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<div class="topSearch-container"> <input id="topSearch" autocomplete="off" class="topSearch form-control input-lg" type="text" name="searchStr" style="color:black" onfocus="if (this.value == 'search for..') {this.value = '';this.style.color='black'}" value="" placeholder="Search PhilPapers"> </div> </form> </li> <li><a href="/web/20210826125148/https://philpapers.org/help/search.html">Syntax</a></li> <li><a href="/web/20210826125148/https://philpapers.org/advanced.html">Advanced Search</a></li> </ul> </div> </div> </div> </div> <script type="text/javascript"> $j(document).ready(ppTypeahead.initialize(".topSearch")); </script> <div id="contentContainer" class=" container panel panel-default"> <div id="content"> <div class="cattop"> <div style="float:right;width:250px;" class="hidden-xs"> <a class="addthis_button" href="https://web.archive.org/web/20210826125148/https://www.addthis.com/bookmark.php?v=250&username=dbourget"><img src="https://web.archive.org/web/20210826125148im_/https://s7.addthis.com/static/btn/v2/lg-share-en.gif" width="125" height="16" alt="Bookmark and Share" style="border:0"/></a><script type="text/javascript" src="https://web.archive.org/web/20210826125148js_/https://s7.addthis.com/js/250/addthis_widget.js#username=dbourget"></script> </div> <div class="ch" style="margin-left:0;font-size:11px;margin-bottom:10px"></div> <h1 class="gh"><a href="/web/20210826125148/https://philpapers.org/browse/philosophy-of-mathematics">Philosophy of Mathematics</a> </h1> <div style="font-size:12px;color:#333;font-weight:bold;margin-bottom:10px;"> Edited by <a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/oystein-linnebo">Øystein Linnebo</a> <span class="affils">(<span class="affil">University of Oslo</span>)</span> </div> <div style="font-size:12px;color:#333;margin-bottom:10px;"> Assistant editor: <a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/sam-roberts-1">Sam Roberts</a> <span class="affils">(<span class="affil">Universität Konstanz</span>)</span> </div> </div> <div class="miniheader" style="font-weight:bold;border-top:1px solid #aaa">About this topic </div> <div class="summaries"> <table class="responsive nospace" style="margin-bottom:10px;width:80%"> <tr> <td style="font-size:12px;width:90px" valign="top"><em>Summary</em></td> <td style="padding-bottom:10px"><p>The philosophy of mathematics studies the nature of mathematical truth, mathematical proof, mathematical evidence, mathematical practice, and mathematical explanation. </p> <p>Three philosophical views of mathematics are widely regarded as the ‘classic’ ones. <em>Logicism</em> holds that mathematics is reducible to principles of pure logic. <em>Intuitionism</em> holds that mathematics is concerned with mental constructions and defends a revision of classical mathematics and logic. Finally, <em>formalism</em> is the view that much or all of mathematics is devoid of content and a purely formal study of strings of mathematical language.  </p> <p>In recent decades, some new views have entered the fray. An important newer arrival is <em>structuralism</em>, which holds that mathematics is the study of abstract structures. A <em>non-eliminative</em> version of structuralism holds that there exist such things as abstract structures, whereas an <em>eliminative</em> version tries to make do with concrete objects variously structured. <em>Nominalism</em> denies that there are any abstract mathematical objects and tries to reconstruct classical mathematics accordingly. <em>Fictionalism</em> is based on the idea that, although most mathematical theorems are literally false, there is a non-literal (or fictional) sense in which assertions of them nevertheless count as correct. <em>Mathematical naturalism </em>urges that mathematics be taken as a <em>sui generis</em> discipline in good scientific standing. </p></td> </tr> </table> <table class="responsive nospace" style="margin-bottom:10px;width:80%"> <tr> <td style="font-size:12px;width:90px" valign="top"><em>Key works</em></td> <td> On the more traditional views, it is hard to beat the selection of readings in <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/BENPOM">Benacerraf & Putnam 1964</a>. Non-eliminative structuralism is defended in <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/RESMAA-3">Resnik 1997</a>, <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/SHAPOM-4">Shapiro 1997</a>, and <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/PARMTA">Parsons 2007</a>. A modal version of eliminative structuralism derives from <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/PUTMWF">Putnam 1967</a> and is developed in <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/HELMWN">Hellman 1989</a>. Two classic defenses of logicism are <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/FRETFO-2">Frege 1953</a> and <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/RUSITM">Russell 1919</a>. A neo-Fregean programme was initiated in <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/WRIFCO">Wright 1983</a>; see the essays collected in <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/HALI">Hale & Wright 2001</a> and, for critical discussion, <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/DUMF">Dummett 