An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.

An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.

A natural extension theorem for strongly continuous mappings, the morphisms in the category of apartness spaces, is proved constructively.

Two new notions of compactness, each classically equivalent to the standard classical one of sequential compactness, for apartness spaces are examined within Bishop-style constructive mathematics.

We investigate separation properties for neighbourhood spaces in some details within a framework of constructive mathematics, and define corresponding separation properties for quasi-apartness spaces. We also deal with separation properties for spaces with inequality.

This paper is dedicated to Prof. Dr. Günter Asser, whose work in founding this journal and maintaining it over many difficult years has been a major contribution to the activities of the mathematical logic community.At first sight it appears highly unlikely that Urysohn's Lemma has any significant constructive content. However, working in the context of an apartness space and using functions whose values are a generalisation of the reals, rather than real numbers, enables us to produce a significant (...) constructive version of that lemma. (shrink)

The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity.

The theory of apartness spaces, and their relation to topological spaces (in the point–set case) and uniform spaces (in the set–set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by a uniform structure.

We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces.

이 글의 목적은 ‘아파트 공동체’를 ‘마을 만들기 운동’의 한 유형으로 이해하고, 아파트를 중심으로 마을 공동체를 활성화할 수 있는 이론적⋅실천적 방안을 제안하는 것이다. 이를 위해 이 글은 ‘치안과 통치’, ‘인정’, ‘공동체와 장소’, ‘거버넌스 마을과 계쟁의 마을’이라는 몇 가지 개념 쌍을 주요 분석 도구로 채택한다.BR 이 글은 다음과 같은 논의를 담고 있다. 이글의 2장은 현대 프랑스 철학자 자크랑시에르(J. Rancière)의 개념들에 입각해 한국의 아파트 건설사를 ‘치안’과 ‘통치’의 관철과정으로 규정한다(2). 이 글의 3장은 ‘인정’ 개념을 통해 아파트 공동체의 가능 조건을 철학적으로 탐색한다. 공동체주의자 찰스 테일러(Ch. (...) Taylor)의 논의로부터 아파트 공동체 형성을 위한 조건들을 추출한다(3). 이 글의 4장은 아파트 공동체를 마을 만들기 운동의 한 유형으로 이해하고, 오늘날 대한민국 사회에서 활발하게 전개되고 있는 마을 만들기 운동의 현황과 전망을 아파트 공동체와 관련지어 점검한다. 이 과정에서 이 글은 마을 만들기 운동의 실천적 방법론으로 자리 잡고 있는 거버넌스(Governance) 개념을 비판적으로 성찰하고, 마을 만들기 운동에 대한 활동가들의 진단을 참조하여 마을 운동의 향방을 가늠해 본다.(4). 이상의 논의를 통해 이 글은 아파트 공동체의 활성화 방안으로 ‘유동적 공동체’와 ‘사건적 주체’라는 두 가지 개념을 제안한다. (shrink)

Apartness spaces were introduced as a constructive counterpart to proximity spaces which, in turn, aimed to model the concept of nearness of sets in a metric or topological environment. In this paper we introduce apartness algebras and apartness frames intended to be abstract counterparts to the apartness spaces of (Bridges et al., 2003), and we prove a discrete duality for them.

이 연구는 우선 집 그 안에 사는 사람의 품성이나 성향 내지 정서를 느끼게 해준다는 점에서 볼 때, 집이야말로 그 어떠한 건축물보다도 또한 사람이 만드는 그 어떤 물리적인 실체보다도 일상생활에서 사람의 감성이 담겨지고 표현되고 계발되어 승화시키는 그릇임을 전제한다. 이러한 전제하에 한국의 대표적인 주거 형태로 자리잡은 아파트의 의미를 전통적인 삶의 주거 구조와 비교하면서, 서구적인 아파트가 토착화되는 과정에서 발생한 변화에 주목하여, 아파트식 주거 구조에 공동체적 계기의 실현을 강조하였다. 한국의 주거문화는 생활 기능적 측면보다는 가족 구성원 중심을 강조한다. 여러 가족 구성원이 한 공간에서 모여 산다는 (...) 것은 구성원간의 서로 다른 욕망의 본질에 의해서 갈등, 분열과 긴장이 일어나게 마련이지만, 이러한 갈등구도는 가족 구성원간의 협력과 정(情)의 공간성에 근거해서 해소되어야 한다. 따라서 아파트형 주거문화에서 개별성과 독립성을 포기하지 않으면서도 공동체성을 살릴 수 있는 공간적 계기가 구성되어야 한다. 여기서 말하는 공동체적 계기의 실현이 전통적인 사회의 공동체성으로의 복귀를 의미하지는 않는다. 즉 이러한 공동체적 계기는 전통적인 의미에서의 공동체성이라기 보다는 현대사회의 특징이 반영된 공동체성으로 변화되어야 할 것이다. 사생활 보호와 안정성에 대한 요구와 더불어 공동체성에 대한 요청이 서로 조화될 수 있는 공동체성이 무엇인지 우리는 생각해 보아야 할 것이다. 그리고 이 연구는 현대 주거 공간의 철학적ㆍ윤리적 의미에 대한 숙고의 필요성을 제시한다. 인간을 포함한 모든 존재자는 자신의 존재에 상응하는 고유한 공간을 지니고 있다. 공간과 존재자는 서로 필연적인 관계를 맺고 있기 때문에 공간의 의미는 존재자의 존재의미와 직결되며, 결국 공간의 위기는 존재자의 위기로 연결될 수밖에 없다. 따라서 좋은 공간이란 인간적인 공간임을 전제하지 않을 수 없으며, 좋은 집은 인간적인 집임을 부정할 수 없을 것이다. (shrink)

