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<span>René Descartes</span> </div> </a> <ul id="toc-René_Descartes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gottfried_Leibniz" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gottfried_Leibniz"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Gottfried Leibniz</span> </div> </a> <button aria-controls="toc-Gottfried_Leibniz-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Gottfried Leibniz subsection</span> </button> <ul id="toc-Gottfried_Leibniz-sublist" class="vector-toc-list"> <li id="toc-Ars_inveniendi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ars_inveniendi"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span><i>Ars inveniendi</i></span> </div> </a> <ul id="toc-Ars_inveniendi-sublist" 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<div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Philosophy that mathematics can be used to define all aspects of the universe</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wallis_-_Opera_mathematica,_1657_-_4611280.tif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Wallis_-_Opera_mathematica%2C_1657_-_4611280.tif/lossless-page1-200px-Wallis_-_Opera_mathematica%2C_1657_-_4611280.tif.png" decoding="async" width="200" height="271" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Wallis_-_Opera_mathematica%2C_1657_-_4611280.tif/lossless-page1-300px-Wallis_-_Opera_mathematica%2C_1657_-_4611280.tif.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/Wallis_-_Opera_mathematica%2C_1657_-_4611280.tif/lossless-page1-400px-Wallis_-_Opera_mathematica%2C_1657_-_4611280.tif.png 2x" data-file-width="2060" data-file-height="2796" /></a><figcaption><a href="/wiki/Book_frontispiece" title="Book frontispiece">Frontispiece</a> of <i>Operum Mathematicorum Pars Prima</i> (1657) by <a href="/wiki/John_Wallis" title="John Wallis">John Wallis</a>, the first volume of <i>Opera Mathematica</i> including a chapter entitled <i>Mathesis Universalis</i>.</figcaption></figure> <p><b><span title="Latin-language text"><i lang="la">Mathesis universalis</i></span></b> (from <a href="/wiki/Greek_language" title="Greek language">Greek</a>: <span lang="el">μάθησις</span>, <span title="Greek-language romanization"><i lang="el-Latn">mathesis</i></span> "science or learning", and <a href="/wiki/Latin_language" class="mw-redirect" title="Latin language">Latin</a>: <i lang="la">universalis</i> "universal") is a hypothetical <a href="/wiki/Universal_science" title="Universal science">universal science</a> modelled on <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> envisaged by <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a> and <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a>, among a number of other 16th- and 17th-century philosophers and mathematicians. For Leibniz, it would be supported by a <i><a href="/wiki/Calculus_ratiocinator" title="Calculus ratiocinator">calculus ratiocinator</a></i>. <a href="/wiki/John_Wallis" title="John Wallis">John Wallis</a> invokes the name as title in his <i>Opera Mathematica</i>, a textbook on <a href="/wiki/Arithmetic" title="Arithmetic">arithmetic</a>, <a href="/wiki/Algebra" title="Algebra">algebra</a>, and <a href="/wiki/Cartesian_geometry" class="mw-redirect" title="Cartesian geometry">Cartesian geometry</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=1" title="Edit section: History"><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:Roomen_-_Universae_mathesis_idea,_1602_-_151336.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Roomen_-_Universae_mathesis_idea%2C_1602_-_151336.jpg/200px-Roomen_-_Universae_mathesis_idea%2C_1602_-_151336.jpg" decoding="async" width="200" height="313" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Roomen_-_Universae_mathesis_idea%2C_1602_-_151336.jpg/300px-Roomen_-_Universae_mathesis_idea%2C_1602_-_151336.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Roomen_-_Universae_mathesis_idea%2C_1602_-_151336.jpg/400px-Roomen_-_Universae_mathesis_idea%2C_1602_-_151336.jpg 2x" data-file-width="2195" data-file-height="3436" /></a><figcaption>Frontispiece of <i>Universae mathesis idea</i> (1602) by <a href="/wiki/Adriaan_van_Roomen" title="Adriaan van Roomen">Adriaan van Roomen</a></figcaption></figure> <p>Descartes' most explicit description of <i>mathesis universalis</i> occurs in <i>Rule Four</i> of the <i><a href="/wiki/Rules_for_the_Direction_of_the_Mind" title="Rules for the Direction of the Mind">Rules for the Direction of the Mind</a></i>, written before 1628.