Hohfeldian Infinities: Why Not to Worry


Hillel Steiner has recently attacked the notion of inalienable rights, basing some of his arguments on the Hohfeldian analysis to show that infinite arrays of legal positions would not be associated with any inalienable rights. This essay addresses the nature of the Hohfeldian infinity: the main argument is that what Steiner claims to be an infinite regress is actually a wholly unproblematic form of infinite recursion. First, the nature of the Hohfeldian recursion is demonstrated. It is shown that infinite recursions of legal positions ensue regardless of whether inalienable rights exist or not. Second, the alleged problems that this might pose for the analysis are discussed. The conclusion is that one should not worry about the recursion as long as one understands correctly the role of the Hohfeldian analysis in normative reasoning.


Hillel Steiner has in a recent article attacked the notion of inalienable rights (Steiner 2013). He does not only employ substantive moral arguments for this purpose, but also arguments that rely directly on the system of analysis developed by Wesley Newcomb Hohfeld. The Hohfeldian scheme can, according to Steiner, be used to show that inalienable rights lead either to logical contradictions or to infinite arrays of legal positions, and this can only be avoided by conceding that all rights are alienable. So runs Steiner’s argument.

A closely similar argument made by Steiner in An Essay on Rights (Steiner 1994) two decades ago was refuted by Nigel Simmonds (1995).Footnote 1 Simmonds’s article alone is sufficient for understanding where the problem in Steiner’s argument lies. A reply to Steiner’s more recent essay has been published in Ethics by Pierfrancesco Biasetti, who also discusses the issue further in a related article (Biasetti 2015a, b).

Though Steiner’s argument is based on a misguided application of Hohfeld, he raises an interesting question about the infinities that are present in the Hohfeldian system. Biasetti concedes Steiner’s point to a certain extent, arguing that the Hohfeldian analysis needs to be modified in order to amend a more general problem that does not pertain to inalienable rights. This is due to a particular feature of the Hohfeldian analysis: any Hohfeldian system contains an infinite number of legal positions. Although Biasetti is correct in that the ‘nonclosure’ of normative positions is an intrinsic feature of the Hohfeldian system—rather than pertaining to the inalienability of rights, as Steiner claims—I disagree with both over whether this is actually a problem.

The Hohfeldian Analysis

The Hohfeldian analysis was devised by Wesley Newcomb Hohfeld, an American legal scholar. He wished to expose how jurists used legal terms, such as the word ‘right’, ambiguously, and how this led to faulty reasoning. Though Hohfeld was a jurist, his framework is equally suitable for the analysis of moral and other normative systems. In the Hohfeldian analysis, normative relations are reduced to eight basic positions, four of which are typically called first-order positions and the other four higher-order positions. It can roughly be said that the first-order positions pertain to whether a given type of action is required, permitted or forbidden in relation to a given party,Footnote 2 whereas higher-order positions concern how normative relations can be changed, and thus relate only indirectly to the permissibility or obligatoriness of physical conduct.

The first-order positions are duty, liberty, claim and no-right. One’s having the duty to φ means that φ-ing—which can be any type of conduct—is obligatory. It also entails that at least one party has a claim (also known as claim-right) to this conduct.Footnote 3 A Hohfeldian duty is thus always held toward someone. For instance, if I have the duty to pay you £500, then you have the claim-right that I pay you £500. These two positions are correlatives: a duty entails at least one claim-right (Fig. 1).Footnote 4 Similarly, liberty and no-right are correlatives. A’s having a liberty to refrain from φ-ing towards B means that A is not duty-bound toward B to φ. Such a liberty is entailed by a no-right, that is, lack of claim. Thus, B holds a no-right in relation to A with regard to A’s φ-ing.

