The Epistemic Theory of Vagueness
The Epistemic Theory of Vagueness
Abstract and Keywords
This chapter addresses the epistemic theory of vagueness, which claims that there are sharp, unknowable boundaries to the application of vague expressions. Some features of Timothy Williamson's elaboration of the epistemic theory are discussed, and reasons not to take the epistemic view are proposed. The epistemic theory confronts and rejects the claim that there are indeterminacies in the application of vague language. If it succeeds, the indeterminacy claim is false. If it fails, its failure may help us to understand the indeterminacy claim. In his account of the relation between meaning and use, Williamson claims that use determines meaning, but that the correct application of words depends on the dispositions of speakers. That view of meaning and use supports what is called the ‘boundary model’, which is a theory of meaning because it explains the application of vague words as determined by a social choice function.
THERE is one simple way to solve the sorites paradox. It is to say that there are sharp boundaries to the application of vague words. In any sorites series there is some counter-instance to the tolerance principle—there is a sharp boundary. The most prominent form of this view holds that we do not or cannot know where those boundaries are; borderline cases are those that are too close to the unknown boundary for us to know which side of the boundary they are on. That is the epistemic theory of vagueness.
I have two purposes in discussing the epistemic theory. The first is to argue that it should be rejected. If it succeeds, then the indeterminacy claim is false, and there is a right answer to any question of the application of vague language used in law-making.
The second purpose is to support two related, controversial claims: that general evaluative and normative considerations are necessarily vague, and that the meaning of a word is (or is analogous to) a rule for its use. These claims support the indeterminacy claim: first, they underpin the notion that the application of vague linguistic expressions is indeterminate in some cases. Secondly, the two claims support the view that the interpretive resources of the law are themselves vague. The latter claim will prepare the ground for the account of the role of interpretation in law in Chapter 8. This argument supports the conclusion that the indeterminacy thesis is not just a point about legal language: vagueness is commonly a feature of legal rights and duties, and is a standard feature of the considerations on which judges ought to act.
I set out in this chapter to support those two claims, by examining and rejecting a type of theory of meaning. I do so by taking advantage of Timothy Williamson’s sophisticated elaboration of the epistemic theory of vagueness. He proposes an account of the relation between meaning and use which supports the epistemic theory. In this chapter 1 give an opposed account of that relation, which supports and elaborates the similarity model of vagueness.
1. The Epistemic Theory
The epistemic theory has the attraction of simplicity. It also has the attractions of vindicating classical logic, of maintaining a simple relationship between classical logic and the meaning of words in a natural language, and of doing nothing obviously innovative with the notion of truth. Its problem is (p.100) that it makes a bizarre claim about the correct application of vague words: it claims that their meanings determine sharp boundaries, which we cannot locate.
The epistemic theory has the consequence that you could lay a hair on the ground so that, all along its length, half of it is close to New York and half of it is not. Or you could, except that you have no way of knowing where the boundary is. The theory solves the paradox at the price of an apparently outlandish account of the meaning of words.
The most straightforward argument for the epistemic theory is to say that things just must be that way, because there is no other way to solve the sorites paradox. The acceptability of a bizarre truth about the meaning of vague words can be deduced from an acceptance of classical logic.1 I will call this argument the ‘logic argument’ (see the discussion of Williamson’s logic argument in Chapter4.3 above).
Epistemic theorists do not restrict themselves to the logic argument.2 They support it with arguments meant to dispel the appearance that their claims about meaning are bizarre. They offer explanations of the meanings of ordinary vague words aimed at unsettling the semanticist hunch that there can be no sharp boundaries to their application. I will call these arguments ‘semantic arguments’.
I will address Williamson’s work; he has given the most compelling statement of the logic argument, and the most systematic semantic arguments in favour of the epistemic theory.3 I conclude that the theory is doomed to make untenable semantic claims, and that it can say nothing in defence of those claims but that they must be true as a matter of logic. That is, the epistemic theory must stake everything on the logic argument. Perhaps that conclusion is fatal for the epistemic theory, because it seems that the logic argument does not require us to assert bivalence for all vague utterances. As Williamson points out, it only requires us not to deny it for any vague utterance (193).
The fate of Williamson’s semantic arguments is not only important for an assessment of the epistemic theory of vagueness. It is also important for an understanding of the relation between meaning and use. It is a familiar notion that the meaning of a word is determined by its use; Williamson interprets that notion as equivalent to the notion that the correct application of (p.101) words supervenes on the dispositions of speakers. Scrutiny of this appeal to supervenience suggests that it gives an unsatisfactory account of meaning—an account that leaves the notion of correct application of words (and therefore the notion of a true statement) unintelligible.
2. Meaning and Use
Wittgenstein gave philosophy of language two slogans: ‘the meaning of a word is its use in the language’ and ‘nothing is hidden’.4 Williamson takes a view that many philosophers share: that the first slogan is sound if it is understood properly, and the second is misguided. He accepts the appeal of the notion that the use of (some) words determines their meaning; in his theory the use of those words also determines sharp boundaries to their correct application. Perhaps any semantic argument for the epistemic theory needs to take some similar approach, because it is hard to imagine what could determine whether a word like ‘thin’ applies to a given object in a given context, other than the use of the word. But it is also hard to imagine how the use of a word like ‘thin’ could determine sharp boundaries to its application, and this seems at a glance to be an objection to the epistemic theory. As Williamson puts it, the objection is that ‘there is no line, for our use leaves not a line but a smear’ (206). I will call this objection to the epistemic theory the ‘use’ objection.
To evaluate the use objection, we need to unpack the notions of determination, of use, and of meaning. In this section 1 will discuss Williamson’s interpretation of those notions: he treats the view that use determines meaning as claiming that the correct application of words like ‘thin’ supervenes on the dispositions of speakers. I will claim that, if this supervenience account is correct, the use of words like ‘thin’ cannot be sharply bounded. On Williamson’s view, that makes it impossible to give an account of vague statements as having a meaning in a natural language: it leads to nihilism about the meaning of vague expressions whose meaning is determined by their use. Section 4 proposes a different interpretation of the notion that use determines meaning—an interpretation that does not support the epistemic theory of vagueness. The account gives reason to think that understanding the vagueness of evaluative language is essential to understanding vagueness in general, and Section 5 addresses the vagueness of evaluative language. Section 6 gives an account of context dependence that is meant to support Sections 4 and 5.
Williamson’s response to the use objection offers an ingenious, austere account of determination: ‘To say that use determines meaning is just to say that meaning supervenes on use’ (206). And that is just to say that there cannot be a change in meaning, or a difference in meaning, without a change or a difference in use. Sameness of use entails sameness of meaning. That, Williamson implies, is all that we can make of the notion that use determines meaning.5 An epistemic theorist can say that sameness of use entails sameness of meaning, so the fact that meaning is determined by use seems to give no reason to doubt that there are precise boundaries to the application of words such as ‘thin’.6
Anyone who wants to reject the epistemic theory will feel an urge to make more of the notion that use determines meaning. It is important to Williamson to insist that nothing more can be made of the connection between meaning and use. He insists that there is no ‘algorithm for calculating’ meaning from use (206),7 no ‘recipe for extracting meaning from use’ (207). But Williamson does not need to say that there is nothing more to the connection: the epistemic approach can say that the nature of the connection is unknowable, at least to humans. The conclusion is that the connection between meaning and use is a mystery. That connection poses no objection to the epistemic theory, because no opponent of that theory can give an account of the connection that shows that the application of vague words is determinate in clear cases, and indeterminate in borderline cases: ‘The epistemic theory of vagueness makes the connection between meaning and use no harder to understand than it already is. At worst, there may be no account to be had, beyond a few vague salutary remarks. Meaning may supervene on use in an unsurveyably chaotic way’ (209). I will argue that if meaning supervenes on use, then there cannot be sharp boundaries to the application of vague words (this section). I will also claim that, whatever difficulties there may be in giving a general philosophical account of the connection between meaning and use, no such difficulties stand in the way of an approach to meaning that is inconsistent with the epistemic theory of vagueness (Section 4). An account of meaning requires a notion of ‘use’ that is different from the way of an approach to meaning that is inconsistent with the epistemic theory of vagueness (Section 4). An account of meaning requires a notion of ‘use’ that is different from the way of an approach to meaning that is inconsistent with the epistemic theory of vagueness (Section 4). An account of meaning requires a notion of ‘use’ that is different from the way of an approach to meaning that is inconsistent with the epistemic theory of vagueness (Section 4). An account of meaning requires a notion of ‘use’ that is different from the way of an approach to meaning that is inconsistent with the epistemic theory of vagueness (Section 4). An account of meaning requires a notion of ‘use’ that is different from Williamson’s.the way of an approach to meaning that is inconsistent with the epistemic theory of vagueness (Section 4). An account of meaning requires a notion of ‘use’ that is different from Williamson’s.
For the purpose of stating the use objection, Williamson ‘provisionally’ identifies use with ‘our dispositions to assent to and dissent from’ a declarative sentence in varying circumstances (we will see that the theory needs to include some additional dispositions). We can call that notion of use ‘useas-dispositions’.
Williamson points out that we may be mistaken in (some of) our dispositions to assent to or dissent from the application of a vague word like ‘thin’. We may even be systematically mistaken. These facts explain the appeal of the supervenience account: Williamson rightly insists that ‘Truth-conditions cannot be reduced to statistics of assent and dissent’ (206). Supervenience seems to allow Williamson to assert a necessary but non-reductionist connection between two sets of properties, without incurring an onus of explaining the way in which one phenomenon determines the other.
Meaning and reference are interchangeable in Williamson’s supervenience account of the connection between meaning and use. He characterizes the use objection as identifying the meaning of a declarative sentence with its truth conditions, and he sets out to show that the epistemic theory can assert that the use of words like ‘thin’ determines truth conditions that set unknowable sharp boundaries to correct application (205).8 If use determines truth conditions, use thereby determines whether it is correct to apply a vague predicate to a given object in a given situation. So to state Williamson’s supervenience claim, we can leave out the notion of meaning, and say that use determines the correct application (to given objects in given contexts) of some vague words.
To summarize, Williamson offers an interpretation of the notion that use determines meaning: the correct application of vague expressions like ‘thin’ supervenes on the dispositions of speakers. It is not quite clear which expressions this supervenience account applies to, although Williamson suggests that it is a general claim. He asserts that ‘A slight shift along one axis of measurement in all our dispositions to use “thin” would slightly shift the meaning and extension of “thin”,’ and he suggests that the point applies generally, unless the meaning of words is ‘stabilized by natural divisions’ (231). Perhaps the claim extends, then, to all terms that are not terms for natural kinds. For the most part, I will leave aside the question of the scope of the supervenience account, and speak of ‘words like “thin” ’. But we should note that it (p.104) is patently obvious that the account must apply to many terms (e.g. ‘rave’) used in formulating laws.
