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On the Nature of Necessary Truths in Jurisprudence: Putting Wittgensteinian Hinges to Use

Published online by Cambridge University Press:  25 February 2021

Yi Tong
Yi Tong, Lecturer of Philosophy, Humanities Department, University of Wisconsin-Platteville, USA.
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Inquiring into the fundamental nature of law has been traditionally formulated as an attempt to answer the question, “What is Law?” Such an inquiry typically proceeds by identifying the necessary features of law. Joseph Raz, for example, writes:

A theory consists of necessary truths, for only necessary truths about the law reveal the nature of the law. We talk of ‘the nature of law’, or the nature of anything else, to refer to those of the law’s characteristics which are of the essence of law, which make law into what it is. That is those properties without which the law would not be law.1

Research Article
© The Author(s), 2021

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I would like to thank Brian Bix for his detailed comments on an earlier version. I am also grateful to RA Duff and Doug Lewis, for their critical comments and questions. This essay, as well as my understanding of the problems discussed in it, could not have progressed into its current form without the generous help from Richard Bronaugh. I would also like to express my gratitude toward Shane Drefcinski, Michael Sharkey, Mary Lenzi, and Melissa Gormley for their collegial support during my work on this project.


1. Joseph Raz, Between Authority and Interpretation: On the Theory of Law and Practical Reason (Oxford University Press, 2009) at 24.

2. Joseph Raz, Ethics in the Public Domain, revised ed (Clarendon Press, 1995) at 215 [Raz, Ethics]. The thesis about law’s necessary claim to authority can also be found in Part I of Joseph Raz, The Morality of Freedom (Clarendon Press, 1986) at 23 [Raz, Morality of Freedom], which includes a more elaborate discussion of authority generally.

3. Brian Bix, Jurisprudence: Theory and Context, 7th ed (Carolina Academic Press, 2015) at 17. Here, Bix calls attention to the status of necessity claims in Raz’s theory, but does not go any further in clarifying or defending the notion of necessity in jurisprudence. However, Bix made one brief suggestion: the kind of necessity involved in legal theory is grounded in a community’s self-understanding and way of life, which is a Wittgensteinian notion. See Brian Bix, “Raz on Necessity” (2003) 22:6 Law & Phil 237 at 555-56 [Bix, Raz on Necessity]. The task of this essay can be understood as an attempt to follow this suggestion and take a step forward.

4. For example, Fine defends the view that there are varieties of necessities, and three main forms are: the metaphysical, the natural, and the normative, none of which is reducible to any other. See Kit Fine, Modality and Tense (Oxford University Press, 2005) at 235. For an attempt trying to connect talk of necessity in jurisprudence with works on necessity in areas, such as metaphysics and epistemology, see Michael Giudice, Understanding the Nature of Law: A Case for Constructive Conceptual Explanation (Edward Elgar, 2015).

5. Raz continues: “Sociology of law provides a wealth of detailed information and analysis of the functions of law in some particular societies. Legal philosophy has to be content with those few features which all legal systems necessarily possess.” Joseph Raz, The Authority of Law: Essays on Law and Morality (Clarendon Press, 1979) at 104-05.

6. Jules Coleman, “Incorporationism, Conventionality, and the Practical Difference Thesis” (1998) 4:4 Legal Theory 381 at 393 n 24 [emphasis in original]. This formulation raises two important questions. First, are we investigating into law or the concept of law? In other words, are the necessary properties of law located in the concept of law or law (the social institution that the concept designates)? Second, does the distinction between “our concept of law” and “the concept of law” have any implication for jurisprudence? Raz, for instance, argues that what we investigate is “our concept of law”, the product of a specific culture. See Raz, supra note 1 at 40. These questions invite reflections on a range of issues on the nature of concepts that must await another time. Suffice it to say that I think the answer to the first question is “both,” and I do not think the second question can be settled without clarifying the concept of a concept, especially how concepts are individuated. Making a distinction between concept and conception can help us clarify the issue, but this is not the place to pursue the point.

7. Julie Dickson, Evaluation and Legal Theory (Hart, 2001) at 17-18. See also Alexy’s statement that “enquiring into the nature of something is to enquire into its necessary properties. Thus, for the question ‘What is the nature of law?’ one may substitute the question ‘What are the necessary properties of law?’”. Robert Alexy, “On the Concept and the Nature of Law” (2008) 21:3 Ratio Juris 281 at 290. A more recent example is from Scott Shapiro, who writes: “[T]o discover the law’s nature … would be in part to discover its necessary properties, that is, those properties that law could not fail to have.” Scott Shapiro, Legality (Harvard University Press, 2011) at 9. Shapiro makes a distinction between Identity Questions and Implication Questions as possible interpretations of what it is we want to know when we inquire into the nature of a thing. For Shapiro, when we ask, “what is the nature of law?” we might be asking what makes law law rather than something else (Identity Question), or we might be asking what necessarily follows from law’s being law (Implication Question). Shapiro may appear to imply that only the second kind of question involves necessary truths by writing: “In this second sense of ‘nature,’ to discover an entity’s nature is in part to discover those properties that it necessarily has. An object has a property necessarily just in case it could not fail to have it.” Ibid at 9. However, this distinction does not affect the general characterization that a theory of the nature of law consists of necessary truths. This is because answers to Identity Questions, the set of properties that make instances of X the things that they are, also take the form of necessary truths. Indeed, how could it be otherwise? Answers to Identity Questions must involve those attributes necessary of law. This is attested to by Shapiro’s own example of water: the identity of water is (necessarily) H2O because being H2O is what makes water water. This example is a paradigm example of what philosophers call “metaphysical necessity.” It is worth noting that the nature and status of this kind of necessity is controversial. See Kit Fine, “Essence and modality” (1994) 8 Philosophical Perspectives 1 and Peter Hanks, “A Puzzle About Necessity” (2008) 68:1 Erkenntnis 129. More on this below.


