The biblical sentence “God is Spirit” (John 4:24) occasioned the development of the Christian doctrine about God as Spirit. But since patristic times “spirit” was interpreted in the sense of Nus, which rather means “intellect.” The biblical concept of spirit (pneuma), however, has its root meaning in referring to “air in movement,” as in breath or storm. The similar concept of pneuma in Stoic philosophy has become the “immediate precursor” (Max Jammer) of the field concept in modern physics, so that (...) the conclusion is suggested that God is spirit as something like a field of force rather than as intellect. This essay argues for such a conception by relating the divine eternity and immensity to the concepts of space and time, the basic requirements of any physical field. God's eternity and immensity are interpreted in terms of undivided infinite space (and time) which is presupposed in all concepts of parts of space or time (or space‐time), therefore in all mathematical and physical measurement. (shrink)

We define a class of productive σ-ideals of subsets of the Cantor space 2 ω and observe that both σ-ideals of meagre sets and of null sets are in this class. From every productive σ-ideal I we produce a σ-ideal I κ , of subsets of the generalized Cantor space 2 κ . In particular, starting from meagre sets and null sets in 2 ω we obtain meagre sets and null sets in 2 κ , respectively. (...) Then we investigate additivity, covering number, uniformity and cofinality of I κ . For example, we show that non(I = non(I ω 1 ) = non(I ω 2 ). Our results generalizes those from [5]. (shrink)

Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have (...) shown that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological space, Cantor space. The current paper produces an alternate proof of the Zhang-Mints result. (shrink)

In this paper, we are interested in parallels to the classical notions of special subsets in defined in the generalized Cantor and Baire spaces (2κ and ). We consider generalizations of the well‐known classes of special subsets, like Lusin sets, strongly null sets, concentrated sets, perfectly meagre sets, σ‐sets, γ‐sets, sets with the Menger, the Rothberger, or the Hurewicz property, but also of some less‐know classes like X‐small sets, meagre additive sets, Ramsey null sets, Marczewski, Silver, Miller, and Laver‐null (...) sets. We notice that many classical theorems regarding these classes can be relatively easy generalized to higher cardinals although sometimes with some additional assumptions. This paper serves as a catalogue of such results along with some other generalizations and open problems. (shrink)

This paper has two parts. In the first, I try to show that Russell's arguments against the thesis of Kant's first antinomy are unsatisfactory; in the second, I argue that the Universe, if transcendentally real, must be finite in both space and time.

It is well known that infinite minimal sets for continuous functions on the interval are Cantor sets; that is, compact zero dimensional metrizable sets without isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on connected linearly ordered spaces enjoy the same properties as Cantor sets except that they can fail to be metrizable. However, no examples of such subsets have been known. In (...) this note we construct, in ZFC, ${2^{\mathfrak{c}}}$ non-metrizable infinite pairwise non-homeomorphic minimal sets on compact connected linearly ordered spaces. (shrink)

We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am Math (...) Soc, in press), as well as of global ${\aleph_0}$ -stability. We conclude with a study of perturbation systems (see Ben Yaacov I, On perturbations of continuous structures, submitted) in the formalism of topometric spaces. In particular, we show how the abstract development applies to ${\aleph_0}$ -stability up to perturbation. (shrink)

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.

We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends Sikora’s (...) [28] investigation of orders on groups in topology and Solomon’s [31] investigation of these orders in computable algebra. Furthermore, we establish that a computable free group Fn of rank n>1 has a bi-order in every Turing degree. (shrink)

We establish some results on the Borel and difference hierarchies in φ-spaces. Such spaces are the topological counterpart of the algebraic directed-complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non-collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω. We also sketch some older applications of these hierarchies and present a new application to the question (...) of characterizing the ω-ary Boolean operations generating a given level of the Wadge hierarchy from the open sets. (shrink)

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of (...) space. Husserl’s Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (shrink)

