{"id":1572,"date":"2009-08-12T14:28:33","date_gmt":"2009-08-12T12:28:33","guid":{"rendered":"http:\/\/deleet.dk\/?p=1572"},"modified":"2009-08-12T14:28:33","modified_gmt":"2009-08-12T12:28:33","slug":"truth-tables-and-necessary-truths","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2009\/08\/truth-tables-and-necessary-truths\/","title":{"rendered":"Truth tables and necessary truths"},"content":{"rendered":"

<\/p>\n

\n

In the essay Validity and necessary truths<\/em> I used truth tables with necessary truths and impossibilities in it. I did it like this:<\/span><\/p>\n\n<\/col>\n<\/col>\n<\/col>\n\n\n\n\n
P<\/td>\n\u25a1Q<\/td>\nP\u2192\u25a1Q<\/td>\n<\/tr>\n
T<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Note that the modal operator is placed in the truth table also. It could also be done like this:<\/p>\n\n<\/col>\n<\/col>\n<\/col>\n\n\n\n\n
P<\/td>\nQ<\/td>\nP\u2192Q<\/td>\n<\/tr>\n
T<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Note that Q is true on all rows. When thinking about a necessary truth or an impossibility we can simply choose only to look at the rows where the proposition is true. The truth table above is a part of this larger truth table:<\/p>\n\n<\/col>\n<\/col>\n<\/col>\n\n\n\n\n\n\n
P<\/td>\nQ<\/td>\nP\u2192Q<\/td>\n<\/tr>\n
T<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
T<\/td>\nF<\/td>\nF<\/td>\n<\/tr>\n
F<\/td>\nT<\/td>\nT<\/td>\n<\/tr>\n
F<\/td>\nF<\/td>\nT<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

We simply only looked at rows 1 and 3.<\/p>\n","protected":false},"excerpt":{"rendered":"

In the essay Validity and necessary truths I used truth tables with necessary truths and impossibilities in it. I did it like this: P \u25a1Q P\u2192\u25a1Q T T T F T T Note that the modal operator is placed in the truth table also. It could also be done like this: P Q P\u2192Q T […]<\/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":[552,553,14,836,1318],"class_list":["post-1572","post","type-post","status-publish","format-standard","hentry","category-logic-philosophy","tag-impossibility","tag-impossible","tag-modal","tag-necessary-truth","tag-truth-table","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/1572","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=1572"}],"version-history":[{"count":0,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/1572\/revisions"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=1572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=1572"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=1572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}