8. Joseph Raz, “On the Nature of Law” (1996) 82:1 Archiv für Rechts-und Sozialphilosophie 1 at 2.

9. Ibid.


10. Both quotes are from Dickson, supra note 7 at 17.

11. Danny Priel, “Jurisprudence and Necessity” (2007) 20:1 Can JL & Jur 173 at 192. Priel’s argument in sections II-IV of the article, in outline, is as follows: a legal theorist trying to identify the necessary properties of law has to either find a minimalist list of features that are shared by all possible (and reasonable) accounts of law, which would make the account too thin to be illuminating, or find the most important features of law as candidates for the necessary features of law according to the theorist, from a particular point of view in a particular society, which would make the account parochial. Further, both alternatives suffer from a deeper problem: there is no non question-begging way to determine what counts as law to begin with. Priel takes these two alternatives outlined here as unsuccessful attempts to respond to a general problem: since people (both theorists and lay people alike) have different attitudes towards what counts as law, the “theorists who wish to give an account of the necessary features of law are like scientists whose disagreement in their explanation of certain phenomena is the result of the fact that they work with samples of different things.” The theorist “does not even have a starting point from which an inquiry can begin.” Ibid at 181-82. One consequence of this deeper problem is that theories of the nature of law are immune from empirical refutation. This echoes a critique by Brian Tamanaha, A Realistic Theory of Law (Cambridge University Press, 2017) at 77-80.


12. Tamanaha, supra note 11 at 65. Tamanaha’s discussion on whether claims about the nature of law are a priori or a posteriori will be addressed in section VII of the text, below.

13. Ibid at 58.


14. Frederick Schauer, The Force of Law (Harvard University Press, 2015) at 40.

15. Brian Bix notes: “[T]he possibility of ‘necessity’ talk in jurisprudence goes hand-in-hand with the possibility of conceptual analysis; if one concludes that one is impossible or inappropriate in discussing law, then likely the other is as well…. [W]ithout a clear understanding of what is meant by a claim of ‘necessity’ in jurisprudence, we cannot begin the process of defending conceptual analysis.” Bix, Raz on Necessity, supra note 3 at 538, 556.

16. For example, in his critique of conceptual analysis in jurisprudence, Brian Leiter seems to equate necessity with analyticity, and assumes that Quine’s attack on the analytic-synthetic distinction also undermines necessity talk in legal theory. See Brian Leiter, Naturalizing Jurisprudence: Essays on American Legal Realism and Naturalism in Legal Philosophy (Oxford University Press, 2007) at 175-76. A similar point is also made in Dennis Patterson, Book Review of Philosophy of Law by Andrei Marmor, (2011) Notre Dame Philosophical Reviews, online at It is worth asking whether Quine’s critique of the analytic-synthetic distinction is relevant to the kind of conceptual methodology of jurisprudence. This is not the place to discuss this question in detail.

17. The logical necessities, presumably the easiest to understand among the three, could just be the logical truths. But as one commentator writes: “As it turns out, it is very hard to think of universally accepted ideas about what the generic properties of logical truths are or should be.” Mario Gómez-Torrente, “Logical Truth” in Edward N Zalta, ed, Stanford Encyclopedia of Philosophy (Fall 2018 Edition), para 1, online at

18. Debates around the nature of necessity in jurisprudence are in a state of confusion partly because of the careless choices of terms. For example, in a recent anthology, Waluchow and Sciaraffa use “conceptual necessity” to refer to the kind of necessary truths discussed in jurisprudence (“Raz holds that a norm cannot, as a matter of conceptual necessity, be authoritative if those subject to it must engage in moral reasoning to determine the norm’s existence and content.”) Wil Waluchow & Stefan Sciaraffa, eds, Philosophical Foundations of the Nature of Law (Oxford University Press, 2013) at xv. In the same volume, Ehrenberg uses “conceptually necessary feature of law.” Ibid at 60. Himma uses the phrase ‘conceptual truth’ to refer to the same thing (“Hart asserts that it is a conceptual truth that primary legal norms generally define legal obligations”). Ibid at 158. These usages seem to diverge from those in general philosophical literature. For example, the phrase ‘conceptual necessity’ is often employed by the larger philosophical community to refer to “analytic truth”—truth in virtue of meaning. A classic example of such truths is: bachelors are unmarried men. However, legal theorists generally deny that they are seeking analytic truths and that their projects are semantic in nature. They prefer, as will be discussed below, a metaphysical use of the term ‘necessity’. This discrepancy amongst the uses of “conceptual necessity” may invite confusions, and explain why some critics think Quine’s attack on the analytic-synthetic distinction also undermines the idea of necessity in jurisprudence. They might have thought that legal theorists are offering conceptual necessities which are truths in virtue of meaning.


