By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with (...) the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces. (shrink)

An error has been found in the cited paper; namely, Theorem 3.1 is false.

Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev ≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev ≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank (...) α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are the co-existential maps introduced in [8]. Co-elementary maps are of level ≥α for all ordinals α; of course in the Boolean context, the co-elementary maps coincide with the maps of level ≥ω. The results of this paper include: (i) every map of level ≥ω is co-elementary; (ii) the limit maps of an ω-indexed inverse system of maps of level ≥α are also of level ≥α; and (iii) if K is a co-elementary class, k ≥ k (K,K) = Lev ≥ k+1 (K,K), then Lev ≥ k (K,K) = Lev ≥ω (K,K). A space X ∈ K is co-existentially closed in K if Lev ≥ 0 (K, X) = Lev ≥ 1 (K, X). Adapting the technique of "adding roots," by which one builds algebraically closed extensions of fields (and, more generally, existentially closed extensions of models of universal-existential theories), we showed in [8] that every infinite member of a co-inductive co-elementary class (such as CH itself, BS, or the class CON of continua) is a continuous image of a space of the same weight that is co-existentially closed in that class. We show here that every compactum that is co-existentially closed in CON (a co-existentially closed continuum) is both indecomposable and of covering dimension one. (shrink)

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.

A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class. K is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed (...) by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y ∈ K and Y is equivalent to X, then Y is homeomorphic to X. As prime example, the closed set taxonomy assigns to each sentence in the first order language of bounded lattices the class of topological spaces whose lattices of closed sets satisfy that sentence. It turns out that every compact two-complex is characterized via this taxonomy in the class of metrizable spaces, but that no infinite discrete space is so characterized. We investigate various natural classification schemes, compare them, and look into the question of which spaces can and cannot be characterized within them. (shrink)

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers ω as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on ω. For example, (...) in every sense of relative ubiquity considered here, the set of dense linear orderings on ω is ubiquitous in the set of linear orderings on ω. (shrink)

The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is unchanged when we move among the lattice bases of a compactum. In this paper we define syntactically the expansive sentences, and show each of them to be base free. We also show that many well-known properties of compacta (...) may be expressed using expansive sentences; and that any property so expressible is closed under inverse limits and co-existential images. As a byproduct, we conclude that co-existential images of pseudo-arcs are pseudo-arcs. This is of interest because the corresponding statement for confluent maps is still open, and co-existential maps are often—but not always—confluent. (shrink)

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and (...) first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of zero-sets are elementarily equivalent then their respective rings of bounded continuous real-valued functions satisfy the same positive-universal sentences. The proof of this uses the technique of constructing ultraproducts as direct limits of products in a category theoretic setting. (shrink)

Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice bases of the space, thereby making model-theoretic tools available to study the defined properties. In this note we are primarily interested in properties of continua related to unicoherence; i.e., properties that speak to the existence of (...) “holes” in a continuum and in certain of its subcontinua. (shrink)

The options in a decision problem generally have outcomes with common features. Putting aside the common features simplifies deliberations, but the simplification requires a philosophical justification that this book provides.

Schelling und Hegel benutzen in ihren philosophischen Texten mathematische und naturwissenschaftliche Modelle wie Unendlichkeit oder Gleichgewicht. Die Strukturen dieser Begriffe liefern einen Massstab fur den Vergleich der Positionen Schellings und Hegels, der fur Schellings Identitatsphilosophie und Hegels erste Jenaer Schriften durchgefuhrt wird. Als wichtigstes Resultat kann eine grundlegende Differenz zwischen beiden Positionen bereits um 1801 nachgewiesen und gezeigt werden, dass diese auf einer unterschiedlichen Auffassung der Rolle des Absoluten beruht.