Note that the claim that a slight change in dispositions would slightly shift the extension of ‘thin’ is a significantly stronger claim than the supervenience claim. To say that correct application supervenes on dispositions is only to say that correct application cannot change without a change in dispositions. That says nothing about the consequences of any change in dispositions; it only states a consequence of identity of dispositions. There is an ambiguity in the claim that a slight shift in ‘all our dispositions to use “thin” ’ would shift the correct application of ‘thin’. Williamson may mean that any change in the base on which meaning supervenes (a base which includes all our dispositions) would shift the correct application of ‘thin’. Or he may mean only to say that the correct application of ‘thin’ would change slightly if all speakers underwent a slight change in dispositions. Either claim would say more than merely that correct application supervenes on dispositions.
I will treat Williamson’s supervenience account as including this stronger claim (in some form); when it is useful to distinguish it from the rest of the account, I will call it ‘the correlation claim’, since it seems to say that a difference (of some kind) in dispositions entails a difference in correct application.
The arguments in this section are all regress arguments. They allege indeterminacies in the base on which (in Williamson’s account) meaning supervenes, and they rely on a claim that the supervenience account lacks resources to eradicate indeterminacies in the supervenience base. Their purpose is to show that Williamson’s epistemic theory cannot maintain a connection between meaning and use. There are two alternative ways in which these arguments can succeed, and there is a third way in which the purpose might be achieved, independently of the regress arguments.
1. The regress arguments succeed if Williamson is committed to the correlation claim. They succeed because, on the correlation claim, if the supervenience base is not sharply bounded, then the correct application of a word like ‘thin’ will not be sharply bounded. If ‘a slight shift along one axis of measurement in all our dispositions to use “thin” would slightly shift the meaning and extension of “thin” ’, then by the same token a slight indeterminacy in what counts as ‘all our dispositions’ would make the extension of ‘thin’ slightly indeterminate. It is not quite clear whether (or in what form) Williamson is committed to the correlation claim; perhaps an epistemic theorist should reject that claim as inconsistent with Williamson’s view that ‘Meaning may supervene on use in an unsurveyably chaotic way’ (209).
2. Even without the correlation claim, the regress arguments succeed if correct application cannot be sharply bounded when the supervenience base is not sharply bounded. And that seems to be the case. Even if correct application supervenes on use in an unsurveyable way, it seems that it can be (p.105) sharply bounded only if it supervenes on a determinate base (i.e. everything must either be part of the base, or not be part of the base). The reason is as follows: if correct application supervenes on use, correct application can change only if use changes. If it is indeterminate whether something counts as use, then there may be two situations in which it is indeterminate whether use is the same in each. Then it will be indeterminate whether it is possible that correct application differs in the two situations. If it is indeterminate whether an expression may correctly apply in one situation and not in another, there is indeterminacy in meaning.
Compare another supervenience relation: the result of a fair election supervenes on the votes. If there is no answer to a question of the form ‘Is this a vote?’, then there is no guarantee of a determinate election result. The election will not give a result, if the result turns on the ballots whose status as votes is indeterminate. Supervenience of correct application of words on dispositions of speakers is similar, except that indeterminacy as to votes entails only the possibility that an election result will be indeterminate (the ballots whose status as votes is indeterminate may not make a difference). In the supervenience account of meaning and use, every indeterminacy in the supervenience base entails indeterminacy in the supervenient property. Elections answer yes/no questions, or select one or more alternatives from a list. If the epistemic theory is to use supervenience to maintain a connection between meaning and use, it needs the relation by which use supervenes on meaning to divide a continuum perfectly sharply (and, in fact, it needs that relation to divide a multiplicity of continua, corresponding to the grounds of application of words like ‘thin’).
3. Even if sharp boundaries could supervene on an indeterminate base, the supervenience account may not protect the epistemic theory against the use objection, if there is more to say about the way in which use determines meaning than merely that correct application supervenes on dispositions of speakers. A crucial aspect of Williamson’s use of the supervenience account is his claim that no one can say more about the way in which use determines meaning than that correct application supervenes on dispositions. In Section 4 I will give an outline account of what more can be said. For the present, we should see that if nothing more can be said, then the notion that use determines meaning is unintelligible. That means that the epistemic theory cannot give an account of any intelligible connection between meaning and use. Its only option is to say that no one can give an account of any such intelligible connection.
Section 2 sets out the regress arguments. Section 3 aims to show the need for a different interpretation of the notion that use determines meaning from Williamson’s. Rather than offering a competing interpretation of that notion, I argue that the supervenience account needs (contrary to some (p.106) suggestions of Williamson’s) to treat some precise dispositional phenomenon as providing a norm for the application of the word, and that no such phenomenon can do that job.
Dispositions Cannot Determine Sharp Boundaries
We can think of dispositions as properties (of speakers, in this case) that correspond to counterfactual propositions: a person has a disposition to behave in a given way in a given situation if and only if he or she would behave in that way in that situation. There may be fatal objections to the very notion that people have such dispositions with regard to the application of words, or that such dispositions have any precise connection with the correct application of words. If we think of dispositions as lawlike generalizations as to what someone will do, there are ordinarily none that are borne out without exception. If we think of dispositions as probabilities, then it is hard to see how sharp boundaries could supervene on them. But I will set aside such potential objections, and accept for the purpose of argument that in any situation a person has a disposition that corresponds to the fact that he or she either would or would not say ‘yes’ to a question of the application of a vague expression in any case. The result seems to be a sharply bounded set of facts on which, in the epistemic theory, the application of words such as ‘thin’ supervenes. Those facts are hidden from us (i) because we do not know precisely what people are disposed to do, and (ii) even if we knew all that, we know of no algorithm that would tell us whether it is correct to apply the word.
There are some good reasons for Williamson to adopt the notion of use-as-dispositions. Suppose, instead, that we thought of use as speech events. That would be fatal for the supervenience account: it would raise a question as to which speech events count as the base on which meaning supervenes. How recent would an utterance have to be for it to count as part of the base? The answer to that question could not be determined by use, on pain of a vicious regress. The supervenience account cannot treat use as a set of speech events, because such a set would necessarily extend across time, and the supervenience account lacks the resources to account for a sharp boundary to the dispositions that count as part of the base. Use-as-dispositions seems to avoid this diachronic problem, because it seems that it can be treated as a purely synchronic notion: the notion is that the application of an expression at any moment supervenes on the dispositions of speakers at that moment. The result is the view that boundaries are unstable: they change as dispositions change. Williamson accepts instability as an insight of the epistemic theory, and not as an objection.9
(p.107) Imagine a speech community of just two people, who speak a language much like English. Suppose that one of them is disposed to say that it is dark at 8.30 one evening, and suppose that the other is not disposed to say so until 8.50. At 8.40 one of them says that it is dark, and the other says that it is not dark. On the supervenience account, this pattern of use determines that one of the two speakers is right (and also which of them is right)—in just the same way that their use of the word ‘dark’ determines whether either of them is right when they both say that it is not dark at noon. What is more, the pattern of dispositions determines a first nanosecond of dark.
If we thought only of the dispositions I have stated, it would seem particularly bizarre to say that the pattern of dispositions determines a first nanosecond of dark. In fact, it would be surveyably false. But there is any number of other facts about the dispositions of the two speakers, in addition to their dispositions to assent to or dissent from statements applying vague expressions—facts about the strength of their dispositions, and their dispositions to defer to each other, or not, etc. The supervenience account needs to appeal to such additional dispositions.
In summary, the supervenience account needs to treat speakers’ dispositions (and not speech events) as use, and it cannot restrict itself to dispositions to assent to or dissent from assertions. It needs to appeal to additional dispositions.
Whose Dispositions? Speech Communities
On the supervenience account, correct application cannot change unless the dispositions of speakers change; if dispositions change, then correct application may (and, according to the correlation claim, does) change. This account implies that, when a speaker in Spokane dies, the truth conditions of statements applying the word ‘thin’ change, and a statement applying the word ‘thin’ in a borderline case in Bombay may switch from true to false. But this semantic butterfly effect is no more bizarre than the notion that there is a sharp boundary to the application of vague words, and it will not bother an epistemic theorist. Note, however, that it is a consequence that arises only if we think of the supervenience base as comprising the dispositions of (something like) all English speakers in the world. Does that make sense?
Williamson treats meaning as supervening on ‘our use’ (206). ‘Our’ is unspecific: ‘we’ could refer to you and me, or everyone, or some class in between. Until it is made specific, there is no sharply bounded supervenience base. The supervenience account needs a sharply bounded speech (p.108) community, and speech communities are not ordinarily sharply bounded. This is not only a geographical problem, but a problem of which foreign language speakers are also English speakers, which children count as competent, which speakers are too eccentric to count, and so on. The indeterminacy will remain whether the language community is simply ‘speakers of English’, or any subdivision. There is no way to define a language community that is non-arbitrary and precise. Perhaps the only viable criterion is mutual intelligibility, and that is extremely vague.
Moreover, use of a language within a community will include different ways of speaking corresponding to ethnic or local differences, social strata, women’s talk, men’s talk, written and spoken language and different genres of writing, formal and informal speech situations, different ways of speaking to grown-ups and children, conventions of exaggeration and understatement in particular situations, tendencies to self-consciousness in various situations, and so on and so on. To treat all the dispositions of members of the community as the supervenience base would be to distort the use of language within a community. But if we treat each of these innumerable ethnolinguistic varieties as a separate language, indeterminacy will arise as to which ‘language’ is being spoken on a particular occasion.
Suppose that there are two towns, Slough and Leighton Buzzard, in each of which people have varying dispositions to apply the word ‘thin’. Suppose that there are precise facts about those dispositions, and that the dispositions of people in Slough are slightly different from the dispositions of people in Leighton Buzzard.
It might seem tempting to say that there are slightly different norms for the use of the word ‘thin’ in Slough and Leighton Buzzard (each of which differs, presumably slightly, from the norm for its use in English in general), and that in his or her idiolect each speaker has his or her own norm for the use of the word. Each of these ‘languages’—English, or Leighton Buzzard English, or Slough English, or an individual speaker’s idiolect—corresponds to a different set of dispositions to apply the word ‘thin’.
Here lurks a problem for the epistemic theory: even if we can affirm the principle of bivalence for any specified ‘language’, a vague statement in a borderline case may be true in one ‘language’, and false in another. A speaker who utters a vague statement in a borderline case may say something that is true in their idiolect, and false in the English of their family, and true in the English of their town, and false in the English of their country, and true in English in general (and there are countless other ‘languages’ corresponding to countless other speech communities we could conceive of the speaker as belonging to). If meaning supervenes on use-as-dispositions, then the sharp boundaries to the application of vague words are not only unstable, they are also relative to a specification of whose dispositions count for the purpose of determining meaning. For any human language, the epistemic theory must (p.109) postulate a large finite number of sharp extensions of vague words, corresponding to a large finite number of speech communities. It makes no sense to talk of the truth value of a statement, except in relation to one specification of the extent of the speech community whose dispositions determine its truth value (and one specification of which ethnolinguistic register is being used, and so on).