We discuss the existence of universal spaces (either in the sense of embeddings or continuous images) for some classes of scattered Eberlein compacta. Given a cardinal κ, we consider the class Sκ of all scattered Eberlein compact spaces K of weight ≤ κ and such that the second Cantor-Bendixson derivative of K is a singleton. We prove that if κ is an uncountable cardinal such that κ = 2<κ, then there exists a space X in Sκ such that (...) every member of Sκ is homeomorphic to a retract of X. We show that it is consistent that there does not exist a universal space (either by embeddings or by mappings onto) in Sω₁. Assuming that ∂ = ω₁, we prove that there exists a space X ∈ Sω₁, which is universal in the sense of embeddings. We also show that it is consistent that there exists a space X ∈ Sω₁, universal in the sense of embeddings, but Sω₁ does not contain an universal element in the sense of mappings onto. (shrink)

INSPIRED by a dynamist Naturphilosophie and looking for a mathematics of the natura naturans, the founders of modern mathematics in Germany made some lasting contributions in the attempt to go beyond perceptible space. Hermann Grassmann’s extension theory, Johann Benedict Listing’s topology, Bernhard Riemann’s non-Euclidean manifold theory, Carl Gustav Jacob Jacobi’s approach to non-mechanistic theory and last but not least Georg Cantor’s transfinite set theory were all influenced by the tradition of Naturphilosophie. One central motivation for the new mathematics (...) was to decipher the so-called “inner side of nature” which was thought to be invisible but nonetheless physical. As a result, mathematics was understood not only in terms of quantity but of morphogenetic quality and as a tool to recognize the intrinsic possibilities of structuring and organizing nature. This essay focuses on the philosophical viewpoints of Christian Samuel Weiss, Justus and Hermann Grassmann, Bernhard Riemann and their reception of Schelling’s philosophy. Riemann deconstructed empiricist theories of space so as to glean the fundamental constitution of space. One result was that a given, fixed and static metric is not necessary for the understanding of space. The underlying topological substratum has no specific metric but is capable of exhibiting any possible metric. Riemann’s claims are compared with Schelling’s theory of space in his “Darstellung des Naturprocesses”. My thesis is that Schelling’s philosophy of the emergence of space can be read in Riemannian terms and that it is an interesting model in the context of modern questions. (shrink)

The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of (...) space. Husserl’s Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and context of Husserl’s own development. (shrink)

In the topological semantics for modal logic, S4 is well-known to be complete for the rational line, for the real line, and for Cantor space: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but also strongly complete, for the rational line. But no similarly easy amendment is available for the real line or for Cantor (...) space and the question of strong completeness for these spaces has remained open, together with the more general question of strong completeness for any dense-in-itself metric space. In this paper, we prove that S4 is strongly complete for any dense-in-itself metric space. (shrink)

ABSTRACT The Great Exhibition of 1851 is generally interpreted as a thoroughly secular event that celebrated progress in science, technology, and industry. In contrast to this perception, however, the exhibition was viewed by many contemporaries as a religious event of considerable importance. Although some religious commentators were highly critical of the exhibition and condemned the display of artifacts in the Crystal Palace as giving succor to materialism, others incorporated science and technology into their religious frameworks. Drawing on sermons, tracts, and (...) the religious periodical press, this essay pays close attention to the ways in which science and technology were endowed with providentialist significance and particularly examines the notion of human progress used by a number of Christian writers, especially Congregationalists, who set scientific and technological progress within a teleological religious perspective. This discussion sheds fresh light not only on the Great Exhibition itself but also on the deployment of natural theology in mid-nineteenth-century Britain. (shrink)

ABSTRACT The Great Exhibition of 1851 is generally interpreted as a thoroughly secular event that celebrated progress in science, technology, and industry. In contrast to this perception, however, the exhibition was viewed by many contemporaries as a religious event of considerable importance. Although some religious commentators were highly critical of the exhibition and condemned the display of artifacts in the Crystal Palace as giving succor to materialism, others incorporated science and technology into their religious frameworks. Drawing on sermons, tracts, and (...) the religious periodical press, this essay pays close attention to the ways in which science and technology were endowed with providentialist significance and particularly examines the notion of human progress used by a number of Christian writers, especially Congregationalists, who set scientific and technological progress within a teleological religious perspective. This discussion sheds fresh light not only on the Great Exhibition itself but also on the deployment of natural theology in mid-nineteenth-century Britain. (shrink)

