The Fraenkel-Mostowski method has been widely used to prove independence results among weak versions of the axiom of choice. In this paper it is shown that certain statements cannot be proved by this method. More specifically it is shown that in all Fraenkel-Mostowski models the following hold: 1. The axiom of choice for sets of finite sets implies the axiom of choice for sets of well-orderable sets. 2. The Boolean prime ideal theorem implies a weakened form of Sikorski's theorem.

Let NBG be von Neumann-Bernays-Gödel set theory without the axiom of choice and let NBGA be the modification which allows atoms. In this paper we consider some of the well-known class or global forms of the wellordering theorem, the axiom of choice, and maximal principles which are known to be equivalent in NBG and show they are not equivalent in NBGA.

In 1945–46, representatives of the U.S. government made similar discoveries in both Germany and Japan, unearthing evidence of unethical experiments on human beings that could be viewed as war crimes. The outcomes in the two defeated nations, however, were strikingly different. In Germany, the United States, influenced by the Canadian physician John Thompson, played a key role in bringing Nazi physicians to trial and publicizing their misdeeds. In Japan, the United States played an equally key role in concealing information about (...) the biological warfare experiments and in securing immunity from prosecution for the perpetrators. The greater force of appeals to national security and wartime exigency help to explain these different outcomes. (shrink)

We study the relationship between the countable axiom of choice and the Tychonoff product theorem for countable families of topological spaces.

We investigate the set theoretical strength of some properties of normality, including Urysohn's Lemma, Tietze-Urysohn Extension Theorem, normality of disjoint unions of normal spaces, and normality of Fσ subsets of normal spaces.

We show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well-ordered families of sets and the axiom of choice for sets are both true, but the axiom of choice is false.

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2math image and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second.

In Zermelo-Fraenkel set theory with the axiom of choice every set has the same cardinal number as some ordinal. Von Rimscha has weakened this condition to “Every set has the same cardinal number as some transitive set”. In set theory without the axiom of choice, we study the deductive strength of this and similar statements introduced by von Rimscha.

This book is a collection of secondary essays on America's most important philosophic thinkers—statesmen, judges, writers, educators, and activists—from the colonial period to the present. Each essay is a comprehensive introduction to the thought of a noted American on the fundamental meaning of the American regime.

We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.

The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice.

We study the Tychonoff Compactness Theorem for several different definitions of a compact space.

We study the relationship between various properties of the real numbers and weak choice principles.

We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.

This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.

We study the relationships between definitions of compactness in topological spaces and the roll the axiom of choice plays in these relationships.

We study statements about countable and well-ordered unions and their relation to each other and to countable and well-ordered forms of the axiom of choice. Using WO as an abbreviation for “well-orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union (...) of countable sets is WO. (shrink)

In set theory without the Axiom of Choice, we investigate the set-theoretic strength of the principle NDS which states that there is no function f on the set ω of natural numbers such that for everyn ∈ ω, f ≺ f, where for sets x and y, x ≺ y means that there is a one-to-one map g : x → y, but no one-to-one map h : y → x. It is a long standing open problem whether NDS implies (...) AC. In this paper, among other results, we show that NDS is a strong axiom by establishing that ACLO ↛ NDS in ZFA set theory. The latter result provides a strongly negative answer to the question of whether “every Dedekind-finite set is finite” implies NDS addressed in G. H. Moore “Zermelo’s Axiom of Choice. Its Origins, Development, and Influence” and in P. Howard–J. E. Rubin “Consequences of the Axiom of Choice”. We also prove that ACWO ↛ NDS in ZF and that “for all infinite cardinals m, m + m = m” ↛ NDS in ZFA. (shrink)

