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The Liar Paradox in Legal Reasoning

Published online by Cambridge University Press:  16 January 2009

J. C. Hicks
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“All Cretans are liars,” said Epimenides—at first sight a common-place scrap of mild xenophobia; about equal to “Taffy was a Welshman, Taffy was a thief” in charity and acumen. Not, one would suppose, a statement calculated to attract close attention from philosophers or logicians, or (despite the introduction of the offence of incitement to racial hatred) from lawyers.

But Epimenides' statement was widely discussed by the best thinkers of classical times and has kept its importance for the foundations of logic until the present century. To understand why, it is necessary to add two facts. First, Epimenides was himself a Cretan. Secondly, his statement was taken to mean not just that all Cretans lied from time to time but that everything ever said by any Cretan was false. It thus implies, in particular, that it is itself false. Not only can this be shown to lead to absurd consequences; it also suggests a simpler form of sentence which heightens the absurdity and best introduces the following discussion. It is: “This statement is false.” If that is true it is false, and if it is false it is true. So we have the paradox of a sentence which breaks no rule of formal grammar, is composed entirely of words whose sense is well understood, combines those words in such a way as to produce an apparently normal and meaningful statement, but turns out on investigation to have something radically wrong with it. We feel inclined to say that it has proved to be “meaningless” or “self-contradictory,” or to involve a “vicious circle.”

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The Cambridge Law Journal , Volume 29 , Issue 2 , November 1971 , pp. 275 - 291
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Copyright © Cambridge Law Journal and Contributors 1971

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References

1 I am indebted to my father-in-law, Rev. J. B. Jennings, for the reminder that the saying itself was current in the post-classical Hellenistic world of the New Testament—see Titus i, 12. Whether an echo of the debate as to its logical status is to be heard in the words “one of themselves … said” is an intriguing speculation.

2 Many involve mathematical concepts, but not all. A number can be found collected in Russell, Bertrand, “Mathematical Logic as based on the Theory of Types” (1908) 30 American Journal of Mathematics 222–262CrossRefGoogle Scholar, and in Northrop, E. N., Riddles in Mathematics (1945)Google Scholar, Chap. 9.

3 Cited in Northrop, loc. cit., and more fully by Dr. I. Tammelo of Sydney in The Lawyer's Logic, issued by the Australian Society of Legal Philosophy (2nd issue, 1967). This work is an experimental model for Dr. Tammelo's forthcoming book, Outlines of Modern Legal Logic (Franz Steiner Verlag GmbH).

4 The writer agrees with Alf Ross, who regards it as equally faulty. (“On Self-reference and a Puzzle in Constitutional Law” (1969) 78 Mind 1, at p. 16.Google Scholar) See the text to note 73, below.

5 Lee v. Bude and Torrington Ry. Co. (1871) L.R. 6 C.P. 576, per Willes J. at p. 582.

6 e.g., the Representation of the People Acts and the Representative Peers (Ireland) Act 1857.

7 e.g., the Parliament Acts 1911 and 1949.

8 e.g., the Septennial Act 1715.

9 [1966] 1 W.L.R. 1234.

10 [1898] A.C. 375.

11 It is true that the Statement includes the words “while treating former decisions … as normally binding,” and so apparently blurs the sharpness of the paradox which would be revealed by the bare statement “this House is never bound by its own decisions,” but as will appear from the more detailed treatment below, this merely complicates, not invalidates, the example.

12 Re Annesley [1926]Google Scholar Ch. 692; Re Ross [1930]Google Scholar 1 Ch. 377.

13 Re Askew [1930] 2 Ch. 259.Google Scholar

14 Cheshire, Private International Law (8th ed.), p. 72, cites as further examples formal and essential validity of marriage, title to foreign land and some cases of title to movables.

15 Although only three examples have been given, it is not to be supposed that the list is exhaustive. For a situation where the courts have explicitly circumscribed the operation of a rule so as to avoid an infinite regress consider the case of notices to produce documents, which do not have to extend to include the production of such notices themselves nor (although this seems a wider exception than is required) of some other notices, such as notices to quit: Doe d. Fleming v. Somerton (1845) 7 Q.B. 58.

16 Northrop, op. cit., Chap. 5.

17 “Mathematical Logic as based on the Theory of Types,” 30 American Journal of Mathematics 222, hereafter cited as “Russell, Theory of Types.”

18 See the Introduction, pp. 35–65, for a discursive account, and pp. 161–167 and 187–199 for the fully rigorous treatment, using symbolic notation. (Page references are to the second edition (1927), paperback version (1962)).

19 Russell, Theory of Types, p. 261.

20 Whitehead and Russell, Principia Mathematica, p. 37.

21 Principia Mathematica, p. 56.

22 e.g., Popper, Karl, “Self-reference and Meaning” (1954) 63 Mind 162.CrossRefGoogle Scholar

23 “On Self-reference and a Puzzle in Constitutional Law” (1969)Google Scholar 78 Mind 1.

