I am grateful to Richard Bronaugh for his helpful comments.

1. Hohfeld, W.N., Fundamental Legal Conceptions (New Haven, CT: Yale University Press, 1919), initially published in (1913) 23 Yale L. J. 16 and (1917) 26 Yale L. J. 710.Google Scholar

2. Part of the burden ofRobinson, R.E., Coval, S.C. & Smith, J.C., “The Logic of Rights” (1983) 33 U.T.L.J. 267 CrossRefGoogle Scholar, is to contrast Hohfeld’s use of ‘fundamental’ with that found within rights theories in designating certain rights or liberties as fundamental.

3. Ibid, at 271 n. 9

4. Kocourek, Albert, “Plurality of Advantage and Disadvantage in Jural Relations”; (1920) 19 Mich. L. Rev. 47 at 56.CrossRefGoogle Scholar

5. O’Reilly, Daniel T., “Are There Any Fundamental Legal Conceptions?” (1999) 49 U.T.L.J. 271 CrossRefGoogle Scholar—a review essay on my book, Rights & Law—Analysis & Theory (Oxford: Hart Publishing, 1997), building on his own previous article, “Using the Square of Opposition to Illustrate the Deontic and Alethic Relations Constituting Rights” (1995) 45 U.T.L.J. 279.Google Scholar

6. Hart, H.L.A., Essays on Bentham (Oxford: Clarendon Press, 1982) at 114.Google Scholar For further use of the device related to present concerns, see Raz, Joseph, The Concept of a Legal System, 1st ed. (Oxford: Clarendon Press, 1970) at 56 (on Bentham)Google Scholar; Mullock, Philip, “The Hohfeldian Jural Opposite” (1971) 13 Ratio 158;Google Scholar Lyons, David, In the Interests of the Governed (Oxford: Clarendon Press, 1973) at 117 (on Bentham);Google Scholar Mullock, Philip, “Logic and Liberty” (1979) 35 Phil. Stud. 217 (on Bentham).CrossRefGoogle Scholar A novel employment of the square of opposition in an attempt to indicate the relationships between different jurisprudential theories is to be found in Burgess Jackson, Keith, “Teaching Legal Theory with Venn Diagrams“ (1998) 29 Metaphilosophy 159 at 168–71.Google Scholar

7. See Londey, David & Johanson, Carmen, “Apuleius and the Square of Opposition” (1984) 29 Phronesis 165;CrossRefGoogle Scholar , Parsons, “The Traditional Square of Opposition—A Biography” (1997) 18 Acta Analytica 23.Google Scholar

8. The problem that preoccupies Parsons, ibid., concerns the treatment of empty terms, but for our purposes the assumption can safely be made that we are never dealing with an empty term (e.g., a duty to stay off Whiteacre, where there is no such place as Whiteacre). What I refer to as the standard form of the square is what Parsons describes as the traditional square of opposition, and it is this form that is invoked by the authors cited above as employing the square to assist in an understanding of law.

9. The symmetry is clearer if we replace ‘no students are hard working’ with the clumsier sounding but semantically identical ‘all students are not hard working’.

10. Robinson, Coval & Smith, supra note 2 at 274-75; O’Reilly, , “Using the Square of Opposition“, supra note 5 at 292–93; Raz, supra note 6 at 56; Lyons, supra note 6 at 120.Google Scholar

11. For example, there will be some students who are not hard working in either the case of no students being hard-working or the case of some being hard-working and some not.

12. It may be thought that the two contradictions can be helpfully explained in terms of a distinction between internal and external negations. However, this does not fully capture the analysis offered by the triangle of possibilities, in that it suggests two separate positions taking us in quite distinct paths away from the compound being negated. The triangle displays in the opposite face to the point representing the initial compound the possibility of recognising that the compound has been negated, without as yet being sure which of the two negations will be reached (we come across some students who are not hard working, so know that the proposition that all students are hard working has been negated, but do not yet know how). The contrast with the square of opposition, is that it inappropriately suggests that the place indicated by the face of the triangle is a definite position, indicated by a point on the square.

13. We could become more sophisticated in our enquiry, for example by asking what proportion o students are hard working. But this further level of enquiry takes place within the elementary category of some-are-and-some-are-not. By contrast, it can be shown that point c within the square of opposition does not provide us with an elementary level for further enquiry because we do not yet know what further enquiry is meaningful. If it turns out that c is subsumed with a, then as all students are hard working it will be meaningless to ask what proportion are hard working; whereas if c is joined with d it will become a meaningful question.

