{"id":504,"date":"2015-02-22T19:37:23","date_gmt":"2015-02-23T00:37:23","guid":{"rendered":"http:\/\/alanrhoda.net\/wordpress\/?p=504"},"modified":"2015-03-29T15:40:01","modified_gmt":"2015-03-29T20:40:01","slug":"correspondence-vs-disquotation","status":"publish","type":"post","link":"http:\/\/alanrhoda.net\/wordpress\/2015\/02\/correspondence-vs-disquotation\/","title":{"rendered":"Correspondence vs. Disquotation"},"content":{"rendered":"

In my previous two posts I have discussed the correspondence theory of truth<\/a> and disquotation principles<\/a>. In this post I’m going to use the former to argue against the latter.\u00a0More specifically, I’m going to argue that the “if and only if” of the disquotation principles should be merely an “only if”. In other words, instead of<\/p>\n

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

    I will argue that we should affirm only<\/p>\n

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    1. <p<\/em>> is true only if\u00a0p<\/em><\/li>\n<\/ol>\n

      and reject<\/p>\n

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      1. <p<\/em>> is true if\u00a0p.<\/em><\/li>\n<\/ol>\n

        (3)\u00a0is more naturally expressed as (4):<\/p>\n

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        1. If p<\/em>\u00a0then <p<\/em>>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

          I’m going to argue that (4) is false, and that therefore (1) is false.<\/p>\n

          Why (4) may seem to be necessarily\u00a0true<\/span><\/b><\/p>\n

          My claim that (4) is false is bound to be met with some skepticism, for many philosophers regard (4) as logically necessary. Before launching into my critique of (4) it will be helpful to begin by giving this perspective its due.<\/p>\n

          Conflating use and mention.<\/span><\/em> One line of thought that may\u00a0lead one to endorse (4) as logically necessary is based on a misreading of it and on a conflation of the use\/mention distinction. Thus, it may be thought that (4) should be read as<\/p>\n

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          1. If p<\/em>\u00a0is true<\/span> then <p<\/em>>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

            But (5)\u00a0is the wrong way to read (4). In my previous post discussing disquotation principles I noted that the variable p<\/em> occurs twice. When p<\/i> occurs in quotes or angle brackets it\u00a0is\u00a0mentioned, but not used <\/em><\/strong>because it functions\u00a0merely as a referring device allowing us to predicate truth of this<\/em>\u00a0truthbearer. In contrast, when p<\/em> occurs without quotes or angle brackets it is\u00a0used, but not mentioned<\/em><\/strong>\u00a0because\u00a0p\u00a0<\/em>is being used to describe a putative state of affairs. To read (4) as\u00a0(5)\u00a0is confused because if we’re going to predicate truth of p<\/em> in the antecedent then we have to refer not<\/em> to the state of affairs described by p<\/em> but\u00a0to p<\/em> itself. So (5) should read like (6):<\/p>\n

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            1. If <p><\/em>\u00a0is true<\/span> then <p<\/em>>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

              Now, (6) is obviously a tautology. As such it is both logically necessary and trivially true. (More exactly, it’s logically necessary that (6) is\u00a0true if<\/em> the proposition it expresses\u00a0exists<\/em>.) And so one who mistakenly reads (4) in this way may come away with the impression that (4) is logically\u00a0necessary. But (6)\u00a0doesn’t say the same thing as (4)<\/em><\/strong>. In (4) the antecedent isn’t saying something\u00a0about<\/em>\u00a0p<\/em> (e.g., that\u00a0p<\/em> is true). Rather, it’s saying something about\u00a0reality<\/em>, i.e.,<\/p>\n

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              1. If\u00a0reality is as <<\/em>p> describes<\/em>, then\u00a0<p<\/em>>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

                Subject to the additional need for quantification\u00a0that I will address shortly, (7) is the correct way to read (4). We can easily see this by considering standard examples of the disquotation principle, such as<\/p>\n

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                1. <The cat is on the mat> is true if and only if\u00a0the cat is on the mat.<\/li>\n<\/ol>\n

                  What (8) says is that the proposition <The cat is on the mat> is true if and only if things are as that proposition describes, that is, if and only if the cat in question really\u00a0is<\/em> on the mat in question.<\/p>\n

                  Taking the existence of propositions for granted<\/em>.<\/span>\u00a0<\/em>Another way in which one might come to regard (4) as logically\u00a0necessary\u00a0is by taking\u00a0the\u00a0existence<\/em> of propositions in general, or of specific propositions, for granted. Of course, if <\/em>a proposition exists then it must have a truth value depending on whether reality is as it describes or not. And so we arrive at (4), that if reality is as a given proposition describes, then that proposition is true.<\/p>\n

                  But\u00a0p<\/em>\u00a0in (4) isn’t a proposition; it is a\u00a0variable<\/em>\u00a0or a placeholder for propositions. To\u00a0evaluate an expression that contains a variable one must ask what the\u00a0domain<\/em> of that variable is. Its domain is the collection of things that can be admissibly plugged into it. In (4) this is the collection of propositions. To make the meaning of (4) fully explicit we must\u00a0make its domain explicit as follows:<\/p>\n

