Vague, So Untrue. David Braun and Theodore Sider Noûs 41 (2007): - PDF

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Vague, So Untrue David Braun and Theodore Sider Noûs 41 (2007): According to an old and attractive view, vagueness must be eliminated before semantic notions (truth, implication, and so on) may

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Vague, So Untrue David Braun and Theodore Sider Noûs 41 (2007): According to an old and attractive view, vagueness must be eliminated before semantic notions (truth, implication, and so on) may be applied. This view call it semantic nihilism was accepted by Frege, but is rarely defended nowadays. 1 This recent neglect is unjustified: the thorny nest of problems surrounding vagueness is best untangled by accepting something like the old The authors formulated the main idea for this paper in Sider wrote a first draft in the Spring of 2001 and presented talks at various places, some under the title Vagueness, Ambiguity and the Application of Logic. Braun and Sider revised the paper significantly during We would like to thank the following for helpful comments: JC Beall, Jiri Benovsky, Sylvain Bromberger, Cian Dorr, Delia Graff, Hilary Greaves, John Hawthorne, Mark Heller, Benj Hellie, Hud Hudson, Jeff King, Karson Kovakovich, Sarah-Jane Leslie, Europa Malynicz, Ned Markosian, Gail Mauner, Vann McGee, Brian McLaughlin, Daniel Nolan, Teresa Robertson, Jennifer Saul, Roy Sorensen, Jason Stanley, Gabriel Uzquiano, Ryan Wasserman, Brian Weatherson, Timothy Williamson, anonymous referees, the participants in Tim Maudlin s seminar on truth, and audiences at Alabama, Alberta, the ANU, Boise State, Calvin, the Creighton Club, UC Davis, Kentucky, Leeds, Massachusetts, Massey, M.I.T., Miami, the New Jersey Regional Association conference, Oxford, the Princeton- Rutgers graduate student conference, Richmond, Southern Illinois at Edwardsville, Stockholm, Syracuse, Virginia, and Western Washington University. 1 Frege (1903, section 56); see also Williamson (1994, section 2.2). The recent literature does contain some related views. Mark Heller s view is somewhat like ours (1990, chapters 3 and 4). Peter Unger (1979a,b,c) claimed that vague sentences like I exist are untrue, but his view was far more radical than ours (e.g.: our existing expressions, at least by and large, fail to make any contact with whatever is there (1979a, p. 249)). See also Dummett (1975) and Wheeler (1975, 1979). An interesting case is David Lewis. Mostly he seems to endorse standard supervaluationism, but some intriguing remarks sound closer to semantic nihilism: Super-truth, with respect to a language interpreted in an imperfectly decisive way, replaces truth simpliciter as the goal of a cooperative speaker attempting to impart information (1993, p. 29 our boldface). Sorensen (2002) suggests that supervaluationists should reject the identification of supertruth with truth, and should hold that no sentence is true. Perhaps he has something like semantic nihilism in mind. Vann McGee and Brian McLaughlin (1995) also reject the identification, but unlike us, try to use supertruth to capture part of our ordinary notion of truth. Closest of all is the view presented by Kirk Ludwig and Greg Ray (2002). Like us, Ludwig and Ray say that vague sentences are untrue, and that vagueness does not require abandoning classical logic. But there are many differences between our theories, the most crucial of which stem from their (implausible, in our view) denial of vagueness in semantic vocabulary. Consequently, they do not develop a theory of ignoring, which is crucial to our account (section 1.2), nor do they address the worries that the view is self-defeating (section 1.4) and inexpressible (section 3.2). 1 Fregean view. If semantic notions such as truth apply only to completely precise sentences, they do not apply to English or any other natural language. Thus, almost no English sentences are true (or false). We defend this seemingly radical and self-refuting conclusion by developing a theory of how vagueness is typically and harmlessly ignored. Section one sets out semantic nihilism. Section two argues for its superiority to the structurally similar theory of supervaluationism. 2 Section three concerns truth. 1. Semantic nihilism 1.1 Semantic indeterminacy and truth An expression is vague if it can be unclear to a speaker informed of all relevant facts whether the expression correctly applies. Imagine a series of patches of color varying continuously from red to pink. A speaker who can see the patches clearly will nevertheless be unsure whether red applies to certain intermediate patches. Like many, we think that vagueness occurs when there exist multiple equally good candidates to be the meaning of a given linguistic expression. Red is vague because there are many color properties that equally deserve to be expressed by red. On our usage, any sentence containing a vague word such as red counts as vague, even if it does not concern a borderline case. We choose this usage because the multiplicity of candidate meanings for red results in a multiplicity of propositions that equally deserve to be the meaning of such a sentence. 