We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number[Formula: see text] of a pair-coloring c:[X]2→2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω, c min and c max, which satisfy [Formula: see text] and prove: Theorem. For every Polish space X and every (...) continuous pair-coloringc:[X]2→2with[Formula: see text], [Formula: see text] There is a model of set theory in which[Formula: see text]and[Formula: see text]. The consistency of [Formula: see text] and of [Formula: see text] follows from [20]. We prove that [Formula: see text] is equal to the covering number of 2 by graphs of Lipschitz functions and their reflections on the diagonal. An iteration of an optimal forcing notion associated to c min gives: Theorem. There is a model of set theory in which ℝ2 is coverable byℵ1graphs and reflections of graphs of continuous real functions; ℝ2 is not coverable byℵ1graphs and reflections of graphs of Lipschitz real functions. Figure 1.1 in the introduction summarizes the ZFC results in Part I of the paper. The independence results in Part II show that any two rows in Fig. 1.1 can be separated if one excludes [Formula: see text] from row. (shrink)

In this paper we show that some standard topological constructions may be fruitfully used in the theory of closure spaces (see [5], [4]). These possibilities are exemplified by the classical theorem on the universality of the Alexandroff's cube for T 0-closure spaces. It turns out that the closure space of all filters in the lattice of all subsets forms a generalized Alexandroff's cube that is universal for T 0-closure spaces. By this theorem we obtain the following characterization of the (...) consequence operator of the classical logic: If is a countable set and C: P() P() is a closure operator on X, then C satisfies the compactness theorem iff the closure space ,C is homeomorphically embeddable in the closure space of the consequence operator of the classical logic.We also prove that for every closure space X with a countable base such that the cardinality of X is not greater than 2 there exists a subset X of irrationals and a subset X of the Cantor's set such that X is both a continuous image of X and a continuous image of X. (shrink)

Dynamic Topological Logic ( $\mathcal{DTL}$ ) is a modal framework for reasoning about dynamical systems, that is, pairs 〈X, f〉 where X is a topological space and f: X → X a continuous function. In this paper we consider the case where X is a metric space. We first show that any formula which can be satisfied on an arbitrary dynamic topological system can be satisfied on one based on a metric space; in fact, this space (...) can be taken to be countable and have no isolated points. Since any metric space with these properties is homeomorphic to the set of rational numbers, it follows that any satisfiable formula can be satisfied on a system based on $\mathbb{Q}$ . We then show that the situation changes when considering complete metric spaces, by exhibiting a formula which is not valid in general but is valid on the class of systems based on a complete metric space. While we do not attempt to give a full characterization of the set of valid formulas on this class we do give a relative completeness result; any formula which is satisfiable on a dynamical system based on a complete metric space is also satisfied on one based on the Cantor space. (shrink)

Unlike Martin‐Löf randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and further, provides a general method for abstracting “bit‐wise” definitions of randomness from Cantor space to arbitrary computable probability spaces. This same method is also applied to give machine characterizations of computable and Schnorr randomness for computable probability spaces, extending the previously known results. (...) The paper contains a new type of randomness—endomorphism randomness—which the author hopes will shed light on the open question of whether Kolmogorov‐Loveland randomness is equivalent to Martin‐Löf randomness. The last section contains ideas for future research. (shrink)

A surprising feature of the White Rose anti-Nazi resistance pamphlets is their appeal to a foundational classical Chinese text, the Laozi (otherwise known as the Daodejing), to buttress their critique of fascism and authoritarianism. I argue that from the perspective of a 1942 educated readership, the act of quoting the Laozi functioned as a subtle and pointed nod to anti-fascist intellectuals in pre-war Germany, many of whom had interpreted the Laozi as an anti-authoritarian and pacifist text. To a sympathetic reader, (...) the Laozi therefore constituted an apt reference point for critiquing National Socialism. I then introduce a complication for this wartime reading of the Laozi from the perspective of its ambiguous reception in ancient Chinese political thought. I more specifically discuss an ancient line of interpretation of the Laozi that points in the direction of authoritarianism — in stark tension with the White Rose message of passive resistance and popular revolt. (shrink)