19. Tamanaha might be an exception. See Tamanaha, supra note 11 at 58-65. However, his conclusion is that to the (limited) extent that legal theorists have reflected on the nature of necessity in law, they “do not agree among themselves on the basis for their assertions, and most have not explained their position at all.” Ibid at 65.


20. For example, as mentioned in notes 16 and 18, one critique of the method of conceptual analysis in jurisprudence relies on Quine’s attack on the analytic-synthetic distinction. This ignores the fact that Quine primarily has logical and conceptual/analytic necessities in mind. It is unclear then how Quine’s critique can be immediately applied in jurisprudence. See Fine, supra note 4 at 3: “Quine often has the logical or analytic modalities in mind (necessity in virtue of logical form or of meaning).”

21. “The central notion involved in any modal characterization of the distinction between essential and accidental properties is that of metaphysical necessity/possibility.” Teresa Robertson & Philip Atkins, “Essential vs Accidental Properties” in Edward N Zalta, ed, Stanford Encyclopedia of Philosophy (Summer 2016 Edition), para 1, online at See also Fine, supra note 7.

22. Tamanaha accurately observes: “Analytical jurisprudents often speak in metaphysical terms.” Tamanaha, supra note 11 at 64. Shapiro is explicit that his project is a metaphysical one. See Shapiro, supra note 7 at 2, 19. For him, the project of analytical jurisprudence is a metaphysical project.

23. For example, Hale writes: “Metaphysical necessities hold true at all possible worlds without qualification or exception.” Bob Hale, “Absolute Necessities” (1996) 10 Philosophical Perspectives 93 at 95.

24. Another example philosophers often use: Gold necessarily has the atomic number 79 (or, there is no metaphysically possible world where gold has an atomic number that is not 79).

25. Here one is reminded of Raz’s claim that “[t]he general theory of law is universal for it consists of claims about the nature of all law, and of all legal systems, and about the nature of adjudication, legislation, and legal reasoning, wherever they may be, and whatever they might be … the truth of the theses of the general theory of law is not contingent on existing political, social, economic or cultural conditions, institutions, or practices.” Raz, supra note 8 at 1. Likewise, Green has claimed that “features necessary to law are those found not only in all existing and historical legal systems, but in all possible ones—or all humanly possible ones.” Leslie Green, “The Morality in Law” Oxford Legal Studies Research Paper No. 12/2013 (24 February 2013) at 33, online at Both Raz and Shapiro, for example, have used the example of water’s being H2O to illustrate essential properties of an object. See Raz, supra note 1 at 27 and Shapiro, supra note 7 at 8-9. Also, in his criticism mentioned earlier, Schauer compares law with birds, a natural kind category, which again encourages the thought that the kind of necessity in jurisprudence is metaphysical in nature. See Schauer, supra note 14.

26. Ronald Dworkin, cited in Tamanaha, supra note 11 at 58. Tamanaha also discusses the ontological difference between law and water at 59-60.

27. Ludwig Wittgenstein, On Certainty, ed by GEM Anscombe & GH von Wright, translated by Denis Paul & GEM Anscombe (Basil Blackwell, 1969). Here, two caveats about my reading of this work are in order. First, since its publication, On Certainty, like Wittgenstein’s other two major works, the Tractatus and the Philosophical Investigations, has aroused intense scholarly debates. See the summary of literature on this book in Avrum Stroll, Moore and Wittgenstein on Certainty (Oxford University Press, 1994) at 5-6. My discussion of the work is highly selective in that it only focuses on ideas that I think would help illuminate jurisprudential methodology. Second, the difficulty of interpreting On Certainty is increased by the fact that it is far from being a finished work. It is a compilation of a series of first-draft notes written in the last year and a half of Wittgenstein’s life. The author did not live to edit and polish them. The last entry was on April 27, 1951, two days before the philosopher’s death. There are noticeable repetitions, omissions, and references to other works or manuscripts throughout the text. What follows is a discussion of some of Wittgenstein’s insights that I believe could be reasonably read off of On Certainty, while trying to avoid exegetical issues. It is, however, unavoidably a philosophical reconstruction.

