{"id":508,"date":"2015-02-17T21:37:39","date_gmt":"2015-02-18T02:37:39","guid":{"rendered":"http:\/\/alanrhoda.net\/wordpress\/?p=508"},"modified":"2015-02-18T21:30:00","modified_gmt":"2015-02-19T02:30:00","slug":"truth-correspondence-and-disquotation","status":"publish","type":"post","link":"http:\/\/alanrhoda.net\/wordpress\/2015\/02\/truth-correspondence-and-disquotation\/","title":{"rendered":"Truth and Disquotation Principles"},"content":{"rendered":"

In my previous post<\/a> I talked about the correspondence theory of truth<\/strong> and its relation to truthmaker theory<\/strong>. I’m going to follow it\u00a0up with a series of posts on various issues concerning truth and ontology that I’ve been mulling over off-and-on over the past several years.\u00a0The current post concerns disquotation principles<\/strong>. I distinguish between sentential and propositional disquotation principles and argue that the latter is of much wider applicability than the former.<\/p>\n

<\/p>\n

Disquotation principles<\/strong><\/span><\/p>\n

Disquotation principles comes in two main forms, (1)\u00a0and\u00a0(2):<\/p>\n

    \n
  1. “p<\/i>” is true if and only if\u00a0p<\/em>.<\/li>\n
  2. <p<\/em>> is true if and only if\u00a0p<\/em>.<\/li>\n<\/ol>\n

    I\u00a0call (1) the\u00a0sentential disquotation principle <\/strong>because in it the variable\u00a0p<\/em>\u00a0is supposed to take the place of a sentence<\/em>, and more specifically, of a declarative sentence or statement. Sentences are strings of symbols that when grammatically well-formed are capable of expressing a complete thought, one that includes both a subject and a predicate.<\/p>\n

    I call (2) the\u00a0propositional disquotation principle<\/strong>\u00a0because in it\u00a0the variable\u00a0p<\/em> is supposed to take the place of a\u00a0proposition<\/em>. Unlike sentences, propositions are not strings of symbols. Rather, they are\u00a0units of meaning<\/em> capable of bearing a truth value. (Concepts like\u00a0green<\/em> are also units of meaning, but it makes no sense to suppose it is true that green<\/em>.) Declarative sentences are typically used to\u00a0express<\/em> propositions, but they are not identical to the propositions they express. To suppose otherwise is\u00a0to confuse the message (the proposition expressed) with the symbolic carrier of the message (the sentence).<\/p>\n

    Sentential disquotiation<\/strong><\/span><\/p>\n

    (1) may seem like a truism, but I will argue that it is true only in\u00a0very limited<\/em> contexts. Consider the following examples:<\/p>\n

      \n
    1. “Buddha was fat” is true if and only if Buddha was fat.<\/li>\n
    2. “Janelle is a curly-haired puppy lover” is true if and only if Janelle is a curly haired puppy lover.<\/li>\n
    3. “1 + 1 = 2” is true if and only if 1 + 1 = 2.<\/li>\n<\/ol>\n

      In each case, on the left-hand side (LHS) is a quoted declarative sentence to which is appended the predicate “is true”. On the right-hand side (RHS) the quoted sentence appears again, but without quotes.<\/p>\n

      Why are there quotes around the sentence on the LHS but not the RHS? The reason for this is because, on the LHS, we want to predicate truth\u00a0of a sentence<\/em>, and so that sentence has to become the subject of a clause. To make it into a subject we have to refer to the sentence as a whole. Putting quotes around it\u00a0allows us to do this.\u00a0It allows us\u00a0to mention<\/em>\u00a0the sentence\u00a0<\/em>without\u00a0using<\/em> it<\/strong>. The clause on the RHS, in contrast, lacks quotes because there the sentence is\u00a0used to describe its\u00a0truth conditions<\/strong>. The two occurrences of\u00a0p<\/em> in (1), therefore, have very different roles. On the LHS “p<\/em>” is used denotatively to single out or\u00a0name<\/em>\u00a0p<\/em>, whereas on the RHS p<\/i> is used connotatively to\u00a0express<\/em>\u00a0p<\/em>.<\/p>\n

      Now, the problem with (1), the reason why it is true only in limited contexts, is because most sentences are not perfectly\u00a0clear and precise as to their meaning<\/em>. One problem, illustrated by (3), is\u00a0vagueness<\/strong>. There is no clear line of demarcation between fat<\/em> and\u00a0non-fat<\/em> persons. Hence, the meaning, and therefore the truth conditions, of “Buddha was fat” are vague. There is no clear demarcation on the RHS between cases in which its truth conditions are fulfilled and cases in which they aren’t. Likewise, there is no clear demarcation on the LHS between cases in which “Buddha was fat” is true and cases in which it isn’t. Consequently, there is no clear demarcation between cases in which the “if and only if” comparative is satisfied and cases in which it isn’t. But then (3) isn’t true, and so neither is (1).<\/p>\n