<sup id="cite_ref-FOOTNOTESasaki2003359_1-0" class="reference"><a href="#cite_note-FOOTNOTESasaki2003359-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Leibniz attempted to work out the possible connections between <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a>, <a href="/wiki/Algebra" title="Algebra">algebra</a>, <a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">infinitesimal calculus</a>, <a href="/wiki/Combinatorics" title="Combinatorics">combinatorics</a>, and <a href="/wiki/Characteristica_universalis" title="Characteristica universalis">universal characteristics</a> in an incomplete treatise titled "<i>Mathesis Universalis</i>" in 1695. </p><p><a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">Predicate logic</a> could be seen as a modern system with some of these <i>universal</i> qualities, at least as far as mathematics and <a href="/wiki/Computer_science" title="Computer science">computer science</a> are concerned. More generally, <i>mathesis universalis</i>, along with perhaps <a href="/wiki/Fran%C3%A7ois_Vi%C3%A8te" title="François Viète">François Viète</a>'s <a href="/wiki/Algebra" title="Algebra">algebra</a>, represents one of the earliest attempts to construct a <a href="/wiki/Formal_system" title="Formal system">formal system</a>. </p><p> One of the perhaps most prominent critics of the idea of <i>mathesis universalis</i> was <a href="/wiki/Ludwig_Wittgenstein%27s_philosophy_of_mathematics" title="Ludwig Wittgenstein's philosophy of mathematics">Ludwig Wittgenstein and his philosophy of mathematics</a>.<sup id="cite_ref-FOOTNOTERhees1970_2-0" class="reference"><a href="#cite_note-FOOTNOTERhees1970-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> As Anthropologist Emily Martin notes:<sup id="cite_ref-FOOTNOTEMartin2013_3-0" class="reference"><a href="#cite_note-FOOTNOTEMartin2013-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style></p><blockquote class="templatequote"><p>Tackling mathematics, the realm of symbolic life perhaps most difficult to regard as contingent on social norms, Wittgenstein commented that people found the idea that numbers rested on conventional social understandings "unbearable".</p></blockquote> <div class="mw-heading mw-heading2"><h2 id="René_Descartes"><span id="Ren.C3.A9_Descartes"></span>René Descartes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=2" title="Edit section: René Descartes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> In Descartes' corpus the term <i>mathesis universalis</i> appears only in the <i><a href="/wiki/Rules_for_the_Direction_of_the_Mind" title="Rules for the Direction of the Mind">Rules for the Direction of the Mind</a></i>.<sup id="cite_ref-FOOTNOTESasaki2003359_1-1" class="reference"><a href="#cite_note-FOOTNOTESasaki2003359-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In the discussion of <i>Rule Four</i>, Descartes' provides his clearest description of <i>mathesis universalis</i>:<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"> <dl><dt>Rule Four</dt> <dt>We need a method if we are to investigate the truth of things.</dt></dl> <p>[...] I began my investigation by inquiring what exactly is generally meant by the term 'mathematics' and why it is that, in addition to arithmetic and geometry, sciences such as astronomy, music, optics, mechanics, among others, are called branches of mathematics. [...] This made me realize that there must be a general science which explains all the points that can be raised concerning order and measure irrespective of the subject-matter, and that this science should be termed <i><b>mathesis universalis</b></i> — a venerable term with a well-established meaning — for it covers everything that entitles these other sciences to be called branches of mathematics. [...] </p> <div class="templatequotecite">— <cite><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a>, <i><a href="/wiki/Rules_for_the_Direction_of_the_Mind" title="Rules for the Direction of the Mind">Rules for the Direction of the Mind</a></i>; translated by <a href="/wiki/John_Cottingham" title="John Cottingham">John Cottingham</a><sup id="cite_ref-FOOTNOTEDescartes198519–20_4-0" class="reference"><a href="#cite_note-FOOTNOTEDescartes198519–20-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></cite></div></blockquote> <div class="mw-heading mw-heading2"><h2 id="Gottfried_Leibniz">Gottfried Leibniz</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=3" title="Edit section: Gottfried Leibniz"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In his account of <i>mathesis universalis</i>, Leibniz proposed a dual method of universal synthesis and analysis for the ascertaining <a href="/wiki/Truth" title="Truth">truth</a>, described in <i>De Synthesi et Analysi universale seu Arte inveniendi et judicandi</i> (1890).