{"id":816,"date":"2008-11-26T12:39:07","date_gmt":"2008-11-26T10:39:07","guid":{"rendered":"http:\/\/deleet.dk\/?p=816"},"modified":"2008-11-26T12:39:07","modified_gmt":"2008-11-26T10:39:07","slug":"formalisering-af-%e2%80%9dder-er-maksimalt-en-ting-der-er-n%c3%b8dvendig%e2%80%9d","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/da\/?p=816","title":{"rendered":"Formalisering af \u201dder er maksimalt en ting der er n\u00f8dvendig\u201d"},"content":{"rendered":"<p><!-- \t -->Et argument som blev fremlagt af Immanuel p\u00e5 FRDB.org. Argumentet er ugyldigt, men det indeholder et interessant pr\u00e6mis. Det er interessant fordi, at pr\u00e6misset er sv\u00e6rt at formalisere.<\/p>\n<p><strong>Argumentet<\/strong><\/p>\n<p>1.&lt; all&gt;p, p is contingent.<br \/>\n2. 1 is necessary( by 1)<br \/>\n3.There is at least one thing that is necessary( by 2).<br \/>\n4.There is at most one thing that is necessary( ?).<br \/>\n5. There is at exactly on thing that is necessary( 3, 4)<a name=\"sdfootnote1anc\" href=\"#sdfootnote1sym\"><sup>1<\/sup><\/a><\/p>\n<p>Det interessante pr\u00e6mis er (4) for hvorledes skal man formalisere det?<\/p>\n<p>Jeg formaliserede resten af argumentet s\u00e5ledes:<\/p>\n<p>Dom\u00e6ne-xy: domme<\/p>\n<p>Fx \u2261 x er kontingent<br \/>\nGx \u2261 x is n\u00f8dvendig<\/p>\n<p>1. (\u2200x)(Fx)<br \/>\n2. \u25a1(\u2200x)(Fx)<br \/>\n3. (\u2203x)(Gx)<br \/>\n4. ?<br \/>\n5. (\u2203!x)(Gx)<\/p>\n<p>P\u00e5 dansk:<\/p>\n<p>1&#8242;. For alle x g\u00e6lder det at, x er kontingent.<br \/>\n2&#8242;. N\u00f8dvendigvis, for alle x g\u00e6lder det at, x kontingent.<br \/>\n3&#8242;. Der eksisterer mindst en x s\u00e5ledes at, x er n\u00f8dvendig.<br \/>\n4&#8242;. ?<br \/>\n5&#8242;. Der eksisterer pr\u00e6cis en x s\u00e5ledes at, x er n\u00f8dvendig.<\/p>\n<p>Det blev foresl\u00e5et af Anaximanchild at forst\u00e5 det s\u00e5ledes:<\/p>\n<p>4&#8242;. There does not exist distinct x,y such that x is necessary AND y is necessary.<a name=\"sdfootnote2anc\" href=\"#sdfootnote2sym\"><sup>2<\/sup><\/a><\/p>\n<p>Dette er dog ingen formalisering, men det giver inspiration til hvordan man kan formalisere pr\u00e6misset. Jeg kom frem til dette:<\/p>\n<p>4. \u00ac((\u2203x)(Gx)\u1d27(\u2203y)(Gy))<\/p>\n<p>P\u00e5 dansk:<\/p>\n<p>4&#8242;. Det er ikke tilf\u00e6ldet, at der eksisterer mindst en x s\u00e5ledes at, x er n\u00f8dvendig og der eksisterer mindst en y s\u00e5ledes at, y er n\u00f8dvendig.<\/p>\n<p>Dog er dette mangelfuldt, da det stadig er muligt for x og y at referere til den samme dom. Dette hul m\u00e5 lukkes. Jeg fandt f\u00f8rst p\u00e5 en metode der er besv\u00e6rlig, men nu jeg har fundet p\u00e5 en anden metode.<a name=\"sdfootnote3anc\" href=\"#sdfootnote3sym\"><sup>3<\/sup><\/a> Ideen er at introducere en relation som fort\u00e6ller, at de ikke er eller refererer til den samme dom:<\/p>\n<p>Rxy \u2261 x er ikke den samme som y<\/p>\n<p>Eller hvis man hellere vil have den positive variant:<\/p>\n<p>Txy \u2261 x er den samme som y<\/p>\n<p>Det skal dermed g\u00e6lde at relationen er enten sand eller falsk alt efter hvilken af ovenst\u00e5ende l\u00f8sninger man valgte. Dermed bliver (4):<\/p>\n<p>4. \u00ac((\u2203x)(Gx)\u1d27(\u2203y)(Gy))\u1d27Rxy<\/p>\n<p>eller<\/p>\n<p>4. \u00ac((\u2203x)(Gx)\u1d27((\u2203y)(Gy))\u1d27Txy)<\/p>\n<p>Fordelen ved den positive variant er at den kan st\u00e5 inden i parentesen sammen med det andet.<\/p>\n<p><a name=\"sdfootnote1sym\" href=\"#sdfootnote1anc\">1<\/a><a href=\"http:\/\/www.freeratio.org\/vbb\/showthread.php?p=5673568#post5673568\">http:\/\/www.freeratio.org\/vbb\/showthread.php?p=5673568#post5673568<\/a><\/p>\n<p><a name=\"sdfootnote2sym\" href=\"#sdfootnote2anc\">2<\/a><a href=\"http:\/\/www.freeratio.org\/vbb\/showthread.php?p=5674260#post5674260\">http:\/\/www.freeratio.org\/vbb\/showthread.php?p=5674260#post5674260<\/a><\/p>\n<p><a name=\"sdfootnote3sym\" href=\"#sdfootnote3anc\">3<\/a><a href=\"http:\/\/www.freeratio.org\/vbb\/showthread.php?p=5674273#post5674273\">http:\/\/www.freeratio.org\/vbb\/showthread.php?p=5674273#post5674273<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Et argument som blev fremlagt af Immanuel p\u00e5 FRDB.org. Argumentet er ugyldigt, men det indeholder et interessant pr\u00e6mis. Det er interessant fordi, at pr\u00e6misset er sv\u00e6rt at formalisere. Argumentet 1.&lt; all&gt;p, p is contingent. 2. 1 is necessary( by 1) 3.There is at least one thing that is necessary( by 2). 4.There is at most [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[424,1021],"class_list":["post-816","post","type-post","status-publish","format-standard","hentry","category-logik-filosofi","tag-formalisering","tag-prdikatslogik"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=\/wp\/v2\/posts\/816","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=816"}],"version-history":[{"count":0,"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=\/wp\/v2\/posts\/816\/revisions"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/da\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}