3 We assume that the properties, relations, and propositions that are candidates for being the meanings of linguistic expressions are precise: any n-tuple of objects either definitely instantiates or definitely fails to instantiate a given n-place relation, and any proposition is either definitely true or definitely false. 4 But the facts that determine meaning (for instance, facts about use, naturalness of properties, and causal relations between speakers and properties) 2 We make no attempt at an exhaustive comparison with other rival theories. The literature contains powerful critiques of these theories (see especially Williamson (1994)), which provide our theory with ample motivation, if it can be adequately defended. 3 The multiplicity of propositions follows automatically, given a structured conception of propositions. 4 Our theory thus cannot capture so-called worldly vagueness, if it exists. 2 do not determine a unique property to be the meaning of red. 5 There is no property that red uniquely expresses, and therefore no unique proposition that a sentence containing red expresses. Vagueness is a type of semantic indeterminacy. 6 Many agree that vagueness results from a multiplicity of candidate meanings. Our distinctive claim concerns the impact of this multiplicity on semantics. The leading idea is that vagueness is a lot like ambiguity. 7 To be either true or false, a sentence must have a unique meaning. Ambiguous sentences do not have unique meanings. Therefore, they are neither true nor false. 8 Similarly, sentences containing vague expressions do not have unique meanings; therefore, they too are neither true nor false. 9 Ambiguity is usually taken to be resolved in context by the intentions of speaker and audience. If vagueness could be eliminated by context then truth and falsity could indeed be achieved. But unlike ambiguity, vagueness is rarely (if ever) totally eliminated in context; and so on our view, utterances are rarely (if ever) true or false. Most agree that vague sentences concerning borderline cases, for instance Five piled stones are a heap, are neither true nor false. Semantic nihilism goes much further: no sentences containing vague terms are either true or false, not even sentences that do not concern borderline cases. None of the following sentences is either true or false: Zero piled stones are a heap. 5 See Lewis (1983, 1984) and Devitt (1984, section 12.4) on content determination. We therefore oppose epistemicists like Sorensen (1988; 2001, chapter 11) and Williamson (1994, section 7.5), who hold that linguistic expressions generally do have unique meanings. We also oppose those like Fara (2000) and Soames (1999, chapter 7), who hold that vague expressions have meanings relative either to contexts, or sets of interests, that generate unique extensions. If the facts that determine meaning are not sufficiently fine-grained to secure sharp cutoffs, supplementing them with facts about the context will not suffice either. 6 Similar points hold for mental items. 7 Vagueness and ambiguity are merely analogous, not identical. The meanings of an ambiguous term cluster into a small number of disjoint groups which must be mastered individually by a competent speaker; in any context of use one has one of these clusters in mind; etc. And perhaps vagueness and ambiguity should be treated at different levels of linguistic analysis, the former being a property of linguistic expressions, the latter a property of sounds. (Thanks to Sylvain Bromberger for discussion.) 8 This is the dominant view about ambiguous sentences and truth values. See Fine (1975, p. 284), for a contrary opinion, and Tye (1989) for a criticism of Fine. 9 Do any sentences lack vagueness altogether? Perhaps mathematical sentences, or sentences constructed out of purely logical vocabulary, such as Everything is self-identical (uttered in a context in which the quantifier is unrestricted). 3 One million piled stones are a heap. If five piled stones are a heap then five piled stones are a heap. Five piled stones are a heap and it is not the case that five piled stones are a heap. These sentences lack truth value for the same reason ambiguous sentences do: lack of a unique meaning. 1.2 Approximate truth and ignoring vagueness We say that an utterance of A man with no hairs on his head is bald is vague, and therefore untrue. There exist some people, Snow is white, and George W. Bush was President of the United States in 2002 are all untrue. Despite this, we do not think of ourselves as defending a radical view. We do not recommend ceasing to speak vague languages. 10 We do not view vagueness as a defect, as Frege did. 11 For all we say, vagueness may be essential for language to be useful. 