{"id":2385,"date":"2011-09-05T01:49:25","date_gmt":"2011-09-05T00:49:25","guid":{"rendered":"http:\/\/emilkirkegaard.dk\/en\/?p=2385"},"modified":"2011-09-05T02:46:15","modified_gmt":"2011-09-05T01:46:15","slug":"john-nolt-logics-chp-11-12","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2011\/09\/john-nolt-logics-chp-11-12\/","title":{"rendered":"John Nolt – Logics, chp. 11-12"},"content":{"rendered":"

I am taking an advanced logic class this semester. Som of the reading material has been posted in our internal system. I’ll post it here so that others may get good use of it as well. The text in question is John Nolt’s Logics<\/em> chp. 11-12. I remade the pdfs so that they ar smaller and most of the text is copyable making for easyer quoting. Enjoy<\/p>\n

John Nolt – Logics, chp 11-12<\/a><\/p>\n

Edit<\/strong> – A comment to the stuff (danish)<\/h3>\n

D\u00e6r st\u00e5r i Nolt kap. 12, at:<\/p>\n

\u201dWe have said so far that the accessibility relation for all forms of alethic<\/p>\n

possibility is reflexive. For physical possibility, I have argued that it is transitive as<\/p>\n

well. And for logical possibility it seems also to be symmetric. Thus the accessibil-<\/p>\n

ity relation for logical possibility is apparently reflexive, transitive, and symmetric.<\/p>\n

It can be proved, though we shall not do so here, that these three characteristics<\/p>\n

together define the logic S5, which is characterized by Leibnizian semantic… That<\/p>\n

is, making the accessibility relation reflexive, transitive, and symmetric has the<\/p>\n

same effect on the logic as making each world possible relative to each.\u201d p. 343<\/p>\n

m\u00e6n min entuisjon sagde maj strakes, at dette var forkert, alts\u00e5, at de er forkert at<\/p>\n

R1. For any world, that world relates to itself. (Reflexsive)<\/p>\n

R2. For any world w1 and for any world w2, if w1 relates to w2, then w2 relates to w1. (Symmetry)<\/p>\n

R3. For any world w1, for any world w2, and for any world w3, if w1 relates to w2, and w2 relates to w3, then w1 relates to w3. (Transitive)<\/p>\n

er \u00e6kvival\u00e6nt m\u00e6d<\/p>\n

R4. For any world w1 and for any world w2, w1 relates to w2. (Omni-relevans)<\/p>\n

M\u00e6n de er ganske r\u00e6gtigt, at ves man pr\u00f8ver at k\u00f8re diverse beviser ig\u00e6nnem, s\u00e5 kan man godt bevise fx (\u25caA\u2192\u2610\u25caA) vha. en mod\u00e6l som er reflexsive, symmetrical og transitive (jaj valgte 1r1, 2r2).<\/p>\n

M\u00e6n stadig er d\u00e6r n\u00e5get galt. Di forsk\u00e6llige verdener er helt isolerede, modsat vad di er i givet R4. Jaj googlede de, og andre har osse bem\u00e6rket de<\/a>:<\/p>\n

\u201dRequiring the accessibility relation to be reflexive, transitive and symmetric is to require that it be an equivalence relation. This isn\u2019t the same as saying that every world is accessible from every other. But it is to say that the class of worlds is split up into classes within which every world is accessible from every other; and there is no access between these classes. S5, the system that results, is in many ways the most intuitive of the modal systems, and is the closest to the naive ideas with which we started.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"

I am taking an advanced logic class this semester. Som of the reading material has been posted in our internal system. I’ll post it here so that others may get good use of it as well. The text in question is John Nolt’s Logics chp. 11-12. I remade the pdfs so that they ar smaller […]<\/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":[701,14,1702,1701],"class_list":["post-2385","post","type-post","status-publish","format-standard","hentry","category-logic-philosophy","tag-logic","tag-modal","tag-s5","tag-textbook","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2385","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=2385"}],"version-history":[{"count":2,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2385\/revisions"}],"predecessor-version":[{"id":2388,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2385\/revisions\/2388"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=2385"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=2385"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=2385"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}