{"id":12806,"date":"2009-02-19T08:50:14","date_gmt":"2009-02-19T08:50:14","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2009\/02\/19\/the-difference-between-possibility-and-contingency\/"},"modified":"2009-02-19T08:50:14","modified_gmt":"2009-02-19T08:50:14","slug":"the-difference-between-possibility-and-contingency","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2009\/02\/19\/the-difference-between-possibility-and-contingency\/","title":{"rendered":"The Difference Between Possibility and Contingency"},"content":{"rendered":"

Over lunch yesterday, Peter Lupu questioned my assertion that possibility and contingency are not the same.  What chutzpah!<\/em> So let me now try to prove to him that they are indeed not the same, though they are of course related.  To put the point as simply and directly as I can, possibility and contingency are not the same because every necessary proposition is possible, but no necessary proposition is contingent.  Perhaps this requires a bit of explanation.<\/font><\/p>\n

We first divide all propositions into two mutually exclusive and jointly exhaustive groups, the noncontingent<\/em> and the contingent<\/em>.  The first group subdivides into two mutually exclusive and jointly exhaustive subgroups, the necessary<\/em> and the impossible<\/em>.  A proposition is necessary (impossible) just in case it is true in every (no) possible world.  A proposition is possible just in case it is true in some possible worlds.  It follows that if proposition p is necessary, then p is possible, but not conversely.<\/font><\/p>\n

Since we know that there are necessary propositions, and since we know that every necessary proposition is a possible proposition, we know that there are necessary propositions which are possible.  But we also know that no necessary proposition is contingent.  It follows that we know that there are possible propositions that are not contingent.  It follows that the extension of 'possible proposition' is different from the extension of 'contingent proposition.'  This suffices to show that possibility and contingency are not the same.  Here are some definitions.  I have included definitions not fomulated  in the imagery of possible worlds for those who are 'spooked' by his imagery.<\/font><\/p>\n

A proposition p is possible =df<\/sub> there is a possible world in which p is true.<\/font><\/span><\/p>\n

A proposition p is possible  =df<\/sub> it is not necessary that p be false.<\/font><\/span><\/p>\n

A proposition p is contingent =df<\/sub> there is a possible world in which p is true and there is a possible world in which p is false.<\/font><\/span><\/p>\n

A proposition p is contingent =df<\/sub> p is both possibly true and possibly false.<\/font><\/span><\/p>\n

Example.  No color is a sound<\/em> is possible but not contingent.  There is a possible world in which it is true, but no possible world in which it is false.  Tom's favorite shirt is red<\/em> is contingent.  There is a possible world in which it is true and a possible world in which it is false.<\/font><\/p>\n

UPDATE (21 February): David Brightly provides a very useful map of the modal terrain in the Comments.<\/font><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Over lunch yesterday, Peter Lupu questioned my assertion that possibility and contingency are not the same.  What chutzpah! So let me now try to prove to him that they are indeed not the same, though they are of course related.  To put the point as simply and directly as I can, possibility and contingency are … Continue reading “The Difference Between Possibility and Contingency”<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[235],"tags":[],"class_list":["post-12806","post","type-post","status-publish","format-standard","hentry","category-modal-matters"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/12806","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=12806"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/12806\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=12806"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=12806"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=12806"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}