It is my hope that the book will be widely read and debated."--Axel Leijonhufvud, UCLA and the University of Trento "This is a major and controversial contribution to macroeconomics that cannot fail to make an impact in several areas.

Purpose This paper aims to formalize long-term trajectories of human civilization as a scientific and ethical field of study. The long-term trajectory of human civilization can be defined as the path that human civilization takes during the entire future time period in which human civilization could continue to exist. -/- Design/methodology/approach This paper focuses on four types of trajectories: status quo trajectories, in which human civilization persists in a state broadly similar to its current state into the distant future; catastrophe (...) trajectories, in which one or more events cause significant harm to human civilization; technological transformation trajectories, in which radical technological breakthroughs put human civilization on a fundamentally different course; and astronomical trajectories, in which human civilization expands beyond its home planet and into the accessible portions of the cosmos. -/- Findings Status quo trajectories appear unlikely to persist into the distant future, especially in light of long-term astronomical processes. Several catastrophe, technological transformation and astronomical trajectories appear possible. -/- Originality/value Some current actions may be able to affect the long-term trajectory. Whether these actions should be pursued depends on a mix of empirical and ethical factors. For some ethical frameworks, these actions may be especially important to pursue. (shrink)

This paper argues that contemporary macroeconomic and finance models suffer from insuperable epistemological flaws and that their empirical difficulties – which are particularly apparent in modeling market participants' expectations – can be traced to economists' core premise that they can adequately specify in probabilistic terms how individuals alter the way they make decisions and how the processes underpinning market outcomes unfold over time. We refer to such accounts of change as determinate. The first part examines how this core premise has (...) derailed the development of macroeconomic analysis for the last four decades. The second part sketches how imperfect knowledge economics (IKE) jettisons conventional models' core premise and how doing so helps to overcome these models' epistemological flaws. By opening economic models to change, that is, at least in part, indeterminate, and by recognizing imperfect knowledge on the part of economists, IKE explores the frontier of what empirically relevant mathematical macroeconomic and finance models can deliver. (shrink)

This note focuses on George Soros's challenge to macroeconomics and finance theory that any valid methodology of social science must explicitly recognize fallibility in a Knightian sense. We use a simple algebraic example to sketch how extant models formalize fallibility. We argue that contemporary theory's epistemological and empirical difficulties can be traced to assuming away fallibility in a Knightian sense. We also discuss how imperfect knowledge economics provides a way to open mathematical models to such fallibility, while preserving economics as (...) an empirical science. (shrink)

In the Catholic understanding of grace perfecting nature, revelation must protect the truths reason might know when reason is in its healthy state, lest reason lose those truths if it lapses into an unhealthy state. For this reason, the supernatural is always part of the definition of the natural, and not just for Christians but for all human beings.

We determine the bivariate probability densities with specified margins and show that the Cohen-Zaparovanny class of positive phase-space density functions, with the quantum mechanical marginal distributions of position and momentum, contains all such densities.

This volume of thirteen essays originated in a conference on Latin philosophy at Columbia University, organized by the editors in 2012. The guiding principle was to examine how writing philosophy in Latin gave a distinctive character to Roman philosophical thinking. The conference was interdisciplinary, involving philosophers and literary scholars, some interested in ancient history as well. In publishing the papers, the editors had in mind as a model Philosophia Togata I and II, the second volume of which is almost (...) twenty years old. More up to date, this volume also aims to fill gaps in the earlier enterprise by devoting one of the four parts to Seneca, not treated as a separate topic there, and by going beyond... (shrink)