{"id":195,"date":"2006-01-29T22:59:00","date_gmt":"2006-01-30T02:59:00","guid":{"rendered":"http:\/\/alanrhoda.net\/wordpress\/?p=195"},"modified":"2006-01-29T22:59:00","modified_gmt":"2006-01-30T02:59:00","slug":"of-unicorns-and-possible-worlds","status":"publish","type":"post","link":"http:\/\/alanrhoda.net\/wordpress\/2006\/01\/of-unicorns-and-possible-worlds\/","title":{"rendered":"Of Unicorns and Possible Worlds"},"content":{"rendered":"

A few posts back<\/a> I suggested that there might be two senses of “exists”: (1) a “there is” sense that functions linguistically as a second-order predicate (i.e., it says of a concept or predicate expression that its extension is non-empty), and (2) an “is actual” sense that functions linguistically as a first-order predicate of individuals.<\/p>\n

I tried to support this distinction by appealing to what seem to be noncontroversial cases of possible but non-actual things (like dinosaurs, unicorns, the WTC, etc.). Consequently, it seems right to say that “There are<\/span> possible things that do not exist<\/span>.” But for that to make sense, what is affirmed by “there are” cannot be what’s denied by “do not exist”. With two senses of “exists”, however, this can be read without contradiction as saying “There are possible things that are not actual.”<\/p>\n

Commentator Ocham disputes my logic. He thinks I’m guilty of fallaciously reasoning from<\/p>\n

(1) Possibly, there are unicorns.
to
(2) There are possible unicorns.<\/p>\n

Perhaps I am guilty of some simple mistake like this, but I don’t think so. In the interests of furthering discussion I’m going to try and restate my argument in more precise logical terms using possible worlds semantics.<\/p>\n

Let A<\/span> be the actual world, let U<\/span> be a possible world accessible from A<\/span>, and let U<\/span> contain unicorns. Then, the following are true:<\/p>\n

(3) It is not the case that unicorns are actual. (b\/c A<\/span> does not contain unicorns)<\/span>
(4) It is possible that unicorns <\/span> are actual. (b\/c U<\/span> does contain unicorns and <\/span>is accessible from A<\/span>)<\/p>\n

I take (4) to say the same thing as (1).<\/p>\n

Notice, we have here two<\/span> distinct possible worlds, A<\/span> and U<\/span>. But if we can have two of a thing, then we can quantify over it. So let’s quantify over possible worlds. The usefulness of this is that it allows us to restate (4) without using any modal qualifiers.<\/p>\n

Let w be a variable that ranges over possible worlds, and let x be a variable that ranges over all individuals within a possible world. Also, let W_ stand for “… is a world”, let U_ stand for “… is a unicorn”, and let _E_ stand for “… exists (is actual) in …”. In these terms, (4) states:<\/p>\n

(4′) (\u2203w)(Ww &<\/span> (\u2203x)(xEw &<\/span> Ux))<\/p>\n

which is just a generalization of the claim that U<\/span> is a possible world that contains unicorns:<\/p>\n

(5) (\u2203w)(Ww &<\/span> w=U<\/span> & (\u2203x)(xEU<\/span> &<\/span> Ux))<\/p>\n

Ex hypothesi<\/span>, the quantifiers (\u2203w) and (\u2203x) cannot mean “is actual” because we’re quantifying over possible worlds and their contents without implying anything about whether they are actual or not. The predicate _E_, however, denotes world-relative actuality<\/span>, which in the actual world A<\/span> reduces to actuality simpliciter<\/span> (i.e., xEA<\/span> \u2194 x is actual).<\/p>\n

In light of the foregoing, my argument for two senses of “exists” can be restated as follows: We can quantify over non-actuals<\/span>. Hence, if, in Fregean terms, existence is simply the denial of the number nought, there must be a sense of “exists” that does not imply actuality. On the other hand, we need to distinguish between actuals and non-actuals. Hence, we need a sense of “exists” that does imply actuality.<\/p>\n","protected":false},"excerpt":{"rendered":"

A few posts back I suggested that there might be two senses of “exists”: (1) a “there is” sense that functions linguistically as a second-order predicate (i.e., it says of a concept or predicate expression that its extension is non-empty), and (2) an “is actual” sense that functions linguistically as a first-order predicate of individuals.\u2026 Read More »<\/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":[],"class_list":["post-195","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/195","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=195"}],"version-history":[{"count":0,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/195\/revisions"}],"wp:attachment":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/media?parent=195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/categories?post=195"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/tags?post=195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}