We provide a general criterion for Fraenkel–Mostowski models of $${\textsf{ZFA}}$$ (i.e. Zermelo–Fraenkel set theory weakened to permit the existence of atoms) which implies “every linearly ordered set can be well ordered” ( $${\textsf{LW}}$$ ), and look at six models for $${\textsf{ZFA}}$$ which satisfy this criterion (and thus $${\textsf{LW}}$$ is true in these models) and “every Dedekind finite set is finite” ( $${\textsf{DF}}={\textsf{F}}$$ ) is true, and also consider various forms of choice for well-ordered families of well orderable sets in these (...) models. In Model 1, the axiom of multiple choice for countably infinite families of countably infinite sets ( $${\textsf{MC}}_{\aleph _{0}}^{\aleph _{0}}$$ ) is false. It was the open question of whether or not such a model exists (from Howard and Tachtsis “On metrizability and compactness of certain products without the Axiom of Choice”) that provided the motivation for this paper. In Model 2, which is constructed by first choosing an uncountable regular cardinal in the ground model, a strong form of Dependent choice is true, while the axiom of choice for well-ordered families of finite sets ( $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ ) is false. Also in this model the axiom of multiple choice for well-ordered families of well orderable sets fails. Model 3 is similar to Model 2 except for the status of $${\textsf{AC}}^{{\textsf{WO}}}_{{\textsf{fin}}}$$ which is unknown. Models 4 and 5 are variations of Model 3. In Model 4 $${\textsf{AC}}_{\textrm{fin}}^{{\textsf{WO}}}$$ is true. The construction of Model 5 begins by choosing a regular successor cardinal in the ground model. Model 6 is the only one in which $$2{\mathfrak {m}} = {\mathfrak {m}}$$ for every infinite cardinal number $${\mathfrak {m}}$$. We show that the union of a well-ordered family of well orderable sets is well orderable in Model 6 and that the axiom of multiple countable choice is false. (shrink)

Paul C. Taylor provides an accessible guide to a well-travelled but still-mysterious area of the contemporary social landscape. The result is the first philosophical introduction to the field of race theory and to a non-biological and situational notion of race. Provides the first philosophical introduction to the field of race theory. Outlines the main features and implications of race-thinking; asks questions such as: What is race-thinking? Don’t we know better than to talk about race now? Are there any races? (...) What is it like to have a racial identity? Engages with the ideas of such important figures as Linda Alcoff, K. Anthony Appiah, W.E.B. Du Bois, Howard Winant, and Naomi Zack. Explores the enduring significance of race in relation to culture, personal relationships and social justice. (shrink)

Teaching at a private, conservative religious institution poses unique challenges for equality, diversity, and inclusivity education (EDI). Given the realities of the student population in the Honors College of a private, religious institution, it is necessary to first introduce students to the contemporary realities of inequality and oppression and thus the need for EDI. This chapter proposes a conceptual framework and pedagogical suggestions for teaching basic concepts of social justice in a team-taught, interdisciplinary social science course. The course integrates four (...) different approaches to justice: theoretical, social scientific, narratological, and experiential. The discussion of the experiential dimension of the course references practical pedagogical strategies for making social justice and inequality real for our students. Understanding the realities of social inequality and its roots can foster a better understanding of the social forces and structures that perpetuate inequality. Furthermore, this approach can plant the intellectual and empathic seeds to challenge in-group bias and hopefully germinate into fruitful interaction with diverse others. Finally, this rich, interdisciplinary encounter with social inequality and justice can prepare students to work for just social structures that will lead to a more inclusive world. (shrink)

Religion, reason, and the enchanted public sphere -- Minor protest(ant)s: Cohen and German-Jewish liberalism -- The dialectic of enchantment: science, religion, and secular reasoning -- Rights, religion, and race: Cohen's ethical socialism and the specter of anti-Semitism -- Enchanted reasoning: self-reflexive religion and minority -- Some minor reflections of enchantment.

At the end of the nineteenth century, Ludwig Edinger completed the first comparative survey of the microscopic anatomy of vertebrate brains. He is regarded as the founder of the field of comparative neuroanatomy. Modern commentators have misunderstood him to have espoused an anti-Darwinian linear view of brain evolution, harkening to the metaphysics of the scala naturae. This understanding arises, in part, from an increasingly contested view of nineteenth-century morphology in Germany. Edinger did espouse a progressionist, though not strictly linear, view (...) of forebrain evolution, but his work also provided carefully documented evidence that brain stem structures vary in complexity independently from one another and across species in a manner that is not compatible with linear progress. This led Edinger to reject progressionism for all brain structures other than the forebrain roof, based on reasoning not too dissimilar from those his successors used to dismiss it for the forebrain roof. (shrink)

Originally published in 1971 by Winthrop Publishers, Inc., this volume provides a discussion and analysis of the theory of natural law as it appears in contemporary political and social thought. This theory of natural law was used from the fifth century B.C. until the end of the eighteenth century to provide a universal, rational standard to determine the nature and limits of political obligation, the evaluation of competing forms of government, and the relation of law and politics to morals.