The paper deals with proximal convergence and Leader's theorem, in the constructive theory of uniform apartness spaces.

I BEGIN WITH A PUZZLE of sorts. Time is one; space is two—at least two. Time comes always already unified, one time. Thus we say “What time is it now?” and not “Which time is it now?” We do not ask, “What space is it?” Yet we might ask: “Which space are we in?”. Any supposed symmetry of time and space is skewed from the start. If time is self-consolidating—constantly gathering itself together in coherent units such (...) as years or hours or semesters or seasons— space is self-proliferating. Take, for example, the dimensionality of space. One dimension in space is represented by a point or a line, whose radically reduced format mocks the extensiveness of cosmic space. Two dimensions, as in a plane figure, also falls far short of our sense that space spreads out indefinitely far beyond the perceiving subject. Only with three dimensions do we begin to approach an adequation between the structure and the sense of space. For then the subject is surrounded by something sufficiently roomy in which to live and move. Indeed, as Aristotle, Kant, and Merleau-Ponty all remark, the three-dimensionality of space directly reflects our bodily state, that is, the fact that as upright beings three perpendicular planes implicitly meet and intersect in us. Even here, proliferation abounds: our bilateral symmetry means that each dimension is doubled: one vertical plane bifurcates into “up” and “down,” the other vertical plane into “front” and “back,” and the horizontal plane into “right” and “left.” Thus subject-centered space is triple, only to be redoubled. Further, if we think of spatiality not as body-based but as locatory—as determined by landmarks and other locales in the environment—the proliferation is more striking still. There are the four cardinal directions, which themselves split easily into the thirty two points of a compass. Nor need we be so arithmetically well-rounded. Even apart from fancy mathematical models of n –dimensional space, and recent technological instantiations of virtual space, there is no end to the number or ways in which we can be oriented in space—in accordance with what Deleuze and Guattari call “the variability, the polyvocity of directions” by which we can move in any given spatial scene. Beyond direction, however, is place. Heidegger remarks that “space has been split up into places.” The fact is that we continually find ourselves immersed in a multiplex spatial network whose nodal points are supplied by particular places. If space is infinitely large, place is indefinitely many. (shrink)

Metaphor plays a unique role in cognitive development by structuring abstract concepts and leading to conceptual change. Existing work suggests early emergence of metaphorical abilities, with five-year-olds understanding and explaining metaphors that involve cross-domain comparisons (e.g., SPACE to TIME). Yet relatively little is known about the factors that explain this developmental change. This study focuses on spatial metaphors for time, and asks whether cognitive and/or verbal factors best explain developmental changes in three- to six-year-old children's comprehension and explanation of (...) metaphors. The results show that children's grasp of the time concept—but not verbal ability—predicts their metaphor comprehension. Verbal ability, on the other hand, is a predictor of metaphor explanation, even after controlling for age. The results thus suggest that cognitive and verbal factors selectively predict children's emerging metaphorical abilities. (shrink)

Following its publication in Germany in 1963, Otto Friedrich Bollnow's Human Space quickly became essential reading within a cross-disciplinary field of subject areas including architecture, anthropology, and philosophy. In this first English translation, Bollnow conceives the human experience of space not merely as a philosophical problem but also as an extension of his research into psychology, human behavior, and the conventional domains of architecture: living in a building, in an apartment, in a house. Human Space is a (...) remarkable investigation of space as we experience it, by a man many consider to be the father of spatial and architectural anthropology. This lush hardcover edition includes an afterword by Joseph Kohlmaier that situates the work in the context of philosophical and architectural discussion. (shrink)

