Matthias and I clearly agree on a great deal: a voluntarist approach to defining public international law is unsatisfactory; any rule of recognition in international law must provide a basis for a link between legality and legitimacy; one of the central contributions that law can make to international society is procedural in nature. However, our respective positions on the utility of a binary distinction between law and not-law have significant impacts on our approaches. We are both concerned, I think, with preserving the autonomy of politics – with ensuring that politics (or, more specifically, international public authority) do not come to be invaded by law. My own concern with preserving the autonomy of law leads me to two conclusions with which Matthias would take issue: that international public authority must be constituted by law; and that the rules which those authorities administer must be treated differently, depending on whether or not they meet a set of formal criteria that legal rules must satisfy. I will also address Matthias's discussion of Lon L. Fuller's internal morality of law and Benedict Kingsbury's concept of publicness in international law. I believe that both sets of concepts may be useful to Matthias's argument and deserve further attention. First, however, I would like to explore what it means, or could mean, to cut off the head of the king.

As noted, both Matthias and I are unconvinced by the prevailing rule of recognition in public international law, grounded in state consent. This I take to be one of the implications of the proposition that we should cut off the head of the king: state consent ought not to be the basis for the validity of legal rules. For Matthias, law, or at least a part of what constitutes law, is defined in functional terms. Distinctions between law (on a voluntarist conception) and not-law are critiqued for their inability to draw attention to any meaningful difference. If I have understood correctly, Matthias would have the definition of law encompass rules that pass muster on a voluntarist conception as well as instruments adopted by international public authorities that, in terms of what they purport to accomplish and how they operate, are not different from state-based law in any meaningful way. But, once this move is accomplished, a second move occurs: the rules, standards, principles, guidelines, etc. that comprise the tools of the trade of international public authorities are removed from the realm of law. Public authority is to be made independent of law – another way in which to understand the proposition that the king must lose his head.

What does it mean to make public authority independent of law? Central to Matthias's argument is that law does not cease to be relevant to exercises of public authority. On the contrary, the legitimacy of exercises of public authority is assessed with the aid of legal rules. One implication is that international public authority is no longer to be seen as constituted by law, though I may be taking Matthias's argument too far here. Matthias wishes to discharge law ‘from the function of identifying authoritative from non-authoritative acts’ and ‘from the function of defining and delimiting the realm of international public authority’. Given Matthias's concern with the legitimacy of public authority, however, this would beg the question as to how public authority is to be constituted.

The main role for law in Matthias's schema is procedural. Law is the main vehicle through which the legitimacy of exercises of international public authority is assured. The rules, standards, and principles against which such exercises are measured are subject to scrutiny through discursive processes. Matthias notes that they could be adopted through the usual channels and become binding international law; it is not clear whether they must have formal, binding status in order to be considered valid rules for the review of exercises of authority, but it would appear that Matthias is more concerned with the legitimacy of these rules, as determined through discursive processes, than with their formal validity. In addition, given his suspicion of the voluntarist conception of international law, and his embrace of discourse as a means of testing the legitimacy of rule candidates, it seems unlikely that his procedural rules would need to have been accepted as binding by states.

One curious aspect of Matthias's argument is his ultimate rejection of Lon Fuller's approach. He acknowledges its promise but ultimately concludes that its standards are too low: in particular, he points to the lack of attention to ‘overlapping or unclear competencies, lack of procedural fairness, judicial review, or adequate representation or participation’. This is quite true, but Fuller's eight criteria are not meant to ensure legitimacy of exercises of authority by public officials – they are criteria for law's internal morality. In any event, Matthias is in good company in his assessment of Fuller's criteria as necessary but not sufficient. Kingsbury and Klabbers, though sympathetic to Fuller's approach, ultimately feel the need to supplement it with a range of other criteria, but this is, at least in part, because these scholars are concerned to maintain the binary distinction between law and not-law, though they seek to identify a new rule of recognition for public international legal rules, being unsatisfied, for different reasons, with the voluntarist approach. Fuller was not particularly concerned about this binary distinction; nor is Matthias. The main role that Matthias grants to law is to provide a means for testing the legitimacy of exercises of international public authority. Matthias could potentially adopt Fuller's approach, emphasizing the interactional aspect, described by Brunnée and Toope in the following terms:

The interactional element in Fuller's thought makes ample room for the discursive processes that Matthias wishes to rely upon to vet the rules through which the legitimacy of exercises of public authority is tested. Fuller's approach would also permit the identification of a rule of recognition that does not depend on state consent, and which would therefore admit into the circle of law a range of rules and instruments currently classified as ‘soft law’. Finally, Fuller's approach is highly attentive to concerns about legitimacy. In short, it seems to be an excellent starting point for accomplishing the range of objectives that Matthias wishes a definition of law to achieve.

My reason for looking beyond Fuller is that I wish to maintain a binary distinction between law and not-law, though I fully share Matthias's concerns with a voluntarist approach to the definition of that boundary. Matthias's arguments against the binary approach do not allay my concerns, partly because he does not paint the advantages of the elimination of the boundary in particularly vivid colours, and partly because I feel he does not adequately address the concerns of those scholars, notably Brunnée, Kingsbury, Klabbers, Koskenniemi, and Toope, who, while supporting a binary distinction between law and not-law, are not satisfied with a voluntarist approach to the rule of recognition. More particularly, I do not believe that Matthias's restricted role for law is the best way to protect the autonomy of politics. The autopoietic conception of the constitution as a structural coupling between law and politics, allowing each to make vital contributions to the other while at the same time preserving the autonomy of both, strikes me as a much better way to achieve one of Matthias's central objectives, ensuring the legitimacy of exercises of public authority.

I mentioned above a doubt as to the means by which international public authority is to be constituted. Here, again, I feel that Matthias may have been too quick to set aside a particularly promising approach, namely Kingsbury's criterion of publicness, which is a viable alternative to a state-centric approach to the constitution of international public authorities. Matthias raises a range of concerns with Kingsbury's approach, notably the apparent circularity of the proposition that actors accept the obligation to respect the principles of publicness when they purport to make law – what is the source of the principles? A way out of this dilemma is presented, I believe, by reference to discursive processes: the principles are not formally binding legal rules, but propositions that must be tested discursively. Like Fuller's eight criteria, they emerge through complex processes of induction, deduction, experience, research, and judgement.

Having dwelt on some important points of divergence in our approaches, I now return to the matter of convergence. The role that Matthias identifies for law – a series of standards or principles used to test the legitimacy of exercises of international public authority – strikes me as a role that law is particularly well suited to play. The expectations that have been heaped on international law's slender shoulders are very often excessive. In my own field, international environmental law, these expectations have tended to lead to an explosion of droit matériel – of substantive, often highly detailed, technical rules that give the impression of identifying boundaries between sustainable and unsustainable activities. The grand principles of international environmental law, such as precaution or common but differentiated responsibilities, are often denigrated for being insufficiently operationalized – for failing to spell out to actors what to do and not to do. Yet, under conditions of scientific uncertainty, and in a society as heterogeneous as international society, it cannot be the function of law to provide the answers to questions about whether a particular use of a water resource is reasonable and equitable, or whether a particular state must or must not adopt a greenhouse-gas emission-reduction target. One of the great strengths of literature on global administrative law and international public authority is the emphasis that is placed on what law can do, and can do well. It is particularly well suited to doing just what Matthias argues should be its central preoccupation, namely providing guidelines, standards, and criteria against which the exercise of international public authority is to be judged.

What attitude to adopt towards soft law? Is it a danger to the integrity of law, to be strenuously resisted, or a part of law, to be embraced? The answer to this question may well be of secondary importance. One of the most important roles of soft law for public international law appears to be to provoke investigation into, and debate about, the nature, sources, validity, and legitimacy of law.