Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary

The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of quantum corrections to the effective action past one-loop necessitates diagramatic techniques. Diagramatic evaluations and higher loop-order renormalisation can be best accomplished on a Riemannian manifold of constant curvature accommodating a boundary of constant extrinsic curvature. In such a context the stated evaluations can be accomplished through a consistent interpretation of the Feynman rules within the spherical formulation of the theory for which the method of images allows. To this effect, the mathematical consequences of such an interpretation are analyzed and the spherical formulation of the Feynman rules on the bounded manifold is, as a result, developed.Comment: 12 pages, references added. To appear in Classical and Quantum Gravit

Miracles, Trust, and Ennui in Barnes’ Predictivism

Eric Barnes’ The Paradox of Predictivism is concerned primarily with two facts: predictivism and pluralism. In the middle part of the book, he peers through these two lenses at the tired realist scarecrow of the no-miracles argument. He attempts to reanimate this weatherworn realist argument, contra suggestions by people like me that it should be abandoned. In this paper, I want to get clear on Barnes’ contribution to the debate. He focuses on what he calls the miraculous endorsement argument, which explains not the success of a specific theory but instead the history of successes for an entire research program. The history of successes is explained by reliable and improving methods, which are the flipside of approximately true background theories. Yet, as Barnes notes, the whole story must begin with methods that are at least minimally reliable. Barnes demands that the realist explain the origin of the minimally reliable take-off point, and he suggests a way that the realist might do so. I contend that his explanation still relies on contingent developments and so fails to completely explain the development of take-off theories. However, this line of argument digs into familiar details of the no-miracles argument and overlooks what’s new in Barnes’ approach. By calling attention to pluralism, he reminds us that we need an account of scientific expertise. This is important, I suggest, because expertise is not indefinite. We do not trust specific experts for everything, but only for things within the bounds of their expertise. Drawing these boundaries relies on our own background theories and is only likely to be reliable if our background theories are approximately true. I argue, then, that pluralism gives us reason to be realists

Risk Regulation and the Faces of Uncertainty

Dr. Walker addresses the difficulty of regulators\u27 working with potentially inaccurate information and clarifies related aspects of decision making by presenting a taxonomy for the kinds of uncertainty inherent in necessarily incomplete data