REIMER‐KIRKHAM S, SHARMA S, PESUT B, SAWATZKY R, MEYERHOFF H and COCHRANE M. Nursing Inquiry 2012; 19: 202–212 Sacred spaces in public places: religious and spiritual plurality in health careSeveral intriguing developments mark the role and expression of religion and spirituality in society in recent years. In what were deemed secular societies, flows of increased sacralization (variously referred to as ‘new’, ‘alternative’, ‘emergent’ and ‘progressive’ spiritualities) and resurgent globalizing religions (sometimes with fundamentalist expressions) are resulting in unprecedented plurality. These shifts (...) are occurring in conjunction with increasing ethnic diversity associated with global migration, as well as other axes of difference within contemporary society. Democratic secular nations such as Canada are challenged to achieve social cohesion in the face of growing religious, spiritual and ethnic diversity. These challenges are evident in the high‐paced, demanding arena of Health care. Here, religious and spiritual plurality enter in, sometimes resulting in conflict between medical services and patients’ beliefs, other times provoking uncertainties on the part of healthcare professionals about what to do with their own religiously or spiritually grounded values and beliefs. In this paper, we present selected findings from a 3‐year study that examined the negotiation of religious and spiritual pluralism in Health care. Our focus is on the themes of ‘sacred’ and ‘place’, exploring how the sacred – that which is attributed as special and set apart as it pertains to the divine, transcendence, God or higher power – takes form in social and material spaces in hospitals. (shrink)

How do past experiences of violence map onto present day narratives of insurgency in northern Mozambique? In the insurgency that began in northern Mozambique in 2017, narratives of past violent encounters and animosity between different ethnic groups sharing the coastal space emerge as a way of making sense of the conflict. This article explores the ways these narratives stem from existing historical tensions between Makonde and Mwani inhabiting the northern districts of Cabo Delgado. Drawing on ethnography and oral history (...) to highlight the continuities in narrative, I will explore the ways in which current violence is interpreted through references to pivotal moments of violence in the past. I will address the historical construction of difference between Makonde and Mwani to consider what it may tell us about the fractures that underpin the insurgency. (shrink)

Based on a small research project conducted in Kuala Lumpur (KL) in July - August 2017, the paper discusses places and practices of young heterosexual Malaysian Muslims dating in KL. In Malaysia, the law (Khalwat law) does not allow for two unrelated people (where at least one of them is Muslim) of opposite sexes to be within ‘suspicious proximity’ of one another in public. This law significantly influences behaviours and activities in urban spaces in KL. However, apart from the legal (...) framework, the faith of urban users seems to influence significantly the way they perceive space and how they behave in the city. The paper questions the analytical usefulness of the notion of public space (as the Western construct) in an attempt to formulate new intellectual coordinates to discuss urban space in a context of the Islamic, post-colonial, tropical, and global city. The ultimate aim of this paper is to start discussing how religious imagination and narratives could lead to formulating a new typology of urban spaces. (shrink)

In this brief excerpt from a forthcoming translation of L’Afrique et ses fantômes and Singe de Kafka, Seloua Luste Boulbina shows how French opposition to the Islamic hijab, as described by Fanon, mirrored British opposition to the Indian practice of sati by claiming to defend women while really defending the interests of European men. This made it difficult, if not impossible, for women to define and assert interests of their own, apart from the perspectives imposed by politically opposed groups of (...) men. Fanon recognized this complex silence. But Fanon also failed to read the perspective motivating the writings of fellow Martinican author, Mayotte Capécia, which prevented him from seeing any independence in women’s capacity for interracial love and prevented him from giving a more complex psychological and political meaning to mixed ancestry. (shrink)

This article gives a brief description of one of the sub-branches of Paganism, Wicca. It describes how sacred space is established and it explores the sacred circle as a symbolic representation of Wiccan cosmology. Physical sacred space thus constructed becomes a 'world apart' from the mundane and a bridge between ordinary physical reality and metaphysical realms. The circle is the outer expression of an imaginai inner world wherein anything is possible. The connection between a bounded, physical space (...) and a limitless otherworld is discussed, using the discourse of the witches and theoretical perspectives on sacred space. (shrink)

Pamela conceived of vulnerability as a capability to enhance our lives in a continual creative process of transformation. She argued for recreating our perception of vulnerability as positive in our lives and in our relationships. I come to this exploration of transformation both as an academic and as Pamela’s sister, exploring my own lived experience of vulnerability and love as a result of her passing, and seeking to understand how her concept of creative transformation can relate to my personal experiences (...) as well as others’ stories of transformation. Pamela describes that an openness to vulnerability creates a space or a threshold for transformation. This space can be dark and disorienting yet as we move through it we have the freedom to make choices that enhance our personal lives as well as the social and political contexts within which we live and work. In my work that encourages a holistic mind–body–spirit view of health and healing I can see how Pamela’s conception of vulnerability as a capability opens us to a creative response for healing. My exploration of vulnerability and creative transformation reveals that Pamela’s work on vulnerability can be applied to creative transformation broadly and is especially relevant in a world currently torn apart by violence and fear. An openness to vulnerability may help the world to evolve toward love and hope. (shrink)

In the Treatise of Human Nature , Hume argues that, because we have adequate ideas of the smallest parts of space, we can infer that space itself must conform to our representations of it. The paper examines two challenges to this argument based on Descartes's and Locke's treatments of adequate ideas, ideas that fully capture the objects they represent. The first challenge, posed by Arnauld in his Objections to the Meditations , asks how we can know that an (...) idea is adequate. The second challenge, implicit in Locke's Essay , asks how an empiricist can characterize an idea as inadequate, as both picking out an object and yet failing to capture it fully. In showing how Hume responds to these challenges, his theory of perceptual representation is explained and his treatment of space is related to his scepticism. His conclusion is shown not to be a characterization of space as it exists wholly apart from our powers of conception. Instead, in an adumbration of Kant, his claim is restricted to space as it appears to us. (shrink)

