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.

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 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.

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.

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.

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.

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.

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

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)

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

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)

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)

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)

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

Many of the most important properties of human groups – including properties that may give one group an evolutionary advantage over another – are properly defined only at the level of group organization. Yet at present, most work on the evolution of culture has focused solely on the transmission of individual-level traits. I propose a conceptual extension of the theory of cultural evolution, particularly related to the evolutionary competition between cultural groups. The key concept in this extension is the emergent (...) group-level trait. This type of trait is characterized by the structured organization of differentiated individuals and constitutes a unit of selection that is qualitatively different from selection on groups as defined by traditional multilevel selection theory. As a corollary, I argue that the traditional focus on cooperation as the defining feature of human societies has missed an essential feature of cooperative groups. Traditional models of cooperation assume that interacting with one cooperator is equivalent to interacting with any other. However, human groups involve differential roles, meaning that receiving aid from one individual is often preferred to receiving aid from another. In this target article, I discuss the emergence and evolution of group-level traits and the implications for the theory of cultural evolution, including ramifications for the evolution of human cooperation, technology, and cultural institutions, and for the equivalency of multilevel selection and inclusive fitness approaches. (shrink)

In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordinary logic (...) of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if <em>x</em> doesn't exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it. (shrink)

The etiological approach to ‘proper functions’ in biology can be strengthened by relating it to Robert Cummins' general treatment of function ascription. The proper functions of a biological trait are the functions it is assigned in a Cummins-style functional explanation of the fitness of ancestors. These functions figure in selective explanations of the trait. It is also argued that some recent etiological theories include inaccurate accounts of selective explanation in biology. Finally, a generalization of the notion of selective explanation allows (...) an analysis of the proper functions of human artifacts. (shrink)

Some ‘naturalist’ accounts of disease employ a biostatistical account of dysfunction, whilst others use a ‘selected effect’ account. Several recent authors have argued that the biostatistical account offers the best hope for a naturalist account of disease. We show that the selected effect account survives the criticisms levelled by these authors relatively unscathed, and has significant advantages over the BST. Moreover, unlike the BST, it has a strong theoretical rationale and can provide substantive reasons to decide difficult cases. This is (...) illustrated by showing how life-history theory clarifies the status of so-called diseases of old age. The selected effect account of function deserves a more prominent place in the philosophy of medicine than it currently occupies. _1_ Introduction _2_ Biostatistical and Selected Effect Accounts of Function _3_ Objections to the Selected Effect Account _3.1_ Boorse _3.2_ Kingma _3.3_ Hausman _3.4_ Murphy and Woolfolk _4_ Problems for the Biostatistical Account _4.1_ Schwartz _5_ Analysis versus Explication _6_ Explicating Dysfunction: Life History Theory and Senescence _7_ Conclusion. (shrink)