Nondeterminacy and Population Ethics

This paper synthesizes a general view out of Derek Parfit’s last views on how to avoid the Repugnant Conclusion and presents the general features of a plausible theory of population ethics based on Parfit’s suggestions. The paper argues that a plausible population axiology provides only partial orderings and implies that some outcomes are nondeterminate in their ranking. The paper shows, first, how the combination of what Parfit calls “imprecise equality” and the “Wide Dual Person-Affecting Principle” allows one to avoid both the Continuum Argument and the Improved Mere Addition Paradox. Second, the paper shows how this is enough to in principle also refute Gustaf Arrhenius’s impossibility theorems. Third, the paper suggests that a plausible population axiology must allow for nondeterminacy, that whatever the substance of the axiology is, it can only provide partial orderings of outcomes, and that if we revise Arrhenius’s adequacy conditions these can condition what a satisfactory population axiology looks like. Finally, the paper illustrates how one can apply normative theories that allow for nondeterminacy and also infer formal constraints on the theories in light of the consequences of their application.

How Hard to Tell? Complexity of Belief Manipulation Through Propositional Announcements

Consider a set of agents with initial beliefs and a formal operator for incorporating new information. Now suppose that, for each agent, we have a formula that we would like them to believe. Does there exist a single announcement that will lead all agents to believe the corresponding formula? This paper studies the problem of the existence of such an announcement in the context of model-preference definable revision operators. First, we provide two characterisation theorems for the existence of announcements: one in the general case, the other for total partial orderings. Second, we exploit the characterisation theorems to provide upper bound complexity results. Finally, we also provide matching optimal lower bounds for the Dalal and Ginsberg operators.

Generalized derivatives and optimization problems for n-dimensional fuzzy-number-valued functions

In this paper, we present the concepts of generalized derivative, directional generalized derivative, subdifferential and conjugate for n-dimensional fuzzy-number-valued functions and discuss the characterizations of generalized derivative and directional generalized derivative by, respectively, using the derivative and directional derivative of crisp functions that are determined by the fuzzy mapping. Furthermore, the relations among generalized derivative, directional generalized derivative, subdifferential and convexity for n-dimensional fuzzy-number-valued functions are investigated. Finally, under two kinds of partial orderings defined on the set of all n-dimensional fuzzy numbers, the duality theorems and saddle point optimality criteria in fuzzy optimization problems with constraints are discussed.

Babbitt’s Beguiling Surfaces, Improvised Inside; Part III: Opportunities

Babbitt’s relatively early composition Semi-Simple Variations (1956) presents intriguing surface patterns that are not determined by its pre-compositional plan, but rather result from subsequent “improvised” decisions that are strategic. This video (the third of a three-part video essay) considers Babbitt’s own conversational pronouncements (in radio interviews) together with some particulars of his life-long musical activities, that together suggest uncanny affiliations to jazz improvisation. As a result of Babbitt’s creative reconceptualizing of planning and spontaneity in music, his pre-compositional structures (partial orderings) fit in an unexpected way into (or reformulate) the ecosystem relating music composition to the physical means of its performance.