This essay is excerpted by Nathan Bupp from Paul Kurtz, The Turbulent Universe (Amherst, N.Y.: Prometheus Books, 2013). Copyright ©2013 by the Estate of Paul Kurtz. All rights reserved. Used by permission of the Estate and the publisher, www.prometheusbooks.com.

A real x is -Kurtz random if it is in no closed null set . We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.

We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, (...) or Schnorr random reals. We show that Low(ML, Kurtz) coincides with the non-DNR degrees, while both Low(CR, Kurtz) and Low(Schnorr, Kurtz) are exactly the non-high, non-DNR degrees. (shrink)

Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.

We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness (...) notions going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set. (shrink)

The weakly random reals contain not only the Schnorr random reals as a subclass but also the weakly 1-generic reals and therefore the n -generic reals for every n . While the class of Schnorr random reals does not overlap with any of these classes of generic reals, their degrees may. In this paper, we describe the extent to which this is possible for the Turing, weak truth-table, and truth-table degrees and then extend our analysis to the Schnorr random and (...) hyperimmune reals. (shrink)

We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. (...) If additionally f is known to have bounded variation, then we show f has Luzin’s if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness. (shrink)

We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. (...) If additionally f is known to have bounded variation, then we show f has Luzin’s if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness. (shrink)

A seminal theorem due to Weyl [14] states that if $(a_n)$ is any sequence of distinct integers, then, for almost every $x \in \mathbb{R}$, the sequence $(a_n x)$ is uniformly distributed modulo one. In particular, for almost every $x$ in the unit interval, the sequence $(a_n x)$ is uniformly distributed modulo one for every computable sequence $(a_n)$ of distinct integers. Call such an $x$ UD random. Here it is shown that every Schnorr random real is UD random, but there are (...) Kurtz random reals that are not UD random. On the other hand, Weyl's theorem still holds relative to a particular effectively closed null set, so there are UD random reals that are not Kurtz random. (shrink)

This work contributes to the program of studying effective versions of “almost-everywhere” theorems in analysis and ergodic theory via algorithmic randomness. Consider the setting of Cantor space {0,1}N with the uniform measure and the usual shift. We determine the level of randomness needed for a point so that multiple recurrence in the sense of Furstenberg into effectively closed sets P of positive measure holds for iterations starting at the point. This means that for each k∈N there is an (...) n such that n,2n,…,kn shifts of the point all end up in P. We consider multiple recurrence into closed sets that possess various degrees of effectiveness: clopen, Π10 with computable measure, and Π10. The notions of Kurtz, Schnorr, and Martin-Löf randomness, respectively, turn out to be sufficient. We obtain similar results for multiple recurrence with respect to the k commuting shift operators on {0,1}Nk. (shrink)

The contributors to this volume were asked the following questions: The term "Humanism" is widely used, as are the terms "ethical" Humanism, "scientific" Humanism and "religious" Humanism. What is Humanism? Can you define it? If there is in your judgment no clear definition in the literature, you may wish to propose one. You may also wish to focus on the relationship of Humanism to atheism, science, its ethical position, or some other theme. Those who have contributed represent a wide spectrum (...) of Humanist opinion in the world today. They are primarily philosophers, psychologists, social scientists, ethical and religious leaders. Among the themes they discuss are historic roots of Humanism, the general problem of definition, the relationship of Humanism to ethics and morality, Humanism and religion, Humanism and atheism and Humanism on the world scene. Most of the varieties of Humanism are represented, including naturalistic Humanism, liberal Humanism, atheistic Humanism, humanistic psychology, behaviourism, Marxism, and Zen. If there is a common thread running throughout this volume, it is the conviction that Humanism is committed to the method of reason as the chief means of solving problems and the belief that mankind can survive and humans can enjoy a significant life. This conviction and this belief, however, can be realized only if men continue to have confidence in their own natural powers and abilities and the courage to use them. (shrink)