Fig. 1

For every regulated action, omission or conduct, A has either a duty or a liberty, and B has either a claim-right or a no-right

There are four higher-order positions: power, disability, liability and immunity. Power means that one can change a legal relation through a volitional act, whereas disability logically means the lack thereof. Similarly, B’s having a liability towards A means that A can change a legal relation that pertains to B, and immunity implies the absence of such a relation.

The Hohfeldian table does not yet tell us how the concept of ‘right’ should be defined, and there is considerable disagreement in this regard. According to Steiner, Hohfeldian claims and immunities are rights, as they entail constraints for the correlative duty-bearers and disability-holders, respectively.Footnote 5 I will here use the term ‘right’ interchangeably with ‘claim’, as the argument I am addressing focuses on the inalienability of claims.

The Hohfeldian framework does not make many normative claims about moral or legal relations, perhaps none at all. It does presuppose certain things, such as the correlativity of claim-rights and duties (the so-called correlativity axiomFootnote 6), but in general the framework is neutral when it comes to evaluative assertions about the content of morality or of a legal system or of another type of normative system. Steiner believes, however, that the Hohfeldian system can be used to show that no rights can be inalienable. His argument is dependent on a particular feature of the Hohfeldian system: that higher-order positions, such as powers and liabilities, can also pertain to other higher-order positions. For instance, if a traffic police officer has the power P1 to impose an obligation O for a driver to stop his or her car, but the police commissioner may fire the officer, then the police commissioner has the power P2 to extinguish the power P1 of the officer. In this case, P1 pertains directly to O, whereas P2 pertains to P1. There is an infinite number of such higher-order relations—for instance, the mayor could have the power P3 to fire the police commissioner and thus extinguish P2—even though at some point the relations most likely become disability-immunity relations. This is the recursion (which Steiner calls the ‘regression’) of higher-order Hohfeldian relations. I will analyse the nature of the Hohfeldian recursion more closely in the third section. I will, however, first present the structure of Steiner’s argument.

Steiner’s Argument

Steiner begins by describing a situation between two parties, Blue and Red, where Red is under the duty not to assault Blue, and Blue holds the correlative claim (that is, right) against Red’s assaulting her. In addition, Blue does not have the power to waive this duty by consenting to the assault, but holds rather the corresponding disability D1. Blue seems to be the holder of an inalienable right. However, Steiner claims that this is not the case:

[Blue’s right is not inalienable] for disabilities entail correlative immunities. So, if Blue is encumbered with D 1, then someone else, say Green, is vested with the correlative immunity, I 1, against Blue’s waiving Red’s duty not to assault Blue. Now, the question we have to ask is this: Is Green’s immunity, I 1, waivable and, if so, by whom? If it is waivable and, moreover, waivable by Green, then Green is in a position to extinguish D1: that is, to release Blue from her disability to waive Red’s duty not to assault her. And if Blue can be thus empowered to waive that duty, then, trivially, that duty is a waivable one, that is, its correlative right is alienable. (Steiner 2013)

I should note that there is a mistake in the passage above; Green does not have an immunity that correlates with D1. The immunity-holders here are Blue and Red themselves. Green does, however, hold a disability D2 to change Blue’s disability D1. This mistake will pose some problems for Steiner’s main argument, a matter to which I will return in ‘Coping with the Infinity’. Steiner then goes on to describe how Black may have a disability D3 to change Green’s disability D2, and Purple may have a disability D4 pertaining to D3, and so on. He concludes as follows:

[T]he sufficiently unmistakable point here is that wherever this otherwise infinite regress stops, it can be stopped only by an immunity which is waivable by the person vested with it. And the exercise of that waiver renders serially possible a succession of waivers—a waiver chain—that terminates in Blue’s being empowered to waive Red’s nonassault duty. And the waivability of that duty entails, once again, that Blue’s right against Red’s assaulting her is not inalienable. (Steiner 2013)

Steiner claims that we are faced with two choices: either we accept that all rights are waivable or we accept the infinite recursion which he calls nonclosure. The problem with nonclosure is, according to Steiner, that there is ‘necessarily insufficient time and/or persons’ to sustain such a normative system, as we could not warrantedly assert whether a right has been waived without first investigating the endless chain of powers and/or disabilities (Steiner 2013).

