Important, unimportant a critical anticipation of the assumptions of legal positivism in Alice in Wonderland

Almost a full century separates Lewis’ Alice in Wonderland (1865) and the second, lengthier and more elaborate edition of Hans Kelsen’s Pure Theory of Law (1960; first edition published in 1934). And yet, it is possible to argue that the former anticipates and critically addresses many of the philosophical assumptions that underlie and are elemental to the argument of the latter. Both texts, with the illuminating differences that arise from their disparate genre, have as one of their key themes norms and their functioning. Wonderland, as Alice soon finds out, is a world beset by rules of all kinds: from the etiquette rituals of the mad tea-party to the changing setting for the cricket game to the procedural insanity of the trial with which the novel ends. Pure Theory of Law, as Kelsen emphatically stresses, has the grundnorm as the cornerstone upon which the whole theoretical edifice rests2. This paper discusses some of the assumptions underlying Kelsen’s argument as an instance of the modern worldview which Lewis satirically scrutinizes. The first section (Sleepy and stupid) discusses Lewis critique of the idea that, to correctly apprehend an object (in the case of Kelsen’s study, law), one has to free it from its alien elements. The second section (Do bats eat cats?) discusses the notion of systemic coherence and its impact on modern ways of thinking about truth, law and society. The third section (Off with their heads!) explores the connections between readings of systems as neutral entities and the perpetuation of political power. The fourth and final section (Important, Unimportant) explains the sense in which a “critical anticipation” is both possible and useful to discuss the philosophical assumptions structuring some positivist arguments. It also discusses the reasons for choosing to focus on Kelsen’s work, rather than on that of Lewis’ contemporary, John Austin, whose The Province of Jurisprudence Determined (published in 1832) remains influential in legal debates today.

Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.