<sup id="cite_ref-FOOTNOTESasaki2003_5-0" class="reference"><a href="#cite_note-FOOTNOTESasaki2003-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEMarciszewski1984_6-0" class="reference"><a href="#cite_note-FOOTNOTEMarciszewski1984-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ars_inveniendi"><i>Ars inveniendi</i></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=4" title="Edit section: Ars inveniendi"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Ars inveniendi</i> (<a href="/wiki/Latin" title="Latin">Latin</a> for "art of invention") is the constituent part of <i>mathesis universalis</i> corresponding to the method of synthesis.<sup id="cite_ref-FOOTNOTESasaki2003_5-1" class="reference"><a href="#cite_note-FOOTNOTESasaki2003-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEMarciszewski1984_6-1" class="reference"><a href="#cite_note-FOOTNOTEMarciszewski1984-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ars_combinatoria"><i>Ars combinatoria</i></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=5" title="Edit section: Ars combinatoria"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Leibniz also identified synthesis with the <i><a href="/wiki/De_Arte_Combinatoria" title="De Arte Combinatoria">ars combinatoria</a></i>, viewing it in terms of the recombination of symbols or human thoughts.<sup id="cite_ref-FOOTNOTESasaki2003_5-2" class="reference"><a href="#cite_note-FOOTNOTESasaki2003-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ars_judicandi"><i>Ars judicandi</i></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=6" title="Edit section: Ars judicandi"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Ars judicandi</i> (<a href="/wiki/Latin" title="Latin">Latin</a> for "art of judgement") is the constituent part of <i>mathesis universalis</i> corresponding to the method of analysis.<sup id="cite_ref-FOOTNOTESasaki2003_5-3" class="reference"><a href="#cite_note-FOOTNOTESasaki2003-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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: 15em;"> <ul><li><i><a href="/wiki/Characteristica_universalis" title="Characteristica universalis">Characteristica universalis</a></i></li> <li><i><a href="/wiki/De_Arte_Combinatoria" title="De Arte Combinatoria">De Arte Combinatoria</a></i></li> <li><i><a href="/wiki/An_Essay_towards_a_Real_Character,_and_a_Philosophical_Language" class="mw-redirect" title="An Essay towards a Real Character, and a Philosophical Language">An Essay towards a Real Character, and a Philosophical Language</a></i></li> <li><i><a href="/wiki/Lingua_generalis" title="Lingua generalis">Lingua generalis</a></i></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 15em;"> <ol class="references"> <li id="cite_note-FOOTNOTESasaki2003359-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESasaki2003359_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESasaki2003359_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSasaki2003">Sasaki (2003)</a>, p. 359.</span> </li> <li id="cite_note-FOOTNOTERhees1970-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERhees1970_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRhees1970">Rhees (1970)</a>.</span> </li> <li id="cite_note-FOOTNOTEMartin2013-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMartin2013_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMartin2013">Martin (2013)</a>.</span> </li> <li id="cite_note-FOOTNOTEDescartes198519–20-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDescartes198519–20_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDescartes1985">Descartes (1985)</a>, pp. 19–20.</span> </li> <li id="cite_note-FOOTNOTESasaki2003-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESasaki2003_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESasaki2003_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTESasaki2003_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTESasaki2003_5-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSasaki2003">Sasaki (2003)</a>.</span> </li> <li id="cite_note-FOOTNOTEMarciszewski1984-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEMarciszewski1984_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEMarciszewski1984_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFMarciszewski1984">Marciszewski (1984)</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Mathesis_universalis&action=edit&section=9" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFFoucault2010" class="citation book cs1">Foucault, Michel (2010). <i>The Order of Things: an archaeology of the human sciences</i>. London: Routledge.