The Problem of Ignorance

Holly Smith (2014) contends that subjective deontological theories – those that hold that our moral duties are sensitive to our beliefs about our situation – cannot correctly determine whether one ought to gather more information before acting. Against this contention, I argue that deontological theories can use a decision-theoretic approach to evaluating the moral importance of information. I then argue that this approach compares favourably with an alternative approach proposed by Philip Swenson (2016)

The prospects for mathematical logic in the twenty-first century

The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.Comment: Association for Symbolic Logi

Measure Recognition Problem

This is an article in mathematics, specifically in set theory. On the example of the Measure Recognition Problem (MRP) the article highlights the phenomenon of the utility of a multidisciplinary mathematical approach to a single mathematical problem, in particular the value of a set-theoretic analysis. MRP asks if for a given Boolean algebra \algB and a property $\Phi$ of measures one can recognize by purely combinatorial means if \algB supports a strictly positive measure with property $\Phi$. The most famous instance of this problem is MRP(countable additivity), and in the first part of the article we survey the known results on this and some other problems. We show how these results naturally lead to asking about two other specific instances of the problem MRP, namely MRP(nonatomic) and MRP(separable). Then we show how our recent work D\v zamonja and Plebanek (2006) gives an easy solution to the former of these problems, and gives some partial information about the latter. The long term goal of this line of research is to obtain a structure theory of Boolean algebras that support a finitely additive strictly positive measure, along the lines of Maharam theorem which gives such a structure theorem for measure algebras

Is the dream solution to the continuum hypothesis attainable?

The dream solution of the continuum hypothesis (CH) would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set theory, a missing axiom, widely regarded as true. Such a dream solution would indeed be a solution, since we would all accept the new axiom along with its consequences. In this article, however, I argue that such a dream solution to CH is unattainable. The article is adapted from and expands upon material in my article, "The set-theoretic multiverse", to appear in the Review of Symbolic Logic (see arXiv:1108.4223).Comment: This article is based upon an argument I gave during the course of a three-lecture tutorial on set-theoretic geology at the summer school "Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments", at the University of London, Birkbeck in August 201

The river sharing problem: A review of the technical literature for policy economists

Water is essential for life. However, the basic problem of water resource allocation has been that water tends to be over-allocated. Demand for water exceeds the available supply. Essentially, the water economy is bankrupt. Bankruptcy problems have been almost exhaustively studied in the literature on economic theory-primarily from the perspective of cooperative game theory. The main concern of this literature has been how to fairly divide up the assets of a bankrupt entity. In water resource economics cooperative game theory has often been employed as a means of analyzing water resource allocation. It was only recently that the problem of directional flow was incorporated into such analyses. This has come to be known as the “river sharing problem” in the theoretical literature. Accounting for the direction of flow in water resource allocation problems has profound implications for policies that wish to facilitate both fair and efficient water allocations. This is the case whether proposed policies are interventionist or market based in nature. There is now a considerable literature on the allocation and distribution of water resources characterized by unidirectional flow. In this paper I critically review and appraise this literature with a view to making it more accessible to applied and policy economists. A key feature of the paper is that the connection between the bankruptcy literature, which has recently also realized the importance of flow, and the river sharing literature is discussed. The current state of the art in game theoretic models of water resource allocation with directional flow is discussed and implications and consequences for water resource policy highlightedRiver sharing problem, Bankruptcy, Cooperative game theory, Water resouyrce allocation, distributive justice

Universal Dynamic Complexity as the Basis for Theoretic Ecology and Unified Civilisation Transition to Creative Global Sustainability

The recently proposed new, universally applicable, rigorously derived and reality-based concept of dynamic complexity provides a unified basis for the causally complete understanding of any real, multi-component and multi-level system of interacting entities, including the case of earth system and global civilisation development. This crucial extension with respect to other existing notions of complexity is obtained due the unrestricted, universally nonperturbative analysis of arbitrary interaction process leading to the new, rigorously derived concept of dynamically multivalued (redundant) entanglement of interacting components. Any real system with interaction is described as a sequence of autonomously emerging "levels of complexity", where each level includes unceasing, dynamically random change of multiple system configurations, or "realisations", each of them resulting from dynamic entanglement of interaction components coming, generally, from lower complexity levels. Dynamic complexity as such is universally defined as a growing function of the number of those explicitly obtained system realisations (or related rate of their change). Mathematically rigorous, realistic and universal nature of unreduced dynamic complexity determines its unique role as a basis for theoretical ecology. This conclusion is confirmed by several directions of universal complexity application to global change understanding and monitoring. They include the rigorously substantiated necessity of civilisation transition to the superior level of complexity involving new, intrinsically unified and causally complete kind of knowledge (initiated by the "universal science of complexity"), qualitatively new kind of material production, social structure, and infrastructure. We show why that new level of civilisation development is intrinsically "sustainable", i. e. characterised by creative, complexity-increasing interaction between "production" and "natural resources" that replaces current contradiction between them