{"id":110,"date":"2006-09-20T02:05:00","date_gmt":"2006-09-20T06:05:00","guid":{"rendered":"http:\/\/alanrhoda.net\/wordpress\/?p=110"},"modified":"2006-09-20T02:05:00","modified_gmt":"2006-09-20T06:05:00","slug":"tense-logic-bivalence-and-open-theism","status":"publish","type":"post","link":"http:\/\/alanrhoda.net\/wordpress\/2006\/09\/tense-logic-bivalence-and-open-theism\/","title":{"rendered":"Tense Logic, Bivalence, and Open Theism"},"content":{"rendered":"<p>In previous blog posts I&#8217;ve discussed two opposing tense logics: (a) Ockhamist and (b) Peircean. Ockhamist tense logic takes as its characteristic axiom the claim that<\/p>\n<blockquote><p>(O) \u25a1(\u2200p)(\u2200t)(\u2200u: u<t )(IS(p,t) \u2192 WAS(WILL(p,t),u))\n\ni.e., necessarily, for all propositions p, and for all times t and u such that u is prior to t, p is the case at t, then at u it was the case that p will be the case at t <\/p><\/blockquote>\n<p>In contrast, Peircean tense logic insists that (O) is a <span style=\"font-style: italic;\">non sequitur<\/span>, and replaces it with:<\/p>\n<blockquote><p>(P) \u25ca(\u2203p)(\u2203t)(\u2203u: u<t )(IS(p,t) \u2227 \u00acWAS(WILL(p,t),u))\n\ni.e., possibly, for some proposition p and some times t and u such that u is prior to t, p is the case at t and it was not the case at u that p will be the case at t<\/p><\/blockquote>\n<p>The basis of the disagreement turns on whether the future tense operator, WILL, carries <span style=\"font-style: italic;\">determinative force<\/span>. In other words, if one is speaking strictly (not loosely) and predicts that something <span style=\"font-style: italic;\">will<\/span> happen, is it implied that the predicted event is necessitated by what obtains at the time the prediction is made? If so, then the Peircean is right. Otherwise, the Ockhamist is right.<\/p>\n<p>Without trying to resolve that particular issue right now, I&#8217;d like to note that there are three possible results if the Peircean is correct, depending on how one answers two questions: (1) are there any propositions about the future that carry absolutely <span style=\"font-style: italic;\">no <\/span>determinative force whatsover, i.e., Ockhamist-style predictions? (2) If so, are these propositions bivalent, i.e., must they be either true or, if not true, then false?<\/p>\n<ul>\n<li>Option 1: Yes on (1). Yes on (2). This means that the future is <span style=\"font-style: italic;\">alethically settled<\/span>, i.e., there is an unchanging set of true Ockhamist-style predictions that completely characterizes the future as of any given time.<\/li>\n<li>Option 2: Yes on (1). No on (2). The future is alethically open (i.e., not alethically settled), but some Ockhamist-style prediction (those pertaining to future contingents) are neither true nor false.<\/li>\n<li>Option 3: No on (1). The future is alethically open and bivalence is preserved because there simply are no Ockhamist-style predictions.<\/li>\n<\/ul>\n<p>Now, suppose one is an open theist. That is, suppose that one affirms the conjunction of (a) monotheism, (b) future contingency, and (c) the incompatibility of future contingency with God&#8217;s knowing the future as wholly determinate and settled. It turns out that there are three major versions of open theism, each corresponding to one of the three options above.<\/p>\n<ul>\n<li>Version 1 &#8211; Involuntary Partial Nescience: God knows all that can be known, but there are truths about the contingent future that simply cannot be known, not even by God. (Richard Swinburne and William Hasker have espoused this view.)<\/li>\n<li>Version 2 &#8211; Non-bivalentist Omniscience: God is fully omniscient, i.e., knowing all and only truths. Ockhamist-style propositions about the contingent future are neither true nor false. (J.R. Lucas, among others, has espoused this view.)<\/li>\n<li>Version 3 &#8211; Bivalentist Omniscience: God is fully omniscience. There are no Ockhamist-style propositions about the contingent future. (Greg Boyd has espoused this view.)<\/li>\n<\/ul>\n<p>Each view faces some challenges. The proponent of version 1 needs to explain how there can be truths that are in principle unknowable. The proponent of version 2 needs to motivate the denial of bivalence and the attendent rejection of standard logic. The proponent of version 3 needs to make a persuasive case that Ockhamist-style predictions are not really propositions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In previous blog posts I&#8217;ve discussed two opposing tense logics: (a) Ockhamist and (b) Peircean. Ockhamist tense logic takes as its characteristic axiom the claim that (O) \u25a1(\u2200p)(\u2200t)(\u2200u: u<\/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":[],"class_list":["post-110","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/110","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=110"}],"version-history":[{"count":0,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/110\/revisions"}],"wp:attachment":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/media?parent=110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/categories?post=110"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/tags?post=110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}