Humankind : a limited company? -- From volume to point: 1. Philosophy, 2. Religion -- Science : specialised but not special -- Cosmic hierarchies -- Consciousness -- Cognition -- In theory -- Back to Genesis -- The beautiful union.

The volume is a collection of essays devoted to the analysis of scientific change and stability. It explores the balance and tension that exist between commensurability and continuity on the one hand, and incommensurability and discontinuity on the other. Moreover, it discusses some central epistemological consequences regarding the nature of scientific progress, rationality and realism. In relation to these topics, it investigates a number of new avenues, and revisits some familiar issues, with a focus on the history and philosophy of (...) physics, and an emphasis on developments in cognitive sciences as well as on the claims of “new experimentalists”. The book constitutes fully revised versions of papers which were originally presented at the international colloquium held at the University of Nancy, France, in June 2004. (shrink)

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)

For many people the existence of God is by no means a sufficiently clear feature of reality. This problem, the fact of divine hiddenness, has been a source of existential concern and has sometimes been taken as a rationale for support of atheism or agnosticism. In this collection of essays, a distinguished group of philosophers of religion explore the question of divine hiddenness in considerable detail. The issue is approached from several perspectives including Jewish, Christian, atheist and agnostic. There is (...) coverage of the historical treatment of divine hiddenness as found in the work of Maimonides, St. John of the Cross, Jonathan Edwards, Kierkegaard, and various Biblical writers. A substantial introduction clarifies the main problems of and leading solutions to divine hiddenness. Primarily directed at philosophers of religion, theologians, and scholars of religious studies, this collection could also serve as a textbook for upper-level courses in philosophy of religion. (shrink)

This article examines how discussions around the new interdisciplinary research area combining neuroscience and education have brought into sharp relief differences in the philosophies of learning in these two areas. It considers the difficulties faced by those working at the interface between these two areas and, in particular, it focuses on the challenge of avoiding 'non-sense' when attempting to include the brain in educational argument. The paper relates common transgressions in sense-making with dualist and monist notions of the mind-brain relationship. (...) It then extends a brain-mind-behaviour model from cognitive neuroscience to include a greater emphasis on social interaction and construction. This creates a tool for examining the potentially complex interrelationships between the different learning philosophies in this emerging new field. (shrink)

This paper argues that many ethical issues in neuroeducational research cannot be appropriately addressed using the principles and guidance available in one of these areas alone, or by applying these in simple combination. Instead, interdisciplinary and public dialogue will be required to develop appropriate normative principles. In developing this argument, it examines neuroscientific and educational perspectives within three broad categories of ethical issue arising at the interface of cognitive neuroscience and education: issues regarding the carrying out of interdisciplinary research, the (...) scrutiny and communication of findings and concepts, and the application of research and associated issues of policy likely to arise in the future. To help highlight the need for interdisciplinary and public discussion, we also report the opinions of a group of educators (comprising trainee teachers, teachers and head teachers) on the neuroeducational ethics of cognitive enhancing drugs, infant screening, genetic profiling and animal research. (shrink)

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.

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

There is increasing interest in research that combines neuroscientific and educational perspectives on learning, but significant philosophical issues divide these perspectives. This article examines the value of such neuroeducational research and how concepts from different perspectives may be interrelated through a ‘level of actions’ model. This model, which encourages a multiperspective approach, may be helpful in avoiding some of the worst transgressions of sense-making in constructing concepts that span neuroscience and education. Application of the model is explored in the context (...) of teaching strategies intended to foster creativity, and its affordances and limitations are discussed. (shrink)

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.

We study theorems from Functional Analysis with regard to their relationship with various weak choice principles and prove several results about them: “Every infinite‐dimensional Banach space has a well‐orderable Hamel basis” is equivalent to ; “ can be well‐ordered” implies “no infinite‐dimensional Banach space has a Hamel basis of cardinality ”, thus the latter statement is true in every Fraenkel‐Mostowski model of ; “No infinite‐dimensional Banach space has a Hamel basis of cardinality ” is not provable in ; “No infinite‐dimensional (...) Banach space has a well‐orderable Hamel basis of cardinality ” is provable in ; (the Axiom of Choice for denumerable families of non‐empty finite sets) is equivalent to “no infinite‐dimensional Banach space has a Hamel basis which can be written as a denumerable union of finite sets”; Mazur's Lemma (“If X is an infinite‐dimensional Banach space, Y is a finite‐dimensional vector subspace of X, and, then there is a unit vector such that for all and all scalars α”) is provable in ; “A real normed vector space X is finite‐dimensional if and only if its closed unit ball is compact” is provable in ; (Principle of Dependent Choices) + “ can be well‐ordered” does not imply the Hahn‐Banach Theorem () in ; and “no infinite‐dimensional Banach space has a Hamel basis of cardinality ” are independent from each other in ; “No infinite‐dimensional Banach space can be written as a denumerable union of finite‐dimensional subspaces” lies in strength between (the Axiom of Countable Choice) and ; implies “No infinite‐dimensional Banach space can be written as a denumerable union of closed proper subspaces” which in turn implies ; “Every infinite‐dimensional Banach space has a denumerable linearly independent subset” is a theorem of, but not a theorem of ; and “Every infinite‐dimensional Banach space has a linearly independent subset of cardinality ” implies “every Dedekind‐finite set is finite”. (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)

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

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 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.

Two theorems are proved: First that the statement“there exists a field F such that for every vector space over F, every generating set contains a basis”implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ℤ2 has a basis implies that every well-ordered collection of two-element sets has a choice function.