{"id":2005,"date":"2010-01-15T01:53:55","date_gmt":"2010-01-15T00:53:55","guid":{"rendered":"http:\/\/emilkirkegaard.dk\/en\/?p=2005"},"modified":"2010-01-15T01:53:55","modified_gmt":"2010-01-15T00:53:55","slug":"similarity-between-pws-and-predicate-logic","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2010\/01\/similarity-between-pws-and-predicate-logic\/","title":{"rendered":"Similarity between PWS and predicate logic"},"content":{"rendered":"<p><!-- \t\t@page { margin: 2cm } \t\tP { margin-bottom: 0.21cm } -->It seems to me that the formulas:<\/p>\n<p style=\"margin-left: 1.25cm;\">1. \u25caP<\/p>\n<p style=\"margin-left: 1.25cm;\">2. (\u2203x)(Fx)<\/p>\n<p>and:<\/p>\n<p style=\"margin-left: 1.25cm;\">3. \u25a1P<\/p>\n<p style=\"margin-left: 1.25cm;\">4. (\u2200x)(Fx)<\/p>\n<p>are quite similar, if we translate the modal propositional ones into PWS. Here is the result:<\/p>\n<p style=\"margin-left: 1.25cm;\">1*. (\u2203w)(Pw)<\/p>\n<p style=\"margin-left: 1.25cm;\">3*. (\u2200w)(Pw)<\/p>\n<p>Translated into a formal-ish english language, they should be read as:<\/p>\n<p style=\"margin-left: 1.25cm;\">1*. There exists a possible world, w, such that P is the case in w.<\/p>\n<p style=\"margin-left: 1.25cm;\">2. There exists an x such that Fx.<\/p>\n<p style=\"margin-left: 1.25cm;\">3*. For all possible worlds, w, P is the case in w.<\/p>\n<p style=\"margin-left: 1.25cm;\">4. For all x, Fx.<\/p>\n<p>The similarity becomes stronger when an interpretation is added to the predicate logic formula though I leave that up to the reader to do.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It seems to me that the formulas: 1. \u25caP 2. (\u2203x)(Fx) and: 3. \u25a1P 4. (\u2200x)(Fx) are quite similar, if we translate the modal propositional ones into PWS. Here is the result: 1*. (\u2203w)(Pw) 3*. (\u2200w)(Pw) Translated into a formal-ish english language, they should be read as: 1*. There exists a possible world, w, such [&hellip;]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[998,1026,1532],"class_list":["post-2005","post","type-post","status-publish","format-standard","hentry","category-logic-philosophy","tag-predicate-logic","tag-pws","tag-similarity","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2005","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/comments?post=2005"}],"version-history":[{"count":1,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2005\/revisions"}],"predecessor-version":[{"id":2006,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2005\/revisions\/2006"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=2005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=2005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=2005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}