{"id":1128,"date":"2009-02-27T00:13:49","date_gmt":"2009-02-26T22:13:49","guid":{"rendered":"http:\/\/deleet.dk\/?p=1128"},"modified":"2009-02-27T00:13:49","modified_gmt":"2009-02-26T22:13:49","slug":"tough-modal-logic-formalization","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2009\/02\/tough-modal-logic-formalization\/","title":{"rendered":"Tough modal logic formalization"},"content":{"rendered":"<p><a href=\"http:\/\/www.freeratio.org\/showthread.php?t=263026\">Source.<\/a><\/p>\n<p>Gamgee wrote:<\/p>\n<p>In the Ontological Argument, Anselm refutes Guanilo&#8217;s Perfect Island criticism by stating that God has Aseity. Anselm does not, as far as i know, make any attempt to prove that God has Aseity, or even if Aseity is logically possible.<\/p>\n<p>I argue that it is not, for the following reason:<\/p>\n<p>1) We accept that God does not exist in the physical world.<\/p>\n<p>2) Therefore, there must exist some realm outside of normal time and space (realm x, for conveniency)<\/p>\n<p>3) God exists in realm x<\/p>\n<p>4) Therefore, God requires realm x to exist so that he can exist in it.<\/p>\n<p>5) Without realm x, God would not exist<\/p>\n<p>6) Therefore, God is contingent upon realm x for his existence. Aseity is false.<\/p>\n<p>Any obvious holes in my logic?<\/p>\n<p>It&#8217;s not that bad but it&#8217;s badly structured. I&#8217;ll help you:<\/p>\n<p><strong>Definitions<\/strong><\/p>\n<p>D:x \u2261 things<\/p>\n<p>D:y \u2261 things<\/p>\n<p>Ex \u2261 x exists<\/p>\n<p>Fxy \u2261 x exists in y<\/p>\n<p>Cxy \u2261 x in contingent upon y.<\/p>\n<p>a \u2261 God<\/p>\n<p>b \u2261 non-physical world<\/p>\n<p>c \u2261 physical world<\/p>\n<p>Desired conclusion: God is contingent upon the non-physical world.<\/p>\n<p>Desired route: Something to do with worlds.<\/p>\n<p><strong>Version one<\/strong><\/p>\n<p>1a. Ea<\/p>\n<p>God exists. (Premise)<\/p>\n<p>2a. \u00acFac<\/p>\n<p>God does not exist in the physical world. (Premise)<\/p>\n<p>3a. (\u2200x)(Ex\u2192(Fxc\u2228Fxb))<\/p>\n<p>For all x, if x exists, then x exists in the physical world or x exists in the non-physical world. (Premise)<\/p>\n<p>4a. \u22a2 Fab (1, 2, 3)<\/p>\n<p>Therefore, God exists in the non-physical world.<\/p>\n<p>5a. (\u2200x)(\u2200y)((Ex\u2192Fxy)\u2227\u00acEy)\u2192\u00acEx<\/p>\n<p>For all x, if x exists in y and y does not exist, then x does not exist.<\/p>\n<p>6a. ((\u2200x)(\u2200y)((Ex\u2192Fxy)\u2227\u00acEy)\u2192\u00acEx)\u2192Cxy<\/p>\n<p>If, for all x, for all y, if, if x exists, then x exists in y and y does not exist, then x does not exist, then x is contingent upon y.<\/p>\n<p>7a. \u22a2 Cab (5, 6)<\/p>\n<p>Therefore, God is contingent upon the non-physical world.<\/p>\n<p>But 5 is false. It says that if x exist, then x does not exist. I got stuck there. Trying to figure out how to formulate it in some other way to avoid this.<\/p>\n<p><strong>Version two<\/strong><\/p>\n<p>1b. Ea\u2192Fab<\/p>\n<p>If God exists, then God exists in the non-physical world. (premise)<\/p>\n<p>2b. (\u2200x)(\u2200y)((Ex\u2192Fxy)\u2227\u00acEy)\u2192\u00acEx<\/p>\n<p>For all x, for all y, if, if x exists, then x exists in y, and y does not exist, then x does not exist. (premise)<\/p>\n<p>3b. ((\u2200x)(\u2200y)((Ex\u2192Fxy)\u2227\u00acEy)\u2192\u00acEx)\u2192Cxy<\/p>\n<p>If for all x, for all y, if, if x exists, then x exists in y, and y does not exist, then x does not exist, then x is contingent upon y. (premise)<\/p>\n<p>And here I got stuck. I couldn&#8217;t find a way to get to Cxy without assuming \u00acEb.<\/p>\n<p><strong>Version three<\/strong><\/p>\n<p>1c. \u00acEb\u2192\u00acEa<\/p>\n<p>If the non-physical world does not exist, then God does not exist. (Premise)<\/p>\n<p>2c. (\u2200x)(\u2200y)(\u00acEy\u2192\u00acEx)\u2192Cxy<\/p>\n<p>If for all x, for all y, if y does not exist, then x does not exist, then x in contingent upon y. (Premise)<\/p>\n<p>3c. \u22a2 Cab (1, 2)<\/p>\n<p>Therefore, God is contingent upon the non-physical world.<\/p>\n<p>This works. Premise two is analytic. Premise one is sometimes true per definition.<\/p>\n<p><strong>Comments<\/strong><\/p>\n<p>This argument was remarkably hard to formalize for me.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Source. Gamgee wrote: In the Ontological Argument, Anselm refutes Guanilo&#8217;s Perfect Island criticism by stating that God has Aseity. Anselm does not, as far as i know, make any attempt to prove that God has Aseity, or even if Aseity is logically possible. I argue that it is not, for the following reason: 1) We [&hellip;]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,19],"tags":[472,489,1021,998,1368,1409],"class_list":["post-1128","post","type-post","status-publish","format-standard","hentry","category-logic-philosophy","category-religion-filosofi","tag-god","tag-gud","tag-prdikatslogik","tag-predicate-logic","tag-verden","tag-world","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/1128","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=1128"}],"version-history":[{"count":0,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/1128\/revisions"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=1128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=1128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=1128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}