1991</a>. Nominalism is often driven by the epistemic challenge due to <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/BENMT">Benacerraf 1973</a> and <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/FIERM">Field 1989</a>, ch. 1 and 7. Field’s classic attempt to vindicate nominalism is <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/FIESWN-2">Field 1980</a>. For a comprehensive overview of the subject, see <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/BURASW">Burgess & Rosen 1997</a>. On fictionalism, see <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/YABTPO-2">Yablo 2010</a>. The indispensability argument derives from Quine but crystallized in <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/PUTPOL">Putnam 1971</a>; for a recent defense, see <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/COLTIO-3">Colyvan 2001</a>. On mathematical naturalism, see <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/MADNIM">Maddy 1997</a> and <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/MADSPA-2">Maddy 2007</a>.</td> </tr> </table> <table class="responsive nospace" style="margin-bottom:0px;width:80%"> <tr> <td style="font-size:12px;width:90px" valign="top"><em>Introductions</em></td> <td><p>Introductory book: <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/SHATAM">Shapiro 2000</a>. Anthologies: <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/BENPOM">Benacerraf & Putnam 1964</a>, <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/HARTPO-18">Hart 1996</a>, <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/BUENWI">Bueno & Linnebo 2009</a>, and <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/MARAHI-3">Marcus & McEvoy 2016</a> (with lots of historical material). Handbook: <a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/SHATOH">Shapiro 2005</a>. </p></td> </tr> <tr> <td></td> <td style="padding-bottom:10px"> </tr> </table> <div id="reflink" class="ll" onclick="simpleReq('/utils/intro_text_refs.html',{cId:47,field:'introductions',noheader:1},function(r) {;$('xp_refs2').update(r);$('xp_refs2').show();;$('reflink').hide();return false})">Show all references</div> <div id="xp_refs2" style="display:none;"></div></td> </div> <a name="content"></a> <div class="miniheader" style="font-weight:bold;border-top:1px solid #aaa"> In this area </div> <table width="100%"> <tr> <td valign="top"> <div style="padding-bottom:5px"> <form id="inside"> <input placeholder="Search inside" class="searchInside" type="text" name="catq" value=""> <input type="hidden" name="sort" value="relevance"> <input type="hidden" name="uncat" value=""> <input type="hidden" name="setAside" value=""> <input type="submit" value="go" class="button"> </form> </div> <div class="ah" style="font-size:14px;margin-bottom:10px;color:#109D49">Subcategories</div> <div class="toc1"> <div class="toc"> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/epistemology-of-mathematics">Epistemology of Mathematics</a><span class="hint"> (<b class="hint">1,197</b> | 227)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/alan-baker">Alan Baker</a></span> <div class="catContent"> <div class="cat cat3"> <a rel="section" class="tocCatName catName3" href="/web/20210826125148/https://philpapers.org/browse/apriority-in-mathematics">Apriority in Mathematics</a><span class="hint"> (<b class="hint">72</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/alexander-c-r-oldemeier">Alexander C. 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class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-nominalism">Mathematical Nominalism</a><span class="hint"> (<b class="hint">213</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-platonism">Mathematical Platonism</a><span class="hint"> (<b class="hint">425</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> <div class="cat cat3"> <a rel="section" 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href="/web/20210826125148/https://philpapers.org/browse/indispensability-arguments-in-mathematics">Indispensability Arguments in Mathematics</a><span class="hint"> (<b class="hint">233</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/numbers">Numbers</a><span class="hint"> (<b class="hint">360</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-nature-of-sets">The Nature of Sets</a>*<span class="hint"> (<b class="hint">251</b> | 98)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> </div></div> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/mathematical-cognition">Mathematical Cognition</a><span class="hint"> (<b class="hint">345</b> | 14)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/lieven-decock">Lieven Decock</a></span> <div class="catContent"> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-intuition">Mathematical Intuition</a>*<span class="hint"> (<b class="hint">133</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/alexander-c-r-oldemeier">Alexander C. R. Oldemeier</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/visualization-in-mathematics">Visualization in Mathematics</a><span class="hint"> (<b class="hint">74</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/silvia-de-toffoli">Silvia De Toffoli</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-cognition-misc">Mathematical