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Vagueness and Legal Theory

Published online by Cambridge University Press:  16 February 2009

Timothy A. O. Endicott
St. Catherine's College, Oxford


The use of vague language in law has important implications for legal theory. Legal philosophers have occasionally grappled with those implications, but they have not come to grips with the characteristic phenomenon of vagueness: the sorites paradox. I discuss the paradox, and claim that it poses problems for some legal theorists (David Lyons, Hans Kelsen, and, especially, Ronald Dworkin). I propose that a good account of vagueness will have three consequences for legal theory: (i) Theories that deny that vagueness in formulations of the law leads to discretion in adjudication (including Dworkin's) cannot accommodate “higher-order” vagueness, (ii) A legal theory should accept that the law is partly indeterminate when it can be stated in vague language, (iii) However, the traditional formulation of the indeterminacy claim, that a vague statement is “neither true nor false” in a borderline case, is misconceived and should be abandoned.

Copyright © Cambridge University Press 1997

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1. Criminal Justice and Public Order Act 1994, ch. 33, §63(1).Google Scholar

2. §63(1)(b).

3. A completed definition would distinguish ambiguity.

4. When they write about the meaning of expressions like “serious distress,” philosophers of language and philosophers of law are generally more interested in puzzles other than imprecision. Here I will focus on imprecision, because of its important consequences for legal theory, and because legal theorists have neglected it. I will follow the usage of philosophers of logic and call it “vagueness” because it is the typifying feature of words that arc vague in the broad sense just proposed. Expressions displaying the semantic features that have interested philosophers of law (which they term “open texture,” “family resemblances,” “contcstability,” etc.) are typically imprecise. It is possible to invent terms that display those features and are not imprecise; but imprecision is the common, characteristic feature of vague words in natural (and therefore in legall) language. For surveys of semantic problems that can be referred to as “vagueness” see Bix, Brian, Law, Language and Legal Determinacy (1993)Google Scholar, and Waldron, Jeremy, Vagueness in Law and Language: Some Philosophical Issues, 82 Cal L. Rev. 509 (1994).CrossRefGoogle Scholar

5. The indeterminacy claim needs to be distinguished from the radical indeterminacy claims of some critical and deconstructionist theorists. The claim that vagueness leads to indeterminacy in some cases is a feature of, for instance, H.L.A. Hart's theory of law, which radical theorists oppose. I discuss claims of radical indeterminacy in Linguistic Indeterminacy, 16 Oxford J. Legal Stud., 667 (1996).Google Scholar

6. I will use “borderline case” as shorthand for “borderline case for the application of a vague expression.” By this I mean a case in which it is unclear, because of the vagueness of an expression, whether the expression applies. I will have to go ahead and use the term without making any further attempt to explain what a borderline case is: That explanation would be a complete account of the nature of vagueness, and this paper is meant to be one fragment of such an account.

7. Joseph Raz formulated the “indeterminacy thesis” in this way in a dispute with Ronald Dworkin about the nature of legal principles: “if the content of the law is exclusively determined by social facts, then the law is gappy; that is, there are legal statements which are neither true nor false.” Legal Principles and the Limits of Law, in Ronald Dworkin and Contemporary Jurisprudence 73Google Scholar (Cohen, Marshall ed., 1983Google Scholar). Cf. Coleman, Jules: “Philosophers generally agree that some sentences involving the application of vague predicates are neither true nor false.”Google ScholarTruth and Objectivity in Law, 1 Legal Theory 33 (1995).Google Scholar For a recent example of a philosopher of language who adopts the position that a vague statement is neither true nor false in a borderline case see Tye, Michael, Sorites Paradoxes and the Semantics of Vagueness, 8 Philosophical Perspectives 188 (1994).CrossRefGoogle Scholar For an argument against the position, see Fine, Kit, Vagueness, Truth and Logic, 30 Synthese 265 (1975).CrossRefGoogle Scholar

8. Book review, 111 Law Q. Rev. 519 (1995)Google Scholar, reviewing Hart, H.L.A., The Conceit of LawGoogle Scholar (2nd ed., Raz, J. and Bulloch, P.A. eds., 1994Google Scholar). It seems that the problem is not actually one of proof. What a plaintiff has to do is to prove facts that support a cause of action. In a borderline case, the plaintiff's problem is not that he or she cannot discharge the burden of proving facts, but that, as the second sentence of the quotation from Lyons suggests, it is unclear whether the facts support a cause of action (cf. the distinction between the prosecution's burden of proof in a criminal case, and a rule that criminal statutes are to be interpreted in favor of the accused).