12 We do not recommend wholesale changes in linguistic practice; our semantic nihilism is intended as a rational reconstruction of existing practice. On our view, ordinary speakers typically and harmlessly ignore vagueness. And when doing so, it is reasonable to speak, in a sense to be defined, the approximate truth. While the facts that determine meaning do not determine a unique proposition as being meant by a vague sentence, they are not entirely impotent. There is typically a cloud of propositions in the neighborhood of a sentence uttered by a vague speaker. Vagueness prevents the speaker from singling out one of these propositions uniquely, but does not banish the cloud. Speaking vaguely (as always), there is a range of legitimate disambiguations for a vague expression. These are objects, properties, relations, or propositions, depending on whether that expression is a name, monadic predicate, polyadic predicate, or sentence (we ignore other grammatical categories for simplicity). When all the legitimate disambiguations of a sentence are true, call that sentence approximately true. 13 An ordinary utterance of A man with no hairs on his head 10 See Unger (1979a). 11 See Dummett (1981, pp ). 12 See Wright (1975, p. 330, p. 335). 13 Calling a sentence approximately true may misleadingly suggest that it uniquely expresses a proposition that is close to or similar to a true proposition. But sentences that 4 is bald is approximately true, despite failing to be true. 14 Truth is usually thought to play a pervasive role in our cognitive lives. Truth (or perhaps known truth) is the goal of successful inquiry: it is what a diligent inquirer must strive to accept. Truth (or perhaps known truth) is the norm of assertion: it is what a cooperative speaker must strive to communicate. 15 Given our picture of semantics, truth is an impossible standard that we never achieve. But it would be pointlessly fussy to enforce this standard to the letter, requiring the (exact) truth. It would rarely be possible to live up to this standard, nor would it be desirable to try, for the differences between the legitimate disambiguations of our sentences are rarely significant to us. As a result, it is usually harmless to ignore vagueness, set it aside, and act as if one s sentence is not vague, but rather expresses a unique proposition. When vagueness is being ignored, the cooperative communicator satisfies her communicative obligations well enough by uttering sentences that are approximately true; a diligent inquirer satisfies her intellectual obligations well enough by accepting sentences that are approximately true. For in such cases, the differences between the legitimate disambiguations do not matter, and each is true. A typical speaker will, for instance, ignore the vagueness in A man with no hairs on his head is bald and treat that sentence as true, since it is approximately true. In so doing she would not, strictly speaking, be living up to her obligation to speak only the truth; but since the sentence is approximately true, she would closely approximate satisfaction of that obligation as closely as anyone ever does. Likewise, cooperative speakers are usually thought to be obliged to deny sentences only when they are false or suffer from some other semantic defect, are approximately true in our technical sense need not express a single proposition uniquely. Moreover, some sentences that are approximately true in the ordinary sense are not approximately true in our technical sense, for example The number of pennies in the jar is 256,291, said of a jar containing 256,292 pennies. 14 Note the parallel with the supervaluationists. Our legitimate disambiguations and approximate truth are structurally similar to their precisifications and supertruth. As with precisifications, the range of legitimate disambiguations of an expression may well vary from context to context. Moreover, following Fine (1975, p. 276), an assignment of legitimate disambiguations to an entire language must coordinate what it assigns to distinct terms. Bob Dylan is identical with Robert Zimmerman should turn out approximately true; thus, Bob Dylan and Robert Zimmerman cannot be simultaneously disambiguated differently. Despite these structural similarities between our theoretical tools, we put those tools to a very different use than do supervaluationists. Most importantly, we do not identify supertruth with truth. See below. 15 At least one of us is suspicious of talk of the norm of assertion. We might speak instead of various goals speakers have, one of which is to communicate truths. 5 such as presupposition-failure or (other) lack of truth value. On our view, when vagueness is ignored, this norm is satisfied well enough if the denied sentence, or its presupposition, is approximately false that is, false on all legitimate disambiguations or the sentence suffers from some failure of truth value unrelated to vagueness. 16 Ordinary speakers do not ignore the vagueness of sentences that concern borderline cases, for instance, Five piled stones are a heap. Here it is evident to any competent speaker that the sentence is untrue because of its vagueness. 