It would be simpler for the epistemic theory to say that all English speakers are members of one speech community, speaking one language—English. But the problem of membership is actually insurmountable for an epistemic theorist who wants to describe people simply as speaking English. To say that the dispositions of all and only English speakers count would be to give a vague specification of the base on which correct application supervenes: it may be unclear whether some young children, and eccentric adults, and students of English as a second language, count as English speakers. It is a specification that can only support the epistemic theory if there is a sharply bounded answer to the question ‘Who counts as an English speaker?’ The epistemic theory will say that every person either is or is not an English speaker, and that we cannot know whether to call some people ‘English speakers’. But ‘English speaker’ and ‘speech community’ seem to be expressions like ‘thin’—in Williamson’s terms, their correct application is not ‘stabilized’ by natural divisions, and it seems that Williamson should say that their correct application supervenes on the dispositions of speakers. But the expression ‘English speaker’ cannot be explained as having a sharp boundary that supervenes on the dispositions of English speakers, because a regress would ensue:
(1) There are sharp boundaries to the correct application of ‘thin’; they supervene on the dispositions of English speakers.
(2) There are sharp boundaries to the correct application of ‘English speaker’ (and, therefore, sharp boundaries to the base on which the correct application of ‘thin’ supervenes); they supervene on the dispositions of English speakers.
(3) There are sharp boundaries to the correct application of ‘English speaker’ (and, therefore, sharp boundaries to the base on which the correct application of ‘English speaker’ supervenes); they supervene on the dispositions of English speakers.
Is this regress vicious? It is not vicious merely in virtue of the fact that it generates an infinite number of unknowably true statements. That need not embarrass an epistemic theorist: if there is even one unknowably true statement, there is an infinite number of unknowably true conjunctive statements. It may seem that an epistemic theorist must simply say that there is an infinite number of unknowable answers to questions about membership in a speech community.
(p.110) But the regress is vicious (at step 2, rather than at an arbitrarily high level), because the dispositions of English speakers may not determine sharp boundaries to the group of English speakers. Each step above step 1 asserts what it also presupposes: that the group of English speakers has sharp boundaries. To illustrate the problem with this regress of dispositions, consider the case of Elfi. I propose that an epistemic theorist who uses the supervenience account of meaning and use needs to admit that the following scenario is possible; the scenario shows that that account cannot portray use as determining sharp boundaries to the application of vague words.
Elfi the borderline English speaker
Imagine a woman called Elfi, who is a borderline case for the correct application of the term ‘English speaker’. No one knows whether it is true or false to say that she is an English speaker. In fact (although no one can know it), her capacities place her so close to the hidden sharp boundary between English speakers and non-English speakers that if her own dispositions are included in the supervenience base, she counts as an English speaker, and if her dispositions are not included in the base, she does not count as an English speaker. Are Elfi’s dispositions part of the supervenience base? They are if she is an English speaker, and they are not if she is not an English speaker. Either way, the dispositions of English speakers cannot answer the question whether Elfi is an English speaker. It is not just that no one can know the answer; it is that, if there is an unknowable answer, it is not supplied by the dispositions of English speakers.
On one interpretation of the correlation claim, Elfi is possible because adding any single speaker’s dispositions to the supervenience base changes the truth conditions of a vague statement. And even on the pure supervenience claim, Elfi is possible because it is possible that those truth conditions will change if the supervenience base changes.
An epistemic theorist might say that, until we have an account of what does make someone an English speaker, there is no support for the notion that it is indeterminate in any case whether someone is an English speaker. And I have not shown that there is no hidden sharp boundary between people who are and are not English speakers. But the problem for the epistemic theory is that the dispositions of English speakers cannot determine whether it is true to say that Elfi is an English speaker. This is not a proof of indeterminacy, but it indicates that the epistemic theory cannot support the claim that it is use that determines the sharp boundaries that the theory postulates.
We should conclude that there is a constraint on the supervenience account: to the extent that use determines meaning, the principle of bivalence can only be affirmed relative to a precise specification of the speakers (p.111) whose dispositions count as ‘use’. Any such specification of the membership of any ordinary speech community (whether it is Leighton Buzzard English speakers or English speakers in general) would be a stipulation. If the truth of a vague statement supervenes on the dispositions of speakers, that statement may be true relative to some specifications of the class of speakers, and false relative to others. Sharp boundaries to membership in the class of speakers cannot supervene on dispositions of speakers. So the principle of bivalence can be affirmed only relative to a stipulation.
That is a dismal conclusion, because the goal of the theory was to apply classical logic to utterances in a natural language. It is impossible to use the supervenience account to do so, and in Williamson’s theory the consequence is that, in natural languages, words whose meaning is determined by use are semantically defective. Those words are incoherent in a natural language.
To solve this problem of membership in a speech community, the epistemic theory could view idiolects alone as semantically adequate. If this works, the notion of a natural language would be rescued as a coherent notion within an idiolect, the extension of ‘English speaker’ within an idiolect would supervene on the dispositions of the individual speaker. But words like ‘thin’ would still have no meaning in a natural language. Think of each person as speaking their own language, and think of their statements as being true or false in their idiolect. Each speaker tries to achieve a rough match with the idiolects of others, but their statements have meaning only within their own idiolects. The problem of specifying membership in a speech community vanishes, at least if we are willing to take it for granted that any speaker has a single set of dispositions.
That approach is not Williamson’s: he insists that ‘linguistic meaning is socially determined’, so that slight differences in dispositions among speakers do not generate multiple meanings (236).10 That insight is patently sound, and it is an argument against the superveniensce account.
Which Dispositions? Mistakes and Other Falsehoods
If we stick to idiolects, we have decided whose dispositions count. But a question remains as to which of a speaker’s dispositions count. We saw that the supervenience base must include more than just dispositions to assent to or dissent from applications of a vague expression. Pertinent dispositions must include dispositions to defer to others, to hesitate and to hedge, to experience various psychological phenomena, and dispositions concerning the use of related expressions, and so on. But not all dispositions can be pertinent to the determination of meaning. If the correct application of ‘thin’ supervenes on (p.112) dispositions, it is plausible to think that it also supervenes on a base that does not include speakers’ dispositions, e.g. to split infinitives. If it is true to say that sharp boundaries supervene on all dispositions of speakers, and some dispositions have nothing to do with the application of ‘thin’ (so that we can say that the application of ‘thin’ cannot change when there is no change except in those dispositions), then it is also true to say that (the same) sharp boundaries supervene on some proper subset of dispositions of speakers.11
The question for the supervenience account is how strong the supervenience claim should be. Does correct application supervene on all dispositions of speakers? on pertinent dispositions of speakers? on dispositions of speakers to assent-dissent? The first claim is too weak, and we have seen that supervenience on dispositions to assent to or dissent from declarative sentences applying the vague word would be too strong. The epistemic theorist needs to make a supervenience claim similar to the second listed above: that correct application supervenes on pertinent dispositions. But ‘pertinent’ is vague, and sharp boundaries to its application cannot supervene on pertinent dispositions of speakers, because a vicious regress would result. The epistemic theory will assert that the application of ‘pertinent’ must be sharply bounded, but it has no semantic argument to account for ‘pertinent’ as bivalent. Sharp boundaries to pertinent dispositions cannot be determined by pertinent dispositions: an account that made such a claim would end in a regress analogous to the regress that led to the Elfi scenario.
Perhaps a more serious problem for the epistemic theory is how to account for mistaken dispositions. Can we make sense of the notion that a person might be disposed to misapply a word? Williamson is, rightly, committed to doing so: he presents the possibility of mistakes as a reason why there is no ‘recipe for extracting meaning from use’ (193); his purpose is to absolve the epistemic theory from the obnoxious burden of having to say how use determines sharp boundaries. He insists that even the agreement of speakers in their dispositions to apply a word ‘does not generally guarantee the correctness of that application. Whole societies can sometimes be mistaken.’12 I have argued that the epistemic theory can only postulate a determinate base for the supervenience of meaning within an idiolect. But the possibility of mistake applies to idiolects too. Unless we abandon the notion of a mistake, and say that a word just applies to whatever a person is disposed to apply it to, we need to admit that a speaker might be disposed to misapply a word.
Williamson suggests that the problem is that someone’s dispositions to apply the word ‘thin’ may be mistaken because a thin person may not look thin for some reason, and a speaker may not be familiar with the relevant (p.113) comparison class (206). Those forms of mistake seem not to pose a basic problem for the epistemic theory: besides his or her disposition not to apply the word ‘thin’ to that person, the speaker will have other dispositions (to make a different judgment in different perceptual conditions or with greater familiarity with the comparison class, to decide that they had misapplied the word, to defer to better-placed speakers … ). The correct application of ‘thin’ in the speaker’s idiolect supervenes on all the speaker’s (pertinent) dispositions. The complexity of dispositions might also account for dispositions to lie, or to be sarcastic, or generous: someone might be disposed to call someone who is not thin ‘thin’, but also to admit in the right circumstances that they were exaggerating.
But the problem of dispositions to misapply a word is more far-reaching: people may misjudge the application of the word ‘thin’, without having any other inconsistent disposition. They may not be thinking straight for a moment, or they may be systematically disposed to exaggerate in a way that is unreflective and thoroughly consistent. It seems that the supervenience account needs an account of dispositions to misjudge that do not arise from unfavourable perceptual conditions or lack of information. But the supervenience account cannot appeal to the dispositions of other speakers, on pain of the regress that would arise if the supervenience account appealed to use in a speech community. And it cannot appeal to dispositions across time, on pain of the same diachronic regress that would arise if a supervenience account tried to adopt the notion of use-as-speech-events.
This point about mistakes has more far-reaching consequences than the impossibility of a recipe or algorithm: it seems that it is not just beyond our capacities, but impossible in principle, to identify sharp boundaries to the application of the word ‘thin’ by reference to the dispositions of speakers. We could not do so without an account of which dispositions are mistaken, and we can have no such account unless we know the application of the word. This is not just an epistemic problem. No being with greater cognitive powers than ours could identify the correct application of a word on the basis of the dispositions of speakers, without already being able to distinguish mistaken dispositions from dispositions that count. So no such being could identify sharp boundaries to the correct application of a word merely on the basis of dispositions.
It seems that the epistemic theory must account for the word ‘thin’ as applying correctly, in a speaker’s idiolect, while the speaker is disposed to do what others (or the speaker at other moments) would call ‘misapplying’ it. But that account is incoherent: it would eliminate the notion of mistaken dispositions, and would thereby eliminate the notion of the correctness of a speaker’s dispositions (a notion which the account uses). ‘Mistaken’ would become a term that has meaning only at a moment within an idiolect, and could not apply to the consistent dispositions of the speaker.