9. Could the court resolve the dispute by applying a presumption that the seller has performed by delivering unless the term is clearly breached (or that the seller has not performed unless the term is clearly fulfilled)? It could do so, but (i) there may be no such presumption and (ii) if there were, that would be a rule of law in addition to the rule imposing the vague term. That is, the case would be resolved by the presumption, and not as a result of the nature of a cause of action based on a vague law (cf. the argument in the text below).

10. Hans Kelsen, General Theory of Norms (Hartney, Michael trans., 1991Google Scholar) [hereafter GTN] 366; cf. Introduction to the Problems of Legal Theory (Paulson, Bonnie Litschewski and Paulson, Stanley L. trans., 1992Google Scholar) [translation of the first, 1934 edition of Reine Rechtslehre, hereafter IPLT] 84, and Pure Theory of Law (Knight, Max trans., 1967Google Scholar) [translation of the second, 1960 edition of Reine Rechtslehre, hereafter PTL] 245–6. The claim in this form seems also to have survived changes in Kelsen's conception of a “gap”: For a discussion of those changes and a critique of Kelsen's doctrine of completeness, see Alchourron, Carlos and Bulygin, Eugenio, Normative Systems (1971), esp. at 129–33.Google Scholar

11. IPLT 85.

12. Unbestimmtheit, translated as “indeterminacy” in IPLT 78–9Google Scholar, “indefiniteness” in PTL 349–50.Google Scholar

13. PTL 351: cf. IPLT 80.

14. Claudio Luzzati has made a convincing argument that Kelsen's “indeterminacy” is not linguistic in nature: Discretion and ‘Indeterminacy’ in Kelsen's Theory of Legal Interpretation, in Hans Kelsen's Legal Theory: A Diachronic Perspective (Gianformaggio, Letizia ed., 1990Google Scholar). Kelsen's list of forms of indeterminacy ((a) to (d) in text above) supports that claim. Kelsen's notion of indeterminacy is an artefact of his preoccupations with the question of whether logic applies to norms, and with the relation between general and individual norms, which cannot be discussed here. It is sufficient for our puqioses that Kelsen's doctrine of indeterminacy, though not a linguistic doctrine, gives his theory a potential device for accounting for linguistic indeterminacy. He used the device in that way when he discussed ambiguity; the discussion here proposes a way of using the same device to give an account of vagueness.

15. Philosophers of language with “supervaluational” theories treat vagueness in this way: For an example, see Fine, , supraGoogle Scholar note 7, and for criticism see Williamson, Timothy, Vagueness (1994), chapter 5.Google Scholar

16. For a defense of the thesis see Dworkin, Ronald, On Gaps in the Law, inGoogle Scholar Controversies About Laws Ontology (Amselek, Paul and MacCormick, Neil eds., 1991), 8490.Google Scholar In a recent debate with Hilary Putnam, Jules Coleman has argued that “Dworkin has abandoned the right-answer thesis,” replacing it in Law's Empire with a “political theory of legitimate authority” that “depends on associative communities exhibiting political virtues and ideals, not on the existence of right answers to legal disputes.” (Supra note 7, at 49–50; a similar argument is made in Coleman, Jules and Leiter, Brian, Determinacy, Objectivity, and Authority, in Law and Interpretation 203Google Scholar (Marmor, Andrei ed., 1995), 214Google Scholar). But On Gaps in the Law displays Dworkin's continuing commitment to the right-answer thesis, and shows that the commitment is not accidental: His theory of legitimacy itself is bound to the right-answer thesis by Dworkin's view that the political virtues he identifies are commensurable. Similarly, in a recent elaboration of his account of philosophical skepticism about morality and aesthetics, Dworkin proposes that the case for indeterminacy claims is weaker in law than in, e.g., aesthetics: Objectivity and Truth: You'd Better Belieiv It, 25 Phil. Pub. Aff. 87 (1996).Google Scholar But in those remarks he makes no categorical claim that there are no cases in which the law gives no single right answer. Putnam makes a different argument against Coleman's view in Replies, 1 Legal Theory 69 (1995).Google Scholar

17. Dworkin, Ronald, No Right Ansurr? in Law, Morality and Society 58Google Scholar (Hacker, P.M.S. and Raz, Joseph eds., 1977) 6769.Google Scholar

18. Raz, Joseph, The Authoriry of Law (1979) 73.Google ScholarCf. Hart's view of the role of interpretation in areas of “open texture”: “Canons of ‘interpretation’ cannot eliminate, though they can diminish, these uncertainties; for these canons are themselves general rules for the use of language, and make use of general terms which themselves require interpretation.” The Concept of Law (2d ed., 1994) 126.Google Scholar