The “happy fish” passage concluding the “Autumn Floods” chapter of the Classical Chinese text known as the Zhuangzi has traditionally been seen to advance a form of relativism which precludes objectivity. My aim in this paper is to question this view with close reference to the passage itself. I further argue that the central concern of the two philosophical personae in the passage – Zhuangzi and Huizi – is not with the epistemic standards of human judgements (the established view since (...) Hansen, “The Relatively Happy Fish”), but with the more basic problem of species-specific perspectives. On my reading, Zhuangzi’s emphatic positionality in the passage – on the dam, accompanied by his friend Huizi – plausibly suggests a circumspect reflection on the limitedness of human knowledge. It is significant that Zhuangzi’s knowledge of fish happiness is avowedly from a certain place, and not absolute. But there is still a sense in which this view is objective: namely, insofar as it adequately accounts for an inherently human perspective on the world. I call this modest form of relativism ‘Species Relativism’, which, crucially, leaves room for objectivity, even though a fully objective (i.e. absolute) view of the world is not accessible to humans. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Uncanonical Dante: The Divine Comedy And Islamic PhilosophyPaul A. CantorThe distorted notions of invisible things which Dante and hisrival Milton have idealized, are merely the mask and the mantlein which these great poets walk through eternity enveloped anddisguised. It is a difficult question to determine how far theywere conscious of the distinction which must have subsisted intheir minds between their own creeds and that of the people.Dante at (...) least appears to wish to mark the full extent of it byplacing Riphaeus, whom Virgil calls justissimus unus, inParadise, and observing a most heretical caprice in hisdistribution of rewards and punishments.—Percy Shelley, A Defence of PoetryIThe case of Dante provides an excellent opportunity to open up the question of the Western canon. In one sense, Dante is the perfect example of a canonical author. His name is one of the few certain to appear on anybody’s short list of the truly central authors in the Western literary tradition. But in another sense Dante can be regarded as uncanonical. In his own day he was widely suspected of being heretical in his religious views, 1 and a careful reading of his works does indeed raise serious doubts about his being the pillar of orthodoxy he is often taken to be today. 2 Out of this interplay between the canonical and the noncanonical Dante, I hope to show that the issue of the Western canon is more complicated than either its defenders or its attackers generally present it.In discussing the issue of the canon, it is important to sort out at the [End Page 138] beginning what we do and do not mean by the term. A canonical work may merely be a work that has been accepted into the literary canon, one that has become a touchstone in the reading and teaching of literature. But the term canonical can suggest something else, that the work is orthodox and somehow represents a central authoritative position in Western culture. The word canonical is so loaded with religious connotations that it is difficult to separate the relatively neutral first meaning of the term from the loaded second meaning. Dante is a case in point. When people refer to him as a canonical author, they usually do not simply mean that he is widely read and taught. Most discussions of Dante today treat him as representing an authoritative cultural moment in the Western tradition, as the supreme embodiment of the medieval mind. Viewed that way, Dante becomes an emblem of everything contemporary critics of the Western canon bitterly hate and reject. The reason they feel that they must attack authors like Dante and displace them from the center of literary study is that these authors have come to stand for orthodoxy and thus seem to enforce the hegemony of Western culture.Critics who wish to champion various forms of non-Western culture have a particular axe to grind with canonical authors like Dante. The contemporary debate over the Western canon seems to be premised on a sharp opposition between Western and non-Western cultures, as if they were complete and irreconcilable antitheses, and even wholly unrelated. One of the principal charges against the Western canon is that it is Eurocentric, that it remains confined within a narrow orbit of European ideas and beliefs, thus excluding all other views of the world. A corrolary of the idea of Eurocentrism is the concept of Orientalism, developed by Edward Said. 3 Said argues that throughout its history, the Occident has defined itself in opposition to the Orient, basing its elevated self-image on a debased vision of the cultural Other. In Said’s argument, the Occident views itself as rational as opposed to an irrational Orient, as emotionally disciplined in contrast to an emotionally uncontrolled Orient, and as masculine over against a feminine Orient.In medieval Europe the Orient was chiefly represented by the Muslim world, and one does not have to look far in medieval literature to find the kinds of orientalist stereotypes about which Said writes. The French Song of Roland contains excellent examples, but even the Divine Comedy seems to... (shrink)

In this paper several problems are raised concerning Ian Barbour's four ways of interrelating science and religion—Conflict, Independence, Dialogue, and Integration—as put forward in such publications as his highly influential Religion in an Age of Science (1990) and widely adopted by other writers in this field. The authors argue that this taxonomy is not very useful or analytically helpful, especially to historians seeking to understand past engagements between science and religion.