The general argument of this section has been that the supervenience account cannot help the epistemic theory, because it supposes that meaning is determined by a pattern of use, and ‘pattern of use’ is vague. It would beg the question against the epistemic theory to say that, because ‘pattern of use’ is vague, the extension of a pattern of use may be indeterminate. But a pattern of use of ‘thin’ cannot have sharp boundaries that are determined by a pattern of use of ‘pattern of use’. The supervenience account has nothing to support the notion that there is a sharply bounded set of dispositions that are pertinent to the application of any vague word—except the logic argument.
Now we face a different and more basic problem: if there were a sharply bounded pattern of use of a word like ‘thin’, what would make it right or wrong to apply the word? As Williamson has pointed out, ‘Our use determines many lines,’13 such as the line between unanimity and lack of unanimity, or between majority assent and less than majority assent. But he points out that there is no reason to think that any such line is the line between truth and falsity (206). Williamson responds to these facts by renouncing reductionism14—implying that the supervenience account does not commit him to identifying any precise dispositional phenomenon as equivalent to the line between truth and falsity. Yet if supervenience is a relation of determination, it seems that Williamson must claim that something about the dispositions of speakers makes it right or wrong to apply a word like ‘thin’, so that some precise dispositional phenomenon is equivalent to the line between truth and falsity, but we cannot know which. And, on the correlation claim, a tiny change in dispositions brings about a tiny change in truth conditions, but we cannot know how.
The question that the supervenience account must face up to is ‘How does meaning supervene on use?’ We cannot demand an answer to the question, but the proposition that there is an unknowable answer needs support. It is impossible in principle for the dispositions of speakers to determine the answer, because it is a question of how the dispositions of speakers determine anything. So this is a final regress argument against the supervenience account: it supposes that the use of a word supplies a norm for its application, but that very notion presupposes a way of supervening, a relation (though we have no algorithm for identifying it) between dispositions and correct application. That relation cannot itself be determined by dispositions. The (p.115) epistemic theory does not need an account of the relation, but it does need to support the view that an unaccountable relation exists.
We might put this problem in the following way: the supervenience account is offered as an interpretation of the slogan that use determines meaning. But supervenience is not a kind of determination; to assert supervenience is only to raise the question ‘What is the relation between the supervenient property and the base?’15 That is an intelligible question, even if the answer is unknowable.
The epistemic response to this sort of objection can be summarized by saying that no one has come up with an account of what makes it correct to call someone ‘thin’ in a clear case (perhaps it is unknowable), and that whatever it is that makes an application (unknowably) correct in a borderline case is just the same as whatever it is that makes it correct in a clear case.16
The problem should not be rejected so quickly, however. The supervenience account is a way of saying that the agreement of speakers (or the consistency of an individual speaker) provides the norm for the use of a word like ‘thin’. Granted that unanimity or majority assent do not make a word apply, it makes sense to ask how much agreement of what sort it takes to constitute the norm for the use of a word. The epistemic theory must say that some precise fact or set of facts about dispositions to apply the word ‘thin’ makes it correct to call one borderline-thin person ‘thin’, and makes it incorrect to call the next person in a sorites series ‘thin’.
An epistemic theorist might say that this interpretation of the supervenience account demands an algorithm for calculating meaning from dispositions, where there is no algorithm. It is no objection to the epistemic theory that people do not have a technique for identifying how use determines sharp boundaries; that is just what the theory claims. But on the epistemic theory, there must be something that we have no technique for identifying—a way in which meaning supervenes on use. That is, a way in which a tiny shift in dispositions can (and, according to the correlation claim, does) make it the case that a word applies to an object that it would not otherwise apply to. Although the supervenience account does not have to explain the way in which dispositions do that, it does have to support the view that there is such a way.
(p.116) But that view is unsupportable. What is wrong with the notion that unanimity decides the application of vague words? Not that we do not know whether vague words apply just when a speech community is unanimous, but that we know that the fact of unanimity does not give anyone a reason to apply the word ‘thin’ in a case in which the phenomenon obtains, while withholding it in an immaterially different case in which the phenomenon does not obtain. This reason for denying that unanimity (or majority assent … ) provides a norm for the use of a word would apply equally to any precise dispositional phenomenon.
Williamson has argued that it cannot be said that a community has not bothered to lay down a precise meaning for an expression, unless we can identify the sense in which speakers have bothered to lay down that the expression applies in clear cases.17 But that is what speakers do in every situation in which they only happen to face clear cases of the application of an expression. We have a word for dogs, and a word for cats, and there is a clear sense in which speakers have bothered to distinguish between cats and dogs. But no one has bothered to provide for intermediate cases between cats and dogs, and if an intermediate case turned up, people would need to decide (i.e. determine) something that has not been decided. There is no ground to suppose that the application of ‘cat’ and ‘dog’ must be determinate in intermediate cases if it is determinate in clear cases: nothing in the practice of using those words bears on intermediate cases. In this regard there is nothing hard to understand about the connection between meaning and use: the use of the word ‘cat’ is in part to distinguish cats from dogs, and that use is fulfilled successfully without drawing a sharp boundary.
The case is similar with, for example, all artefact terms. People ordinarily deal with clear cases of cars, pianos, houses, and telephones. There is nothing bizarre or baffling about the borderline cases that are encountered in factories, building sites, or wrecking yards. A partly dismantled piano presents speakers with a manageable question of whether to extend the application of a term from the clear cases in which it is used; not with an unanswerable question as to whether its application extends to the new case.
Speakers bother to distinguish between cats and dogs without bothering to lay down a rule for intermediate cases. They bother to lay down the application of the word ‘piano’ to clear cases, without bothering about when the pieces in the factory become a piano, or when a piano stops existing. If that is the best way to describe those cases, it may be best to give a similar description of the use of words whose application lies on a natural spectrum, such as ‘dark’ and ‘thin’, in which there is nothing at all unusual about borderline cases. We bother to lay down a distinction between salient alternatives; why not say that we do not bother to lay down a rule for borderline cases? The (p.117) epistemic theory can reject that view by cleaving to the logic argument, but it cannot appeal to the unaccountable supervenience of meaning on use to reject that view. There is no defence of the epistemic theory on the ground that the connection between meaning and use is hard to explain.
I do not mean that there are no philosophical difficulties in giving an account of the relation between meaning and use. I mean that the use objection is not met by Williamson’s account of use, because there is nothing mysterious about the proposition that the use of the word ‘cat’ lays down a rule for clear cases, and does not lay down a rule for cases intermediate between cats and dogs. The use of words for biological species and of words for artefact terms gives an answer to questions of application in clear cases. That use does not answer questions of the application of the expression in borderline cases. There is a clear and simple sense in which speakers have bothered to answer the question of the application of the words ‘car’, ‘piano’, and ‘house’ in clear cases, and have not bothered to do so in borderline cases. The dispositions that people no doubt have in borderline cases do not provide a complete guide to the correct application of the word.
We could put that very point in terms of the use objection, by saying that the use of vague words does not lay down a sharp boundary to their correct application. Properly understood, the use objection claims that the use of words provides a norm for their correct application, but rejects the notion that dispositions provide a sharply bounded norm. The added element that is needed in an account of the relation between the meaning of words and their use is the notion that use can provide a norm—a reason, on which a speaker could act, for applying or withholding a word. The tolerance principle is attractive because it seems that no trivial change in the grounds relevant to the application of a vague word could guide a speaker to apply the word in one case and withhold it in the other, in the way that norms are capable of guiding behaviour.
The obstacle to the notion that the dispositions of speakers determine a sharp boundary to the correct application of vague words is this: even if it made sense to say that the speakers in a community are (unknowably) disposed to withhold the word ‘thin’ from one borderline thin person, and to apply it to another person who is thinner in a trivial degree, that fact would not give any speaker a reason to apply and withhold the word in the same way.
The response that an epistemic theory could make to the objection in this form is obvious: it is to say that no one understands the relation between meaning and use well enough to make these claims about norms, and to challenge an opponent to explain the normativity of language use in a way that reveals indeterminacies in borderline cases of the application of vague words. So Section 4 explores some features of the ways in which use can provide a norm for the application of words.
Two Senses of ‘Norm’
Words such as ‘rule’, ‘practice’, and ‘norm’ share a familiar ambiguity between their descriptive and prescriptive senses. A fish may be bigger than the norm, and a person may violate a norm. This descriptive-prescriptive distinction is a distinction between what is normal and what is normative (between the way something is done, and the way to do something). So we can talk of what the police do as a rule, and of what a rule requires ox permits the police to do.
I will differentiate the descriptive and prescriptive senses of such words by writing, for example, ‘D-norm’ and ‘P-norm’. It makes sense to ask, ‘what is the norm for the use of the word “thin” in Slough?’ and to mean to ask either what is done in Slough, or what it is correct (from some point of view) to do in Slough—to ask for the D-norm or the P-norm. Of course, it also makes sense to ask such a question without differentiating; in fact, to differentiate between P-norms and D-norms is to raise questions about a relation that is ordinarily taken for granted.
The supervenience account has the advantage of offering a simple account of that relation. We can think of it as claiming that the meaning of a word like ‘thin’ is a P-norm for the use of the word, requiring that behaviour conform to the D-norm (use-as-dispositions) for the use of the word. On that account, when you use a word like ‘thin’, it is correct to do precisely what is done.
The supervenience account will not yield a precise P-norm if the argument of Section 3 is sound, because there is no precise D-norm for the use of a word like ‘thin’. A D-norm is a regularity of conduct; in any pattern of conduct as complex as the use of the word ‘thin’, there is any number of regularities. The argument of Section 3 was that no such regularity counts as the D-norm for the use of a word like ‘thin’. The phrase ‘as a rule’ is vague, and sharp boundaries to its application cannot supervene on dispositions. There would be a precise D-norm only if membership in the speech community were specified, and there were some sharply bounded set of pertinent dispositions. Most strikingly, there is no precise D-norm unless mistaken dispositions are counted out of the supervenience base. The notion of a mistake is itself a normative notion, and the possibility of mistakes upsets the notion that it is correct to do precisely what is done.
There are further reasons for thinking that there are no sharp, unknowable boundaries to the P-norm for the application of a word like ‘thin’. Even if the notion of a precise D-norm for ‘thin’ made sense, there is a basic objection to the notion that a P-norm is a requirement that behaviour should conform precisely to the D-norm. It might be thought that that simple account of the relation between D-norms and P-norms does make sense: that people try to conform in their linguistic behaviour to the D-norm for their community. On (p.119) this view, the D-norm is what they are aiming at, but because of their limited linguistic capacities, it is impossible for them to apply the P-norm reliably in borderline cases.