28. Wittgenstein, supra note 27 at the preface. A more detailed list of Moore’s propositions can be found in Moore’s original papers. See GE Moore, “A defense of Common Sense” in Philosophical Papers (Collier Books, 1959) at 32 and “Proof of an External World” ibid at 126. As Wittgenstein’s notes develop, various examples of the same type are given by Wittgenstein himself: “Every human being has parents” (Wittgenstein, supra note 27 at 211), “For months I have lived at address A” (ibid at 70), “There is an island, Australia” (ibid at 159), and “Trees do not gradually change into men and men into trees” (ibid at 513).


29. Wittgenstein, supra note 27 at 125.

30. GH von Wright, Wittgenstein (University of Minnesota Press, 1983) at 170.

31. Wittgenstein, supra note 27 at 243. This shows that perhaps Moore’s propositions require a different kind of grounding. See my discussion in section IV below.

32. Ibid at 17.


33. Ibid at 54. The German here is: nicht mehr denkbar. Literally: no longer thinkable.


34. Ibid at 56.


35. Ibid at 32.


36. Ibid at 24.


37. Ibid at 84, 134.


38. Ibid at 111. Wittgenstein makes a conceptual point here that is similar to the one made earlier, about looking at my hands to confirm that I have two hands. If we were even uncertain about whether the Earth has existed for a long time before my birth, and needed special investigations to assemble evidence for this conclusion, then, whatever evidence we might gather, it is unclear whether the evidence could be any surer than this conclusion.


39. Ibid at 93.


40. Ibid [emphasis added].


41. Ibid at 162 [emphasis added].


42. The “as a whole” part is my addition. Wittgenstein’s discussion of a world-picture is very loose and sketchy, and not without inconsistencies. The world-picture is “the substratum of all my enquiring and asserting.” Ibid. But if the world-picture is defined simply (and loosely) as “everything I have seen or heard” (Ibid at 93, where the idea of a world-picture is first introduced), which is hardly a definition, then it could not be the case that no part of it could be open to doubt. I doubt if there is any better way to make Wittgenstein’s idea of a world-picture more precise.


43. Ibid at 83.


44. Ibid at 94.


45. Ibid at 162.


46. Ibid at 190. The German here is aufhindeuten, to suggest or indicate.


47. Ibid at 341 [final emphasis added]


48. Ibid.


49. Ibid at 299, 357.


50. Ibid at 95.


51. Ibid at 92.


52. Ibid at 96 [emphasis added].


53. Ibid at 97.


54. Ibid at 162.


55. “The picture of the Earth as a ball is a good picture, it proves itself everywhere, it is also a simple picture—in short, we work with it without doubting it.” Ibid at 147 [last emphasis added]. The role the world-picture plays in our life is not qua a set of propositions, but rather a praxis. Von Wright writes: “The fragments of a world-picture underlying the uses of language are not originally and strictly propositions at all. The pre-knowledge is not propositional knowledge. But if this foundation is not propositional, what then is it? It is, one could say, a praxis.” Von Wright, supra note 30 at 178. These points will become more evident below.


56. Wittgenstein, supra note 27 at 96.

57. Ibid at 211.


58. Ibid at 136, 167.


59. Ibid at 136.


60. Ibid at 410.


61. See WVO Quine, “Two Dogmas of Empiricism” in From a Logical Point of View (Harper & Row, 1961) at 20. First published as WV Quine, “Two Dogmas of Empiricism” (1951) 60:1 Philosophical Review 20.

62. Wittgenstein, supra note 27 at 475.

63. Stroll, supra note 27 at 145-46.

64. I say “usually” because the formation of a world-picture could be, at least for some parts of it, a process of knowledge acquisition. For example, that there is a big island called Australia (one of Wittgenstein’s examples) might be a part of my world-picture now, but I may have learned it as a bit of knowledge in a world geography class. See Wittgenstein, supra note 27 at 159.

65. Ibid at 87.


66. In Philosophical Investigations, Wittgenstein remarks that a certain custom or form of life has to be assumed for a game to be recognizable as a game, but that custom itself is not part of the game. See Ludwig Wittgenstein, Philosophical Investigations, 3rd ed, translated by GEM Anscombe (Blackwell Publishing, 1953/2001) at sections 199, 200, 204.

67. We may run an argument similar to the one discussed above (see von Wright, supra note 30 and Wittgenstein, supra note 27 at 111) to reach the same conclusion from another direction: if the hinges are in the same category as the other beliefs and knowledge, then they would in principle be open to doubt and thus require further evidence and proof to support or ground them. But it is not clear in that case what other evidence or proof we could use to support or ground a hinge belief, because what can be more certain than a hinge?

68. To say, then, as Moore did, that one knows such a proposition with absolute certainty, involves confusion. It follows that calling hinges beliefs or propositions would be problematic too. The problem will be more conspicuous when I argue below that Raz’s necessity claim should be understood as a hinge of legal practice and discourse. However, I will keep referring to hinges as beliefs and propositions. See my response to this problem (the first objection) in section IX.

