbol" title="Non-logical symbol">non-logical</a></li> <li><a href="/wiki/Variable_(mathematics)" title="Variable (mathematics)">variable</a></li></ul></li> <li><a href="/wiki/Term_(logic)" title="Term (logic)">Term</a></li> <li><a href="/wiki/Theory_(mathematical_logic)" title="Theory (mathematical logic)">Theory</a> <ul><li><a href="/wiki/List_of_mathematical_theories" title="List of mathematical theories"><span style="font-size:85%;">list</span></a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="nowrap">Example <a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic<br />systems</a> <span style="font-size:85%;">(<a href="/wiki/List_of_first-order_theories" title="List of first-order theories">list</a>)</span></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>of <a href="/wiki/True_arithmetic" title="True arithmetic">arithmetic</a>: <ul><li><a href="/wiki/Peano_axioms" title="Peano axioms">Peano</a></li> <li><a href="/wiki/Second-order_arithmetic" title="Second-order arithmetic">second-order</a></li> <li><a href="/wiki/Elementary_function_arithmetic" title="Elementary function arithmetic">elementary function</a></li> <li><a href="/wiki/Primitive_recursive_arithmetic" title="Primitive recursive arithmetic">primitive recursive</a></li> <li><a href="/wiki/Robinson_arithmetic" title="Robinson arithmetic">Robinson</a></li> <li><a href="/wiki/Skolem_arithmetic" title="Skolem arithmetic">Skolem</a></li></ul></li> <li>of the <a href="/wiki/Construction_of_the_real_numbers" title="Construction of the real numbers">real numbers</a> <ul><li><a href="/wiki/Tarski%27s_axiomatization_of_the_reals" title="Tarski's axiomatization of the reals">Tarski's axiomatization</a></li></ul></li> <li>of <a href="/wiki/Axiomatization_of_Boolean_algebras" class="mw-redirect" title="Axiomatization of Boolean algebras">Boolean algebras</a> <ul><li><a href="/wiki/Boolean_algebras_canonically_defined" title="Boolean algebras canonically defined">canonical</a></li> <li><a href="/wiki/Minimal_axioms_for_Boolean_algebra" title="Minimal axioms for Boolean algebra">minimal axioms</a></li></ul></li> <li>of <a href="/wiki/Foundations_of_geometry" title="Foundations of geometry">geometry</a>: <ul><li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean</a>: <ul><li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i></a></li> <li><a href="/wiki/Hilbert%27s_axioms" title="Hilbert's axioms">Hilbert's</a></li> <li><a href="/wiki/Tarski%27s_axioms" title="Tarski's axioms">Tarski's</a></li></ul></li> <li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean</a></li></ul></li></ul> <ul><li><i><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proof_theory" title="Proof theory">Proof theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Formal_proof" title="Formal proof">Formal proof</a></li> <li><a href="/wiki/Natural_deduction" title="Natural deduction">Natural deduction</a></li> <li><a href="/wiki/Logical_consequence" title="Logical consequence">Logical consequence</a></li> <li><a href="/wiki/Rule_of_inference" title="Rule of inference">Rule of inference</a></li> <li><a href="/wiki/Sequent_calculus" title="Sequent calculus">Sequent calculus</a></li> <li><a href="/wiki/Theorem" title="Theorem">Theorem</a></li> <li><a href="/wiki/Formal_system" title="Formal system">Systems</a> <ul><li><a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic</a></li> <li><a href="/wiki/Deductive_system" class="mw-redirect" title="Deductive system">deductive</a></li> <li><a href="/wiki/Hilbert_system" title="Hilbert system">Hilbert</a> <ul><li><a href="/wiki/List_of_Hilbert_systems" class="mw-redirect" title="List of Hilbert systems">list</a></li></ul></li></ul></li> <li><a href="/wiki/Complete_theory" title="Complete theory">Complete theory</a></li> <li><a href="/wiki/Independence_(mathematical_logic)" title="Independence (mathematical logic)">Independence</a> (<a href="/wiki/List_of_statements_independent_of_ZFC" title="List of statements independent of ZFC">from ZFC</a>)</li> <li><a href="/wiki/Proof_of_impossibility" title="Proof of impossibility">Proof of impossibility</a></li> <li><a href="/wiki/Ordinal_analysis" title="Ordinal analysis">Ordinal analysis</a></li> <li><a href="/wiki/Reverse_mathematics" title="Reverse mathematics">Reverse mathematics</a></li> <li><a href="/wiki/Self-verifying_theories" title="Self-verifying theories">Self-verifying theories</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Model_theory" title="Model theory">Model theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Interpretation_(logic)" title="Interpretation (logic)">Interpretation</a> <ul><li><a href="/wiki/Interpretation_function" class="mw-redirect" title="Interpretation function">function</a></li> <li><a href="/wiki/Interpretation_(model_theory)" title="Interpretation (model theory)">of models</a></li></ul></li> <li><a href="/wiki/Structure_(mathematical_logic)" title="Structure (mathematical logic)">Model</a> <ul><li><a href="/wiki/Elementary_equivalence" title="Elementary equivalence">equivalence</a></li> <li><a href="/wiki/Finite_model_theory" title="Finite model theory">finite</a></li> <li><a href="/wiki/Saturated_model" title="Saturated model">saturated</a></li> <li><a href="/wiki/Spectrum_of_a_theory" title="Spectrum of a theory">spectrum</a></li> <li><a href="/wiki/Substructure_(mathematics)" title="Substructure (mathematics)">submodel</a></li></ul></li> <li><a href="/wiki/Non-standard_model" title="Non-standard model">Non-standard model</a> <ul><li><a href="/wiki/Non-standard_model_of_arithmetic" title="Non-standard model of arithmetic">of arithmetic</a></li></ul></li> <li><a href="/wiki/Diagram_(mathematical_logic)" title="Diagram (mathematical logic)">Diagram</a> <ul><li><a href="/wiki/Elementary_diagram" title="Elementary diagram">elementary</a></li></ul></li> <li><a href="/wiki/Categorical_theory" title="Categorical theory">Categorical theory</a></li> <li><a href="/wiki/Model_complete_theory" title="Model complete theory">Model complete theory</a></li> <li><a href="/wiki/Satisfiability" title="Satisfiability">Satisfiability</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li> <li><a href="/wiki/Strength_(mathematical_logic)" title="Strength (mathematical logic)">Strength</a></li> <li><a href="/wiki/Theories_of_truth" class="mw-redirect" title="Theories of truth">Theories of truth</a> <ul><li><a href="/wiki/Semantic_theory_of_truth" title="Semantic theory of truth">semantic</a></li> <li><a href="/wiki/Tarski%27s_theory_of_truth" class="mw-redirect" title="Tarski's theory of truth">Tarski's</a></li> <li><a href="/wiki/Kripke%27s_theory_of_truth" class="mw-redirect" title="Kripke's theory of truth">Kripke's</a></li></ul></li> <li><a href="/wiki/T-schema" title="T-schema">T-schema</a></li> <li><a href="/wiki/Transfer_principle" title="Transfer principle">Transfer principle</a></li> <li><a href="/wiki/Truth_predicate" title="Truth predicate">Truth predicate</a></li> <li><a href="/wiki/Truth_value" title="Truth value">Truth value</a></li> <li><a href="/wiki/Type_(model_theory)" title="Type (model theory)">Type</a></li> <li><a href="/wiki/Ultraproduct" title="Ultraproduct">Ultraproduct</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity (logic)">Validity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computability_theory" title="Computability theory">Computability theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Church_encoding" title="Church encoding">Church encoding</a></li> <li><a href="/wiki/Church%E2%80%93Turing_thesis" title="Church–Turing 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 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