I propose that this view of vagueness should be replaced with a different account of the connection between meaning and use, based on a different understanding of the notion of ‘use’. ‘Use’, too, has senses that are descriptive (‘the use of heroin has increased’) and prescriptive (‘what’s the use of that?’). We can talk of what use someone has made of a hammer (as a doorstop, paperweight … ) and also of the use, or point, or purpose of a hammer. The supervenience account employs the descriptive sense of ‘use’, when it claims that use-as-dispositions determines meaning. I will argue that the supervenience account cannot generate sharp boundaries because a precise D-norm, if there were one, could not supply the descriptive content of a precise P-norm. In broad terms, the claim is that the connection between meaning and use must be understood as a connection between meaning and the use that is to be made of words. It is a connection between meaning and the use that people have made of words just in so far as that gives a reason for the use of words.
For a community to have a customary rule is for it to use a regularity of behaviour as a guide to behaviour. Anything that is used as a guide to behaviour can be used as a guide to behaviour. This basic point about customary rules is an obstacle to an epistemic theory of the requirements of a vague customary rule.
Customary rules can be complex and subtle, and their requirements can depend on context in complex and subtle ways. Moreover, it can be difficult to distinguish between customary rules and the requirements of morality. There are all sorts of things that members of a community would never think of doing, and that would provoke hostility if someone were mad enough to try them—yet it may be unclear whether to say that those things are prohibited by a customary rule.
Is there a customary rule against shouting in an ordinary conversation? If the members of a community tend not to do so, perhaps they are not following a customary rule, but simply tend (in this respect) to act decently. Or perhaps they are following a customary rule that prohibits something which would be wrong even without the rule. Perhaps we can say that there is a customary rule when the regularity is itself a reason for the conduct in question (when the regularity defines good behaviour, rather than merely reflecting a tendency to behave well).18 Suppose that in Singapore, and not in (p.120) Switzerland, people regularly take off their shoes when they enter someone else’s house. Are Singaporeans simply more considerate (or fussier) than the Swiss? It may be better to say that acting considerately requires taking off your shoes in Singapore, but not in Switzerland (or that it is fussy to take off your shoes in Switzerland, but not in Singapore)—that taking off your shoes is required by a customary rule in Singapore.
The question is complicated in at least three ways:
1. The Singaporeans we have imagined might conceive of themselves as acting for background moral reasons. Perhaps a customary rule exists when, from the point of view of the members of the community, the regularity is a reason, even if the members of the community think of something else as a conclusive reason. The notion of something being a reason from the point of view of people who think they are acting on some other reason may seem puzzling. But to think of an example we only have to think of an instance of behaviour that is clearly governed by a customary rule, even if the participants in the custom think that they behave alike because they happen to concur in wisdom, or decency, or élan.19
2. It is the attitudes and responses of members of the community that make a regularity of behaviour into a customary rule; there is a vast multiplicity of forms and intensities of such attitudes and responses, and there is no clear answer to the question ‘What form, intensity, and consistency of attitudes does it take to distinguish a customary rule from a mere regularity of behaviour with no normative force?’ We might say, again, that all it takes is that the members of the community treat the regularity as a reason for conformity to the regularity. This account does nothing to diminish the unclarity. But that is a virtue, because the unclarity is a genuine feature of some rulegoverned behaviour.
3. We can certainly say that there is a customary rule when there would be no reason to act in a certain way, if other people were not doing so; but what counts as a customary rule requiring you to do what you have other reasons (even conclusive reasons) for doing? The answer, again, seems to be the community’s use of the regularity of behaviour as a reason in itself.
The use of a regularity as a reason for action is a feature of customary rules that survives the complications and uncertainties that accompany an attempt to give an account of customary rules. It may help us to understand vagueness.
Imagine a precise customary rule, requiring workers to stop work when the five o’clock bell rings. We can say that the requirements of the rule supervene on the behaviour of the members of the community. The requirements of the (p.121) rule can change only if the behaviour changes. But we have not yet said enough about the connection between the behaviour of the members of the community, and the requirements of the rule. We can also say that the people treat the regularity of conduct in their community as a reason to stop work. We can put it that the rule consists in the way they treat that regularity. There is no customary rule if they all stop work at the same time merely for some other reason (e.g. if they do so to comply with an agreement with their employer, or because they want to work as long as they can and still catch a train that leaves just after five). The D-norm is the fact that they tend to stop work when the bell rings,20 and the P-norm is the use of the D-norm as a reason to stop when the bell rings.
Imagine a vague customary rule: a rule governing how long people should stay at parties. Suppose that people tend not to stay too long at parties, and they tend to criticize people who stay too long. And they act in these ways not (or not only) for background moral reasons, but because staying too long at parties is not what people do.
How long is too long? That may depend on the type of party, and its size, and the sort of people who are there, and so on. Subject to such forms of context dependence, we might say that the requirements of the rule supervene on facts such as how long people actually stay at parties (and on what it takes to provoke criticism, and so on). But we can say more about the connection between the behaviour of the members of the community, and the requirements of the rule: no precise facts about how long people stay at parties make any precise difference to the requirements of the rule. The point is not simply that knowing such precise facts is unhelpful because we do not know how to calculate the rule’s requirements from them. The point is that knowing precise facts is unhelpful because no one uses any precise facts about the community’s behaviour as a precise guide to their behaviour, and the use of the community’s behaviour as a guide is the rule (the P-norm is a way to use the D-norm).
The rule only requires what people use it as a guide to do. People’s behaviour has a role in answering the question ‘What is correct, what is in accord with the rule?’ An action cannot go against the rule unless the regularity can be used to assess the action as wrong. And a person complies with the rule only if he or she uses the regularity as a guide to action. People do not use anything as a guide that they cannot use as a guide. So they do not use inaccessibly precise facts as a guide. Even if there were such a thing as the precise D-norm for staying at parties, the P-norm would not be precise. The difference between the vague customary rule and the precise customary rule is that (p.122) it is possible to use the D-norm of leaving when the bell rings as a precise guide to action.
The regularities of behaviour that people use as guides to conduct, and the ways they use them, vary widely within and among communities, and little can be said about them in general. As well as being vague or precise, customary rules can be very rigid or very flexible, and the potential variety of their content is unlimited. But we can make the general point that such normative practices presuppose the notion that the regularity is a justification for conduct, and people do not use anything to justify their conduct that they cannot use. The application of vague rules such as the one we have considered is subject to a built-in qualification of materiality: there is no such thing as an immaterial breach of such a rule. The precise rule makes sense of saying, ‘he stopped work before he should have, but only by five seconds’, but the vague rule does not make sense of saying, ‘he stayed longer than he should have at the dinner party, but only for five seconds’.21 The vague rule makes sense of deciding to leave a party, and it also makes sense of judging people as rude, or annoying, or overly scrupulous. But increments that do not matter cannot make the difference between action in accord with the rule and action contrary to the rule.
That claim leads to a sorites paradox for the requirements of vague customary rules. So an epistemic theorist has to say that the claim is incorrect, or else that the alleged customary rule is incoherent. There is a readily apparent epistemicist response to the claim: that it begs the question by relying on a tendentious definition of a rule. An epistemic theorist might say that the P-norm is a requirement of conformity to the D-norm; people are reliably right in identifying the D-norm (and therefore the P-norm) only in clear cases, because the behaviour is not all known, and is so complex, and because there is no algorithm for identifying the D-norm. It is possible to stay a second too long at a party, though no one can know that that is impolite, because no one can reliably identify it as too long. is a requirement of conformity to the D-norm; people are reliably right in identifying the D-norm (and therefore the P-norm) only in clear cases, because the behaviour is not all known, and is so complex, and because there is no algorithm for identifying the D-norm. It is possible to stay a second too long at a party, though no one can know that that is impolite, because no one can reliably identify it as too long.
necessarily unreliable. And it claims that there is no sharp boundary to the requirements of a vague customary rule, because (i) there is no difference between what the customary rule requires, and what people use the rule to guide them to do, and (ii) people do not use the rule as a guide to do anything that they cannot use it as a guide to do. People will certainly be unreliable in identifying D-norms—e.g. in guessing at the answer to any question such as ‘How many seconds did the average guest spend at dinner parties last year?’ And individuals can also be unreliable in answering the (p.123) P-question ‘Is it time to go home yet?’ That unreliability accounts for the possibility that someone might misbehave without meaning to misbehave. But the possibility of unreliability gives no reason to think that the rule has unknowable requirements.
To conceive of a P-norm as requiring conformity to a precise D-norm would ignore the role that the regularity (the D-norm) plays in the life of the community—its use. If (contrary to the claims of Section 3) any sharply bounded period of time counted as the D-norm, deviating very slightly from it could not count as going against the rule, because the D-norm could not be used as a standard by which to guide or evaluate conduct. And the use of a regularity to guide or to evaluate conduct is all that a customary rule is. There is nothing more to a customary rule, though there is more to questions such as whether it should be followed. A customary rule does not draw distinctions that the members of the community do not draw, and it cannot draw distinctions that they cannot draw.
We could say that customary rules provide a useful analogue with which to compare the meaning of a word like ‘thin’: both consist in the community’s use of a regularity as a guide to conduct. Or we could say that that similarity is a reason to say that the meaning of an expression is a customary rule. The notion that the meaning of a word is a rule for its use sounds like an obviously false Wittgensteinian gesture, and several writers have argued against it.22 When Wittgenstein says, ‘we are not equipped with rules for every possible application’ of a word (PI 80), and that ‘the application of a word is not everywhere bounded by rules’ (PI 84), he seems to imply that the application of a word is governed by rules in some cases. He seems to have thought, roughly, that the meaning of a word is a set of rules for its use—a set of rules that do not answer every possible question of its application.
The meaning of a word is certainly not a rule in Raz’s sense of a protected reason for action:23 there is nothing for it to be protected from. That distinguishes it from customary rules such as the rule against staying too long at parties, which is a reason not to act for certain other reasons. The fact that ‘dark’ applies to conditions sufficiently similar to pitch blackness does not exclude reasons to use the word differently, because there are no such reasons.24 Moreover, the meaning of words carries none of the complex normative equipment that (other) rules carry: there are no duties or rights or (p.124) powers. There is just one big, complex, remarkably pure coordination problem, to which a natural language is a complex solution.
We may view the meaning of a word as a customary rule, or only as sharing with customary rules a central normative feature: the use of a regularity of behaviour as a general guide to action. On either account, a theory of the practice of using a word must use the basic concept of normative theory, the concept of a guide to action. On either account, an epistemic theory of the application of words like ‘thin’ faces thesame objections as an epistemic account of the requirements of a vague customary rule.
Use determines the correct application of a word just to the extent that it gives a reason to apply or not to apply the word. On this view, meaning is what you know when you know how to use a word.
