{"id":1708,"date":"2009-09-17T16:03:29","date_gmt":"2009-09-17T14:03:29","guid":{"rendered":"http:\/\/deleet.dk\/?p=1708"},"modified":"2009-09-17T16:03:29","modified_gmt":"2009-09-17T14:03:29","slug":"explicating-epistemic-possibility","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2009\/09\/explicating-epistemic-possibility\/","title":{"rendered":"Explicating epistemic possibility"},"content":{"rendered":"

It is clear that when we use the phrase \u201cIt is possible that…\u201d it is not in all cases used to express mere alethic possibility, that is, \u201cIt is logically possible that p.\u201d [\u25caP] Other times it is used to express what is called epistemic possibility, that is, \u201cFor all we (or I) know p might be true.\u201d. It preliminarily seems like a good idea to explicate this as \u201cIt is compatible with everything we know that p is true and that p is false.\u201d.1<\/sup><\/a> But this is an improper explication as pointed out in Possible Worlds.<\/em>2<\/sup><\/a><\/span><\/p>\n

Consider the example of Goldbach’s Conjecture (GC), that is, that every even number greater than 2 is the sum of two prime numbers.3<\/sup><\/a> A mathematician might say that it is possible that (GC) is true. If we explicate that as suggested above, then we get that (GC) <\/span>and<\/em> not-(GC) is consistent with everything we know. We may formalize this explication as: <\/span><\/p>\n

(\u2200P)(EP\u2194\u25ca[P\u2227(\u2200n)Q<\/span>1<\/span><\/sub>\u2227Q<\/span>2<\/span><\/sub>\u2227Q<\/span>3<\/span><\/span><\/sub>\u2227…\u2227Q<\/span>n<\/span><\/sub>\u2227([\u2200Q][KQ])<\/span>]) where \u201cEP\u201d means \u201cP is epistemically possible\u201d, \u201cKQ\u201d means \u201cQ is known\u201d.4<\/sup><\/a><\/span><\/p>\n

However, since (GC) is a mathematical proposition, then it is either necessarily true, or necessarily false. If it is necessarily true, then it’s negation is not consistent with everything we know. All necessary falsehoods are inconsistent with any proposition.5<\/sup><\/a> If (GC) is false, then (GC) is necessarily false, and, thus it is not consistent with everything we know. If (GC) is true, then it is necessarily true, but then the claim that it is false is necessarily false and thus not consistent with everything we know. I note that this objection applies when one deals with non-contingent propositions.<\/span><\/p>\n

The authors of <\/span>Possible Worlds<\/em> suggest instead that epistemic possibility should be explicated without alethic terms at all. They suggest the plain explication of: We (or I) do not know that (GC), and we do not know that not-(GC).<\/span><\/p>\n

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1<\/a>Simplifying \there. It is possible to formulate it without assuming bivalence.<\/div>\n

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2<\/a>N. \tSwartz, R. Bradley, 1979, pp. 229-230.<\/div>\n

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3<\/a>Some \texamples: 4 is the sum of 1 and 3. 6 is the sum of 3 and 3. 8 is the \tsum of 5 and 3. Etc. \thttp:\/\/en.wikipedia.org\/wiki\/Goldbach%27s_Conjecture<\/a><\/div>\n

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4<\/a>This \tis a bit complicated because it uses propositions as variables and \tpropositions are written in the upper case in formalizations. It is \tto be read as: For all propositions, that P is epistemically \tpossible is logically equivalent with that it is logically possible \tthat (P and Q1<\/sub> and Q2<\/sub> and Q3<\/sub> etc, \tand that for all Q’s, Q is known.<\/div>\n

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5<\/a>To \tsay that two propositions are consistent is to say that they are \tboth true in some possible world, but a necessary falsehood is not \ttrue in any possible world, thus, it is not true together with any \tother proposition in any possible world. Hence, it is not consistent \twith any proposition. More about this in chapter 1 of Possible \tWorlds.<\/em><\/div>\n","protected":false},"excerpt":{"rendered":"

It is clear that when we use the phrase \u201cIt is possible that…\u201d it is not in all cases used to express mere alethic possibility, that is, \u201cIt is logically possible that p.\u201d [\u25caP] Other times it is used to express what is called epistemic possibility, that is, \u201cFor all we (or I) know p […]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27],"tags":[343,369,474],"class_list":["post-1708","post","type-post","status-publish","format-standard","hentry","category-epistemology","tag-epistemic-possibility","tag-explication","tag-goldbachs-conjecture","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/1708","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/comments?post=1708"}],"version-history":[{"count":0,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/1708\/revisions"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=1708"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=1708"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=1708"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}