69. Wittgenstein, supra note 27 at 106.

70. Ibid at 166 [emphasis added].


71. Ibid at 253.


72. Ibid at 144.


73. Ibid at 204.


74. Ibid at 140, 141, 144.


75. Ibid at 144, 152.


76. Ibid at 190.


77. Ibid at 343. Of course, it does not follow that this is the only hinge, or that there will not be more local hinges, ones specific to a particular discourse or practice. As I argue below, necessary truths in jurisprudence are hinges of our legal practice.


78. The phrase ‘practicable dependence’ was suggested to me by Richard Bronaugh.

79. Wittgenstein, supra note 27 at 248.

80. Ibid at 204.


81. Wittgenstein, supra note 66, at section 217.

82. Wittgenstein, supra note 27 at 204.

83. Ibid at 7. See also ibid at 148: “Why do I not satisfy myself that I have two feet when I want to get up from a chair? There is no why. I simply don’t. This is how I act” [emphasis added]. The “satisfy myself” part translates the German “überzeuge ich mich davon;” an alternative translation would be “convince myself.”


84. Ibid at 147.


85. Ibid at 159.


86. Ibid at 513.


87. Danièle Moyal-Sharrock, Understanding Wittgenstein’s On Certainty (Palgrave Macmillan, 2004) at 97.

88. It would be beyond the scope of this essay to try to offer an explanation of a social practice. But there are clear paradigms: law and politics are social practices while mathematics and geology are not, though, in all cases, one can speak of truths. They might be thought of as different forms of inquiry, with different objectives, as Aristotle sets out in his Nichomachean Ethics. See Aristotle, The Nicomachean Ethics, translated by David Ross, ed by Lesley Brown (Oxford University Press, 2009) at 1140b. In any case, no sharp distinction between an inquiry and a social practice is intended in the above discussion.

89. Richard Bronaugh has informed me that the Wittgensteinian ideas expounded above echo those of RG Collingwood, a perhaps unjustly neglected historian and philosopher, especially ideas from his 1940 book, An Essay on Metaphysics. Collingwood’s discussion is about the nature of metaphysics. In a rather formal manner, Collingwood lays down the following theses and definitions central to his project: (1) every statement is made in answer to a question; (2) that which is stated is called a proposition; (3) every question involves a presupposition; (4) the fact that something causes a question to rise is called the “logical efficacy” of that thing. (For instance, “this mark on a stone is an intentional inscription and means something” has logical efficacy in causing the following question to rise, “what does it mean?”); (5) the logical efficacy of a supposition does not depend upon the truth of what is supposed, or even on its being thought true, but only on its being supposed; (6) a presupposition is either relative or absolute; (7) a presupposition is relative if it stands to one question as its presupposition, and to another as its answer; absolute if, to all questions to which it is related, it stands as a presupposition, never as an answer; (8) it follows, from (1), (2), (3), and (7) that absolute presuppositions are not propositions. See RG Collingwood, An Essay on Metaphysics (Oxford University Press, 2002 [1940]) at 21-33. For Collingwood, metaphysics is about recovering the absolute presuppositions of the sciences, where “science” is to be understood as “a body of systematic and orderly thinking about a determinate subject-matter.” Since the sciences change historically, metaphysics is a historical discipline. For example, “all events have causes” is an absolute presupposition of Newtonian physics, though not one of Einsteinian physics. Ibid at 4, 47, 51.

Bronaugh suggests that Wittgenstein’s hinge propositions bear resemblance to those Collingwood calls “absolute presuppositions.” Indeed, they share several similarities: (i) they are presupposed by an inquiry or science for its intelligibility (i.e., for the questions within it to be meaningful, answerable, and determinate questions, and therefore cannot be doubted); (ii) they are of a different category from those surrounding them, as they are not propositions and thus are neither true or false; (iii) they are not verifiable, that is to say, the idea of verification does not apply to them; (iv) they have a historical dimension as they, along with the sciences, change over time. When it comes to social practices, Collingwood would perhaps also agree that (v) its presuppositions—the necessary truths about law, as I shall argue—are revealed in our ways of acting.

I find the comparisons with Collingwood illuminating and intriguing, and some of his ideas (since they are in a more sharpened form) may be even more helpful than Wittgenstein for my purpose of elucidating jurisprudential methodology (see infra note 110 for a suggestion about what conceptual analysis might be in legal theory, a suggestion inspired by Collingwood’s writings). These comparisons suggest further lines of inquiry; however, two obvious differences between the two thinkers might be noted at this point: a) Collingwood’s project, as he makes clear in the preface of An Essay on Metaphysics, is about the nature of metaphysics, while Wittgenstein has no such concern; b) the formal aspect of Collingwood’s work makes it resemble Wittgenstein’s Tractatus (a style the later Wittgenstein would not approve). As a result of this formal approach, some conclusions, notably item (8) mentioned above, deductively follow from or are legislated by the other propositions and definitions in Collingwood’s system. Wittgenstein’s approach to these conclusions, presumably similar in nature to what Collingwood has in mind, is very different. For a useful discussion of why Collingwood might still be relevant today, some difficulties internal to the theses sketched above, as well as a partial comparison with Wittgenstein on some important points, see Bernard Williams, “An Essay on Collingwood” in Myles Burnyeat, ed, The Sense of the Past: Essays in the History of Philosophy (Princeton University Press, 2006) at 341.