Remember the speech community of two speakers, one of whom was disposed to apply the word ‘dark’ at 8.30 p.m., and the other not until 8.50. That scenario was an attempt to concoct a surveyable pattern of dispositions to apply a word. The intuitive objection to the epistemic theory is that it is surveyably arbitrary to say that this pattern of dispositions determines a sharp boundary to the use of the word. It is arbitrary in the sense that the pattern of use gives no reason to say that one or the other speaker is incorrect when their dispositions disagree. By the same token, the facts that one speaker started applying the word at 8.30, and the other at 8.50 do not give either of them any reason to apply the word ‘dark’, or reason to withhold it, at 8.40.
The use objection cannot succeed in that simple form, because on the epistemic theory, something is hidden in this situation: each speaker’s ‘whole pattern’ of the use of the word ‘dark’ is inaccessible, even to the speaker. So it is not surveyably arbitrary to say that sharp boundaries supervene on the dispositions of these two speakers to use the word ‘dark’, because their dispositions are not surveyable.
All that can be said in response is that, given the dispositions mentioned, there is no reason to think that any other fact about their use of the word would justify a claim that it is true to say ‘it is dark’ at 8.40, or that it is false. An epistemic theorist might say that no one has said what it would take to justify such a claim in a clear case (and might suggest that, whatever that is, it justifies making true statements (though it does so unknowably) in borderline cases too). But without saying what would justify the application of the word ‘dark’, we can say that it would take something intelligible to those speakers as justifying a distinction in the application of the word. An epistemic theorist can say that the reason is just that it is dark, and the property of darkness just must have sharp boundaries because of the logic argument. That approach would abandon the notion that use determines meaning. (p.125) What the epistemic theory cannot say is that the reason is that the light conditions fit the D-norm for ‘dark’.
On the view that I have proposed, the notion that correct application supervenes on dispositions cannot support the epistemic claim that there are sharp boundaries to the correct application of words. Moreover, it cannot help to make sense of the notion that use determines meaning. Use determines meaning in the sense that a regularity of behaviour is treated as a reason for applying an expression. We should remodel the supervenience account’s conception of use: dispositions matter just in so far as they justify applications of expressions, and they can justify applications of expressions only to the extent that they are intelligible to speakers as providing a justification. So an expression’s D-use (what is done with an expression) determines meaning only in so far as it can show speakers what to do with an expression (its P-use).
It might seem that the argument presented here is verificationist, because it claims that there can be no unknowable truths about what statements mean. Williamson sees verificationism as a tacit prejudice against the epistemic theory, and he curtly rejects it.25 But I do not think that the argument made here is verificationist in any objectionable sense.
Did the Earl of Orkney cross the Atlantic in 1398? There may be no way for people today to find out. For human beings, it is an unknowable truth or an unknowable falsehood that he did so. It would be a form of verificationism to say it cannot be true or false because we have no way of finding out.
But here it is a fact that is unknowable, and not a norm. Meaning is normative if it is the use of regularities as guides to behaviour. The notion of an unknowable norm makes no sense, if norms are capable of guiding behaviour. We can accept the notion of unknowable facts, without accepting the notion of unknowable norms.26 It would make no sense to assert normative consequences for unknowable facts about the dispositions of speakers. The argument does not claim that a proposition is not true unless it is verifiable; it claims that a word does not apply to a known object unless it is intelligible to speakers that it should apply. It may be true, yet unknowable for people living today, that the Earl of Orkney was thin. But it cannot be true, yet unknowable for people who know TW, that TW is thin. It may be controversial, and (p.126) the controversy may be irresolvable, but the question is different in this respect from the question whether the Earl of Orkney was thin.
If there were a precise D-norm, it would be unknowable. As Williamson says, the whole pattern of a community’s D-use is inaccessible to speakers (and in fact, the whole pattern of any one speaker’s use is inaccessible to that speaker). But it would still be false that the P-norm can be unknowable. There is much that you cannot know about what you and others have done with the word ‘thin’, but none of that inaccessible information would help in deciding what to do with the word.
4. The Vagueness of Evaluation
General normative, aesthetic, and value terms are generally vague. We can construct sorites series for the application of ‘right’, ‘good’, ‘beautiful’, and gerundives such as ‘to be done’, and so on. Presumably most thick evaluative concepts (‘brave’, ‘tolerant’, ‘rude’ … ) are vague too. This feature of evaluative expressions is not an accidental feature of human languages. ‘Right’ and ‘wrong’ are vague because they are abstract terms used to evaluate practical decisions, and the considerations relevant to practical decisions are very commonly susceptible to sorites paradoxes. There is no precise amount of time that you should spend with your children. There is no precise mean between being stingy and being profligate. On most mornings you have good reason to get out of bed, but only in special circumstances is there a first second at which you ought to get out of bed. The wise person will not brush his or her teeth all day, but will not ordinarily view any particular stroke as the last stroke of the toothbrush that reason requires.
Reasons for action are not necessarily vague: if you ought to watch all of a TV show that starts at 5 p.m., then you ought to be watching at 5 p.m. But basic reasons (e.g. that the show is gripping … ) are vague. We might say that first-order reasons for action are precise only when they are pegged to some precise phenomenon.27 And evaluative terms such as ‘perfect’ (and reasons to do something perfectly) may not be vague, depending on the context (e.g. on whether there are incommensurable requirements of perfection). But ‘perfect’ does not become meaningless when it is vague. So it is no exaggeration to say that vagueness is a characteristic feature of general evaluative language. Although there are some precise reasons for action, all the language in which we could conceivably talk in general terms about general (p.127) reasons (and about rationality) is vague. For that reason I will talk of the vagueness of evaluation, and not just of evaluative language.
This is one of the most interesting aspects of vague language, but philosophers concerned with vagueness have had little to say about it. There are two reasons why the vagueness of evaluation is important for understanding vagueness in general: first, value terms can be used to formulate sorites paradoxes that stubbornly resist Williamson’s anti-paradox techniques; secondly, evaluative presuppositions underlie context dependence, and perhaps all use of vague descriptive terms. The first of these considerations is an objection to the epistemic theory, and the second is a reason for thinking that the objection is fundamental and general.28
Evaluational Sorites Paradoxes
A good cook is making a batch of soup, and it needs salt. The quantity of salt matters: a good batch of soup this size will have more than a teaspoon and less than a tablespoon of salt. But however much salt is added, no marginal grain of salt makes the difference between a good batch of soup and a batch of soup that is not good. That is the case partly because tastes differ, but it is also because, whatever your taste, it will not be better or worse suited if one grain of salt is added to the soup. The cook knows that no single marginal grain of salt matters.
That reasoning leads to a sorites paradox for the application of the term ‘good’. It is a stubborn paradox because of the role of knowledge in this situation: the point is that the conditional premiss in this form of the sorites paradox is known to be true. Consider the following propositions:
(1) The cook knows that it matters whether the soup is good or not.
(2) The cook knows that one grain of salt does not matter.
(3) Therefore, the cook knows that one grain of salt cannot make the material difference between good soup and soup that is not good.
(4) Therefore, the cook knows that, if the soup is good, it will still be good if one grain of salt is added to the pot.
There may be situations in which the cook does not know whether to say that the soup is good or not (cases that appear to the cook to be borderline cases for the application of ‘good’); in such a situation, (4) is still true. The uncertainty is as to whether x i is good (and it will also be unclear whether x i+1 is good). There is no uncertainty as to whether x i+1 is good if x i is good.
(p.128) One grain of salt probably makes no perceptible difference to the soup at all. But that is not essential to this form of the paradox. The cook may find that adding an eighth of a teaspoon of salt makes a noticeable difference, but not a sufficient difference to justify drawing the significant distinction between soup that is good and soup that is not. Either way, the ‘doesn’t matter’ paradox arises. So this paradox is stronger than forms of the sorites paradox that are based on indiscriminability, because it can apply when the inductive step makes a noticeable difference. This form of the paradox claims that a discriminable difference may not matter, and that if it does not matter, it cannot justify the distinction between good soup and soup that is not good (a distinction that does matter). If two batches of soup are not significantly different, one cannot be good if the other is not good, because that is a significant difference.
Williamson’s strategy for resolving sorites paradoxes is to replace the paradoxical tolerance principle:
(TP) If x i is F, then x i+1 is F
with the non-paradoxical ‘margin for error principle’:
(Ep) If x i is known to be F, then x i+1 is F.29
That strategy fails if the above argument is sound, because the argument yields
(TP’) It is known that if x i is F, then x i+1 is F.
In this situation the tolerance principle is itself an evaluative proposition, which the cook knows to be true.
An epistemic theorist might respond (i) by pointing out that an evaluative judgment may be justified, without some agent knowing that it is justified, and (ii) by disputing the claim that there must be a material difference between soup that is good and soup that is not good. It may matter a little if the soup is a little too salty, and a great deal if the soup is much too salty.
These potential responses do not succeed:
(i) Since the epistemic theory must say that one batch of soup can be good, and another not good, when there is no difference that anyone could use to justify an evaluative distinction between them, the theory has to claim that justifications of evaluative judgments can be not just unknown to a particular agent, but unknowable to any agent. That would make evaluation unintelligible.
(ii) It is true that it might be a disaster if the soup is horrible, and no big problem if the soup is not good but not horrible. But it typically matters whether the soup is good, and it never matters (p.129) whether an extra grain of salt has been added.
This evaluational form of the sorites paradox does not apply only to matters of taste. It is very far-reaching: similar claims could be made about almost any sort of practical decision about how much or how soon or how often … to do something unimportant or something vital. It is a form of the paradox that can be formulated using all the basic general terms of practical reason, such as ‘reasonable’, ‘right’, ‘wrong’, and so on.
The choices are stark for an epistemic theorist. I propose that we cannot make sense of the meaning of evaluative expressions if we attempt to assert bivalence for them. But the epistemic theorist is committed to saying that they are meaningless if we deny bivalence, and that a neutral attitude to bivalence is not an option.
Consequences of the Vagueness of Evaluation
The vagueness of evaluation has an important implication for pragmatic vagueness (above, Chapter 3.10). Because ‘suitable’, ‘appropriate’, ‘reasonable’, and all such terms are vague, the epistemic theory must extend to pragmatic vagueness. It must either assert bivalence for all phenomena of pragmatic vagueness, or claim that all the language in which we describe those phenomena (and all the general language in which they could conceivably be described) is incoherent.
A related ramification of the role of evaluation in pragmatic vagueness is that evaluative considerations are needed to account for context dependence, as I will claim in Section 6.
Finally, the vagueness of evaluation has general importance for understanding vague language, because evaluative presuppositions underlie the use of vague descriptive terms as well as terms like ‘good’. Such a conclusion is inescapable if we accept the view proposed in Section 4, that the meaning of a word shares normative features with customary rules. We could formulate a ‘good soup’ paradox for the requirements of the customary rule against staying too long at parties. By the same token, we could formulate a good soup paradox for the correct application of ‘thin’ or ‘red’. Words such as ‘thin’ and ‘red’ are useful (good) for drawing significant distinctions. The purpose of drawing a distinction using the word ‘red’ cannot be accomplished via a trivial step. Drawing the distinction has a point that it would not have if x i were red and x i+1 were not red. It may matter whether something is distinguished as red, in a way that demands justification. Something that reflects light only at 6562 Ångstroms can be trivially different in colour from something that reflects light only at 6563 Ångstroms. But if ‘red’ is used to draw material distinctions that may require justification, then (p.130) something that is red cannot be trivially different in colour from something that is not red.