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                  1. For all propositions\u00a0p<\/em>, if p<\/em>\u00a0accurately\u00a0describes reality then\u00a0p<\/em>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

                    (Since the quantifier explicitly identifies p<\/em> as a proposition, and since all instances of p<\/em> in (9) are cases in which\u00a0p<\/em> is mentioned, but not used<\/em>\u2014so that there are no\u00a0possible use<\/em>\/mention<\/em> conflations to worry about\u2014I have dropped the angle brackets for notational simplicity.)<\/p>\n

                    It must be observed, however, that (9) doesn’t commit us to the existence of propositions, any more than<\/p>\n

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                    1. For all hobbits\u00a0h<\/em>, if\u00a0h<\/em>\u00a0lives at Bag End, then\u00a0h<\/em>\u00a0is named\u00a0<\/em>Bilbo<\/li>\n<\/ol>\n

                      commits us to the existence of hobbits. For all (9) tells us, the domain of\u00a0p<\/em>, the collection of propositions, could be\u00a0empty<\/em>.<\/p>\n

                      Neither (9), (7), (4), nor (1) entitles us to take the existence of\u00a0any given proposition, or any propositions at all, for granted. Assuming the existence of propositions may seem like an innocuous assumption. After all, we know<\/em> that propositional units of meaning exist. We contemplate and express them all the time. But the thought that (4) is a logically\u00a0<\/em>necessary<\/em> truth requires quantifying not just over\u00a0actual<\/em> propositions (some of which we know to exist), but also over logically possible worlds<\/em>. In other words, the claim is that<\/p>\n

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                      1. For\u00a0all logically possible worlds w<\/em> and for all propositions\u00a0p<\/em>,\u00a0if p<\/em>\u00a0accurately\u00a0describes reality in w<\/em>\u00a0then\u00a0p<\/em>\u00a0<\/em>is true at w<\/em>.<\/li>\n<\/ol>\n

                        But what if it’s logically possible that there be an\u00a0empty<\/em> world, one in which nothing exists? Or what if it’s logically possible that there be a world in which there are no minds<\/em>, and thus no propositions? That (4) is necessarily true requires not just the obviously correct assumption that some propositions exist, but the far from obvious assumption that it is logically necessary that some propositions exist. Perhaps that’s right. But one can’t establish it by appealing to (4) on pain of begging the question.<\/p>\n

                        Why (4) is false<\/span><\/strong><\/p>\n

                        Having argued that (4) is not, or at least is not obviously, a logically necessary truth, I’m now going to argue that it is in fact\u00a0false<\/em>. It is false, I say, because it conflicts with the correspondence theory of truth, which rests on much firmer intuitive grounds.<\/p>\n

                        According to the correspondence theory, truth is a relation of correspondence between a\u00a0truthbearer<\/strong> and a\u00a0truthmaker<\/strong>. The fundamental truthbearers are propositions. Accordingly, for a proposition to be true both<\/em><\/strong> the proposition and a corresponding truthmaker<\/em> must exist. (In the special case of analytic propositions, the proposition is it’s own truthmaker.) But look again at what (4) says.\u00a0As glossed in (7) it says that<\/p>\n

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                        1. If\u00a0reality is as <<\/em>p> describes<\/em>, then\u00a0<p>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

                          The antecedent “reality is as <p> describes” assumes a truthmaker<\/em> for <p><\/em> but\u2014and here’s the crucial point\u2014it doesn’t assume the existence of <<\/em>p><\/em>. It therefore\u00a0gives us only half<\/i> of what’s required for <p<\/em>> to be true. It gives us a truthmaker for <p<\/em>> but not <p<\/em>> itself, the truthbearer. Consequently, (7) is false\u2014and with it (1), (4), (9), and (11) as well. That reality is as <p<\/em>> describes is\u00a0necessary but not sufficient<\/em><\/strong> for <p<\/em>>’s being true. It must\u00a0also<\/em> be the case that <p<\/em>> exists.<\/p>\n

                          We should replace (4), therefore, with<\/p>\n

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                          1. If\u00a0p<\/em>\u00a0and <p<\/em>> exists, then\u00a0<p<\/em>>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

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

                            Now, as I’ve said above, in the actual world we can safely take the existence of many propositions for granted. But we cannot use principles like (4) to establish the existence of propositions in all logically possible worlds. Moreover, even in the actual world we must be careful not to assume that just because we can create declarative sentences that\u00a0seem to express<\/em> propositions that they actually do so. Lewis Carroll’s famous nonsense poem\u00a0Jabberwocky<\/a><\/em> contains many statements that could be used to express propositions. We might think to plug some of these into (4), for example,<\/p>\n

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                            1. If the slithy toves did gyre and gimble in the wabe\u00a0then <The slithy toves did gyre and gimble in the wabe>\u00a0<\/em>is true.<\/li>\n<\/ol>\n

                              But since “the slithy toves did gyre and gimble in the wabe” is nonsense it doesn’t express a proposition. To apply (4), then, we must be able to do two things:<\/p>\n