{"id":3576,"date":"2018-08-08T18:50:18","date_gmt":"2018-08-08T20:50:18","guid":{"rendered":"http:\/\/w3.ufsm.br\/ppgf\/?p=3576"},"modified":"2018-08-08T18:50:18","modified_gmt":"2018-08-08T20:50:18","slug":"palestra-do-prof-dr-john-mumma-california-state-university-of-san-bernardino","status":"publish","type":"post","link":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/2018\/08\/08\/palestra-do-prof-dr-john-mumma-california-state-university-of-san-bernardino","title":{"rendered":"Palestras do Prof. Dr. John Mumma (California State University of San Bernardino)"},"content":{"rendered":"<p><a href=\"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-content\/uploads\/sites\/556\/2019\/03\/Cartaz_Mumma_Semresumo.jpg\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-content\/uploads\/sites\/556\/2019\/03\/Cartaz_Mumma_Semresumo.jpg\" alt=\"\" width=\"1239\" height=\"1754\" class=\"aligncenter size-full wp-image-3575\" \/><\/a><\/p>\n<p>A representational semantics for elementary geometry<\/p>\n<p>Tarskian model theory provides a topic-neutral standard for determining whether the inference of a mathematical claim follows logically from others.  Drawing on John Etchemendy&#8217;s The Concept of Logical Consequence, I discuss how the commonly accepted Tarskian standard applies to the proofs of elementary geometry and explore the prospects for an alternative, topic-specific approach to understanding the logical validity of the proofs.<\/p>\n<p>The first talk will be devoted to explicating Etchemendy&#8217;s distinction between interpretational and representational semantics, and highlighting how the Tarskian standard presumes an interpretational semantics.<\/p>\n<p>In the second talk, I will present an approach for providing a representational semantics for elementary geometry.  I explain how the semantics is inspired by Ken Manders&#8217; seminal analysis of Euclid&#8217;s diagrammatic proofs, provide the central formal ideas of the semantics, and discuss the issues that would need to be addressed to for the semantics to be fully worked out.  I close by considering the prospects for a topic-specific representational semantics in other mathematical subjects.<\/p>\n<p>List of references:<\/p>\n<p>J. Avigad, E. Dean, and J. Mumma.  &#8216;A Formal System for Euclid&#8217;s Elements&#8217; The Review of Symbolic Logic,  vol. 2, no. 4, Dec. 2009.<\/p>\n<p>K. Manders &#8216;The Euclidean diagram.&#8217; In Mancosu, P., editor. The Philosophy of Mathematical Practice. Oxford, UK: Oxford University Press, pp. 80\u2013133, 2008.<\/p>\n<p>J. Etchemendy, chapters 1 and 2 of The Concept of Logical Consequence, CSLI publications, 1999.<\/p>\n<p>J. Etchemendy, &#8216;Reflections on Consequence,&#8217; In Douglas Patterson (ed.), New Essays on Tarski and Philosophy. Oxford University Press. pp. 263&#8211;299, 2008.<\/p>\n<p>A. Tarski &#8216;What is Elementary Geometry&#8217; In Henkin, L., Suppes, P., and Tarski, A., editors. The Axiomatic Method: With Special Reference to Geometry and Physics (first edition). Amsterdam, the Netherlands: North-Holland, pp. 16\u201329.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A representational semantics for elementary geometry Tarskian model theory provides a topic-neutral standard for determining whether the inference of a mathematical claim follows logically from others. Drawing on John Etchemendy&#8217;s The Concept of Logical Consequence, I discuss how the commonly accepted Tarskian standard applies to the proofs of elementary geometry and explore the prospects for [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3575,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,2],"tags":[28],"class_list":["post-3576","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-eventos","category-noticias","tag-john-mumma"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/posts\/3576","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/comments?post=3576"}],"version-history":[{"count":0,"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/posts\/3576\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/media?parent=3576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/categories?post=3576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ufsm.br\/cursos\/pos-graduacao\/santa-maria\/ppgf\/wp-json\/wp\/v2\/tags?post=3576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}