Decision-Theoretic Consequentialism and the Desire-Luck Problem

Jackson (1991) proposes an interpretation of consequentialism, namely, the Decision Theoretic Consequentialism (DTC), which provides a middle ground between internal and external criteria of rightness inspired by decision theory. According to DTC, a right decision either leads to the best outcomes (external element) or springs from right motivations (internal element). He raises an objection to fully external interpretations, like objective consequentialism (OC), which he claims that DTC can resolve. He argues that those interpretations are either too objective, which prevents them from giving guidance for action, or their guidance leads to wrong and blameworthy actions or decisions. I discuss how the emphasis on blameworthiness in DTC constraints its domain to merely the justification of decisions that relies on rationality to provide a justification criterion for moral decisions. I provide examples that support the possibility of rational but immoral decisions that are at odds with DTC’s prescription for right decisions. Moreover, I argue what I call the desire-luck problem for the external element of justification criterion leads to the same objection for DTC that Jackson raised for OC. Therefore, DTC, although successful in response to some objections, fails to provide a prescription for the right decision

On matrix differential equations in the Hopf algebra of renormalization

We establish Sakakibara's differential equations in a matrix setting for the counter term (respectively renormalized character) in Connes-Kreimer's Birkhoff decomposition in any connected graded Hopf algebra, thus including Feynman rules in perturbative renormalization as a key example.Comment: 22 pages, typos correcte

The splitting process in free probability theory

Free cumulants were introduced by Speicher as a proper analog of classical cumulants in Voiculescu's theory of free probability. The relation between free moments and free cumulants is usually described in terms of Moebius calculus over the lattice of non-crossing partitions. In this work we explore another approach to free cumulants and to their combinatorial study using a combinatorial Hopf algebra structure on the linear span of non-crossing partitions. The generating series of free moments is seen as a character on this Hopf algebra. It is characterized by solving a linear fixed point equation that relates it to the generating series of free cumulants. These phenomena are explained through a process similar to (though different from) the arborification process familiar in the theory of dynamical systems, and originating in Cayley's work