This article traces the origins of Kenneth Wilson's conception of effective field theories (EFTs) in the 1960s. I argue that what really made the difference in Wilson's path to his first prototype of EFT are his long-standing pragmatic aspirations and methodological commitments. Wilson's primary interest was to work on mathematically interesting physical problems and he thought that progress could be made by treating them as if they could be analyzed in principle by a sufficiently powerful computer. The first point explains (...) why he had no qualms about twisting the structure of field theories; the second why he divided the state-space of a toy model field theory into continuous slices by following a standard divide-and-conquer algorithmic strategy instead of working directly with a fully discretized and finite theory. I also show how Wilson's prototype bears the mark of these aspirations and commitments and clear up a few striking ironies along the way. (shrink)

There is no question, of course, that music is a temporal art. Stravinsky, noting that it is inconceivable apart from the elements of sound and time, classifies it quite simply as "a certain organization in time, a chrononomy."1 His definition stands as part of a long and honored tradition that encompasses such diverse figures as Racine, Lessing, and Schopenhauer. Schopenhauer, putting the case in its strongest terms, remarks that music is "perceived solely in and through time, to the complete exclusion (...) of space," thus making explicit the opposition between time and space and ruling out the latter as a possible area for legitimate musical experience. Yet anyone familiar with the philosophical and theoretical literature dealing with music must be struck by the persistence with which spatial terminology and categories appear. Indeed, it would seem to be impossible to talk about music at all without invoking spatial notions of one kind or another. Thus in discussing even the most elementary aspects of pitch organization—and among the musical elements, only pitch, we should remember, is uniquely musical—one finds it necessary to rely upon such spatially oriented oppositions as "up and down," "high and low," "small and large" , and so on. Space, then, pace Schopenhauer, apparently forms an inseparable part of the musical experience. · 1. Igor Stravinsky, Poetics of Music in the Form of Six Lessons, trans, Arthur Knodel and Ingolf Dahl , p. 28. Robert P. Morgan is active as both a music composer and theorist. A professor of music at the University of Chicago, he is currently composing a concerto for flute, oboe, and string orchestra to be performed at Swarthmore College. His previous contribution to Critical Inquiry, "On the Analysis of Recent Music," appeared in the Autumn 1977 issue. Anthony Gilbert responds to the current essay in "Musical Space: A Composer's View". (shrink)

The generally agreed upon principle that legality and ethics can come apart is frequently overlooked in our professional ethics education and decision-making procedures. The crux of the issue is that we teach in our philosophy classes that the law can sometimes be unethical, but then clearly state in nursing codes of ethics that students should always follow the law. The law could no doubt give us some reason to choose action A over action B, but in professional contexts we frequently (...) treat the law as a side-constraint that limits the logical space of choices to exclude even consideration of action B. If B is the mandatory action, this in effect forces professionals to do something unethical by preventing them from ever seeing the ethical action as an option. This is a problem. Ultimately we concede that there might be an irresolvable tension in competing normative interests in ethics and the law, though we suggest that a more nuanced approach to ethical code formation could help alleviate the issue somewhat. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:62. 'HUME ON SPACE AND GEOMETRY': ONE RESERVATION In so far as Rosemary Newman disagrees with any2 thing said in my 'Infinite Divisibility in Hume's Treatise ' - which seems, happily, not to be so very far - I hasten to report that I am now persuaded. Thus my suggested reason for refusing to allow that an impression of blackness could give rise to the idea of extension (...) was not, after all, 3 Hume's. And no doubt his conviction that whatever ^s capable of being divided in_ infinitum, must consist of an infinite number of parts (T26) was in part sustained by "the atomistic type of phenomenalism advanced in the first Part 4 of Book I of the Treatise". For to any objection that this nowadays so plainly unacceptable conviction had been accepted as obviously correct by such formidable predecessors as Berkeley and Hobbes, it could be replied that they too had their commitments to their own brands of atomism. In her further comments upon "Hume's phenomenalist atomism" Newman notices, as "a very curious claim", his statement that when - like the true philosopher he was! - he locked at a table:- My senses convey to me only the impressions of colour 'd points, dispos 'd in a certain manner (T34). So I was sorry that she seems to have missed the bold priority claim which, referring to the same passage, I made on Hume's behalf in that article: "Anyone familiar with the theories and the paintings of Seurat might also mischievously characterize the Hume of this Section as 'the Father of Pointillisme' "! But at the end of her paper, although I think only at the end, Newman begins to go very wrong indeed. She says: "Turning to the Enquiry there is little to indicate any shift in Hume's opinion of geometry as a body of synthetic but necessary knowledge." After remarking that Hume does not repeat "any of his earlier arguments" against infinite divisibility "nor those in support of a system of mathematical 63. points", she notices that, in the paragraph characterizing propositions stating only the relations of ideas, geometry "is classed as a science alongside arithmetic and algebra (E25) ".7 Next she quotes the end of that paragraph, and at once comments: "Flew thinks that in the Enquiry Hume is to be seen as 'restoring pure geometry to its place alongside Q the other two elements in the trinity',..." Newman does not, so far as I can see, offer any reason for dismissing this suggestion - apart, that is, from asserting that the paragraph from which she has just quoted "can be interpreted so as to remove any apparent inconsistency with the claim that the impossibility of conceiving the negation of a geometrical axiom has the same ground in the Enquiry as in the Treatise, namely, the invariant character of sensible space." She just tells us that "Where geometry is concerned I follow Atkinson's opinion in finding no reason to suppose that 9 Hume abandoned the Treatise stand." This I find, to say the least, surprising since the very sentence of Hume's Philosophy of Belief from which she quoted my contrary opinion does provide what I still consider to be a quite decisive reason. Since she does not discuss either my reason or the Hume passage to which I was referring, I can here do nothing else or better than repeat myself; adding only and by the way that Professor Atkinson's paper 'Hume on Mathematics' was published a year before that book:Besides restoring pure geometry to its place alongside the other two elements of the trinity, the Inquiry also sketches an account of applied mathematics. This is something the earlier book did not provide at all. 'Every part of mixed mathematics proceeds on the supposition that certain laws are established by nature in her operations, and abstract reasonings are employed, either to assist experience in the discovery of these laws or to determine their influence in particular instances... Thus it is a law of motion, discovered by experience, that the moment or force of any body in motion is in 64. the compound ratio or proportion of its solid contents and its velocity, and, consequently... (shrink)