Infinite Recursion of Higher-Order Relations

An important difference between the concepts of recursion and regress is that whereas with recursion we know what A is and then use it to define B, in the case of regress we do not know what A is and need B to define A. The regress becomes infinite if we also need C to define B, and so on, infinitely. Infinite regress is characteristically problematic, as it never manages to establish A (or B, or C…), whereas infinite recursion does not suffer from such problems. The sequentiality that the Hohfeldian system exhibits is clearly a case of recursion, for the definition of claims and duties is not dependent on any higher-order positions, and higher-order positions are defined in relation to lower-order positions. This is essentially why the Hohfeldian infinity is not problematic, either: it is built on solid ground.

Every Hohfeldian recursion begins from a deontic relation between two Hohfeldian parties. This relation consists of a duty and a claim-right or a liberty and a no-right with regard to a particular action. For the purposes of this article, I will call such a relation a base relation.Footnote 7 In addition, the N-order relation contains some N − 1-order parties as N-order liability-holders or immunity-bearers, and at least some of those individuals are also N − 2-order parties, except where N = 2. Thus, both the Hohfeldian N-level relations and the Fibonaccian N-level numbers are defined by reference to the relations or numbers at the N − 1 and N − 2 levels, except where N = 1 or N = 2.Footnote 8

For example, if Red has a duty not to assault Blue (N = 1), and Green has a disability to alter this relation (N = 2), but the Legislator has a power to alter Green’s disability (N = 3), then the Legislator’s power pertains necessarily both to Green’s disability towards Red and Blue, and to Red and Blue’s immunities towards Green. Therefore this third-order power concerns both second-order and first-order parties, even if these individuals are of course comprised in the third-order relation itself as third-order parties, that is, as third-order liability-bearers.Footnote 9 It is also interesting to note that higher-order positions pertaining to any lower-level relation are always held by every Hohfeldian subject, which is why the number of relations grows exponentially except in the trivial case where there is only one Hohfeldian subject. I exemplify this in Fig. 2.

Fig. 2

The recursion of Hohfeldian higher-order entitlements, exemplified up until third order

In the diagram, there exist only three Hohfeldian subjects: Red, Green and Blue. We can see that there are thus 3 s-order relations and 32 = 9 third-order relations—the number of relations (represented by arrows) grows exponentially. In accordance with my way of counting, at a given order the number of relations that pertain to a given base relation is P n1, where P is the number of existing Hohfeldian subjects—that is, entities encompassed in Hohfeldian relations—and n is the order in question. The number of Hohfeldian relations pertaining to a given base relation that exist altogether at n-order and all the orders under it (the so-called partial sum) can be calculated using summation:

$$\mathop \sum \limits_{i = 1}^{n} \left( {P^{i - 1} } \right) = P^{0} + P^{1} + P^{2} + P^{3} + \cdots + P^{n - 1} \quad P \in {\mathbb{N}}^{0}$$

Summation can also show us conclusively the infinite number of Hohfeldian relations that pertain to a given base relation, even where there is only one Hohfeldian subject.Footnote 10 The infinite series below does not have a sum, as it tends to infinity, as long as P ≠ 0 (meaning that there must be at least one Hohfeldian subject; otherwise there are no Hohfeldian relations at all).

$$\mathop \sum \limits_{i = 1}^{\infty } \left( {P^{i - 1} } \right) = P^{0} + P^{1} + P^{2} + P^{3} + \cdots \quad P \in {\mathbb{N}}^{0}$$

Due to the exponential nature of the recursion, I am not certain that the metaphor of a spiral that is used by Simmonds (1995) is the most suitable way of describing this phenomenon; it resembles rather a tree, which is why I will henceforth refer to any series of recursive higher-order modalities that pertain to a given base relation as a recursive tree.