It might be objected that what matters depends on the situation, and that it might matter (it might matter enormously) whether something reflects light at 6562 or 6563 Ångstroms. Yet the difference in colour is trivial. So the fact that it may matter whether something is red does not mean that the difference between something that is red and something that is not red cannot be a trivial difference in colour.
One difference between ‘reflecting light at 6562 Ångstroms’ and ‘red’ is the generality of ‘red’. It applies generally not only by applying to a range of hues, but also by applying to a range of intensities and saturations, so that there are various grounds of application. But it might be objected that we could construct precise general predicates such as ‘between 6500 and 6600 Ångstroms’. We could also construct precise compound predicates with saturation and intensity components. Let us call some such predicate ‘red+’. The epistemic theory claims that ‘red’ is like ‘red+’, except that the boundaries of its application are determined by dispositions rather than by stipulation. It might matter whether something is red+, so the fact that it may matter whether something is red does not mean that the good soup paradox applies to ‘red’.
The difference between ‘red’ and ‘red+’ is that we can explain the meaning of ‘red’ by pointing to paradigms and saying that it applies to them, and to things that are sufficiently similar in relevant respects. Even if the same objects that serve as paradigms of ‘red’ are also red+, we could not explain the meaning of ‘red+’ in the same way: things must resemble the paradigms in a particular way to be red+. In fact, there are no paradigm red+ objects (no objects that are useful for explaining the meaning of ‘red+’). ‘Red’ is different because knowing its meaning involves knowing how to make judgments of similarities to paradigms. Its meaning cannot be explained more completely than by saying that it applies to things that are sufficiently similar in relevant respects to paradigm cases. The requirements of relevance and sufficiency are evaluative considerations. ‘Red’ is not ordinarily an evaluative term, but its use presupposes the evaluative considerations involved in judgments of relevance and sufficiency. To say that ‘red’ is like ‘red+’ (except that its sharp boundaries of application are determined by dispositions) is to make the use of the word inexplicable.
So we could formulate a paradox just like the good soup paradox, using ‘red’ instead of ‘good’. And like the good soup paradox, it would be stronger than the indiscriminability paradoxes that writers have formulated using ‘red’. Perhaps we can make the good soup paradox entirely general, by applying it to the notion of truth, as Dorothy Edgington has suggested: ‘The difference between a true and a false judgment is meant to be a difference that matters. Yet for any putative line, there will be no significant (p.131) difference—no difference which matters—between things just either side of it.’30 In summary, there is no value-free understanding of language, because of (i) pragmatic vagueness of purposes for which words are used and (ii) context dependence and (iii) the role of evaluative considerations in the use of descriptive language. The intractability of evaluational sorites paradoxes is not only an argument against applying the epistemic theory to evaluative expressions; it is an argument against the epistemic theory. This book offers no theory either of value or of morality, and it is not the place to refute moral theories that allege that there is no such thing as the correct application of moral expressions (as moral truth). But we can say something about a moral theory: no theory should claim that there are sharp boundaries in all contexts to the correct application of general evaluative expressions.
5. Context Dependence and Vagueness
An account of vagueness needs to deal with the fact that people apply the same vague expression differently in different contexts (see Chapter 3.10 above). The complexities of context dependence are unlimited, but we can simplify matters by focusing on three forms. First, vague words are often ‘syncategorematic’: a sandcastle may be large even if it is smaller than a house that is not large. Secondly, the application of vague words may depend on the comparison class. A large house in Stow-on-the-Wold may be smaller than a house in San Jose that is not large. Thirdly, the application of vague words depends on the purposes of the people who are communicating: it may be true to call a house ‘large’ if you are talking about living in it by yourself, and false if you are talking about living with six children.31
For these three reasons and others, a vague expression can apply and fail to apply to the same object in different contexts. That fact points out a similarity between vague and ambiguous expressions: both vague words like ‘large’ and ambiguous words like ‘hot’ have multiple senses. It might be thought that context dependence is simply a form of ambiguity, distinct from and irrelevant to vagueness. Proponents of bivalence can offer a neat account of ambiguity: bivalence is maintained, because an ambiguous statement can be both true and false, as long as it is true in a different sense from the sense in which it is false. So it might seem that the epistemic theory can (p.132) treat context dependence as ambiguity, and claim that vagueness is only a feature of fully disambiguated context-dependent expressions.
Williamson suggests such an approach. He discusses arguments that vagueness is context dependence and rejects them, pointing out that a knowledge of the context in which a vague statement is uttered will not enable anyone to identify the truth of the statement in a borderline case (215). His conclusion is that the epistemic account is needed to preserve bivalence: that vagueness is ‘reduced but not eliminated by context’ (281). In Williamson’s view, ‘Vagueness and context dependence are separate phenomena’ (215). The implication is that context dependence is a form of relativity, which poses no more threat to the principle of bivalence than ambiguity poses. Once the context is fixed, vagueness remains. I will claim that the problem is worse than this view suggests, because ordinarily nothing will count as fixing the context precisely.
On the epistemic theory, it seems that a context-dependent expression has as many senses —and there are as many sharp boundaries to its application— as there are contexts. How many contexts are there? How many senses and sharp boundaries are there for, for example, the word ‘thin’? Comparison classes and the purposes of speakers vary along a multitude of continua. The number must be infinite. The notion of an infinite number of sharp boundaries to the application of ‘thin’ or ‘small’ might sound bizarre and objectionable in itself, but an epistemic theorist will insist that it is neither: any account of the application of a word like ‘small’ or ‘thin’ will have to account for its varying as the context varies. If the context can vary infinitely, then the application of the word must vary infinitely. Any account of the application of vague words needs to account for the relativity of context dependence, and there is nothing objectionable in this regard in the epistemic account.
But in fact there is reason to conclude that context dependence does not just impose a trivial requirement of relativity, but presents a fundamental problem for the epistemic theory. The problem is that contexts are typically unspecific. If you say that you have found a small house, you may do so without specifying the standard (the sense in which you are using ‘small’). You may not specify the comparison class, and you may not specify the purposes that you have in mind. And although the context may be a guide to the relevant standard, there may be nothing in the context to supply a fully specific standard. The context may or may not be a guide to the truth of the statement. Even on the epistemic theory, the truth of your statement will depend on a standard that is not supplied. If the sense of ‘small’ is unspecified, then your statement has no specific truth value. What you say will, in a borderline case, be true on some standards and false on others, and there will be no precise answer to the question ‘What is the standard?’
The epistemic theory could treat context-dependent expressions as semantically incomplete, and conclude that statements using them are (p.133) semantically defective unless their sense is specified. But that approach would defeat the epistemic project of ‘applying’ classical logic to natural languages. In fact, it would even defeat the fall-back epistemic project I suggested earlier, of applying classical logic to idiolects. Context dependence is a characteristic feature of vague words, and we commonly make statements using vague words without specifying the sense in which we are using them. When we do specify a sense, respects typically remain in which that sense is unspecific: ‘small for a family of seven’ is more specific than ‘small’, but it is still unspecific. An indefinite variety of further qualifications could be added to the specification. It would be impossible to add all those qualifications, and no one talking about houses needs to do so. But without them, the correct application of vague words like ‘large’ and ‘small’ depends on something that has not been specified. Yet for an epistemic theorist to view those statements as lacking truth value would mean concluding that much vague discourse is semantically defective.
The alternative is for the epistemic theory to claim that the context on which the application of vague expressions depends is always (or at least characteristically) fully specific. An epistemic theorist might say that every vague statement has a truth value that depends on the context, and that to make a vague statement without specifying a fully specific purpose, and comparison class, and so on, is to speak indexically, appealing to the salient standard—the standard appropriate to the context of utterance.
It might sound odd to suggest that the truth of a statement depends on what amounts to a conversational maxim (a maxim that the statement means, for example, ‘large with respect to the comparison class that is salient in this context’). But we can keep that maxim in its place by saying that the truth of a statement depends on its sense, that a vague context-dependent statement may have a multitude of senses, and that the salient sense is the sense which ought (by conversational convention) to be ascribed to a speaker’s utterance.
But that approach will not solve the problem of unspecificity: the salient sense of a statement—the sense it has in the context of the utterance—is itself characteristically unspecific. First, the comparison class is typically unspecific: it will generally include the house next door, and it may not include every house in the world. What determines the extension of the comparison class? It may be determined by an express stipulation, but ordinarily it is limited just by relevance. To judge what comes within the comparison class is not to answer a question of fact whose precise answer is unknowable, but to make an evaluative judgment concerning what matters for the purpose in question. This fact ties the unspecificity of context dependence to the vagueness of evaluation (see above).
Secondly, on the epistemic approach suggested here, the truth of a statement that a house is large may depend partly on the purposes for which (p.134) someone is calling it ‘large’.32 There may be no specific answer, in a context, to the question ‘Large for what purpose?’ The context of utterance will typically rule out some purposes, and may make some purpose or purposes salient (such as ‘for a home for a family of seven’). But ordinarily no such purpose made salient by the context will be fully specific. Perhaps there is ordinarily nothing that would count as a fully specific purpose, when the purposes concern people’s general needs and complex activities. The purpose of living with six children certainly makes a difference, and will often be all that is needed to determine whether a particular house counts as large for that purpose. But that purpose leaves a great deal unspecified, and not merely unknown. The conclusion must be that context-dependent expressions are not fully disambiguated by context. To the extent that that is the case, the principle of bivalence cannot be asserted for context-dependent expressions. It would be like asserting bivalence for statements reporting the length of periods of time in heartbeats.
It is possible to succeed (or to fail) in some cases in finding a large house in spite of the unspecificity in the standard—just as a year really is longer than 10 million heartbeats. What is not possible is to conceive of the application of the expression ‘large house’ as bivalent, when the context does not supply a standard. If the epistemic theory admits that conclusion, and asserts the principle of bivalence only for specified standards, then it faces the objection that most vague utterances (specifically, all context-dependent utterances, when the context is not fully specific) are semantically incomplete.
6. Conclusion: Putting a Price on Bivalence
If one abandons bivalence for vague utterances, one pays a high price.
(Williamson, Vagueness, 186)
We stalwarts of two-valued logic buy its sweet simplicity at no small price in respect of the harboring of undecidables.
(Quine, ‘What Price Bivalence?’ (1981) 78 Journal of Philosophy 90, 91)
… how can [logic] lose its rigour? Of course not by our bargaining any of its rigour out of it.
