{"id":205,"date":"2018-09-09T17:54:58","date_gmt":"2018-09-09T17:54:58","guid":{"rendered":"http:\/\/www.srfa.ro\/rrfa\/?p=205"},"modified":"2018-09-12T17:43:09","modified_gmt":"2018-09-12T17:43:09","slug":"motivating-categories-a-side-effect-of-structural-realism-by-andrei-sipos","status":"publish","type":"post","link":"https:\/\/www.srfa.ro\/rrfa\/motivating-categories-a-side-effect-of-structural-realism-by-andrei-sipos\/","title":{"rendered":"Motivating Categories: a Side Effect of Structural Realism by ANDREI SIPO\u015e"},"content":{"rendered":"<a href=\"https:\/\/www.srfa.ro\/rrfa\/wp-content\/uploads\/2018\/09\/sipos.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-toolbar=\"bottom\" data-toolbar-fixed=\"off\">sipos<\/a>\n<p><a href=\"https:\/\/www.srfa.ro\/rrfa\/wp-content\/uploads\/2018\/09\/sipos.pdf\" target=\"_blank\" rel=\"noopener\">Download PDF<\/a><\/p>\n<p><strong>Abstract<\/strong>. In this paper I discuss Jonathan Bain\u2019s answer to the argument against<br \/>\nradical ontic structural realism (OSR) based on the idea that a structure is an<br \/>\nisomorphism class and thus cannot be the only thing that exists. I examine Bain\u2019s<br \/>\nproposal of replacing the set-theoretic approach to OSR with a categorial<br \/>\napproach and argue that several of his argumentative moves are deficient. First,<br \/>\nBain seems to define wrongly some of the mathematical concepts involved in<br \/>\ncategory theory, for instance that of \u2018maximal ideal\u2019, and he also attempts to use<br \/>\nthese concepts in ways that would be detrimental to OSR itself. Both of these<br \/>\ndeficiencies undermine his claims. Second, the very form of Bain\u2019s argument is, to<br \/>\nsome point, self-defeating, since defining any category whatsoever presupposes<br \/>\nsome fixed set-theoretic framework.<\/p>\n<p><strong>Keywords<\/strong>: ontic structural realism, mathematical structuralism, category<br \/>\ntheory, set theory.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>REFERENCES<\/strong><\/p>\n<p>Bain, J. (2013). Category-theoretic structure and radical ontic<br \/>\nstructural realism. Synthese 190: 1621-1635.<br \/>\nCartan, H., Eilenberg, S. (1956). Homological algebra. Princeton<br \/>\nUniversity Press.<br \/>\nEilenberg, S., Mac Lane, S. (1945). General theory of natural<br \/>\nequivalences. Transactions of the American Mathematical<br \/>\nSociety 58: 231-294.<br \/>\nGrothendieck, A. (1960). \u00c9l\u00e9ments de g\u00e9om\u00e9trie alg\u00e9brique. I. Le<br \/>\nlangage des sch\u00e9mas. Publications Math\u00e9matiques de l\u2019IH\u00c9S<br \/>\n4: 5-228.<br \/>\nKan, D.M. (1958). Adjoint functors. Transactions of the American<br \/>\nMathematical Society 87: 294-329.<\/p>\n<p>Landry, E.M. (2012). Methodological Structural Realism. In E.M.<br \/>\nLandry, D.P. Rickles (eds.), Structural Realism: Structure,<br \/>\nObject and Causality, Springer.<br \/>\nLawvere, F.W. (1971). Quantifiers and sheaves. Actes du Congr\u00e8s<br \/>\nInternational des Math\u00e9maticiens (Nice, 1970) 1: 329-334.<br \/>\nLawvere, F.W. (1964). An elementary theory of the category of sets.<br \/>\nProceedings of the National Academy of Sciences of the<br \/>\nUnited States of America 52: 1506-1511.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Download PDF Abstract. In this paper I discuss Jonathan Bain\u2019s answer to the argument against radical ontic structural realism (OSR) based on the idea that a structure is an isomorphism class and thus cannot be the only thing that exists. I examine Bain\u2019s proposal of replacing the set-theoretic approach to OSR with a categorial approach&hellip; <\/p>\n<p><a class=\"more-link\" href=\"https:\/\/www.srfa.ro\/rrfa\/motivating-categories-a-side-effect-of-structural-realism-by-andrei-sipos\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[84,83,82,85],"class_list":["post-205","post","type-post","status-publish","format-standard","hentry","category-andrei-sipos","tag-category-theory","tag-mathematical-structuralism","tag-ontic-structural-realism","tag-set-theory","xfolkentry","clearfix"],"_links":{"self":[{"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/posts\/205","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/comments?post=205"}],"version-history":[{"count":2,"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/posts\/205\/revisions"}],"predecessor-version":[{"id":223,"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/posts\/205\/revisions\/223"}],"wp:attachment":[{"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/media?parent=205"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/categories?post=205"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.srfa.ro\/rrfa\/wp-json\/wp\/v2\/tags?post=205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}