{"id":20,"date":"2009-09-25T18:05:00","date_gmt":"2009-09-25T22:05:00","guid":{"rendered":"http:\/\/alanrhoda.net\/wordpress\/?p=20"},"modified":"2013-09-22T21:12:27","modified_gmt":"2013-09-23T01:12:27","slug":"the-modal-openness-of-the-future","status":"publish","type":"post","link":"http:\/\/alanrhoda.net\/wordpress\/2009\/09\/the-modal-openness-of-the-future\/","title":{"rendered":"The Modal Openness of the Future"},"content":{"rendered":"<p>There&#8217;s a simple and valid argument for fatalism based on a proposition which most analytic philosophers would accept. The assumption is this<\/p>\n<ul>\n<li>There is an actual world, alpha, which contains a complete history. Unlike other merely possible worlds, alpha is the possible world that &#8220;obtains&#8221;.<\/li>\n<\/ul>\n<p>For the sake of argument I take this assumption for granted.<\/p>\n<p>Now, <i>fatalism<\/i> can be understood as the doctrine that no events have an intermediate chance of occurring. By a &#8216;chance&#8217; I mean a single-case objective probability. By an &#8216;intermediate&#8217; chance I mean a value between zero and one. If the chance of an event is one, then it is unpreventable&#8211;it&#8217;s guaranteed to happen. If the chance of an event is zero, then its non-occurrence is unpreventable&#8211;it&#8217;s guaranteed not to happen. Fatalism simply says that, for any event, its chance of occurring is either zero or one.<\/p>\n<p>Now, consider the actual world, alpha. This includes a complete history. Hence, for every possible event E, either alpha entails that E occurs, or alpha entails that E doesn&#8217;t occur. If alpha entails that E occurs, then the chance of E&#8217;s occurring given alpha equals one. If alpha entails that E does not occur, then the chance of E&#8217;s occurring given alpha equals zero. Using CH() to represent the chance function, this means that for arbitrary E, either<\/p>\n<ol>\n<li>CH(E | alpha) = 0, or<\/li>\n<li>CH(E | alpha) = 1.<\/li>\n<\/ol>\n<p>Now, what is the chance of alpha? That is, what is the chance that alpha obtains or that alpha is the case? Obviously, it&#8217;s got to be one. In general, the chance that anything <i>is<\/i> the case has got to be either zero or one. Consider my sitting at time T. If it is the case that I sit at t, then the chance that I sit at T is one. It&#8217;s too late to prevent it. Likewise, if it is the case that I stand at T, then the chance that I sit at T is zero. It&#8217;s too late to bring it about that I sit at T. Thus, since alpha (in its entirety) obtains, and thus is the case, we get<\/p>\n<ol start=\"3\">\n<li>CH(alpha) = 1.<\/li>\n<\/ol>\n<p>But from 2 and 3 there follows<\/p>\n<ol start=\"4\">\n<li>CH(E) = 1.<\/li>\n<\/ol>\n<p>And from 1 and 3 there follows<\/p>\n<ol start=\"5\">\n<li>CH(E) = 0.<\/li>\n<\/ol>\n<p>Hence, E is not a future contingent. Since the argument holds for arbitrary E, fatalism is thereby established.<\/p>\n<p>To avoid fatalism the initial assumption must be rejected. We must either deny that there is an actual world (i.e., we must deny that any possible world which includes a complete history obtains), or we must deny that possible worlds must include a complete history, in particular, a complete future history. Call that denial the <i>modal openness of the future<\/i> thesis. I maintain that the future is modally open. As contingencies are resolved, the modal changes. Things that <i>were<\/i> possible may not <i>now <\/i>be possible. Things that <i>are<\/i> necessary may not always <i>have been<\/i> necessary.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There&#8217;s a simple and valid argument for fatalism based on a proposition which most analytic philosophers would accept. The assumption is this There is an actual world, alpha, which contains a complete history. Unlike other merely possible worlds, alpha is the possible world that &#8220;obtains&#8221;. For the sake of argument I take this assumption for\u2026 <span class=\"read-more\"><a href=\"http:\/\/alanrhoda.net\/wordpress\/2009\/09\/the-modal-openness-of-the-future\/\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[4,3,5],"class_list":["post-20","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-modality","tag-openfuture","tag-possibleworld"],"_links":{"self":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/20","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/comments?post=20"}],"version-history":[{"count":1,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/20\/revisions"}],"predecessor-version":[{"id":250,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/20\/revisions\/250"}],"wp:attachment":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/media?parent=20"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/categories?post=20"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/tags?post=20"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}