The development of evolutionary approaches to psychology from Classical Ethology through Sociobiology to Evolutionary Psychology is outlined and the main tenets of today's Evolutionary Psychology briefly examined: the heuristic value of evolutionary thinking for psychology, the massive modularity thesis and the monomorphic mind thesis.

The sociotechnical domain is the realm of scientists, the communities and institutions they form, and the tools and instruments they use to create, disseminate, and preserve knowledge. This paper reviews current scientonomic theory concerning this domain. A core scientonomic concept is that of an epistemic agent. Generally, an agent is an entity capable of intentional action—action that has content or meaning due to its purposeful direction towards a goal. An epistemic agent is one whose actions are the taking of epistemic (...) stances, such as acceptance or rejection, towards epistemic elements, like theories or questions. An epistemic agent must semantically understand the propositions in question, and their alternatives, and choose among them with reason, with the motive of acquiring knowledge. The most obvious example of an epistemic agent is an individual human being. Rejecting the network of practitioners view, current scientonomic theory argues that appropriately organized communities of scientists can also function as epistemic agents. Communal epistemic agents are of particular scientonomic importance. Whereas the methods of theory assessment of individual scientists can be idiosyncratic, scientonomic theory contends that the taking of epistemic stances by scientific communities is a lawful, rule governed process. A second concept of central importance is that of an epistemic tool. A physical object or system is an epistemic tool for some epistemic agent if there is a procedure by which the tool can provide an acceptable source of knowledge under the method employed by that agent. (shrink)

Paul E. Griffiths argues that most research on the emotions has been as misguided as Aristotelian efforts to study "superlunary objects" - objects...

Although physicalism has been the dominant position in recent work in the philosophy of mind, this dominance has not prevented a small but growing number of philosophers from arguing that physicalism is untenable for several reasons: both ontologically and epistemologically it cannot reduce mentality to the realm of the physical, and its attempts to reduce subjectivity to objectivity have thoroughly failed. The contributors to After Physicalism provide powerful alternatives to the physicalist account of the human mind from a dualistic point (...) of view and argue that the reductive and naturalistic paradigm in philosophy has lost its force. The essays in this collection all firmly engage in a priori metaphysics. Those by Uwe Meixner, E. J. Lowe, John Foster, Alvin Plantinga, and Richard Swinburne are concerned with ways to establish the truth of dualism. Essays by William Hasker, A. D. Smith, and Howard Robinson deal with the relation between physicalism and dualism. Benedikt Paul Göcke argues that the “I” is not a particular and Stephen Priest that “I have to understand myself not as a thing but as no-thing-ness.” In the final essay, Thomas Schärtl argues that there are limits to dualism as indicated by the concept of resurrection. By including two classical essays by Plantinga and Swinburne, the volume conveniently brings together some of the best and the newest thinking in making the philosophical case for dualism. "Seven of these essays are by eminent philosophers: Lowe, Foster, Plantinga, Swinburne, Hasker, Smith, and Robinson, each recapitulating his well-known position in the debate. To have these seven essayists together under one cover constitutes a remarkable book, which can be used as a textbook in philosophy of mind as well as in philosophy of religion courses, and which also opens up the debate in an original way among colleagues at an advanced level." —Fergus Kerr, University of Edinburgh. (shrink)

The relationship between individuals’ creativity and their ethical ideologies appears to be complex. Applying Forsyth’s (1980, 1992) personal moral philosophy model which consists of two independent ethical ideology dimensions, idealism and relativism, we hypothesized and found support for a positive relationship between creativity and relativism. It appears that creative people are less likely than non-creative people to follow universal rules in their moral decision making. However, contrary to our hypothesis and the general stereotype that creative people are less caring about (...) others, we found a positive relationship between creativity and idealism. These findings indicate that highly creative people are likely to be what Forsyth called “situationists,” individuals with both an ethic of caring and a pragmatic moral decision-making style. The finding that creative individuals tend to be situationists, and particularly that they tend to be high in idealism, appears to refute the line of reasoning that argues for a “creative personality” characterized in part by social insensitivity. Understanding the relationship between creativity and ethical ideologies has important implications for researchers, managers and teachers. (shrink)