17 Heap would have to be more precise than it in fact is in order for the sentence to be true. Speakers thus refrain from uttering or accepting this sentence. For the same reason they refrain from uttering its negation, Five piled stones are not a heap. 18 Suppose that, despite the manifest vagueness and untruth of Five piled stones are a heap, a speaker decided to ignore its vagueness and utter it anyway. That speaker would then badly fail in her duty as a cooperative communicator, for she would not even be approximately satisfying the norm of assertion to speak only the truth: while some legitimate disambiguations of her sentence are true, others are false. Truth is the norm of assertion is an oversimplification. As Grice (1989) points out, cooperative speakers sometimes do not strive to speak the truth. A speaker may ironically utter Smith is a fine friend despite not accepting that sentence, expecting his hearer to accept the sentence Smith is not a fine friend. On Grice s view, the speaker implicates a truth even though the sentence uttered is false. Consider also the phenomenon of loose talk explored by relevance theorists. 19 A cooperative speaker may utter His face was square, believing that this sentence is false, but intending to communicate some other true sentence. Grice and the relevance theorists thus provide a refined norm of assertion, according to which speakers are obliged to communicate truths in a broad sense. On our view, the sentences communicated in this broad sense are not true. Nevertheless, the communicated sentences are often approximately 16 When vagueness is not ignored, a speaker might deny a sentence she takes to be untrue because of vagueness. 17 This will be justified on nearly any proto-theory of vagueness the speaker may have internalized the speaker need not implicitly accept semantic nihilism. 18 They may deny the sentence, and may also deny its negation, and may even express these denials with the seemingly contradictory sentence Five piled stones is not a heap, and it s not not a heap either. Thanks to Brian Weatherson for this example. This may be an instance of metalinguistic negation. See Horn (1989). 19 See Sperber and Wilson (1986). 6 true. Thus, speakers who ignore vagueness closely approximate satisfaction of the refined norm by communicating approximate truths. We use the term ignore in a technical way. To ignore the vagueness of an expression is to fail to take account of its vagueness and the impact of its vagueness on its truth. When ignoring the vagueness of a sentence, a speaker uses it (and accepts or rejects it) as if it both lacked vagueness and had a truth value. Ordinary speakers usually do not think about vagueness at all, and therefore usually ignore vagueness, in our technical sense. We call this unconscious ignoring. Even philosophers regularly fail to think about vagueness, and so in daily life regularly unconsciously ignore vagueness. Not all ignoring is unconscious. A theorist can consciously realize that chair is vague, and say There is a chair in the next room, though he knows full well that its vagueness deprives it of truth. He might utter it because he is speaking to hearers who are not aware of the impact of vagueness on truth. He might utter it consciously trying to approximate the norm of uttering truths. His uttering the sentence may lead his hearers to accept it, which is a result he may well desire, since he knows that it is impractical to get them to accept (exactly) true sentences. His uttering the sentence may also lead his hearers to perform desirable actions, such as fetching a chair. Altogether, uttering the sentence is likely to be preferable to lapsing into complete silence. Such a theorist is engaging in what we call conscious ignoring. 20 Of course there are intermediate cases for instance, people who know that a term is vague but do not share our view about the nature of vagueness. We still count them as ignoring vagueness, for they use, accept, and deny sentences as if their vagueness did not undermine their truth. We close this section with some final remarks about the relationship between our theory and pragmatics. Our theory is not intended to be a pragmatic theory of vagueness. Ignoring, in our sense, should not be subsumed under any of the standard mechanisms posited by semanticists or pragmaticists to account for communication in context. Ignoring vagueness is merely using sentences as if they were not vague (and so as if they were not truth-valueless). This is usually done unconsciously, by speakers who are oblivious to vagueness. Nor is there any need for theorists like us to exploit any of the standardly discussed pragmatic mechanisms, when we shift from ignoring vagueness to attending to 20 Like the teacher who ignores the raised hand of a persistent student, one can decide to ignore vagueness, in our sense, even when vagueness has been made salient, contrary to Lewis s (1996) Rule of Attention. 7 vagueness, and then back again. Semanticists and pragmaticists can theorize in peace, without taking account of our theory (and our theory need not bend to fit theirs). These theorists usually igno
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