How does an object persist through change? How can a book, for example, open in the morning and shut in the afternoon, persist through a change that involves the incompatible properties of being open and being shut? The goal of this reader is to inform and reframe the philosophical debate around persistence; it presents influential accounts of the problem that range from classic papers by W. V. O. Quine, David Lewis, and Judith Jarvis Thomson to recent work by contemporary philosophers. (...) The authors take on the question of persistence by examining three broad approaches: perdurantism, which holds that change over time is analogous to change over space; exdurantism, according to which identity over time is analogous to identity across possible worlds; and endurantism, which holds that ordinary objects persist by enduring. Each of these approaches appears to be coherent, but each also has its own metaphysical problems. Persistence includes papers that argue for perdurantism, exdurantism, or endurantism, as well as papers that explore some metaphysical difficulties challenging each account. In this way the collection allows readers to balance the trade-offs of each approach in terms of intuitiveness, theoretical attractiveness, and elegance.Contributors:Yuri Balashov, William Carter, Graeme Forbes, Sally Haslanger, Katherine Hawley, H. S. Hestevold, Mark Hinchliffe, Mark Johnston, Roxanne Marie Kurtz, David K. Lewis, Ned Markosian, D. H. Mellor, W. V. O. Quine, Theodore Sider, Richard Taylor, Judith Jarvis Thomson, Peter van Inwagen, Dean Zimmerman. (shrink)

This book has been written for our time of need. It is an affirmative declaration of human values at a time of crisis in what the author regards as the great moral revolution of our age. It began when Paul Kurtz published the four-page Humanist Manifesto II in The Humanist magazine. The reaction was volcanic. The New York Times carried an extensive front-page story on it, as did hundreds of newspapers throughout the United States and abroad. The controversy is (...) unabated. Theologians throughout the country continue to attack and defend the Manifesto. In Russia, Andrei Sakharov, one of the signers of the Manifesto, was given a warning about his collaboration with Western liberals, and then subjected to a large-scale attack in the Soviet Press. The generative ideas presented in the controversial Manifesto are fully developed in this powerful book. In Part I, Kurtz takes us on a tour of the chief religious and moral philosophies available to Western man at this time. He gives detailed critiques of Christian theism and of Marxism. He shows how the original humanism of Marx has been betrayed in the Communist nations. "The crux of the tragedy of modern Communist societies is that they have abandoned these fundamental human rights . . ." In Part II, "The Humanist Alternative," Kurtz brilliantly develops a positive viewpoint, a dynamic presentation of the elements of "the good life" in which we may realize "the human potential and the fullness of being." The author here describes the virtues of the sensual life, the joys and benefits of physical pleasure, and the various ways by which we achieve true self-realization. This section concludes with chapters on libertarianism, the principle of equality, and the democratic ethic inherent in the humanist philosophy. In Part III the author provides an arresting exposition of international problems and their intelligent solution. He stresses the global consciousness of the humanist outlook and its allegiance to all humanity, and demonstrates how the methods of reason can be applied in our personal lives and in world affairs. (shrink)

SPECIAL SECTION PHYSICIAN-ASSISTED SUICIDE, PRO AND CON.

Editors’ Introduction: Radical Philosophy and Politics Amid the Climate Crisis and the Coronavirus Pandemic for Radical Philosophy Review.

Discussions of reproducibility are casting doubts on the credibility of experimental outcomes in the life sciences. Although experimental evolution is not typically included in these discussions, this field is also subject to low reproducibility, partly because of the inherent contingencies affecting the evolutionary process. A received view in experimental studies more generally is that standardization (i.e., rigorous homogenization of experimental conditions) is a solution to some issues of significance and internal validity. However, this solution hides several difficulties, including a reduction (...) of external validity and reproducibility. After explaining the meaning of these two notions in the context of experimental evolution, we import from the fields of animal research and ecology and suggests that systematic heterogenization of experimental factors could prove a promising alternative. We also incorporate into our analysis some philosophical reflections on the nature and diversity of research objectives in experimental evolution. (shrink)

Do activist trade and industrial policies offer developing countries a viable alternative to either neoliberal or mercantilist development regimes? We hope to answer the question by, first, distinguishing the “open economy industrial policies” in vogue today from either their “closed economy” predecessors—i.e., import-substituting industrialization—or more orthodox approaches to development policy making; second, tracing the growth of nontraditional exports from Latin America and the Caribbean to the diffusion of more active approaches in the 1990s; and, third, accounting for activism’s apparent success (...) in an otherwise inauspicious spatial and temporal context by identifying three distinct limits to rent-seeking in the open economy: infant exporter maturation; the costs of government support; and the reactions of foreign rivals. (shrink)