This paper reexamines the historical debate between Leibniz and Newton on the nature of space. According to the traditional reading, Leibniz (in his correspondence with Clarke) produced metaphysical arguments (relying on the Principle of Sufficient Reason and the Principle of Identity of Indiscernibles) in favor of a relational account of space. Newton, according to the traditional account, refuted the metaphysical arguments with the help of an empirical argument based on the bucket experiment. The paper claims that Leibniz’s and (...) Newton’s arguments cannot be understood apart from the distinct dialectics of their respective positions vis-à-vis Descartes’ theory of space and physics. Against the traditional reading, the paper argues that Leibniz and Newton are operating within a different metaphysics and different conceptions of “place,” and that their respective arguments can largely remain intact without undermining the other philosopher’s conception of space. The paper also takes up the task of clarifying the distinction between true and absolute motion, and of explaining the relativity of motion implied by Leibniz’s account. The paper finally argues that the two philosophers have different conceptions of the relation between metaphysics and science, and that Leibniz’s attempt to base physical theory on an underlying metaphysical account of forces renders his account of physics unstable. (shrink)

The aim of the article is to present a model of causal relations that is based on what is known about human causal reasoning and that forms guidelines for implementations in robots. I argue for two theses concerning human cognition. The first is that human causal cognition, in contrast to that of other animals, is based on the understanding of the forces that are involved. The second thesis is that humans think about causality in terms of events. I present a (...) two-vector model of events, developed by Gärdenfors and Warglien, which states that an event is represented in terms of two main components – the force of an action that drives the event, and the result of its application. Apart from the causal mapping, the event model contains representations of a patient, an agent, and possibly some other roles. Agents and patients are objects (animate or inanimate) that have different properties. Following my theory of conceptual spaces, they can be described as vectors of property values. At least two spaces are needed to describe an event, an action space and a result space. The result of an event is modeled as a vector representing the change of properties of the patient before and after the event. In robotics the focus has been on describing results. The proposed model also includes the causal part of events, typically described as an action. A central part of an event category is the mapping from actions to results. This mapping contains the central information about causal relations. In applications of the two-vector model, the central problem is how the event mapping can be learned in a way that is amenable to implementations in robots. Three processes are central for event cognition: causal thinking, control of action and learning by generalization. Although it is not yet clear which is the best way to model how the mappings can be learned, they should be constrained by three corresponding mathematical properties: monotonicity (related to qualitative causal thinking); continuity (plays a key role in activities of action control); and convexity (facilitates generalization and the categorization of events). I argue that Bayesian models are not suitable for these purposes, but some more geometrically oriented approach to event mappings should be used. (shrink)

An urbanely written dialogue which convincingly demonstrates the "compartmentalized" character of a number of modern cosmologies. The implications and inconsistencies of biological and physical views of nature, space and time take up the first part of the book; the second turns to an examination of a Steineresque mysticism, a puzzling emphasis since the objections raised to it in the text itself are never satisfactorily answered. Barfield's major polemic point, the need for more communication among intellectual disciplines as they examine (...) their basic assumptions, is presented with cogency and esprit.--C. L. B. (shrink)