      Another problem facing (1) is that of ambiguity<\/strong>. Ambiguity occurs when there are multiple distinct meanings and no clear way to choose between them. (4) is an example of ambiguity.\u00a0What exactly is the sentence saying about Janelle (my daughter)? Is it saying that she has curly hair and that she loves puppies? Or it it saying that she loves puppies that have curly hair? Both interpretations are grammatically admissible. Hence, there is no unique<\/em>\u00a0set of truth conditions for (4). The “only if” part of the comparative, therefore, cannot be satisfied. But then (4) isn’t true, and so neither is (1).<\/p>\n

      We could try to save (1) by appealing to context, to speaker’s intentions, or to what a typical speaker would\u00a0normally<\/em> mean by using a sentence in a context to fix an exact<\/em>, unique<\/em>, and correct<\/em>\u00a0interpretation of the sentence. But there’s no reason to think that such appeals will, in all cases, yield an exact, unique, and correct interpretation. After all, erudite scholars who are keenly sensitive to matters of context and the nuances of language have been debating for centuries<\/em> about how best to interpret certain passages of the Bible or of Shakespeare. Moreover, the moment we appeal to things like context, intentions, and common usage we are in effect admitting that\u00a0sentences<\/em>, in and of themselves,\u00a0don’t<\/em> have exact and unique meanings. But that’s what (1) assumes. It assumes that the meaning, and therefore the truth conditions, of any given declarative sentence are exactly fixed by the sentence<\/em>. And this just isn’t so.<\/p>\n

      The least unproblematic<\/em> cases for (1)\u00a0are cases like (5) in which the sentence in question is absolutely clear and precise. There is no vagueness or ambiguity in “1 + 1 = 2”. We can specify exactly<\/em> what the sentence means and therefore what it takes for the sentence to be true. It is no accident that Tarski, the man responsible for developing and promoting (1), was a mathematical logician. Mathematical expressions are formulated in an artificial mathematical language designed<\/em> for precision and logical rigor.\u00a0So, to the extent that (1) is true, it is true only with respect to logically rigorous contexts of this sort in which we don’t have to worry about vagueness and ambiguity.<\/p>\n

      Propositional disquotation<\/strong><\/span><\/p>\n

      The angle brackets on the LHS of (2) function in the same way as the quotes in (1). They allow us to refer to or denote\u00a0p<\/em> without connotatively expressing\u00a0p<\/em>. <p<\/em>> on the LHS names<\/em> a proposition. p<\/em> on the RHS\u00a0expresses<\/em>\u00a0the proposition named by <p<\/em>>. The reason for using angle brackets instead of quotes is to make clear that <p<\/em>> is not referring to a sentence, but to a proposition.<\/p>\n

      (2) is far<\/em> more plausible than (1) because propositions suffer from none of the limitations of sentences. Unlike sentences, which often have no clear meaning, a proposition\u00a0is identical<\/strong> to its meaning<\/em>. Propositions, by their very nature, exclude vagueness and ambiguity.<\/p>\n

      Propositions do have an important practical limitation, however. The difficulty is that we have no way to communicate <\/em>propositions or to identify<\/i>\u00a0which proposition we have in mind without expressing\u00a0our thoughts in sentential terms. And this ultimately brings vagueness and ambiguity (and figurative language etc.) back into the mix. So even if (2) is true, we often can’t know for certain whether we’ve applied<\/em> it correctly, for we often can’t know for certain whether we’re all talking about the\u00a0same<\/em> proposition.<\/p>\n

      Concluding remarks<\/strong><\/span><\/p>\n

      So far I have argued that, of the two disquotation principles, (2) has much<\/em> more to be said for it than (1). Indeed, many philosophers would regard (2) not only as\u00a0obviously<\/em>\u00a0true but also as logically<\/em>\u00a0necessary<\/em>.\u00a0In my next post I will argue that this view is\u00a0actually\u00a0quite mistaken.<\/p>\n","protected":false},"excerpt":{"rendered":"

      In my previous post I talked about the correspondence theory of truth and its relation to truthmaker theory. I’m going to follow it\u00a0up with a series of posts on various issues concerning truth and ontology that I’ve been mulling over off-and-on over the past several years.\u00a0The current post concerns disquotation principles. I distinguish between sentential\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":[32,56],"tags":[59,57,51,58],"class_list":["post-508","post","type-post","status-publish","format-standard","hentry","category-truth","category-use-vs-mention","tag-ambiguity","tag-disquotation","tag-truth","tag-vagueness"],"_links":{"self":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/508","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=508"}],"version-history":[{"count":11,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/508\/revisions"}],"predecessor-version":[{"id":521,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/508\/revisions\/521"}],"wp:attachment":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/media?parent=508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/categories?post=508"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/tags?post=508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}