24 Tammelo, The Lawyer's Logic (see note 3 above).

25 See Hare, R. M., The Language of Morals (1952), pp. 24–27Google Scholar, and “Imperative Sentences” in (1949) 58 Mind 30Google Scholar; Hall, E. W., What is Value? (1952)Google Scholar, Chap. 6; Hofstadter, A. and McKinsey, J. C. C., “The Logic of Imperatives” in (1939) 6 Philosophy of Science 446CrossRefGoogle Scholar; Ross, Alf, “Imperatives and Logic” in (1944) 11 Philosophy of Science 30CrossRefGoogle Scholar; Wright, G. H. V., “Deontic Logic” in (1951) 60 Mind 1CrossRefGoogle Scholar; and Storer, T., “The Logic of Value Imperatives” in (1946) 13 Philosophy of Science 25.CrossRefGoogle Scholar

26 Cf. Ross, loc. cit., pp. 41–42.

27 Ross, answering Hart's doubt on this point, is confident that they do not: “The rule against self-reference is concerned with the meaning of a speech-act and is independent of whether the meaning content is used to state how the world is or to prescribe how it ought to be” (“On Self-reference and a Puzzle in Constitutional Law” (1969) 78 Mind 1, at p. 19Google Scholar).

27a Vauxhall Estates Ltd. v. Liverpool Corporation [1932] 1 K.B. 733.Google Scholar

28 Ellen Street Estates Ltd. v. Minister of Health [1934] 1 K.B. 590.Google Scholar

29 Att.-Gen. for New South Wales v. Trethowan [1932]Google Scholar A.C. 526.

30 Another case commonly cited in this context is McCawley v. The King [1920]Google Scholar A.C. 691 but it does not seem to add anything of interest.

31 Harris v. Dönges [1952] 1 T.L.R. 1245Google Scholar (sub nom. Harris v. Minister of Interior, 1952 2 S.A. 428Google Scholar); Minister of Interior v. Harris, 1952 4 S.A. 769Google Scholar and Collins v. Minister of Interior [1957] 1 S.A. 552.Google Scholar See also Ndlwana v. Hofmeyr [1937]Google Scholar A.D. 229, the periodical literature concluding with and cited in Wade, H. W. R., “The Basis of Legal Sovereignty” [1955]Google Scholar C.L.J. 172, and the Annual Survey of South African Law (1956).Google Scholar

32 See Madzimbamuto v. Lardner-Burke, 1966 4 S.A.L.R. 62Google Scholar (first instance); 1968 2 S.A.L.R. 284 (on appeal); and [1968] 3 All E.R. 561 (Privy Council).

33 Harris v. Dönges, supra.

34 See the remarks of Viscount Sankey L.C. on the theoretical possibility of repealing the Statute of Westminster 1931, in British Coal Corporation v. The King [1935] A.C. 500, at p. 520.Google Scholar

35 In “Evil and Omnipotence” (1955) 64 Mind 200, 211Google Scholar, J. C. Mackie conversely cites the paradox of sovereignty to illustrate his thesis.

36 (1802) 7 Ves.Jun. 137.

37 e.g., London Street Tramways v. L.C.C. [1898] A.C. 375; Young v. Bristol Aeroplane Co. [1944]Google Scholar K.B. 718; R. v. Taylor [1950] 2 K.B. 368Google Scholar and R. v. Gould [1968] 2 Q.B. 65.Google Scholar

38 Supra, note 9.

39 At 70 L.Q.R. 471 and in Salmond on Jurisprudence, 11th ed. The editor of the 12th edition takes a different view (see pp. 159–160).

40 Supra, note 37.

41 Salmond on Jurisprudence, 11th ed., p. 187.

42 Ibid., p. 188.

43 2nd ed. p. 207.

44 The fact that to make this a meaningful statement of the doctrine in any particular system would entail defining “certain courts” (twice) and “authoritatively stated” does not affect the argument. The special case where the “certain court” is the same in both instances is that of stare decisis.

45 It is interesting that Hart, H. L. A., in The Concept of Law (1961)Google Scholar, although not discussing precisely the same problem, finds it important to make exactly this distinction between what he calls “primary” and “secondary” rules, the latter being “on a different level from the primary rules, for they are all about such rules” (p. 92; his italics), and applies it to the problems of parliamentary sovereignty (p. 146) and precedent (p. 150).

46 Falconbridge, J. D., in Essays on the Conflict of LawsGoogle Scholar (2nd ed.), points to the similarity between the problem of renvoi and characterisation (p. 53).

47 For recognition of the circular or infinitely regressive nature of the result see Falconbridge, op. cit., pp. 179, 183, 187. See also Dicey and Morris, Conflict of Laws (8th ed.), p. 67, and the references cited in notes 80 and 82 on p. 68; also Cheshire, Private International Law (8th ed.), p. 60. Contra, Rabel, The Conflict of Laws (2nd ed.), p. 80.