Boundaries have gained analytical prominence in sociology of science. Notably, there have been studies on how academics differentiate themselves from outsiders in order to secure their legitimacy. In university departments, scholars engage in boundary work to defend their intellectual communities and institutional resources. While boundary struggles are characteristic of academia, they rarely result in departmental restructuring. This article examines a case where a theoretical divide between social and cultural anthropologists and biological anthropologists led to a departmental split. The study reveals (...) a shift from peaceful coexistence to a full-blown conflict between two intellectual communities and asks, what circumstances gave rise to the activation of a latent intellectual boundary? Drawing on interview data, I demonstrate how changes in the distribution of faculty and the alignment of intellectual, seniority, and gender differences activated the latent boundary. After its activation, scholars engaged in boundary work and expressed their intellectual differences in faculty meetings and interactions with colleagues, which led to arguments about the department’s identity that hampered the unit’s operation. The study shows how boundary work among scholars can pull apart the fabric of a department, causing intellectual identities to diverge and the organization to split. (shrink)

Through publicness we offer a reconceptualization of marginality in the city, one that makes apparent the “inherent porosity” of the boundaries that organize urban life (Harvey 2006, 19). Our analysis attends to moments of publicness during fieldwork spent in various spaces within the city of Ottawa, Ontario, with individuals who use drugs and/or panhandle. Much of this research took place in central neighborhoods of Ottawa, which serve as the public image of the nation’s capital: Lowertown to the East of Parliament (...) Hill, and Centretown to the South. These neighborhoods hold the largest concentration of national and historical monuments in the city. They also contain the largest concentration of public marginality, including a cluster of homeless shelters and harm reduction services. In this article we examine this paradox of urban marginality and the limits of exclusion for conceptualizing it. While marginal individuals are deemed invisible, unimportant, and apart from “normal” city life, they are present and visible, perhaps more visible than anyone else. Even from marginal positions individuals remain affective participants in the space of the city, and constitutive of the urban experience. (shrink)

Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit (...) the major milestones in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces. (shrink)

Some Philosophical Prehistory of General Relativity As history, my remarks will form rather a medley. If they can claim any sort of unity (apart from a ...

This paper deals with the perception of depth in two-dimensional pictures. Two indirect theories of perception, the Mainstream Theory and the Projection Theory, are compared with a direct Adverbial Theory. Apart from seeming to be the philosophical counterpart to present-day empirical theories of perception, the first two theories seem to be tailor-made to deal with this phenomenon, where the perceived space is certainly not out there, on or behind the canvas: they claim that pictorial space is constructed by (...) the brain as the direct object of perception. In contrast, the Adverbial Theory seems unsuited to deal with this phenomenon. I argue, however, that both constructivist theories are incoherent. They misconstrue the intentionality of perception, and fail to attend to the perceptual experience itself. The version of the Adverbial Theory that I defend claims that nothing needs to be constructed: the picture is the direct object of perception, but we perceive it in a certain way. The brain creates no pictorial space; there is only a perceptual experience as of a three-dimensional scene. The Adverbial Theory can thus account for the empirical data, without suffering from coherence problems. (shrink)

We are, Julia Kristeva writes, strangers to ourselves; and indeed much of contemporary theory describes the human condition as one of alienation. Eloquently arguing that we cannot explain the developement of individuality or subjectivity apart from its social context, Kelly Oliver makes a powerful case for recognizing the social aspects of alienation and the psychic aspects of oppression.