Cognition, Misc</a><span class="hint"> (<b class="hint">17</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/phenomenology-of-mathematics">Phenomenology of Mathematics</a><span class="hint"> (<b class="hint">72</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/numerical-cognition">Numerical Cognition</a><span class="hint"> (<b class="hint">168</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/oliver-marshall">Oliver Marshall</a></span> </div> </div></div> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/mathematical-truth">Mathematical Truth</a><span class="hint"> (<b class="hint">221</b> | 17)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/mark-balaguer">Mark Balaguer</a></span> <div class="catContent"> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/analyticity-in-mathematics">Analyticity in Mathematics</a><span class="hint"> (<b class="hint">24</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/axiomatic-truth">Axiomatic Truth</a><span class="hint"> (<b class="hint">60</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/objectivity-of-mathematics">Objectivity Of Mathematics</a><span class="hint"> (<b class="hint">55</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/daniel-waxman">Daniel Waxman</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-truth-misc">Mathematical Truth, Misc</a><span class="hint"> (<b class="hint">65</b>)</span> </div> </div></div> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/set-theory">Set Theory</a><span class="hint"> (<b class="hint">2,132</b> | 397)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/toby-meadows">Toby Meadows</a></span> <div class="catContent"> <div class="cat cat3"> <a rel="section" class="tocCatName catName3" href="/web/20210826125148/https://philpapers.org/browse/the-nature-of-sets">The Nature of Sets</a><span class="hint"> (<b class="hint">251</b> | 98)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> <div class="catContent"> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-iterative-conception-of-set">The Iterative Conception of Set</a><span class="hint"> (<b class="hint">45</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/ontology-of-sets">Ontology of Sets</a><span class="hint"> (<b class="hint">50</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-nature-of-sets-misc">The Nature of Sets, Misc</a><span class="hint"> (<b class="hint">58</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/rafal-urbaniak">Rafal Urbaniak</a></span> </div> </div></div> <div class="cat cat3"> <a rel="section" class="tocCatName catName3" href="/web/20210826125148/https://philpapers.org/browse/axioms-of-set-theory">Axioms of Set Theory</a><span class="hint"> (<b class="hint">39</b> | 6)</span> <div class="catContent"> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/axiomatic-truth">Axiomatic Truth</a>*<span class="hint"> (<b class="hint">27</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-axiom-of-choice">The Axiom of Choice</a><span class="hint"> (<b class="hint">5</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-axiom-of-constructibility">The Axiom of Constructibility</a><span class="hint"> (<b class="hint">0</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-axiom-of-determinacy">The Axiom of Determinacy</a><span class="hint"> (<b class="hint">0</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-axiom-of-infinity">The Axiom of Infinity</a><span class="hint"> (<b class="hint">6</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/new-axioms-in-set-theory">New Axioms in Set Theory</a><span class="hint"> (<b class="hint">9</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/large-cardinals">Large Cardinals</a>*<span class="hint"> (<b class="hint">9</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/nonstandard-axiomatizations">Nonstandard Axiomatizations</a><span class="hint"> (<b class="hint">3</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/independence-results-in-set-theory">Independence Results in Set Theory</a><span class="hint"> (<b class="hint">6</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/axioms-of-set-theory-misc">Axioms of Set Theory, Misc</a><span class="hint"> (<b class="hint">4</b>)</span> </div> </div></div> <div class="cat cat3"> <a rel="section" class="tocCatName catName3" href="/web/20210826125148/https://philpapers.org/browse/cardinals-and-ordinals">Cardinals and Ordinals</a><span class="hint"> (<b class="hint">449</b> | 325)</span> <div class="catContent"> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-continuum-hypothesis">The Continuum Hypothesis</a><span class="hint"> (<b class="hint">49</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/large-cardinals">Large Cardinals</a><span class="hint"> (<b class="hint">60</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/cardinals-and-ordinals-misc">Cardinals and Ordinals, Misc</a><span class="hint"> (<b class="hint">15</b>)</span> </div> </div></div> <div class="cat cat3"> <a rel="section" class="tocCatName catName3" href="/web/20210826125148/https://philpapers.org/browse/set-theory-as-a-foundation">Set Theory as a Foundation</a><span class="hint"> (<b class="hint">223</b> | 37)</span> <div class="catContent"> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/russells-paradox">Russell's