90. This distinction can be traced back to Hume’s distinction between relations of ideas and matters of fact, the former can be known a priori while the latter cannot. See David Hume, An Enquiry Concerning Human Understanding, 3rd edition, PH Nidditch, ed (Clarendon Press, 1975) at section IV.

91. Joseph Raz, among others, explicitly denies that the nature of law can be discerned by inquiring into the meaning of the word ‘law’. See Raz, supra note 1 at 19-20, 29-30.

92. See Hale, supra note 23 for a discussion of this issue.

93. Kit Fine writes: “The metaphysically necessary truths can then be identified with the propositions which are true in virtue of the nature of all objects whatever.” Fine, supra note 7 at 9. See also, “a metaphysical necessity has its source in the identity of objects; it is true, or necessary, in virtue of the objects with which it implicitly deals.” Ibid at 7.


94. It is worth noting that in On Certainty, Wittgenstein also takes traditionally accepted necessary propositions—analytic/linguistic, logical, and mathematical ones—to be hinges. Discussing these is a task for a different occasion. See Moyal-Sharrock, supra note 87 at 102 for a discussion of this point. For discussions of Wittgenstein’s notion of logical necessity, see Michael Dummett, “Wittgenstein’s Philosophy of Mathematics” (1959) 68:3 Philosophical Review 324 and Barry Stroud, “Wittgenstein and Logical Necessity” (1965) 74:4 Philosophical Review 504.

95. This means we need to reconceive the role of experience in our understanding of necessity and hence in conceptual analysis overall. A fuller treatment of this topic will have to be left for a different occasion. I offer some initial thoughts in section VII below.

96. I thank Doug Lewis for help clarifying this point.

97. See Brian Bix, “Joseph Raz’s Approach to Legal Positivism” in Torben Spaak & Patricia Mindus, eds, The Cambridge Companion to Legal Positivism (Cambridge University Press, [forthcoming in 2021]) at section 5.

98. Raz, Ethics, supra note 2 at 215.

99. Bix, Raz on Necessity, supra note 3 at 538.

100. Wittgenstein, supra note 27 at 411.

101. Ibid.


102. Ibid at 144, 152.


103. Ibid at 87 [emphasis added].


104. Ibid at 419.


105. See Section IX below for a discussion of Matthew Kramer’s view that Raz’s claim can be doubted.

106. Wittgenstein, supra note 27 at 190.

107. This echoes Scott Shapiro’s point that conceptual analysis in jurisprudence proceeds by identifying truisms about law. See Shapiro, supra note 7 at 13-16; Wittgenstein, supra note 27 at 87.

108. Raz, Ethics, supra note 2 at 215-16.

109. A few things are worth noting here about Raz’s claim and his methodology. First, that law necessarily claims legitimate authority is, of course, not the same as that law has legitimate authority necessarily. Second, Raz’s claim, while revealing one necessary feature of law, is not the same as a sufficient explanation of the nature of law. The discussion above shows that when we try to identify the nature of law (i.e., when we ask, “What is Law?” we could study “What is the law?”—the actual operations of the legal system, and investigate what is presupposed in those operations). In that language-game, the actual legal practice, we find that law’s de facto claim to legitimate authority is presupposed of necessity. The presupposition is about the intelligibility of the practice (e.g., it cannot claim illegitimate authority—that makes no sense) in the language-game we play. However, we might think this insufficient. We might think that to sufficiently explain the nature of law, we need an explanation of, for example, what constitutes legitimacy and what it is for law to have legitimate authority. That is misguided. The presupposition is what is needed here as revealing a part of the nature of law. There might be different philosophical theories of what counts as legitimate, but the question of what constitutes legitimacy is irrelevant here because it is the claiming of legitimate authority that counts. That is the bedrock. I thank Richard Bronaugh for the clarification here.

110. See Kenneth Einar Himma, “Conceptual Jurisprudence: An Introduction to Conceptual Analysis and Methodology in Legal Theory” (2015) 26 Revus 65 at 72. Understanding necessary truths about law as presuppositions of a social practice also provides us with an opportunity to rethink about the nature of conceptual analysis in jurisprudence (an approach both Raz and Hart, among many other legal theorists, have adopted; for criticism of this approach in jurisprudence, see Leiter, supra note 16). Here Collingwood’s ideas (see generally supra note 89) can also shed light on the nature of conceptual analysis. For Collingwood, analysis is about “disentangling and rearranging questions” or “detecting presuppositions” (Collingwood, supra note 89 at 39-40). This presents a different model for thinking about analysis, where it does not aim at analytic truths. Many of the objections to this method in jurisprudence assume that it does.

