Default Invariance: Naïve Category of Law and Finance

Default invariance is the idea that default does not change at any scale of law and finance. Default is a conserved quantity in a universe where fundamental principles of law and finance operate. It exists at the micro-level as part of the fundamental structure of every financial transaction, and at the macro- level, as a fixed critical point within the relatively stable phases of the law and finance cycle. A key point is that default is equivalent to maximizing uncertainty at the micro-level and at the macro-level, is equivalent to the phase transition where unbearable fluctuations occur in all forms of risk transformation, including maturity, liquidity and credit. As such, default invariance is the glue that links the micro and macro structures of law and finance. In this essay, we apply naïve category theory (NCT), a type of mapping logic, to these types of phenomena. The purpose of using NCT is to introduce a rigorous (but simple) mathematical methodology to law and finance discourse and to show that these types of structural considerations are of prime practical importance and significance to law and finance practitioners. These mappings imply a number of novel areas of investigation. From the micro- structure, three macro-approximations are implied. These approximations form the core analytical framework which we will use to examine the phenomena and hypothesize rules governing law and finance. Our observations from these approximations are grouped into five findings. While the entirety of the five findings can be encapsulated by the three approximations, since the intended audience of this paper is the non-specialist in law, finance and category theory, for ease of access we will illustrate the use of the mappings with relatively common concepts drawn from law and finance, focusing especially on financial contracts, derivatives, Shadow Banking, credit rating agencies and credit crises.

Giving guilt: the aneconomy of law and justice

The concept of guilt is seen here as debt beyond repayment. Following Derrida, the gesture of giving is placed in the economy of gift, an aneconomical gift that is not part of the exchange cycle. At the same time, guilt is linked to desire, the desire to give and to be free from guilt. Desire is described as the urge to cross over, to apprehend the non-identical and to give oneself away. In this reinforced crossing, where the improbability of giving conditions the improbability of reaching out, guilt and its impetus are found locked up in claustrophobic self-reference. For this reason, the author consults Kierkegaard and Luhmann whose contributions show that the gesture of giving acquires its relevance not so much on account of its recipient, but precisely because of the absence of such a recipient. The combination of an absent recipient and an absented giver fills the gift with an emptiness that can only be channelled back upon itself, in the autopoietics of guilt. This is exactly the fate of the law, which can deal with the guilty but never with guilt (in the above sense). In its attempt to give away guilt, the law attempts to become other than itself: justice. The improbability of crossing over becomes more obvious than ever.

Critical autopoiesis and the materiality of law

Autopoietic theory is increasingly seen as a candidate for a radical theory of law, both in relation to its theoretical credentials and its relevance in terms of new and emerging forms of law. An aspect of the theory that has remained less developed, however, is its material side, and more concretely the theory’s accommodation of bodies, space, objects and their claim to legal agency. The present article reads Luhmann’s theory of autopoietic systems in a radical and material manner, linking it on the one hand to current post-structural theorisations of law and society, and on the other hand extending its ambit to accommodate the influx of material considerations that have been working their way through various other disciplines. The latter comprises both a materialisation of the theory itself and ways of conceptualising the legal system as material through and through. This I do by further developing what I have called Critical Autopoiesis, namely an acentric, topological, post-ecological and posthuman understanding of Luhmann’s theory, that draws on Deleuzian thought, feminist theory, geography, non-representational theory, and new material and object-oriented ontologies. These are combined with some well-rehearsed autopoietic concepts, such as distinction, environment and boundaries; Luhmann’s earlier work on materiality continuum; more recent work on bodies and space; as well as his work on form and medium in relation to art. The article concludes with five suggestions for an understanding of what critical autopoietic materiality might mean for law.

Spacing abstraction: capitalism, law and the metropolis

In considering contemporary accounts of the interrelations of economic, legal and urban forms of social relations in the emergence of a global capitalist modernity, this paper argues that politico-juridical imaginaries of new forms of transnational universality have tended to be limited by virtue of both an anachronistic recourse to spatial models of the polis and a failure to confront the ineliminability of abstraction to any idea of global social interconnectivity. In such terms, it argues, Lefebvre’s famous call for a ‘right to the city’ needs to be reinscribed as a properly modern right to the metropolis; one that would allow us to conceive of the possibility of new kinds of relation between individual and collective subjectivity and the development of abstract social forms.

Spatial justice: law and the geography of withdrawal

While spatial justice could be the most radical offspring of law’s recent spatial turn, it remains instead a geographically informed version of social justice. The majority of the existing literature on the subject has made some politically facile assumptions about space, justice and law, thereby subsuming the potentially radical into the banal. In this article, I suggest that the concept of spatial justice is the most promising platform on which to redefine, not only the connection between law and geography, but more importantly, the conceptual foundations of both law and space. More concretely, the article attempts two things: first, a radical understanding of legal spatiality. Space is not just another parameter for law, a background against which law takes place, or a process that the law needs to take into consideration. Space is intertwined with normative production in ways that law often fails to acknowledge, and part of this article is a re-articulation of the connection. Second, to suggest a conception of spatial justice that derives from a spatial law. Such a conception cannot rely on given concepts of distributive or social justice. Instead, the concept of spatial justice put forth here is informed by post-structural, feminist, post-ecological and other radical understandings of emplacement and justice, as well as arguably the most spatial of philosophical discourses, that of Deleuze–Guattari and the prescribed possibilities of space as manifold.

The sound of a breaking string: critical environmental law and ontological vulnerability

This is a thought-provoking contribution on the space of ontological vulnerability as the awareness of being existentially exposed. This space, conceptualised as a space of ‘the middle’ (as opposed, emphatically, to ‘the centre’) offers an opportunity to think away from the sterile debate on eco/anthropocentricity and from such limiting hierarchies as animal/human, human/environmental, natural/artificial. This new, vulnerable position of the middle allows the reconfiguration of ecological processes, and more specifically the position of environmental law in relation to them. Environmental law now finds itself amidst a new, moving, ‘open ecology’ of social, biological and ecological processes. This is a new, radical conceptualisation of what the author has called ‘critical environmental law,’ based upon an epistemology of observation and an ontology of being part of this open ecology. Environmental law, in this light, is simultaneously reformulated as an invitation to disciplinary and ontological openness and yet a call to remain immanent within existing legal structures. This finds expression in four critical environmental positions that set the stage for the further elaboration of a critical environmental law.