In _The Preparation of the Novel_, a collection of lectures delivered at a defining moment in Roland Barthes's career, the critic spoke of his struggle to discover a different way of writing and a new approach to life. _The Neutral_ preceded this work, containing Barthes's challenge to the classic oppositions of Western thought and his effort to establish new pathways of meaning. _How to Live Together_ predates both of these achievements, a series of lectures exploring solitude and the degree of (...) contact necessary for individuals to exist and create at their own pace. A distinct project that sets the tone for his subsequent lectures, _How to Live Together_ is a key introduction to Barthes's pedagogical methods and critical worldview. In this work, Barthes focuses on the concept of "idiorrhythmy," a productive form of living together in which one recognizes and respects the individual rhythms of the other. He explores this phenomenon through five texts that represent different living spaces and their associated ways of life: Émile Zola's _Pot-Bouille_, set in a Parisian apartment building; Thomas Mann's _The Magic Mountain_, which takes place in a sanatorium; André Gide's _La Séquestrée de Poitiers_, based on the true story of a woman confined to her bedroom; Daniel Defoe's _Robinson Crusoe_, about a castaway on a remote island; and Pallidius's _Lausiac History_, detailing the ascetic lives of the desert fathers. As with his previous lecture books, _How to Live Together_ exemplifies Barthes's singular approach to teaching, in which he invites his audience to investigate with him -- or for him -- and wholly incorporates his listeners into his discoveries. Rich with playful observations and suggestive prose, _How to Live Together_ orients English-speaking readers to the full power of Barthes's intellectual adventures. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Taking Up Space:Museum Exploration in the Twenty-First CenturyTiffany Sutton (bio)Museums have become a crucible for questions of the role that traditional art and art history should play in contemporary art. Friedrich Nietzsche argued in the nineteenth century that museums can be no more than mausoleums for effete (fine) art.1 Over the course of the twentieth century, however, curators dispelled such blanket pessimism by showing that what keeps historical (...) art museums, both comprehensive and modern, "alive" and relevant in the modern art world are the things that curators do with the artworks in their collections.2 In certain cases, I will argue in this article, the focus on artworks and the relationship between them can be rewardingly shifted onto the spatial aspect of the museum. I will try to show what such a shift of focus entails, show that it involves a gestalt shift (in Wittgenstein's terms, the "dawning of an aspect"), and illustrate the limits within which this can arise.3 The foremost of these limiting factors is museum architecture, and I will discuss this to the extent that it determines the limits of what curators can do. How architects do things with museums, however, lies outside the scope of this article.An Art Historical Heuristic Gets a Curatorial MakeoverNineteenth-century art museums typically were vast, labyrinthine, and built to assume the shape of a comprehensive art historical narrative, so they were easy targets for ideologues drawn to vibrant modern artworks and the controversy surrounding them. At the turn of the twentieth century new commercial galleries developed a distinctively modern mode of display in which individual artworks were showcased with plenty of space around them.4 Had existing museums changed their ways to accommodate these developments, the momentum of a new aesthetic of flatness, surface, [End Page 87] and yet purer forms of conceptualism would have been lost. It was not a time for absorption and deflation: new museums, no less monumental and historical but smaller and with fewer volumes, were commissioned to give modern art the appearance of a fresh start.5 The weightless upward mobility of Frank Lloyd Wright's Guggenheim Museum in Manhattan, modeled in 1945 and opened to the public in 1959, consummated this trend of the first half of the twentieth century and gave it its purest form. What the building spurt revealed was that as art changes, it demands to be reflected in its surroundings, not merely accommodated. That the response was to build new museums rather than new wings suggests the inner workings of the principle—call it "curatorial heuristic one"—that, whereas art history is fluid and simply flows forward with new developments, museums are not of this nature; they can become effete.The curatorial revision of this heuristic was a century in coming. As often happens when emerging movements are yet underdetermined, modernism suppressed in its beginnings the background factor that would seem to entail the end of modern art when finally brought into focus: the very context of display that had once set it apart. Duchamp's Readymades (1913) gave the initial nod (or wink) to the gallery context; it was, however, ignored, as a suppressed punch line, until art history was ready to concede the importance of the context of display—not in the gallery, but in the museum—to a site-specific artwork by Richard Serra: his Splashing and Prop (1968). With the museum's framing context and, concomitantly, the importance of the curator's work conceded, the barrier that had kept lesser masterpieces in the basement (or out of the museum) were removed. Unearthed, these began to circulate, and attention centered on the relation in which they stood to better-known artworks, either as suppressed alternates or as descendants of an artistic lineage. So postmodern sprawl began, with the display of multiple alternative art histories drawing, as modernism had, on available display conventions for periodizing according to internal principles (period, school, genre, style) such that detection of them devolved upon the viewer.When public uses for the new public museums began to diversify (from an historical/educational focus to aesthetic/educational and cultural/political ones), principles for ordering artworks were... (shrink)

Metaphors of positions, spectrums, perspectives, viewpoints, and polarization reflect the same model, which treats beliefs—and the people who hold them—as points in space. This model is deeply rooted in quantitative research methods and influential traditions of Continental philosophy, and it is evident in some qualitative research. It can suggest that deliberation is difficult and rare because many people are located far apart ideologically, and their respective positions can be explained as dependent variables of factors like personality, partisanship, and demographics. (...) An alternative model treats a given person’s beliefs as connected by reasons to form networks. People disclose the connections among their respective beliefs when they discuss issues. This model offers insights about specific cases, such as discussions conducted on two US college campuses, which are represented here as belief-networks. The model also supports a more optimistic view of the public’s capacity to deliberate. (shrink)

While Sigmund Freud and Maurice Merleau‐Ponty both acknowledge the role that spatiality plays in human life, neither pays any explicit attention to the intersections of race and space. It is Franz Fanon who uses psychoanalysis and phenomenology to provide an account of how the psychical and lived bodily existence of black people is racially constituted by a racist world. More precisely, as I argue in this paper, Fanon's work demonstrates how psychical and bodily spatiality cannot be adequately understood apart (...) from the environing space of the social world. For Fanon, body, psyche, and world mutually influence and constitute each other. In a raced and racist world, therefore, the lived bodily experience and the unconscious of human beings will be racially and racist‐ly constituted as well. This will show you how in psychoanalysis we take spatial ways of looking at things seriously. Sigmund Freud1 Sigmund Freud, “The Question of Lay Analysis,” in volume 20 of The Standard Edition of the Complete Psychological Works of Sigmund Freud, ed. and trans. James Strachey (London: The Hogarth Press, 1959), 195. Everything throws us back on to the organic relations between subject and space, to that gearing of the subject onto his world which is the origin of space. Maurice Merleau‐Ponty2 Maurice Merleau‐Ponty, Phenomenology of Perception, trans. Colin Smith (New York: Routledge, 1962), 251. Hence we are driven from the individual back to the social structure. If there is a [neurotic] taint, it lies not in the “soul” of the individual but rather in that of the environment. Franz Fanon3 Franz Fanon, Black Skin, White Mask, trans. Charles Lam Markmann (New York: Grove Press, 1967), 213. (shrink)

