{"id":10670,"date":"2011-05-27T13:36:38","date_gmt":"2011-05-27T13:36:38","guid":{"rendered":"https:\/\/maverickphilosopher.blog\/index.php\/2011\/05\/27\/can-a-noncontingent-proposition-entail-a-contingent-proposition\/"},"modified":"2011-05-27T13:36:38","modified_gmt":"2011-05-27T13:36:38","slug":"can-a-noncontingent-proposition-entail-a-contingent-proposition","status":"publish","type":"post","link":"https:\/\/maverickphilosopher.blog\/index.php\/2011\/05\/27\/can-a-noncontingent-proposition-entail-a-contingent-proposition\/","title":{"rendered":"Does Any Noncontingent Proposition Entail a Contingent Proposition?"},"content":{"rendered":"

This post continues the discussion in the comment thread of an earlier post<\/a>.   <\/span><\/p>\n

Propositions divide into the contingent and the noncontingent.  The noncontingent divide into the necessary and the impossible.  A proposition is contingent iff it is true in some, but not all, broadly logical possible worlds, 'worlds' for short.   A proposition is necessary iff it is true in all worlds, and impossible iff it true in none.  A proposition p entails a proposition q iff there is no world in which p is true and q false.<\/span><\/p>\n

The title question divides into two:  Does any impossible proposition entail a contingent proposition?  Does any necessary proposition entail a contingent proposition?<\/span><\/p>\n

As regards the first question, yes.  A proposition A of the form p & ~p<\/em> is impossible.  If B is a contingent proposition, then there is no possible world in which  A is true and B false.  So every impossible proposition entails every contingent proposition.  This may strike the reader as paradoxical, but only if he fails to realize that 'entails' has all and only the meaning imputed to it in the above definition.<\/span><\/p>\n

As for the second question, I say 'No' while Peter Lupu says 'Yes.'  His argument is this:<\/span>
1. *Bill = Bill* is necessary.<\/span>
2. *Bill = Bill* entails *(Ex)(x = Bill)*<\/span>
3. *(Ex)(x = Bill)* is contingent.<\/span>
Ergo<\/span>
4. There are necessary propositions that entail contingent propositions.<\/span><\/p>\n

Note first that for (2) to be true, 'Bill' must have a referent and indeed an existing referent.  'Bill' cannot be a vacuous (empty) name, nor can it have a nonexisting 'Meinongian' referent.  Now (3) is surely true given that 'Bill' is being used to name a particular human being, and given the obvious fact that human beings are contingent beings.  So the soundness of the argument rides on whether (1) is true.<\/span><\/p>\n

I grant that Bill is essentially<\/em> self-identical: self-identical in every world in which he exists.  But this is not to say that Bill is necessarily<\/em> self-identical: self-identical in every world.  And this for the simple reason that Bill does not exist in every world.  So I deny (1).  It is not the case that Bill = Bill in every world.  He has properties, including the 'property' of self-identity, only in those worlds in which he exists. <\/span><\/p>\n

My next post will go into these matters in more detail.<\/span><\/p>\n

Addendum 28 May 2011<\/strong>.  Seldom Seen Slim weighs in on Peter's argument as follows:<\/span><\/p>\n

<\/p>\n

\n
I believe your reply to Peter is correct. It follows from how we should define constants in 1st order predicate logic. A domain or possible world is constituted by the objects it contains. Constants name those objects. If a domain has three objects, D = {a,b,c}, then the familiar expansion for identity holds in that domain, i.e., (x) (x = x) is equivalent to a = a and b = b and c = c. But notice that this is conditional and the antecedent asserts the existence in D of (the objects named by) a, b, and c. Thus premise 2 of Peter's argument is actually a conditional: IF a exists in some domain D, then a = a in D. The conclusion (3) must also be a conditional: if a exists in D , then something  in D is self-indentical. That of course does not assert the existential Peter wants from (x)(x = x). Put simply, a = a presumes [presupposes] rather than entails that a exists.<\/div>\n<\/blockquote>\n

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

This post continues the discussion in the comment thread of an earlier post.   Propositions divide into the contingent and the noncontingent.  The noncontingent divide into the necessary and the impossible.  A proposition is contingent iff it is true in some, but not all, broadly logical possible worlds, 'worlds' for short.   A proposition is necessary iff it … Continue reading “Does Any Noncontingent Proposition Entail a Contingent Proposition?”<\/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":[108,235],"tags":[],"class_list":["post-10670","post","type-post","status-publish","format-standard","hentry","category-logica-docens","category-modal-matters"],"_links":{"self":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/10670","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=10670"}],"version-history":[{"count":0,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/posts\/10670\/revisions"}],"wp:attachment":[{"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/media?parent=10670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/categories?post=10670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maverickphilosopher.blog\/index.php\/wp-json\/wp\/v2\/tags?post=10670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}