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Order+of+Things%3A+an+archaeology+of+the+human+sciences&rft.place=London&rft.pub=Routledge&rft.date=2010&rft.aulast=Foucault&rft.aufirst=Michel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMathesis+universalis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarciszewski1984" class="citation journal cs1">Marciszewski, Witold (1984). "The principle of comprehension as a present-day contribution to mathesis universalis". <i>Philosophia Naturalis</i> (21): 525–526.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophia+Naturalis&rft.atitle=The+principle+of+comprehension+as+a+present-day+contribution+to+mathesis+universalis&rft.issue=21&rft.pages=525-526&rft.date=1984&rft.aulast=Marciszewski&rft.aufirst=Witold&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMathesis+universalis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMartin2013" class="citation journal cs1">Martin, Emily (2013). "The Potentiality of Ethnography and the Limits of Affect Theory". <i>Current Anthropology</i>. <b>54</b> (S7): 156. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F670388">10.1086/670388</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:143944116">143944116</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Current+Anthropology&rft.atitle=The+Potentiality+of+Ethnography+and+the+Limits+of+Affect+Theory&rft.volume=54&rft.issue=S7&rft.pages=156&rft.date=2013&rft_id=info%3Adoi%2F10.1086%2F670388&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A143944116%23id-name%3DS2CID&rft.aulast=Martin&rft.aufirst=Emily&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMathesis+universalis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRhees1970" class="citation book cs1">Rhees, Rush (1970). <i>Discussions of Wittgenstein</i>. New York: Schocken.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discussions+of+Wittgenstein&rft.place=New+York&rft.pub=Schocken&rft.date=1970&rft.aulast=Rhees&rft.aufirst=Rush&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMathesis+universalis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSasaki2003" class="citation book cs1">Sasaki, Chikara (2003). "<span class="cs1-kern-left"></span>'Mathesis Universalis' in the Seventeenth Century". <i>Descartes's Mathematical Thought</i>. Boston Studies in the Philosophy of Science. Vol. 237. pp. 359–418. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-94-017-1225-5_10">10.1007/978-94-017-1225-5_10</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-481-6487-5" title="Special:BookSources/978-90-481-6487-5"><bdi>978-90-481-6487-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%27Mathesis+Universalis%27+in+the+Seventeenth+Century&rft.btitle=Descartes%27s+Mathematical+Thought&rft.series=Boston+Studies+in+the+Philosophy+of+Science&rft.pages=359-418&rft.date=2003&rft_id=info%3Adoi%2F10.1007%2F978-94-017-1225-5_10&rft.isbn=978-90-481-6487-5&rft.aulast=Sasaki&rft.aufirst=Chikara&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMathesis+universalis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDescartes1985" class="citation book cs1"><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes, René</a> (20 May 1985). "Rules for the Direction of the Mind". <i>The Philosophical Writings of Descartes</i>. Translated by <a href="/wiki/John_Cottingham" title="John Cottingham">Cottingham, John</a>. Cambridge University Press. pp. 7–78. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FCBO9780511805042.004">10.1017/CBO9780511805042.004</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Rules+for+the+Direction+of+the+Mind&rft.btitle=The+Philosophical+Writings+of+Descartes&rft.pages=7-78&rft.pub=Cambridge+University+Press&rft.date=1985-05-20&rft_id=info%3Adoi%2F10.1017%2FCBO9780511805042.004&rft.aulast=Descartes&rft.aufirst=Ren%C3%A9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMathesis+universalis" class="Z3988"></span></li></ul> </div> <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=Mathesis_universalis&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Raul Corazzon's Ontology web page: <a rel="nofollow" class="external text" href="https://www.ontology.co/mathesis-universalis.htm"><i>Mathesis Universalis</i> with a bibliography</a></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 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href="/wiki/Calculus_ratiocinator" title="Calculus ratiocinator">Calculus ratiocinator</a></i></li> <li><i><a href="/wiki/Characteristica_universalis" title="Characteristica universalis">Characteristica universalis</a></i></li> <li><a href="/wiki/Compossibility" title="Compossibility">Compossibility</a></li> <li><a