Now that we have specified what the Hohfeldian infinite recursion is all about, we may address Steiner’s arguments.

Coping with the Infinity

Steiner identifies two problems with the Hohfeldian infinite recursion: firstly, it renders the ascertainment of any inalienable right impossible, for there is a never-ending chain of potential powers-to-waive that need to be verified before one can say with certainty that such a right actually exists; secondly, Steiner claims that the infinity entails a contradiction. I will first assess the second claim:

The oddity of this infinite regression essentially derives from the fact that it entails a contradiction. Thus, (1) it is necessarily true—true by definition—that each disability entails one and only one corresponding immunity; (2) therefore it is necessarily true that the number of disabilities is equal to the number of immunities; (3) but in the case of Blue’s allegedly inalienable right, the number of immunities is one less than the number of disabilities, because (a) Blue is a disability-holder, but not an immunity-holder, and (b) all immunity-holders are (allegedly) also disability-holders. (Steiner 2013)

As I have already noted in the ‘Steiner's Argument’ section, this putative contradiction is simply a misapplication of Hohfeld at (3a). Blue is indeed an immunity-holder; in the case of an inalienable claim, Blue holds this immunity M towards himself in the second order, and an immunity-that-M-be-altered towards every Hohfeldian subject in the third order, and so on.Footnote 11 Fig. 2 may bring clarity to why the situation Steiner describes is impossible. Green cannot have an immunity against Blue’s waiving Red’s duty not to assault Blue. In every higher-order relation, there are always three parties—one ‘active’ party (with a power or a disability) and two ‘passive’ partiesFootnote 12 (with liabilities or immunities)—and the passive parties of an N-level relation must be the same as in the N − 1-level relation that the N-level relation pertains to.Footnote 13 In the case of second-order relations, the passive parties must always be the same individuals as the parties in the base relation. As Green is an ‘outsider’ with regard to Red’s duty toward Blue, Green cannot have an immunity in the second order (even though he must have either a second-order power or disability). So there is no contradiction.

What about Steiner’s claim—accepted by Biasetti—that there is necessarily insufficient time to sustain normative systems with infinite recursion? We should firstly note that the Hohfeldian infinite recursion obtains completely, regardless of whether a power-to-waive exists at some point in the tree or not. Except perhaps in very odd normative systems, in any Hohfeldian recursive tree there is always a limited number of powers and an infinite number of disabilities. This fact is wholly independent of the inalienability of rights. Steiner is of course right, to an extent, when stating that ‘endorsers of the belief that there can be inalienable rights […] must either reject the Hohfeldian logic of correlative relations embedded in rights discourse or embrace infinite regressiveness—nonclosurein the sets of rules constituting that domain’ (Steiner 2013, pp. 238–239). This is true insofar as ‘regressiveness’ is understood correctly as ‘recursion’. But this does not only concern those who assert that inalienable rights exist: both the proponents and opponents of the notion of inalienable rights who hope to use the Hohfeldian system must accept the infinity embedded in it.Footnote 14 However, should we be worried about this feature of the system? Steiner thinks so, as does Biasetti, who writes:

Problems arise […] with the ‘vertical’ infinity entailed by the nonclosure of the secondary rules made up of [higher-order positions]. Things get unmanageable with this kind of infinity because it is impossible to determine definitively who is in charge of changing the normative positions. (Biasetti 2015a)

We should firstly note that as we are talking about recursion and not regression, the existence of claims and other first-order positions can easily be established in the Hohfeldian framework. However, what worries Steiner and Biasetti is not the existence of claims but rather the ascertainment of whether such claims are inalienable. According to this line of argument, claims cannot be inalienable, because that would assume a non-closed system, and if we had such a system we would not be able to ascertain the existence of a claim-right. Biasetti even sets out to propose different amendments to the Hohfeldian system to rectify this issue. (Biasetti 2015a, b). These amendments may very well lead to an improved system overall; I cannot address them here. However, the fact that there may be better systems for analysing normative relations does not imply that the Hohfeldian system would be fundamentally defective in any way. In fact, I do not see the Hohfeldian infinite recursion as a problem at all.