Paradox</a><span class="hint"> (<b class="hint">97</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/gianluca-longa">Gianluca Longa</a></span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/set-theory-and-logicism">Set Theory and Logicism</a><span class="hint"> (<b class="hint">14</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/gianluca-longa">Gianluca Longa</a></span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/set-theoretic-constructions">Set-Theoretic Constructions</a><span class="hint"> (<b class="hint">16</b>)</span> </div> <div class="cat cat4"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/set-theory-as-a-foundation-misc">Set Theory as a Foundation, Misc</a><span class="hint"> (<b class="hint">59</b>)</span> </div> </div></div> </div></div> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/areas-of-mathematics">Areas of Mathematics</a><span class="hint"> (<b class="hint">8,609</b> | 7,340)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/dirk-schlimm">Dirk Schlimm</a></span> <div class="catContent"> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/algebra">Algebra</a><span class="hint"> (<b class="hint">63</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/analysis">Analysis</a><span class="hint"> (<b class="hint">47</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/category-theory">Category Theory</a><span class="hint"> (<b class="hint">465</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/shay-logan">Shay Logan</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/geometry">Geometry</a><span class="hint"> (<b class="hint">221</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/logic-and-philosophy-of-logic">Logic and Philosophy of Logic</a>*<span class="hint"> (<b class="hint">84,641</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/aleksandra-samonek">Aleksandra Samonek</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/number-theory">Number Theory</a><span class="hint"> (<b class="hint">213</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/william-d-alessandro">William D'Alessandro</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/set-theory">Set Theory</a>*<span class="hint"> (<b class="hint">2,132</b> | 397)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/toby-meadows">Toby Meadows</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/topology">Topology</a><span class="hint"> (<b class="hint">188</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/areas-of-mathematics-misc">Areas of Mathematics, Misc</a><span class="hint"> (<b class="hint">72</b>)</span> </div> </div></div> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/theories-of-mathematics">Theories of Mathematics</a><span class="hint"> (<b class="hint">877</b> | 54)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/roy-t-cook">Roy T. Cook</a></span> <div class="catContent"> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/logicism-in-mathematics">Logicism in Mathematics</a><span class="hint"> (<b class="hint">172</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/gianluca-longa">Gianluca Longa</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/formalism-in-mathematics">Formalism in Mathematics</a><span class="hint"> (<b class="hint">70</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/intuitionism-and-constructivism">Intuitionism and Constructivism</a><span class="hint"> (<b class="hint">341</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/predicativism-in-mathematics">Predicativism in Mathematics</a><span class="hint"> (<b class="hint">26</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-naturalism">Mathematical Naturalism</a><span class="hint"> (<b class="hint">63</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-finitism">Mathematical Finitism</a><span class="hint"> (<b class="hint">31</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/theories-of-mathematics-misc">Theories of Mathematics, Misc</a><span class="hint"> (<b class="hint">120</b>)</span> </div> </div></div> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/history-philosophy-of-mathematics">History: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">425</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/erich-reck">Erich Reck</a></span> </div> <div class="cat cat2" style="margin-bottom:15px"> <a rel="section" class="tocCatName catName2" href="/web/20210826125148/https://philpapers.org/browse/philosophy-of-mathematics-miscellaneous">Philosophy of Mathematics, Miscellaneous</a><span class="hint"> (<b class="hint">3,470</b> | 974)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/sorin-bangu-1">Sorin Bangu</a></span> <div class="catContent"> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/explanation-in-mathematics">Explanation in Mathematics</a><span class="hint"> (<b class="hint">87</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/gianluca-longa">Gianluca Longa</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-infinite">The Infinite</a><span class="hint"> (<b class="hint">305</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/erich-reck">Erich Reck</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/the-application-of-mathematics">The Application of Mathematics</a><span class="hint"> (<b