14. O’Reilly, “Are There Any Fundamental Legal Conceptions?”, supra note 5.

15. Hart, supra note 6; and other works cited in supra note 6; Bentham, Jeremy, Of Laws in General, H.L.A. Hart, ed., (London: Athlone Press, 1970) at 95.Google Scholar

16. For example, a permission to enter is synonymous with no requirement not to enter.

17. O’Reilly, “Are There Any Fundamental Legal Conceptions?”, supra note 5 at 276.

18. This represents the distinction Feinberg, Joel has recognised between a half-liberty and a full liberty in Rights, Justice and the Bounds of Liberty (Princeton, NJ: Princeton University Press, 1980) at 157. The recognition of half-liberties is also to be found in O’Reilly, “Using the Square of Opposition”, supra note 5.CrossRefGoogle Scholar

19. O’Reilly, “Are There Any Fundamental Legal Conceptions?”, supra note 5 at 276.

20. The terminology is Feinberg’s—see supra note 18.

21. O’Reilly, “Are There Any Fundamental Legal Conceptions?”, supra note 5 at 275. This faithfully represents the view Hohfeld himself puts forward.

22. Hart, supra note 6 at 115.

23. Bentham, supra note 15 at 97. What keeps Bentham from the triangle in his analysis of the will is his insistence that there are always two aspects present. But this is done at the expense of keeping the redundant c when we have a or the redundant d when we have b (see figure 3)—or, in his terminology, commanded and unprohibited; prohibited and uncommanded. However, Bentham does not make the mistake of treating a (half-)liberty (c or d—unprohibited or uncommanded) as a stable legal position. Bentham notes that, ‘A non-command [d] of itself does not necessarily include either a prohibition or a permission … it must be accompanied with one or other of them.’ And subsequently (at 98-99) Bentham indicates that where the legislator expressly indicates one of c or d (the undecisive mandates) then the other must be assumed if the legislator has not expressly indicated in addition a or b (the decisive mandates).

24. 1 should say that in this essay I treat conception as synonymous with concept, in accordance with what i take to be Hohfeld’s use of the term. Elsewhere I have argued against a narrower use of conception, in the phrase ‘conceptions of a concept’ (see, e.g., Halpin, Andrew, Reasoning with Law (Oxford: Hart Publishing, 2001) at 162–65).Google Scholar

25. The social aspect of legal duties prevails even in the case of apparently self-regarding duties, in that there exists a concern among other members of society for the well-being of the duty holder (whether altruistic or related obliquely to their own concerns, e.g., not to see medical resources wasted); and the legal entitlement of the general public to the conduct of the duty holder is then expressed through the enforcement rights, etc. of public officials. These enforcement rights may on closer analysis be revealed as a complex aggregate of Hohfeldian conceptions (e.g., the official may have a duty to enforce in some circumstances, or a discretionary power to do so). Although this additional complexity may require us to extend the simpler analysis of the Hohfeldian rightduty paradigm, for reasons referred to in Rights & Law, supra note 5, ch. II, this will not be at the price of having to recognise further fundamental conceptions.

26. A square of opposition could be constructed for rights, but for reasons that will by now be familiar it will collapse into a triangle of possibilities.

27. Cp. supra note 25.

28. O’Reilly, “Are There Any Fundamental Legal Conceptions?”, supra note 5 at 276.

29. Ibid. at272n4.

30. If we posit a more sophisticated deontic operator, such as a Kelsenian operator of normative authorisation, there is still a need to recognise the third element. Whatever the operator might be imagined to be, something is required beyond the subordinate and dominant positions of the two parties, otherwise legal relationships would have to be regarded as entirely consensual. The great danger in seeing the deontic operator as a matter of normative authorisation, and then analysing the content of the legal norms in terms of duties, rights, etc., is to lose sight of the third element altogether.

31. This is the mere negation referred to at supra note 21. The issue of whether a liberty can be reduced to (the absence of) a duty in this way causes problems for Wright, Georg Henrick von, Norm and Action (London: Routledge and Kegan Paul, 1963) at 85–92 Google Scholar in dealing with the question whether ‘permissive norms’ are definable in terms of ‘obligation norms’ and in his use of negation, at 140. Mullock, “The Hohfeldian Jural Opposite”, supra note 6 at 160 suggests that Hohfeld’s analysis can be regarded as an “informal and legal precursor of von Wright’s deontic logic“.

32. For discussion of legal powers see chs. 11:7 & III of Rights & Law, supra note 5.

33. See supra note 25, and Rights & Law, supra note 5 at 31.

34. At the end of the second section.

35. A theme advanced in Rights & Law, supra note 5.

36. 1 owe this illustration to discussion with Roger Brownsword.

37. For more on this, see ch. II of Rights & Law, supra note 5; cp. O’Reilly, “Using the Square of Opposition“, supra note 5 at 301–03, and Robinson, Coval & Smith, supra note 2 at 277.

38. The suggestion has been influential for having been made by Joseph Raz in his analysis of legal rights—for discussion see Rights & Law, supra note 5 at 247 n 187. Arguably, Kelsen does a similar thing in dispensing with right in favour of duty—see ibid, at 4 n6. Either move can be regarded as illustrating the tendency to lose sight of the third element mentioned in supra note 30.