(Wittgenstein, Philosophical Investigations, 108)
Williamson and Quine both see themselves as stalwarts of bivalence. Yet to Williamson, Quine’s approach is ‘close to global nihilism’ (298 n. 2). There (p.135) seem to be two issues: (i) whether it is even coherent to refuse to assert bivalence—to buy or sell two-valued logic, and (ii) how to drive a good bargain. I do not know how to address issue (i); perhaps the best approach for an epistemic theorist is to claim (unlike Williamson) that a coherent theory of semantics must assert bivalence.
As regards issue (ii), Williamson and Quine agree that the cost of abandoning bivalence is to lose its ‘sweet simplicity’, ‘simplicity of theory’ (Quine33), or ‘simplicity, power, past success, and integration with theories in other domains’ (Williamson 186).
Their disagreement is that Williamson denies that there is a cost to be paid for asserting bivalence. If Williamson is right, then there is nothing to count against the elegance of bivalence. Quine says that the cost of asserting bivalence is disregarding the facts, and treating ordinary expressions as if their application were bivalent.34 If the argument of this chapter is right, Quine is right about the cost of asserting bivalence: it means ignoring the reasons to deny that there are sharp boundaries to the application of ordinary vague expressions. I have argued that Williamson’s supervenience account of meaning and use cannot dispel that view.
If there are costs to be paid both for asserting and for denying bivalence, it is unclear what would decide the question. It is beyond the scope of this book to try to assess the value of applying classical logic to natural languages, and if there is any such value, it is undoubtedly incommensurable with the cost of asserting bivalence.35 Both Quine and Williamson view the question as theoretical, and Quine explicitly compares the question to questions of theoretical physics. But classical logic does not have the form of a scientific theory, and if it is falsified by vagueness, it is not falsified in the way that, for example, the steady state theory of the universe was falsified by the discovery of the cosmic background radiation. So I do not know how to address this aspect of issue (ii) either—except to say that the reasons for denying that there are sharp boundaries to the application of vague expressions are cogent, and to leave logic to take care of itself.
So I propose to take a neutral attitude to bivalence (and neither to assert it nor to deny it in particular borderline cases). If there are frequently no clear borderline cases of the application of vague expressions (see chapter5.5), a neutral attitude is appropriate in individual borderline cases, and consistent with the denial of sharp boundaries.
To avoid the paradox of trivalence, this neutral attitude should not picture (p.136) indeterminacy as an area within which neutrality is appropriate. This approach should deny that there is any gap between true and false statements, and also that there is a sharp boundary between them. If we represent the application of words spatially (as a segment on a line, or an area on a plane, or a solid in a space), this conjunction of denials seems nonsensical: it is like trying to picture two geometrical figures on a plane that do not overlap, do not share a boundary, and are not separated by a space. So the approach I propose cannot take spatial metaphors too seriously as a description of the application of vague words: it needs to abandon the notion of boundaries, instead of saying that it is indeterminate where the boundaries are. Chapter 7 discusses that approach.
For law, the consequences of this chapter are three: first, we have seen reasons to support the indeterminacy claim against the strongest challenge that philosophers of logic have mounted against it. I do not propose that champions of classical logic such as Williamson have failed in providing classical logic with a defence that it needs. Whether classical logic needs defence is a question outside the scope of this book. Secondly, we have seen reason to think that the general evaluative and normative linguistic expressions that the law uses are necessarily vague. Not only that, but because any conceivable expressions of that kind would be vague, we have reason to think that general evaluative and normative considerations are necessarily vague. This claim will play an important part in the discussion of the role of interpretation in law in Chapter 8 of Vagueness. Finally, we have seen that the context dependence of legal language supports the indeterminacy claim.
(1) Cf. Mark Platts: the tolerance principle ‘is false, since … paradoxes would be generated by its truth.’ Ways of Meaning (London: Routledge & Kegan Paul, 1979), 230.
(2) Williamson suggests that they do not need to do so, and that it would not be helpful if they did: ‘there is no need to insist, unconstructively, that there must be something wrong with the objections to bivalence in borderline cases’. Vagueness (London: Routledge, 1994), 186.In this chapter 1 will refer to Williamson’s book by page numbers in parentheses.
(3) A third strand in Williamson’s work has been to remove an objection he had seen to the epistemic theory, by explaining ‘what makes us ignorant’ (xi; Ch. 8 is his answer). I will not address that argument.
(4) Philosophical Investigations, trans. G.E. M. Anscombe (Oxford: Blackwell, 1953), sects. 43, 435.
(5) Cf. ‘“Meaning is use”: that is, semantic facts concerning a language supervene on facts about the linguistic behaviour of masters of that language.’ R. M. Sainsbury, and Timothy Williamson, ‘Sorites’, in Bob Hale and Crispin Wright (eds.), A Companion to the Philosophy of Language (Oxford: Blackwell, 1997), 458,480.
(6) Cf. Williamson, ‘What Makes it a Heap?’ (1996) 44 Erkenntnis 327, 331:‘The epistemic theorist can accept the … supervenience thesis and apply it to the borderline case.’
(7) Cf. ‘algorithm for calculating reference’. Williamson, ‘Wright on the Epistemic Conception of Vagueness’ (1996) 56 Analysis 39,42.
(8) However, meaning and truth conditions are not equivalent in the epistemic theory (a precise stipulative definition of ‘thin’ would change the meaning of ‘thin’, but might not change its extension (205,214)).
(9) But note that the instability that Williamson accepts (231) is not a consequence of adopting a synchronic notion of dispositions: he appears to take the view that meaning continually changes as a diachronically extended pattern of use changes. As Williamson presents it,the supervenience account is vulnerable to the diachronic problem: he says,‘What you mean by ‘thin’ does not depend solely on what you would say in your present circumstances and mood’(231).
(10) Cf. ‘what individual speakers mean by a word can be parasitic on its meaning in a public language’ (211).
(11) Another way of putting the same objection is that the correlation claim, which says that a shift in dispositions would shift the meaning of an expression, needs an account of which dispositions it applies to.
(13) ‘Vagueness and Ignorance’ (1992) 66 Proceedings of the Aristotelian Society (suppl.) 145, 155.In fact, if the argument so far presented succeeds, dispositions determine no lines such as unanimity or majority assent, unless there are sharp bounds to the speech community and to the pertinent dispositions of each speaker, and the problem of mistakes is solved, and so on.
(15) Cf. Jaegwon Kim, Supervenience and Mind (Cambridge: Cambridge University Press, 1993), 167:‘there is no single kind of dependence that underlies all cases in which supervenience holds’. Kim concludes that ‘Mind-body supervenience … does not state a solution to the mind-body problem; rather it states the problem itself (Ibid. 168). On Kim’s view, the task for a theory of mind is to explain what kind of dependence relates mind and body. My point here is that it makes sense to ask what kind of determination relates use and meaning, and that the epistemic theory has to claim that the question has an answer, although it will insist that no human being can know what the answer is.
(16) See ‘What Makes it a Heap?’, n. 6 above. And cf. Sainsbury and Williamson: ‘Since no theorist of any kind … has given any such detailed account [of how meaning supervenes on use], the fact that the epistemic theorist has not should not count against the theory.’ ‘Sorites’,n. 5 above, 480.
(17) Identity and Discrimination (Oxford: Blackwell, 1990), 107.
(18) Cf. Hart (CL 255–6) and Dworkin (TRS 53ff; LE 145), and Raz’s distinction between acting on a general reason and following a rule (PRN 57).
(19) Picture any peculiar custom that has no point except to dramatize a distinction between people (such as lawyers wearing wigs), and you have an example of a customary rule—a practice in which the regularity functions as a reason for behaviour, even if participants in the practice think of themselves as acting on other reasons.
(20) It would be more complete to say that the D-norm is a complex variety of related regularities of behaviour including regularities of action, criticism, self-justification … That complexity takes nothing away from the precision of the rule being discussed: to describe all those forms of behaviour is to describe what is done with the precise phenomenon of the bell.
(21) No doubt it is possible to imagine circumstances in which someone leaves a dinner party five seconds later than they should have. I am claiming that it is not possible to imagine that they do so in virtue of violating a customary rule about how long to stay at parties, unless such a rule is pegged to a precise phenomenon (like the five o’clock bell rule).
(22) A vehement example is Paul Ziff, Semantic Analysis (Ithaca, NY: Cornell University Press, 1960), 35:thinking of language as a rule-governed activity ‘can produce, can be the product of, nothing but confusion’. A similar example, but without the exasperation, is Bede Rundle, Wittgenstein and Contemporary Philosophy of Language (Oxford: Blackwell, 1990), 5:rules are an ‘overworked notion’
(23) PRN 191.
(24) If there are ever reasons not to apply the word ‘dark’ when it is dark, they are reasons not to tell the truth (or reasons to speak figuratively … ), and not reasons to diverge from the regularity that constitutes the D-norm for application of the word ‘dark’. If they are excluded, they are excluded by reasons to speak the (literal) truth, and not by the P-norm for ‘dark’.
(26) Is a secret law purporting to create an offence an unknowable mandatory norm? No: it is intelligible, even if it is always false, to say that a secret law justifies an arrest and punishment. But it is unintelligible to say that the ‘offender’ had an unknowable reason not to commit the purported offence. (Except in the sense that the existence of the law might make it more likely that a sanction would be imposed on him—that is an unknown reason.) That is why publicity of laws is one of the requirements of the rule of law.
(27) Cf. Ch. 5.4 above. It would be rash to say that protected reasons are typically more than trivially vague. Whether they are vague or precise is a contingency that depends on the vagueness or precision of a directive, promise, etc. But protected reasons are often vague, and Ch.9.2 argues that legal systems necessarily include vague rules.
(28) A potential puzzle that the vagueness of evaluation poses for Williamson is that it is false to say that the dispositions of speakers determine sharp boundaries to the application of a word like ‘good’, and it is not clear what could support a semantic argument that the epistemic theory applies to evaluative expressions. That puzzle cannot be explored here.
(30) ‘Vagueness by Degrees’, in Rosanna Keefe and Peter Smith (eds.), Vagueness: A Reader (Cambridge, Mass.: MIT Press, 1997), 299.
(31) The second and third forms of context dependence mentioned here can be thought of as forms of syncategorematic meaning, the question being ‘What is the category to which the object must be taken to belong for the purpose of a statement describing it?’ That question is answered partly by comparison class and purpose (that’s big for a house, for a house in Stow-on-the-Wold, for a family of seven … ).
(32) As examples of features of context on which the extension of ‘thin’ might depend, Williamson cites ‘the purpose at hand, the salient comparison classes, previous uses of it in conversation, and so on’ (214).
(33) ‘What Price Bivalence?’ (1981) 78 Journal of Philosophy 90, 91.
(34) ‘Bivalence requires us … to view each general term, e.g. “table”, as true or false of objects even in the absence of what we in our bivalent way are prepared to recognise as objective fact.’ Ibid. 94.