Steiner and Biasetti’s way of looking at the matter asserts the primacy of the Hohfeldian system over moral and legal rules and principles. We ought to bear in mind, however, that the Hohfeldian system is merely a tool for modelling rules and principles on the level of individuals. These norms can be formulated in ways that settle the question of how many powers can be found in the higher orders of a recursive tree. Let us take the example of an imaginary constitutional amendment:

  1. 1.

    No human beings that reside in the territory of this country may torture any other human beings that reside in the territory of this country.

  2. 2.

    The duty prescribed in (1) is nonwaivable.

  3. 3.

    This amendment, including this provision, cannot be repealed.

For any two human beings that reside in the territory of the country in question—let us call them H1 and H2—the statute leads to at least the following Hohfeldian positions:

  • H1 is under the duty D to refrain from torturing H2, and H2 has the corresponding claim-right C toward H1 (and vice versa, but I will disregard that here).

  • Every Hohfeldian subject (including H2) has a disability toward H1 and H2 to extinguish D and R.

  • There is an infinite number of disabilities in this recursive tree.

The infinite recursion can therefore easily be formulated as rules using quantifiers such as ‘no one else’, ‘only’ and so on. When such quantifiers are used explicitly or implicitly, there is no need to go through an infinite number of higher-order modalities to ascertain that a right is inalienable. The very meaning of the proposition ‘Right R is inalienable’ implies that powers-to-waive do not exist in the recursive tree in question. (Formally, this can be expressed using first-order predicate logic.)

Steiner proposes that the Hohfeldian ‘nonclosure’ could be resolved if we reject the existence of inalienable rights. This attempt is, however, not successful. Biasetti, on the other hand, correctly identifies infinite recursion as a necessary feature of any Hohfeldian system, but is needlessly troubled about this. As long as the role of the Hohfeldian analysis in normative reasoning is understood correctly, the infinite recursion of higher-order positions is nothing to worry about.


  1. 1.

    These essays are the earliest discussions of which I am aware where the nature of the Hohfeldian recursion has implications for a substantive normative issue. The issue has been addressed in some other writings, but usually very tangentially.

  2. 2.

    For a discussion of the relational nature of Hohfeldian first-order positions, see Van Duffel (2012).

  3. 3.

    This is the so-called correlativity axiom of the Hohfeldian system, according to which duties are always accompanied by claims, and vice versa. This axiom is sometimes questioned. I will not address this discussion in this paper. See Kramer (1998, p. 22).

  4. 4.

    Hohfeld himself would actually have said that a duty always correlates with exactly one claim-right. Here, I am employing Kramer’s modification of Hohfeld, according to which a single duty can correlate with multiple claim-rights. This does not affect my argument.

  5. 5.

    Steiner (2013, p. 233f) addresses the question of how rights should be identified among the Hohfeldian positions.

  6. 6.

    See note 3.

  7. 7.

    It is of course the case that one’s exercise of one’s power is either permitted, required or forbidden (or both required and forbidden). For instance, a judge has not only the power but also the duty to sentence the accused in accordance with the law. However, the judge’s duty to exercise this power is a completely new base relation, with new ensuing recursion: everyone either has the power or the disability to change the judge’s duty, and so on. Duty-claim and liberty-no-right relations are always base relations.

  8. 8.

    I have chosen to represent Hohfeldian higher-order relations as one relation that pertains to three parties: the power-holder and the two liability-bearers. At least two of these parties can be the same individual, for example if one holds a power to change one’s own entitlement. I prefer this way of presentation because every Hohfeldian power or disability always involves the ability or lack of ability to alter two positions. It could also be understood as two separate relations that can only be altered simultaneously.