111. This leaves aside the question whether conceptual analysis in general is a priori or a posteriori. The answer is underdetermined at this point, because necessary truths may only account for a fraction of the results of conceptual analysis.

112. For an overview of a priori justification and objections to it, see Bruce Russell, “A Priori Justification and Knowledge” in Edward N Zalta, ed, Stanford Encyclopedia of Philosophy (19 May 2014), online at For a summary of critiques of a priori justification, especially in connection with the method of conceptual analysis in jurisprudence, see Himma, supra note 110 and Leiter, supra note 16.

113. Priel writes: “[I]t is more reasonable to suggest that explicating the nature of law involves looking at some cases of actual law and trying to find their essential features by reflecting on them.” Priel, supra note 11 at 177. See also Giudice, supra note 4 at 96-98 and Tamanaha, supra note 11.

114. Giudice gives three examples that he thinks might actually fit Kripke’s examples of natural kinds (e.g., “water is necessarily H2O”): Hart’s Union of Primary and Secondary Rules Thesis; Hart’s description of the Minimum Content of Natural Law Thesis as a “natural necessity”; and Hart’s The Open Texture Thesis. See Giudice, supra note 4 at 99-100. Tamanaha picks on the idea of natural necessity (i.e., there necessarily exists rules in human groups that protect property and persons), but he thinks even if such a search is promising, it “must be established on empirical grounds, not by reasoning from intuitions and concepts.” Tamanaha, supra note 11 at 64.

115. Giudice, supra note 4 at 105.

116. Hilary Putnam, “The Analytic and the Synthetic” in Herbert Feigl & Grover Maxwell, eds, Minnesota Studies in the Philosophy of Science (University of Minnesota Press, 1962) vol III at 358. The example here is one of Putnam’s. It is strikingly similar to the example from Wittgenstein discussed above. In addition, Putnam’s argument also echoes central themes of On Certainty.

117. Ibid at 363. Putnam continues by saying that with regard to the hypothesis about the age of the Earth, “it is not happy to ask if they are analytic or synthetic.” They are what Putnam calls “framework principles.” Putnam uses the phrase ‘systematic import’ to characterize this kind of principles. For example, “[w]e can barely conceive of a conceptual system which did not include the idea of a past.” Ibid at 365. I think these principles can be understood as “hinge propositions.”


118. Ibid at 366-67.


119. This is modified from Frederick Schauer, Thinking like a Lawyer (Harvard University Press, 2009) at 62. It is a restatement of Raz, Ethics, supra note 2 at 212-13.

120. The example is from Andrei Marmor, Philosophy of Law (Princeton University Press, 2011) at 1.

121. Putnam, supra note 116 at 364.

122. Wittgenstein, supra note 27 at 273-4 [emphasis added].

123. I think this distinction holds the key to understanding a qualm in legal theory: sometimes it is hard to determine whether a legal theorist such as John Austin is making empirical claims or conceptual ones. See Brian Bix, “Joseph Raz and Conceptual Analysis” (2007) 6:2 APA Newsletter on Philosophy of Law 1 at 1. Conceptual claims can involve experience.

124. Kant’s distinction is between two kinds of a priori. “[I]t is customary to say of many a cognition derived from experiential sources that we are capable of it or partake in it a priori, because we do not derive it immediately from experience, but rather from a general rule that we have nevertheless itself borrowed from experience.” Immanuel Kant, Critique of Pure Reason, edited and translated by Paul Guyer & Allen Wood (Cambridge University Press, 1998) at 136-37. Kant also draws a similar distinction, between the a priori simpliciter and the a priori secundum quid, in Metaphysik Mrongovius. See ibid at 717 n 9 for Guyer & Wood’s editorial notes. The a priori secundum quid (“a priori in some sense”) could be thought of as a posteriori necessity discussed in this essay.


125. Ibid at 137.


126. Wittgenstein, supra note 27 at 603. “I am taught that under such circumstances this happens. It has been discovered by making the experiment a few times. Not that this would prove anything to us if it weren’t that this experience was surrounded by others which combine with it to form a system.”

127. This structure reflects our general understanding of what law is. It is hence an important feature of the second kind of general, structured experience that it plays a constitutive role in our concepts. It is as if the experience is fossilized, fused into our general understanding of law (i.e., our concept of law). “The propositions of mathematics might be said to be fossilized ….” Hence our reflective general experience related to legal authority and our concept of legal authority are inseparable from each other. Ibid at 657.


128. Giudice, supra note 4 at 97-98. Giudice’s reference to the quote from Raz’s argument was discussed in the previous section of this essay.