Deleuze's concept of 'becoming' provides the key to his notoriously complex metaphysics, yet it has not been systematized until now. Bankston tracks the concept of becoming and its underlying temporal processes across Deleuze's writings, arguing that expressions of becoming(s) appear in two modes of temporality: an appropriation of Nietzsche's eternal return (the becoming of the event), and Bergsonian duration (the becoming of sensation). Overturning the criticisms launched by Žižek and Badiou, with conceptual encounters between Bergson, Nietzsche, Leibniz, Borges, Klossowski, (...) and Proust, the newly charted concept of double becoming provides a roadmap to the totality of Deleuze's philosophy. Bankston systematizes Deleuze's multi-mirrored universe where form and content infinitely refract in a vital kaleidoscope of becoming" -- Amazon.com. (shrink)

The ontologies of Slavoj Žižek and Gilles Deleuze are incommensurable. Rather than appropriate one at the expense of the other, this essay uses Žižek’s notion of parallax to think the two philosophers together, without mediation. Both Deleuze and Žižek provide mirrored philosophical images, with the point of divergence being absolute lack. Deleuze argues that lack, or the being of negation, is an error of representational understanding, while Žižek conceives his philosophy as being driven by absolute lack. A stark opponent of (...) Žižek’s precursor, Hegel, Deleuze rejects opposition as a constitutive feature of reality. However, Žižek mirrors Deleuze’s very concepts in his Lacanian reading of Hegel, while said concepts retain identical terms. For instance, Žižek calls l’objet petit a “difference,” while his term for absolute negation is “repetition,” and finally, he refers to his philosophical system as the “non-All”. These singular concepts in Žižek’s thought share an identical language with that of Deleuze. Deleuze’s philosophy is one of “difference,” while its mode of proliferation is “repetition,” and finally, he often refers to his philosophy as the “One-All”. Mapping these common terms that do not denote a common language, but incommensurable, inverse logics, it becomes evident that Deleuze and Žižek are mirror images of one another, infinitely fragmenting across the expanse of their respective positions. Thus, by triangulating ontology from their unique perspectives, a new ontological shift emerges—one that resists mediation and admixture. (shrink)

The study of anarchism as a philosophical, political, and social movement has burgeoned both in the academy and in the global activist community in recent years. Taking advantage of this boom in anarchist scholarship, Nathan J. Jun and Shane Wahl have compiled twenty-six cutting-edge essays on this timely topic in New Perspectives on Anarchism.

The first book-length study of a leading tenth-century Ismaili theoretician Abu Ya'qub al-Sijistani.

Zusammenfassungen der Referate in französischer Sprache.

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of (...) an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement. (shrink)

Die MISCELLANEA MEDIAEVALIA präsentieren seit ihrer Gründung durch Paul Wilpert im Jahre 1962 Arbeiten des Thomas-Instituts der Universität zu Köln. Das Kernstück der Publikationsreihe bilden die Akten der im zweijährigen Rhythmus stattfindenden Kölner Mediaevistentagungen, die vor über 50 Jahren von Josef Koch, dem Gründungsdirektor des Instituts, ins Leben gerufen wurden. Der interdisziplinäre Charakter dieser Kongresse prägt auch die Tagungsakten: Die MISCELLANEA MEDIAEVALIA versammeln Beiträge aus allen mediävistischen Disziplinen - die mittelalterliche Geschichte, die Philosophie, die Theologie sowie die Kunst- und (...) Literaturwissenschaften sind Teile einer Gesamtbetrachtung des Mittelalters. (shrink)

The centrality of death rituals has in anthropologically informed studies of Buddhism been little documented. The current volume brings together a range of perspectives on Buddhist death rituals including ethnographic, textual, historical and theoretically informed accounts, and presents the diversity of the Buddhist funeral cultures of mainland Southeast Asia and China. It arises out of the University of Bristol's Centre for Buddhist Studies research project Buddhist Death Rituals in Southeast Asia and China, funded by the United Kingdom's Arts and Humanities (...) Research Council. This project involved extensive new research in Thailand, Laos and China. Other items from that project included several public exhibitions, extensive stills photographs, and several video films. The project-team produced two 30 minutes films on the ghost festival in Laos and China, one on urban funerals in Chiang Mai (Thailand) and several shorter clips dealing with funeral cultures in Laos, Thailand and China. Most of this material (and an extensive bibliography on the topic) is available free of charge from the project website located at the webpage of the Department of Theology and Religious Studies (Centre for Buddhist Studies) at the University of Bristol. (shrink)

This article contends that the evolution toward interdisciplinary collaboration that we are witnessing in the sciences must also occur in the humanities to ensure their very survival. That is, humanists must be open to working with scientists and social scientists interested in similar research questions and vice versa. Digital humanities is a positive first step. Complexity science should be the next step. Even though much of the ground-breaking work in complexity science has been done in the natural sciences and mathematics, (...) it can, if critically adapted, provide the needed metaphor for a broad integration of disciplines, humanistic and otherwise. Given its almost a-disciplinary nature, a complexity approach to the research problems in the humanities necessarily breaks down silos. Moreover, it can restore and reframe the seamless intellectual fabric sought by researchers before the atomization of the various disciplines in the nineteenthcentury academy. (shrink)

Forced to Fail traces the long legal history of first racial segregation, and then racial desegregation in America. The authors explain how rapidly changing demographics and family structure in the United States have greatly complicated the project of top-down government efforts to achieve an "ideal" racial balance in schools. It describes how social capital—a positive outcome of social interaction between and among parents, children, and teachers—creates strong bonds that lead to high academic achievement.