19. Bix, , supra note 4, at 3132Google Scholar; or Sainsbury, Mark, Is There Higher-Order Vagueness? 41 Phil. Q. 167 (1991).CrossRefGoogle Scholar Hilary Putnam makes a similar objection to Dworkin, in Are Moral and Legal Values Made or Discovered? 1 Legal Theory 5 (1995)Google Scholar, and Replies (supra, note 16, at 7677).Google Scholar

20. Dworkin, Ronald, Is There Really No Right Answer in Hard Cases? inGoogle ScholarDworkin, , A Matter of Principle 119 (1986)Google Scholar [AMP]. Note that some philosophers of language have also argued that there is first-order vagueness but no such thing as higher-order vagueness; see Wright, Crispin, Is Higher Order Vagueness Coherent? 53 Analysis 129 (1992).CrossRefGoogle Scholar My argument can only succeed against Dworkin if it would also succeed against Wright, but I will not address Wright's position directly. For an argument against Wright's position, see Edgington, Dorothy, Wright and Sainsbury on Higher-onter Vagueness, 53 Analysis 193 (1992).CrossRefGoogle Scholar

21. AMP 130.

22. Id.

23. Id. 405 n. 3.

24. Id. 130.

25. R cannot escape this predicament even by positing an infinite number of truth-values, corresponding—say—to the real numbers from 0 to 1. A rule of construction similar to Dworkin's rule could eliminate vagueness, by requiring that the rule is to be applied only when the degree of truth of the antecedent of die rule is 1.

26. AMP 405 n.3

27. It is tempting to deny this claim: After all, someone who is in any shadow of a doubt is in doubt Suppose that we show someone a sorites series of concerts, starting with a concert that clearly fits the definition of a rave, and moving by imperceptible reductions in volume to a concert that clearly does not fit the definition. Our subject will be in no doubt that the first concert is a rate, and at some point in the series there will presumably be a single first concert about which he or she feels some doubt. So it may seem that any speaker will find three sharply bounded classes of case: Cases in which x is undoubtedly ø, cases in which x is undoubtedly not ø, and cases in which there is some doubt. But this tempting view should be rejected. The fact that there is a first case in which our subject experiences doubt does not mean that there is a sharp boundary to the doubtful cases, because there is no reason why he or she should not have started experiencing doubt at a different point in the series, and because a rational speaker will not say, “I have no doubts whatever about that case, but I'm not sure about this imperceptibly different case.” “Doubtful” is vague. For a similar argument against the appearance that there can be no higher-order vagueness, see Williamson, , supra note 15, at 161.Google Scholar

28. This fact about conventional logic might be taken to indicate that we should make up a new logic, in which the external negation “I do not assert that p” can be represented. That possibility would amount to inventing a three-valued logic, a strategy discussed below (note 31).

29. AMP 121.

30. Id. 122.

31. Here I have adapted the argument in Williamson, , supra note 15, at 187.Google Scholar As Williamson points out, the argument only works if the equivalent in his argument of p “says something.” It does not work if we replace p with, e.g., gibberish: Nonsense cannot be true or false, and the conclusion (5) would not be a contradiction, but just meaningless. For Williamson's argument that a vague statement in a borderline case “says something,” see id. at 195.

32. Note that three-valued logics can be constructed in which there is no contradiction in saying that a statement is neither true nor false: For discussion of examples dating back to C.S. Peirce, see Williamson, , supraGoogle Scholar note 15, chapter 4. A further example is G.H. von Wright's truth logic (von Wright, Georg Henrik, Truth and Logic, in Truth, Knowledge and Modalities 26 (1984)Google Scholar; I am grateful to Jose Juan Moreso and Pablo Navarro for pointing this out). Such logics yield a third option: Instead of presenting Vs claim as an external negation with classical logic or an internal negation with classical logic, as I have proposed in the text, we could interpret Vs claim as an external negation, with a non-classical logic that countenances external negations (truth logic, for example, represents truth by means of a modal operator that has the effect of allowing external negation of assertions within the logic). Possible objections to using three-valued logics to deal with vagueness are that (i) they replace the ordinary notions of “true” and “false” with artificial properties somewhat akin to the ordinary notions of “clearly true” and “clearly false,” (ii) they cannot cope with higher-order vagueness, and (iii) they ignore the reason given in the text below for not asserting that the utterance of a vague sentence in a borderline case is neither true nor false. Those objections cannot be developed here; it is enough for the present argument if R has available an alternative to Vs trivalence.

33. The obvious stratagem would be to reject the disquotational principle (2). For Williamson's argument against rejecting disquotation, see id. at 190–92, and for a proposal that someone like V could reinterpret the principle, see Wright, Crispin, The Epistemic Conception of Vagueness, 33 S.J. Phil. (Supp.) 133 (1994).CrossRefGoogle Scholar

34. An approach with which Williamson has no patience: “no attempt will be made to argue with those who think it acceptable to contradict oneself.” Id. at 189.