129. Tamanaha, supra note 11 at 64 [emphasis added].

130. Giudice, supra note 4 at 102.

131. In trying to establish Hart’s Union of Primary and Secondary Rules Thesis as a posteriori, Giudice says that Hart “engages in observation of the character and functions which legal systems serve in societies.” But right on top of the word ‘observation’, he adds the following footnote, offering a response to an anticipated objection: “Albeit observation which has been accumulated from familiarity with modern municipal legal systems, so in this sense one might object that Hart is still engaging in armchair analysis devoid of actual empirical investigation. I think this objection is fundamentally misguided, as Hart (like anyone else) certainly had to become acquainted, through experience, with modern municipal legal systems before he could reflect on their nature.” Ibid at 99. This response fails for multiple reasons. If Hart had to “become acquainted, through experience,” with modern municipal legal systems to establish his thesis, then it could be said that a mathematician must “become acquainted, through experience,” with numbers to do number theory. But this does not make number theory a posteriori. The anticipated objection has force here exactly because it is pointing to two kinds of experiences that can be understood along lines suggested above.


132. Tamanaha, supra note 11 at 64 [emphasis added].

133. Raz, supra note 8 and Raz, supra note 1.

134. I am aware that even within one society there might be multiple co-existing concepts of law. See Bix, supra note 123 at 3. Again, this is not the place to deal with the question.

135. However, a theory of law makes universal claims, attempting to recover the essential features of law, purporting to apply to all law, wherever and whenever it is found. A theory of law is both parochial and universal. See Raz, supra note 8 at 2. Raz’s “universal” here is different from a much more ambitious use of “universal” discussed in this paragraph.

136. See Bernard Williams, Shame and Necessity (University of California Press, 2008) at ch 3.

137. Even here, we might say that they are necessary truths contingent on the human condition (mathematical truths then have the same character. Nothing prevents us from imagining that aliens use an alternative mathematics).

138. Wittgenstein, supra note 27 at 95.

139. Ibid at 92.


140. Language-games are rooted in our form of life (Wittgenstein, supra note 66 at 148) and will undergo change as a result of the changes in our form of life. “When language-games change, then there is a change in concepts” (Wittgenstein, supra note 27 at 65).

141. The change might happen in other ways. A necessary and indubitable proposition can be directly refuted. Wittgenstein’s example (i.e. no one has been far away from the surface of the Earth) (a hinge in his world-picture when he was writing), is an example of a different possibility. It was a hinge in an old world-picture, but not any more in our own time.

142. Austin did not seem to use the language of necessity explicitly. See John Austin, The Province of Jurisprudence Determined and the Uses of the Study of Jurisprudence (Hackett, 1998) at 350. Austin characterizes his jurisprudential project of giving an account of the nature of law as one that provides a “definition of positive law.” But it is not implausible to think that propositions of his theory take the form of necessary truths.

143. This again echoes Collingwood’s idea that the presuppositions of an inquiry or practice, and in turn metaphysics, whose business is to recover those presuppositions, have a historical and cultural dimension. See Collingwood, supra note 89 at 60 and Raz, supra note 1 at 17-46.

144. Wittgenstein, supra note 27 at 96 [emphasis added].

145. Ibid at 97.


146. Ibid at 410. This aspect, I think, brings Wittgenstein’s thought close to Quine’s holism.


147. I thank Richard Bronaugh for making this problem explicit.

148. As Wittgenstein puts it, “[i]f the true is what is grounded, then the ground is not true, nor yet false”. See Wittgenstein, supra note 27 at 205 [emphasis in original]. See Collingwood, supra note 89. Collingwood says something similar about absolute presuppositions: they are not propositions, and they are neither true nor false. The response given here would also apply to similar qualms about Collingwood’s absolute presuppositions.

149. I thank Brian Bix for raising this point. For relevant discussions of this point, see Brian Bix, supra note 97 at section 4.1.3.

150. See Matthew Kramer, “Requirements, Reasons, and Raz: Legal Positivism and Legal Duties” (1999) 109:2 Ethics 375 [Kramer, “Requirements”]. For an unabridged version of Kramer’s argument, see Matthew Kramer, In Defense of Legal Positivism: Law without Trimmings (Oxford University Press, 1999) at ch 4.

151. Kramer, “Requirements”, supra note 150 at 398.

152. Raz, Morality of Freedom, supra note 2 at 27.

153. Ibid.


154. Kramer, “Requirements”, supra note 150 at 387-99.

155. Green made this point in Leslie Green, “Legal Positivism” in Edward N Zalta, ed, Stanford Encyclopedia of Philosophy, (17 December 2019) at sect. 4.2, online at

156. Raz, Morality of Freedom, supra note 2 at 27.

157. See HLA Hart, The Concept of Law, 2nd ed (Oxford University Press, 1994 [1961]) at 18-78.

158. Williams, supra note 136 at 103-129.

159. Ibid.


160. See, for example, Ronald Dworkin, Taking Rights Seriously (Harvard University Press, 1977) at 14-45; Ronald Dworkin, Law’s Empire (Harvard University Press, 1986) at 243; Hans Kelsen, Introduction to the Problems of Legal Theory, translated by Bonnie L Paulson & Stanley L Paulson (Clarendon Press, 1992) at 63-75. The last two points of clarification are responses to critical questions posed by Brian Bix, RA Duff, and comments from Doug Lewis. I thank Bix, Duff, and Lewis for their very helpful questions and comments.

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