{"id":11123,"date":"2010-11-16T15:13:35","date_gmt":"2010-11-16T15:13:35","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/11\/16\/a-logic-problem\/"},"modified":"2010-11-16T15:13:35","modified_gmt":"2010-11-16T15:13:35","slug":"a-logic-problem","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2010\/11\/16\/a-logic-problem\/","title":{"rendered":"A Logic Problem"},"content":{"rendered":"

Consider this argument:<\/span><\/p>\n

   1. A necessary truth is true.<\/span>
   2. Whatever is true is possibly true.<\/span>
   3. Whatever is possibly true could be false.<\/span>
   Therefore<\/span>
   4. A necessary truth could be false.<\/span>
   <\/span>
A sound argument is one that satisfies two conditions: its premises are all true, and the reasoning it embodies is correct. Is the above argument sound?<\/span><\/p>\n

If not, what has gone wrong in the argument? Answer below the fold.
\n<\/span><\/p>\n

<\/p>\n

There is nothing wrong with the formal logic of the argument.  So if there is a mistake it is because of the falsity of one or more if the premises.  Premise 1 is plainly true.  A proposition true in every possible world is true in the actual world.  Premise 2 is also obviously true.  If a proposition is true, then it is possible that it is true:  if a proposition is true in the actual world, then it is true in at least one possible world.  Premise 3, however, is false: Every necessary truth is possibly true, but no necessary truth is false in any possible world.  And so the argument, having a false premise, is not sound.  <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Consider this argument:    1. A necessary truth is true.   2. Whatever is true is possibly true.   3. Whatever is possibly true could be false.   Therefore   4. A necessary truth could be false.   A sound argument is one that satisfies two conditions: its premises are all true, and the reasoning it embodies is correct. Is the … Continue reading “A Logic Problem”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[108],"tags":[],"class_list":["post-11123","post","type-post","status-publish","format-standard","hentry","category-logica-docens"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11123","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/comments?post=11123"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/11123\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=11123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=11123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=11123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}