It is widely believed that the ancient Greeks thought that Thales was the first philosopher, and that they therefore maintained that philosophy had a Greek origin. This paper challenges these assumptions, arguing that most ancient Greek thinkers who expressed views about the history and development of philosophy rejected both positions. I argue that not even Aristotle presented Thales as the first philosopher, and that doing so would have undermined his philosophical commitments and interests. Beyond Aristotle, the view that Thales was (...) the first philosopher is attested almost nowhere in antiquity. In the classical, Hellenistic, and post-Hellenistic periods, we witness a marked tendency to locate the beginning of philosophy in a time going back further than Thales. Remarkably, ancient Greek thinkers most often traced the origins of philosophy to earlier non-Greek peoples. Contrary to the received view, then, I argue that (1) vanishingly few Greek writers pronounced Thales the first philosopher; and (2) most Greek thinkers did not even advocate a Greek origin of philosophy. Finally, I show that the view that philosophy originated with Thales (along with its misleading attribution to the Greeks in general) has roots in problematic, and in some cases manifestly racist, eighteenth-century historiography of philosophy. (shrink)

In the late 1810s and 1820s the Edinburgh phrenologists were largely concerned with trying to establish phrenology as the true science of mind. They challenged the accepted theories about the nature of mind and the brain; in turn, phrenology was attacked by the proponents of Scottish common-sense philosophy and by some medical men. The ensuing debate, which is discussed as an example of conflict between incommensurable world-views, involved a wide range of contentious theological, philosophical, scientific and methodological issues.

Some people will confront Alzheimer's with a measure of resignation, a determination to struggle against the progressive debilitation and to extract whatever comforts and benefits they can from their remaining existence. They are entitled to pursue that resolute path. For other people, like myself, protracted maintenance during progressive cognitive dysfunction and helplessness is an intolerably degrading prospect. The critical question for those of us seeking to avoid protracted dementia is how best to accomplish that objective.One strategy is to engineer one's (...) own death while still mentally competent to do so (even in the stage of mild dementia). If I were to use a preemptive strategy in the face of a dementia diagnosis, I would probably choose to stop eating and drinking, a process known as voluntarily stopping eating and drinking. An alternative tactic for avoiding prolonged dementia would be to allow oneself to decline into moderate dementia—thus losing capacity to perform self‐deliverance or even to make serious medical decisions—but before getting to that point to provide advance instructions rejecting prospective life‐sustaining medical interventions. These advance instructions would authorize palliative but not curative measures. My current personal instructions define the point of intolerable cognitive decline triggering medical nonintervention as “mental deterioration to a point when I can no longer read and understand written material such as a newspaper or financial records such as a checkbook.” These instructions dictate allowing my demise at a point of moderate dementia when I may not be perceptibly suffering, when I may still be getting some rudimentary satisfaction from my debilitated life, and when I no longer recall the preoccupation with personally intolerable indignity that motivated my instructions. Can I expect that my advance instructions will be implemented in those circumstances? Is it lawful, and is it moral for a surrogate decision‐maker and associated caregivers to allow an uncomprehending, ostensibly content but demented individual to die? My analysis herein contends that it is not only lawful and moral but also legally required to implement clear, considered advance instructions even at a stage of moderate dementia. (shrink)

Carlos F. Gomez, Regulating Death New Yorrk: Free Press, 1991, xx +172 pp.

A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.

Science and Christianity Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-011-9544-2 Authors Geoffrey Cantor, Science and Technology Studies, University College London, Gower Street, London, WC1E 6BT UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

The idea of an inevitable conflict between science and religion was decisively challenged by John Hedley Brooke in his classic Science and Religion: Some Historical Perspectives. Almost two decades on, Science and Religion: New Historical Perspectives revisits this argument and asks how historians can now impose order on the complex and contingent histories of religious engagements with science. Bringing together leading scholars, this volume explores the history and changing meanings of the categories 'science' and 'religion'; the role of publishing and (...) education in forging and spreading ideas; the connection between knowledge, power and intellectual imperialism; and the reasons for the confrontation between evolution and creationism among American Christians and in the Islamic world. A major contribution to the historiography of science and religion, this book makes the most recent scholarship on this much misunderstood debate widely accessible. (shrink)