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

Extant theoretical work on the political resource curse implies that dependence on resource revenues should decrease autocracies’ likelihood of democratizing but not necessarily affect democracies’ chances of survival. Yet most previous empirical studies estimate models that are ill-suited to address this claim. We improve upon earlier studies, estimating a dynamic logit model that interacts a continuous measure of resource dependence with an indicator of regime type using data from 166 countries, covering the period from 1816-2006. We find that an increase (...) in resource dependence at time t - 1 increases the likelihood of autocratic persistence at t, but has no appreciable effect on democratic survival. We go beyond existing empirical studies to show that increases in resource dependence have persistent and substantial cumulative effects on autocracies' likelihood of becoming democratic over the long-term, showing that the total effect of resource dependence on regime type is much larger than the short-term (one period) effect indicates. (shrink)

Paul Weithman offers a fresh, rigorous, and compelling interpretation of John Rawls's reasons for taking his so-called "political turn.".

_A Communion of Subjects_ is the first comparative and interdisciplinary study of the conceptualization of animals in world religions. Scholars from a wide range of disciplines, including Thomas Berry (cultural history), Wendy Doniger (study of myth), Elizabeth Lawrence (veterinary medicine, ritual studies), Marc Bekoff (cognitive ethology), Marc Hauser (behavioral science), Steven Wise (animals and law), Peter Singer (animals and ethics), and Jane Goodall (primatology) consider how major religious traditions have incorporated animals into their belief systems, myths, rituals, and art. Their (...) findings offer profound insights into humans' relationships with animals and a deeper understanding of the social and ecological web in which we all live. Contributors examine Judaism, Christianity, Islam, Hinduism, Buddhism, Jainism, Daoism, Confucianism, African religions, traditions from ancient Egypt and early China, and Native American, indigenous Tibetan, and Australian Aboriginal traditions, among others. They explore issues such as animal consciousness, suffering, sacrifice, and stewardship in innovative methodological ways. They also address contemporary challenges relating to law, biotechnology, social justice, and the environment. By grappling with the nature and ideological features of various religious views, the contributors cast religious teachings and practices in a new light. They reveal how we either intentionally or inadvertently marginalize "others," whether they are human or otherwise, reflecting on the ways in which we assign value to living beings. Though it is an ancient concern, the topic of "Religion and Animals" has yet to be systematically studied by modern scholars. This groundbreaking collection takes the first steps toward a meaningful analysis. (shrink)

General information -- The animals themselves -- Philosophical arguments -- Laws -- Political realities -- Social realities -- Education and the arts -- Contemporary sciences -- Major figures and organizations in the animal rights movement -- The future of animal rights.

Animal studies is a growing interdisciplinary field which seeks to understand how humans study and conceive of other-than-human animals, and how these conceptions have changed over time, across cultures, and among various scholarly modes of inquiry. Until now, this growing field has lacked a comprehensive introductory text appropriate for new scholars. Animal Studies: An Introduction fills this deficiency, providing the first holistic survey of the field.

This chapter presents an opinionated account of how to understand the contributions of experience, especially with respect to the role of cognitive science, in developing and assessing metaphysical theories of reality. I develop a methodological basis for the idea that, independently of work in experimental philosophy focused on explications of concepts, contemporary metaphysical theories with a role for experiential evidence can be fruitfully connected to empirical work in psychology, especially cognitive science. My argument is not that cognitive science should replace (...) the metaphysician’s use of a priori theorizing and ordinary experience as a guide to metaphysical reality. Rather, we should enrich our perspective on a priori theorizing and ordinary experience as a guide to metaphysical reality by drawing on any relevant work in cognitive science. (shrink)

Introduction -- A significant life -- Constructing a methodology -- The method under assault -- Politics as practice -- Political theory as political practice -- Conclusion.