href="/wiki/Difference_(philosophy)" title="Difference (philosophy)">Difference</a></li> <li><a href="/wiki/Dynamism_(metaphysics)" title="Dynamism (metaphysics)">Dynamism</a></li> <li><a href="/wiki/Identity_of_indiscernibles" title="Identity of indiscernibles">Identity of indiscernibles</a></li> <li><a href="/wiki/Individuation" title="Individuation">Individuation</a></li> <li><a href="/wiki/Law_of_continuity" title="Law of continuity">Law of continuity</a></li> <li><a href="/wiki/Leibniz_wheel" title="Leibniz wheel">Leibniz wheel</a></li> <li><a href="/wiki/Leibniz%27s_gap" title="Leibniz's gap">Leibniz's gap</a></li> <li><a href="/wiki/Leibniz%27s_notation" title="Leibniz's notation">Leibniz's notation</a></li> <li><i><a href="/wiki/Lingua_generalis" title="Lingua generalis">Lingua generalis</a></i></li> <li><i><a class="mw-selflink selflink">Mathesis universalis</a></i></li> <li><a href="/wiki/Pre-established_harmony" class="mw-redirect" title="Pre-established harmony">Pre-established harmony</a></li> <li><a href="/wiki/Principle_of_plenitude" title="Principle of plenitude">Plenitude</a></li> <li><a href="/wiki/Principle_of_sufficient_reason" title="Principle of sufficient reason">Sufficient reason</a></li> <li><i><a href="/wiki/Salva_veritate" title="Salva veritate">Salva veritate</a></i></li> <li><a href="/wiki/Theodicy" title="Theodicy">Theodicy</a></li> <li><a href="/wiki/Transcendental_law_of_homogeneity" title="Transcendental law of homogeneity">Transcendental law of homogeneity</a></li> <li><a href="/wiki/Rationalism" title="Rationalism">Rationalism</a></li> <li><a href="/wiki/Universal_science" title="Universal science">Universal science</a></li> <li><i><a href="/wiki/Vis_viva" title="Vis viva">Vis viva</a></i></li> <li><a href="/wiki/Well-founded_phenomenon" class="mw-redirect" title="Well-founded phenomenon">Well-founded phenomenon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/De_Arte_Combinatoria" title="De Arte Combinatoria">De Arte Combinatoria</a></i> <span style="font-size:85%;">(1666)</span></li> <li><i><a href="/wiki/Discourse_on_Metaphysics" title="Discourse on Metaphysics">Discourse on Metaphysics</a></i> <span style="font-size:85%;">(1686)</span></li> <li><i><a href="/wiki/New_Essays_on_Human_Understanding" title="New Essays on Human Understanding">New Essays on Human Understanding</a></i> <span style="font-size:85%;">(1704)</span></li> <li><i><a href="/wiki/Th%C3%A9odic%C3%A9e" title="Théodicée">Théodicée</a></i> <span style="font-size:85%;">(1710)</span></li> <li><i><a href="/wiki/Monadology" title="Monadology">Monadology</a></i> <span style="font-size:85%;">(1714)</span></li> <li><a href="/wiki/Leibniz%E2%80%93Clarke_correspondence" title="Leibniz–Clarke correspondence">Leibniz–Clarke correspondence</a> <span style="font-size:85%;">(1715–1716)</span></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" 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<li><a href="/wiki/History_of_pseudoscience" title="History of pseudoscience">Pseudoscience</a></li> <li><a href="/wiki/History_and_philosophy_of_science" title="History and philosophy of science">History and philosophy of science</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="8" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Johannes-kepler-tabulae-rudolphinae-google-arts-culture.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Johannes-kepler-tabulae-rudolphinae-google-arts-culture.jpg/80px-Johannes-kepler-tabulae-rudolphinae-google-arts-culture.jpg" decoding="async" width="80" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Johannes-kepler-tabulae-rudolphinae-google-arts-culture.jpg/120px-Johannes-kepler-tabulae-rudolphinae-google-arts-culture.jpg 1.5x, 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title="Scientific Revolution">Scientific Revolution</a></li> <li><a href="/wiki/Science_in_the_Age_of_Enlightenment" title="Science in the Age of Enlightenment">Age of Enlightenment</a></li> <li><a href="/wiki/Romanticism_in_science" title="Romanticism in science">Romanticism</a></li> <li><a href="/wiki/19th_century_in_science" title="19th century in science">19th century in science</a></li> <li><a href="/wiki/20th_century_in_science" title="20th century in science">20th century in science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By culture</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_science_and_technology_in_Africa" title="History of science and technology in Africa">African</a></li> <li><a href="/wiki/History_of_science_and_technology_in_Argentina" title="History of science and technology in Argentina">Argentine</a></li> <li><a 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