48 The full theory would be a little more complicated. Briefly, any doctrine of renvoi is necessarily a “third-order” rule if it prescribes which conflicts (second-order) rule is to prevail. Theoretically, that need not give rise to the possibility of contradictions in every form of renvoi, but it can in the “foreign court” form, where the conflicts rules prescribed include the renvoi (third order) rules of the country designated.

49 It is doubtless not coincidental that this accompanies a corresponding revival of interest in the same relationship by professional logicians and philosophers. See, for example, Perelman, C. P., The Idea of Justice (1963)Google Scholar, and Hintikka, K. J. K., “Remarks on a Paradox” (1958) Archiv für Rechts-und-Sozialphilosophie 514.Google Scholar

50 Reference has already been made to Alf Ross's important article “On Self-reference and a Puzzle in Constitutional Law” (1969) 78 Mind 1.Google Scholar It is invaluable on the general problem of self-reference, but the particular “puzzle” which he tackles is one specific to a written constitution, and his solution does not seem applicable to the paradox of parliamentary sovereignty as described above.

51 Collected in The Lawyer's Logic (see note 3 above).

52 Tammelo, I., “The Antinomy of Parliamentary Sovereignty” (1958) Archiv für Rechts-und-Sozialphilosophie 495.Google Scholar

53 Ibid., p. 503.

54 Ibid., p. 502, note 24.

55 Ibid., p. 504.

56 Ibid., p. 504.

57 Ibid., p. 506.

58 Ibid., p. 505.

59 Ibid., p. 506.

60 Ibid., p. 505.

61 See “Affinities and Antinomies in Jurisprudence” [1964]Google Scholar C.L.J. 266; “Logical translations in the Law” (1965)Google Scholar Minn.L.R. 447, and “The Compleat Wrangler” (1966) 50 Minn.L.R. 1001.Google Scholar Among many valuable insights, the particularly pregnant suggestion may be noted that Gödel's incompleteness theorem applies equally to all three fields of study (“Affinities and Antinomies [etc.],” p. 281, and “The Compleat Wrangler,” p. 1002).

62 “Affinities and Antinomies [etc.],” p. 281, and “The Precedence of Precedents” [1968]Google Scholar C.L.J. 35.

63 “Logic and law, the Precedence of Precedents” (1967) 51 Minn.L.R. 655.Google Scholar

64 Supra, note 9.

65 “Logic and Law [etc.],” p. 657.

66 Supra, note 37.

67 Supra, notes 41 and 42.

68 “Logic and Law [etc.],” p. 659.

69 Ibid., p. 661.

70 Ibid., p. 668.

71 Ibid., p. 669.

72 It is not clear that the Court of Appeal have avoided it in their treatment of Rookes v. Barnard [1964]Google Scholar A.C. 1129 in Broome v. Cassell [1971] 2 W.L.R. 853.Google Scholar

73 Ibid., p. 661.

74 It is suggested that these considerations support the view that a similar rule holds in propositional logic (see note 4 above).

75 See the text immediately following note 48 above.

76 Although as Falconbridge points out (op. cit., p. 179) it should in principle have done so whenever there was no evidence as to the foreign theory of renvoi, by virtue of the rule that foreign law agrees with English where the contrary is not proved.

77 It can be argued that all puzzles of this type can be resolved in a practical sense by such a process of “deciding” ad hoc what shall be the scope of the terms employed whenever paradoxical results cause trouble.

78 Cf. Dicey and Morris, op. cit., p. 68; Cheshire, op. cit., p. 58.

79 Conway v. Rimmer [1967] 1 W.L.R. 1031, at p. 1037Google Scholar, and Eastwood v. Herrod [1968] 3 W.L.R. 593, at p. 600.Google Scholar

80 [1944] K.B. 718.

81 See the comments of Russell L.J. in Conway v. Rimmer (supra) at p. 1051.

82 A phrase much used in the Rhodesian UDI cases. See, e.g., per Beadle C.J. 1968 2 S.A.L.R. at p. 314.

83 “Confirms,” for other writers have expressed substantially the same conclusion from different standpoints. See, e.g., Hart, H. L. A., The Concept of Law (1961), pp. 147–149Google Scholar; Wade, H. W. R., “The Basis of Legal Sovereignty” [1955] C.L.J. 172, at pp. 192 and 197Google Scholar; Friedmann, W., “Trethowan's case” (1950) 24 Aust.L.J. 103, at p. 107Google Scholar; and Kolts, G., “Constitutional Crisis and Basic Norm” (1953) 1 Sydney L.R. 64, at p. 65.Google Scholar

84 See note 52 and the text following, above.

* I am very grateful to my friend Rev. Kenneth B. Wilson, B.A., M.Litt., for commenting on a draft of this article from the standpoint of a logician.