35. Supra note 23.

36. This objection to my argument would be consistent with Dworkin's views: He treats the “neither true nor false” formulation as characterizing the thesis that there are gaps in the law (i.e., the thesis that there is often no right answer to a legal dispute): “the theory that says there are gaps in the law is the theory that says there are some, perhaps many, concrete propositions of law … which are neither true nor false.” On Gaps in the Law, supra note 16, at 84.Google Scholar

37. See Williamson, , supra note 15 (esp. chapter 7).Google Scholar

38. See Dworkin, Ronald. Laws Empire 31, 45 (1986).Google Scholar

39. Id. at 702. On the distinction between concepts and conceptions, see also Dworkin, , Taking Rights Seriously 134 (1977), and AMP 128.Google Scholar

40. Laws Empirk, supra note 38, at 204.Google Scholar

41. AMP 130.

42. Id. at 131.

43. Taking Rights Seriously, supra note 39, at 24.Google Scholar

44. Id. at 26.

45. Id. at 38.

46. See supra note 39. Note that, when he makes the argument that indeterminacy arising from vagueness can be eliminated by a rule of construction, he expressly puts aside his account of concepts that admit of different conceptions, for the purpose of argument: AMP 128.

47. Taking Rights Seriously, supra note 39, at 128.Google Scholar In Laws Empire (supra note 38) Dworkin seems to maintain the same distinction: He calls vagueness a “semantic defect” (p. 17; see also p. 351), and sees no semantic defect in words for concepts that admit of different conceptions.

48. Twenty-four-hour solitary confinement is cruel. So is 23-hour-59-minute solitary confinement. By a standard sorites series we can reach the conclusion that one minute of solitary confinement per day (or none at all) is cruel. Similar sorites series could be constructed for “courteous,” “fair,” and so on.

49. See Laws Empire, supra note 40, at 164.Google Scholar

50. And the deficit in integrity will not be made good by any justification of the outcome on the grounds of justice: There is no material difference in the justice of convicting one defendant and the justice of convicting the next defendant in the series.

51. That consequence will be avoided, however, if courts replace a vague standard with a precise standard, e.g., by specifying a period within which an action will be treated as having occurred “within a reasonable time” for the purposes of an enactment using that phrase.

52. Hilary Putnam says that a vague statement in a borderline case “may have no determinate truth value” (Are Moral and Legal Values Made or Discovered?, supra note 19, at 6). That shrewd formulation is consistent with the claim I make, as Putnam can be interpreted as saying not that the statement has no truth value, but that it is indeterminate which truth value the statement has.

53. The extent of the indeterminacy will be determined by the size of the increments with which a sorites series can be constructed. Consider two premises: “Any person who is 0.1 mm shorter than a tall person is tall” and “Any person who is 1 cm shorter than a tall person is tall.” We could construct a version of the sorites paradox with either. If the latter is true, the word “tall” is vaguer (there is more indeterminacy in its application) than if only the first is true. If not even the first is true, then the word “tall” might as well be precise. It seems to be a necessary feature of vague words that there is no precise answer to the question “What is the largest increment with which a sorites series can be constructed?” That means that the extent of the indeterminacy arising from vagueness is necessarily indeterminate.

54. For example, some standards of materiality (de minimis etc.) are vague, but the vagueness may not be substantial.

55. Cf. the somewhat more complex problem in R u Monopolies and Mergers Commission, ex p. South Yorkshire Transport Ltd., [1993] 1 WLR 23 (House of Lords).Google Scholar

56. See, e.g., Hart, supra note 18, chapter 7.Google Scholar

57. On the value of vagueness see Waldron, , supra note 4, at 534–10Google Scholar and Hart, supra note 18, at 128ff.Google Scholar

58. At least, in most cases. There could be borderline cases for the application of an ostensibly precise blood-alcohol standard. By “precision” here I mean precision by comparison to a vague standard such as a prohibition on “driving while intoxicated.”

59. We could minimize vagueness with, e.g., a rule that police may use no force (though we would not eliminate it, since it is unclear whether some actions are forceful). But there are reasons to allow (and even to require) the police to use force in some situations. If the law is only to prohibit inappropriate force, a general standard is bound to be vague.

60. See AMP 120.

61. Finnis, John, Natural Law and Natural Rights 280 (1980)Google Scholar; see also p. 269, re the “no gaps” postulate.

62. So, for example, if a legal system suffers from all-or-nothing rules of negligence liability, it does not need to abandon juridical bivalence: It needs a sensible scheme of contributory negligence.

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