  9. 9.

    The first-order parties (Red and Blue) are encompassed by the power of the Legislator due to their involvement in the second-order relation. This does not change the fact that the first-order parties and the second-order passive parties (that is, holders of liabilities and/or immunities) must be the same individuals, which is why the passive parties of the third-order relation must include the individuals who are first-order parties.

  10. 10.

    I am assuming here that one can be in a Hohfeldian deontic relation with oneself. This is certainly not logically contradictory, even if it can of course be argued that deontic relations can only exist in a community of individuals.

  11. 11.

    Steiner’s claim that Blue is not an immunity-holder here might stem from the fact that he seems to think that one cannot hold a disability or a power toward oneself, as he points out elsewhere in the article: ‘[W]e need to ask the Hohfeldian question of who holds the immunity correlatively entailed by the disability which this inalienability is. We know that it cannot be the rights-holder him- or herself, since correlativity is a relation obtaining between two different persons: one cannot have rights against oneself’ (Steiner 2013, p. 243). However, it is relatively obvious that one can hold powers toward oneself; otherwise one would be wholly incapable of altering one’s own normative position. It would therefore be odd to argue that one can hold powers toward oneself but not their opposites, disabilities.

  12. 12.

    Using my method of counting the relations, there is one power or disability and two liabilities or immunities. There can just as well be two powers or disabilities; this is simply a matter of bookkeeping.

  13. 13.

    One should bear in mind that the Hohfeldian subject who is the active party can also be (but need not be) either of the passive parties; one may occupy several positions in a single Hohfeldian relation.

  14. 14.

    Biasetti notes this, too: ‘It would seem, therefore, that nonclosure is not an exclusive byproduct of inalienable rights: the Hohfeldian framework is itself nonclosed and naturally entails an infinite number of elements’ (Biasetti 2015a, p. 148).


  1. Biasetti, Pierfrancesco. 2015a. Infinite regress and Hohfeld: A comment on Hillel Steiner’s ‘Directed duties and inalienable rights’. Ethics 126: 139–152.

    Article  Google Scholar 

  2. Biasetti, Pierfrancesco. 2015b. Hohfeldian normative systems. Philosophia. doi:10.1007/s11406-015-9637-z.

    Google Scholar 

  3. Kramer, Matthew H. 1998. Rights without trimmings. In A debate over rights. Philosophical enquiries, ed. Matthew H. Kramer, 7–112. Oxford: Oxford University Press.

    Google Scholar 

  4. Simmonds, N. E. 1995. The analytical foundations of justice. Cambridge Law Journal 54: 306–341.

    Article  Google Scholar 

  5. Steiner, Hillel. 1994. An essay on rights. Oxford: Blackwell.

    Google Scholar 

  6. Steiner, Hillel. 2013. Directed duties and inalienable rights. Ethics 123: 230–244.

    Article  Google Scholar 

  7. Van Duffel, Siegfried. 2012. The nature of rights debate rests on a mistake. Pacific Philosophical Quarterly 93: 104–123.

    Article  Google Scholar 

Download references


I would like to extend my sincere gratitude to my supervisor Matthew Kramer, whose extensive comments on several versions of this paper were highly useful. In addition, I wish to thank Nigel Simmonds for his illuminating observations on the paper and the anonymous reviewer who provided very thorough and detailed comments on the manuscript. The Kone Foundation funds my PhD project for which I am thankful.

Author information



Corresponding author

Correspondence to Visa A. J. Kurki.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kurki, V.A.J. Hohfeldian Infinities: Why Not to Worry. Res Publica 23, 137–146 (2017). https://doi.org/10.1007/s11158-016-9322-5

Download citation


  • Jurisprudence
  • Philosophy of law
  • Rights
  • Wesley Newcomb Hohfeld
  • Inalienable rights
  • Infinite regress