{"id":145,"date":"2023-12-10T22:41:06","date_gmt":"2023-12-11T03:41:06","guid":{"rendered":"https:\/\/sites.nd.edu\/yuanshan-li\/?page_id=145"},"modified":"2026-03-30T19:20:20","modified_gmt":"2026-03-30T23:20:20","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/yuanshan-li\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n<p>My research is in mathematical philosophy (broadly construed). This includes philosophical questions that arise from mathematics, the application of mathematics to philosophy, and the history of these investigations.<\/p>\n\n\n\n<p>Recently I&#8217;ve been focusing on philosophical topics related to the Axiom of Choice, such as the notion of constructivity and the axiom&#8217;s applications in analysis and probability theory. I also have interests in the philosophy of science.<\/p>\n\n\n\n<p>My philosophy advisor is <a href=\"https:\/\/jdh.hamkins.org\/\">Joel David Hamkins<\/a> and my math advisor is <a href=\"https:\/\/www.nramseymath.com\/\">Nick Ramsey<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"329\" src=\"https:\/\/sites.nd.edu\/yuanshan-li\/files\/2025\/02\/linfini-1024x329.jpg\" alt=\"\" class=\"wp-image-211\" srcset=\"https:\/\/sites.nd.edu\/yuanshan-li\/files\/2025\/02\/linfini-1024x329.jpg 1024w, https:\/\/sites.nd.edu\/yuanshan-li\/files\/2025\/02\/linfini-300x96.jpg 300w, https:\/\/sites.nd.edu\/yuanshan-li\/files\/2025\/02\/linfini-768x247.jpg 768w, https:\/\/sites.nd.edu\/yuanshan-li\/files\/2025\/02\/linfini-1536x494.jpg 1536w, https:\/\/sites.nd.edu\/yuanshan-li\/files\/2025\/02\/linfini-2048x659.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>La Le\u00e7on<\/em>, Eug\u00e8ne Ionesco<\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Research Papers<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8220;Are nonmeasurable sets significant for epistemology?&#8221; <em>Synthese<\/em>, 2025. <a href=\"https:\/\/philpapers.org\/rec\/LIANSE\">Preprint<\/a> <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s11229-025-05256-4\">Journal<\/a><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Recent and Upcoming Talks<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mar 28, 2026, <em>On Finite Additivity<\/em>, 25th\u00a0Pitt-CMU Graduate Conference in Philosophy<\/li>\n\n\n\n<li>Mar 27, 2026, <em>Bayesian Convergence with Finite Additivity<\/em>, <a href=\"https:\/\/francescazafforablando.com\/pfew\">Pittsburgh Formal Epistemology Workshop<\/a><\/li>\n\n\n\n<li>Dec 10, 2025, <em>Finite Additivity, Axiom of Choice, and Bayesian Convergence<\/em>, IU Bloomington Logic Seminar<\/li>\n\n\n\n<li>Jul 7, 2025, <em>Poincar\u00e9&#8217;s Chalk and Lebesgue&#8217;s Measure<\/em>, <a href=\"https:\/\/voidprove.github.io\/BISFORM2025\/\">BISFORM 2025<\/a>, Peking University<\/li>\n\n\n\n<li>Jun 17, 2025, <em>Rigor, Formalizability, and Values in Mathematics<\/em>, <a href=\"https:\/\/appsa2025taiwan.mystrikingly.com\/\">APPSA-LMPST Taiwan Conference<\/a>, National Yang Ming Chiao Tung University<\/li>\n\n\n\n<li>Jul 11, 2024, <em><a href=\"http:\/\/sites.nd.edu\/yuanshan-li\/files\/2024\/07\/Poster-Yuanshan-Li.pdf\">The Number of Models of Unstable Theories without Choice<\/a><\/em>, Poster Session of <a href=\"https:\/\/120ac.set-theory.info\/home\">&#8220;120 Years of Choice&#8221; Conference<\/a>, University of Leeds<\/li>\n\n\n\n<li>Feb 29, 2024, <em>Poincar\u00e9&#8217;s Dilemma and the Notion of Rigor<\/em>, &#8220;Rigor and the Growth of Knowledge&#8221; Conference, <a href=\"http:\/\/www.sphere.univ-paris-diderot.fr\/\">Laboratoire SPHere<\/a>, Universit\u00e9 Paris Cit\u00e9<\/li>\n\n\n\n<li>Feb 2, 2024, <em>Poincar\u00e9&#8217;s Chalk and Lebesgue&#8217;s Measure<\/em>, UC Irvine Graduate Conference in Philosophy<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Notes<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>My <a href=\"http:\/\/sites.nd.edu\/yuanshan-li\/files\/2024\/04\/Borel-Conjecture.pdf\">note<\/a> on the Borel conjecture. The note contains a writeup for a proof of the independence of the Borel conjecture from ZFC. It follows the first proof of this result due to Laver.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>My research is in mathematical philosophy (broadly construed). This includes philosophical questions that arise from mathematics, the application of mathematics to philosophy, and the history of these investigations. Recently I&#8217;ve been focusing on philosophical topics related to the Axiom of Choice, such as the notion of constructivity and the axiom&#8217;s applications in analysis and probability &hellip; <a href=\"https:\/\/sites.nd.edu\/yuanshan-li\/research\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Research<\/span><\/a><\/p>\n","protected":false},"author":4419,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-145","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Research - Yuanshan Li (Tom)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sites.nd.edu\/yuanshan-li\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research - Yuanshan Li (Tom)\" \/>\n<meta property=\"og:description\" content=\"My research is in mathematical philosophy (broadly construed). 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