class="hint">243</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/nora-berenstain">Nora Berenstain</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/history-of-mathematics">History of Mathematics</a><span class="hint"> (<b class="hint">466</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-practice">Mathematical Practice</a><span class="hint"> (<b class="hint">292</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/silvia-de-toffoli">Silvia De Toffoli</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/philosophy-of-mathematics-general-works">Philosophy of Mathematics, General Works</a><span class="hint"> (<b class="hint">461</b>)</span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/mathematical-explanation">Mathematical Explanation</a>*<span class="hint"> (<b class="hint">152</b>)</span><span class="toc-eds"><a class="person" href="https://web.archive.org/web/20210826125148/https://philpeople.org/profiles/gianluca-longa">Gianluca Longa</a></span> </div> <div class="cat cat3"> <a rel="section" class="tocCatName catName4" href="/web/20210826125148/https://philpapers.org/browse/philosophy-of-mathematics-misc">Philosophy of Mathematics, Misc</a><span class="hint"> (<b class="hint">642</b>)</span> </div> </div></div> <p><h3>History/traditions: Philosophy of Mathematics</h3><ul class="toc normal" style=""><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/history-philosophy-of-mathematics">History: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">425</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/ancient-greek-and-roman-philosophy-of-mathematics">Ancient Greek and Roman Philosophy of Mathematics</a><span class="hint"> (<b class="hint">23</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/medieval-philosophy-of-mathematics">Medieval Philosophy of Mathematics</a><span class="hint"> (<b class="hint">17</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/hobbes-philosophy-of-mathematics">Hobbes: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">27</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/hume-philosophy-of-mathematics">Hume: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">67</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/locke-philosophy-of-mathematics">Locke: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">30</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/kant-philosophy-of-mathematics">Kant: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">395</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/17th18th-century-philosophy-of-mathematics">17th/18th Century Philosophy of Mathematics</a><span class="hint"> (<b class="hint">16</b> | 16)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/19th-century-philosophy-of-mathematics">19th Century Philosophy of Mathematics</a><span class="hint"> (<b class="hint">19</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/frege-philosophy-of-mathematics">Frege: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">352</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/20th-century-philosophy-of-mathematics">20th Century Philosophy of Mathematics</a><span class="hint"> (<b class="hint">15</b>)</span></li><li><a rel="section" class="catName" href="/web/20210826125148/https://philpapers.org/browse/husserl-philosophy-of-mathematics">Husserl: Philosophy of Mathematics</a><span class="hint"> (<b class="hint">124</b>)</span></li></ul> </div> </td> <td valign="top" style="padding-left:5px" class="visible-lg"> <div class="sideBox" style="float:right;max-width:500px"> <div class="sideBoxH">Also in this area</div> <div class="sideBoxC"> <div class="ah"><a href="?uncat=1">Entries to categorize (1583)</a></div> <p> <div class="ah"><a href="?recent=1&sort=added">Most recently added 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Smith</span></a> - <span class="pubYear">2003</span> - <span class="pubInfo"> <em class="pubName">Southern Journal of Philosophy</em> 41 (3):411-449.</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eNAWAF" onclick="ee('click','NAWAF')" onmouseover="ee('over','NAWAF')" onmouseout="ee('out','NAWAF')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/NAWAF"><span class="articleTitle recTitle">Aristotelian Finitism.</span></a><a class="discreet" title="View other works by Tamer Nawar" href="/web/20210826125148/https://philpapers.org/s/Tamer%20Nawar"><span class="name">Tamer Nawar</span></a> - <span class="pubYear">2015</span> - <span class="pubInfo"> <em class="pubName">Synthese</em> 192 (8):2345-2360.</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eTABCYS" onclick="ee('click','TABCYS')" onmouseover="ee('over','TABCYS')" onmouseout="ee('out','TABCYS')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/TABCYS"><span class="articleTitle recTitle">Cónicas y Superficies Cuádricas.</span></a><a class="discreet" title="View other works by Jonathan Taborda" href="/web/20210826125148/https://philpapers.org/s/Jonathan%20Taborda"><span class="name">Jonathan Taborda</span></a> & <a class="discreet" title="View other works by Jaime Chica" href="/web/20210826125148/https://philpapers.org/s/Jaime%20Chica"><span class="name">Jaime Chica</span></a> - <span class="pubYear">manuscript</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eCHUIIM" onclick="ee('click','CHUIIM')" onmouseover="ee('over','CHUIIM')" onmouseout="ee('out','CHUIIM')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/CHUIIM"><span class="articleTitle recTitle">Intuition in Mathematics.</span></a><a class="discreet" title="View other works by Elijah Chudnoff" href="/web/20210826125148/https://philpapers.org/s/Elijah%20Chudnoff"><span class="name">Elijah Chudnoff</span></a> - <span class="pubYear">2014</span> - <span class="pubInfo"> In Barbara Held & Lisa Osbeck (eds.), <em><a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/OSBRI">Rational Intuition</a></em>. Cambridge University Press.</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eMAXLIT-2" onclick="ee('click','MAXLIT-2')" onmouseover="ee('over','MAXLIT-2')" onmouseout="ee('out','MAXLIT-2')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/MAXLIT-2"><span class="articleTitle recTitle">Logic in the Tractatus.</span></a><a class="discreet" title="View other works by Max Weiss" href="/web/20210826125148/https://philpapers.org/s/Max%20Weiss"><span class="name">Max Weiss</span></a> - <span class="pubYear">2017</span> - <span class="pubInfo"> <em class="pubName">Review of Symbolic Logic</em> 10 (1):1-50.</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eSEWTCA" onclick="ee('click','SEWTCA')" onmouseover="ee('over','SEWTCA')" onmouseout="ee('out','SEWTCA')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/SEWTCA"><span class="articleTitle recTitle">The Case Against Infinity.</span></a><a class="discreet" title="View other works by Kip Sewell" href="/web/20210826125148/https://philpapers.org/s/Kip%20Sewell"><span class="name">Kip Sewell</span></a> - <span class="pubYear">manuscript</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eEVNFOT" onclick="ee('click','EVNFOT')" onmouseover="ee('over','EVNFOT')" onmouseout="ee('out','EVNFOT')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/EVNFOT"><span class="articleTitle recTitle">Frege on Truth, Beauty and Goodness.</span></a><a class="discreet" title="View other works by Simon Evnine" href="/web/20210826125148/https://philpapers.org/s/Simon%20Evnine"><span class="name">Simon Evnine</span></a> - <span class="pubYear">2003</span> - <span class="pubInfo"> <em class="pubName">Manuscrito</em> 26 (2):315-330.</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eWOLWOG" onclick="ee('click','WOLWOG')" onmouseover="ee('over','WOLWOG')" onmouseout="ee('out','WOLWOG')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/WOLWOG"><span class="articleTitle recTitle">Wittgenstein on Gödelian 'Incompleteness', Proofs and Mathematical Practice: Reading Remarks on the Foundations of Mathematics, Part I, Appendix III, Carefully.</span></a><a class="discreet" title="View other works by Wolfgang Kienzler" href="/web/20210826125148/https://philpapers.org/s/Wolfgang%20Kienzler"><span class="name">Wolfgang Kienzler</span></a> & <a class="discreet" title="View other works by Sebastian Sunday Grève" href="/web/20210826125148/https://philpapers.org/s/Sebastian%20Sunday Grève"><span class="name">Sebastian Sunday Grève</span></a> - <span class="pubYear">2016</span> - <span class="pubInfo"> In Sebastian Sunday Grève & Jakub Mácha (eds.), <em><a href="https://web.archive.org/web/20210826125148/https://philpapers.org/rec/SUNWAT">Wittgenstein and the Creativity of Language</a></em>. Basingstoke, UK: Palgrave Macmillan. pp. 76-116.</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> <li id="eMACAMU" onclick="ee('click','MACAMU')" onmouseover="ee('over','MACAMU')" onmouseout="ee('out','MACAMU')" class="entry"><span class="citation"><a href="/web/20210826125148/https://philpapers.org/rec/MACAMU"><span class="articleTitle recTitle">Programming Planck Units From a Virtual Electron; a Simulation Hypothesis (Summary).</span></a><a class="discreet" title="View other works by Malcolm Macleod" href="/web/20210826125148/https://philpapers.org/s/Malcolm%20Macleod"><span class="name">Malcolm Macleod</span></a> - <span class="pubYear">2018</span> - <span class="pubInfo"> <em class="pubName">Eur. Phys. J. Plus</em> 133:278.</span></span><span class="toggle" style="display:none" data-target="extras">details</span><div class="extras"></div></li> </div> </div> </div> </p> <p> <div class="sideBox"> <div class="sideBoxH"> Jobs in Philosophy of Mathematics </div> <div class="sideBoxC"> <div> <a href="https://web.archive.org/web/20210826125148/http://philjobs.org/job/show/17653"><b>Marc Sanders Foundation</b></a> </div> <div> Sanders Media Fellows </div> <div> <a href="https://web.archive.org/web/20210826125148/http://philjobs.org/job/show/16898"><b>the University of Hong Kong</b></a> </div> <div> Professor/Associate Professor/Assistant Professor in Philosophy </div> <div> <a href="https://web.archive.org/web/20210826125148/http://philjobs.org/job/show/17709"><b>Dartmouth College</b></a> </div> <div> Postdoctoral Fellowships at the Society of Fellows </div> <div> <a href="https://web.archive.org/web/20210826125148/http://philjobs.org/job/show/17693"><b>Hobart and William Smith Colleges</b></a> </div> <div> Visiting Assistant Professor </div> <div> <a href="https://web.archive.org/web/20210826125148/http://philjobs.org/job/show/17697"><b>Princeton University</b></a> </div> <div> Laurance S. 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