A new and comprehensive look at the reasons behind successful or failed nation building Nation Building presents bold new answers to an age-old question. Why is national integration achieved in some diverse countries, while others are destabilized by political inequality between ethnic groups, contentious politics, or even separatism and ethnic war? Traversing centuries and continents from early nineteenth-century Europe and Asia to Africa from the turn of the twenty-first century to today, Andreas Wimmer delves into the slow-moving forces that encourage (...) political alliances to stretch across ethnic divides and build national unity. Using datasets that cover the entire world and three pairs of case studies, Wimmer's theory of nation building focuses on slow-moving, generational processes: the spread of civil society organizations, linguistic assimilation, and the states' capacity to provide public goods. Wimmer contrasts Switzerland and Belgium to demonstrate how the early development of voluntary organizations enhanced nation building; he examines Botswana and Somalia to illustrate how providing public goods can bring diverse political constituencies together; and he shows that the differences between China and Russia indicate how a shared linguistic space may help build political alliances across ethnic boundaries. Wimmer then reveals, based on the statistical analysis of large-scale datasets, that these mechanisms are at work around the world and explain nation building better than competing arguments such as democratic governance or colonial legacies. He also shows that when political alliances crosscut ethnic divides and when most ethnic communities are represented at the highest levels of government, the general populace will identify with the nation and its symbols, further deepening national political integration. Offering a long-term historical perspective and global outlook, Nation Building sheds important new light on the challenges of political integration in diverse countries. (shrink)

Continuing the study of apartness in lattices, begun in [8], this paper deals with axioms for a product a-frame and with their consequences. This leads to a reasonable notion of proximity in an a-frame, abstracted from its counterpart in the theory of set-set apartness.

Toward the end of his monograph The Craftsman, the American philosopher Richard Sennett describes two different ways of building a house.1 The designer of the first house is the philosopher Ludwig Wittgenstein, and the designer of the second house is the architect Adolf Loos. Though both men embrace the same principles of the New Realism—"purity," "simplicity," and "honesty"—the results of these two builders are fundamentally different. Wittgenstein was not satisfied at all with his abode in the end. Though he says (...) it has "good manners," he accuses it of lacking a great deal of "primordial life." Therefore the Jewish philosopher will never build a house again, apart from his hut in Norway and his one house on the .. (shrink)

In _The Preparation of the Novel_, a collection of lectures delivered at a defining moment in Roland Barthes's career (and completed just weeks before his death), the critic spoke of his struggle to discover a different way of writing and a new approach to life. _The Neutral_ preceded this work, containing Barthes's challenge to the classic oppositions of Western thought and his effort to establish new pathways of meaning. _How to Live Together_ predates both of these achievements, a series of (...) lectures exploring solitude and the degree of contact necessary for individuals to exist and create at their own pace. A distinct project that sets the tone for his subsequent lectures, _How to Live Together_ is a key introduction to Barthes's pedagogical methods and critical worldview. In this work, Barthes focuses on the concept of "idiorrhythmy," a productive form of living together in which one recognizes and respects the individual rhythms of the other. He explores this phenomenon through five texts that represent different living spaces and their associated ways of life: Émile Zola's _Pot-Bouille_, set in a Parisian apartment building; Thomas Mann's _The Magic Mountain_, which takes place in a sanatorium; André Gide's _La Séquestrée de Poitiers_, based on the true story of a woman confined to her bedroom; Daniel Defoe's _Robinson Crusoe_, about a castaway on a remote island; and Pallidius's _Lausiac History_, detailing the ascetic lives of the desert fathers. As with his previous lecture books, _How to Live Together_ exemplifies Barthes's singular approach to teaching, in which he invites his audience to investigate with him--or for him--and wholly incorporates his listeners into his discoveries. Rich with playful observations and suggestive prose, _How to Live Together_ orients English-speaking readers to the full power of Barthes's intellectual adventures. (shrink)

Working within the framework of Bishop's constructive mathematics, we will show that it is possible to define compactness in a more general setting than that of uniform spaces. It is also shown that it is not possible to do this in a topological space.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Cartographic Memory: Social Movement Activism and the Production of Space by Juan HerreraAída R. GuhlincozziCartographic Memory: Social Movement Activism and the Production of Spaceby juan herrera Durham, N.C.: Duke University Press, 2022Juan Herrera’s historical recounting of Latino activism in Fruitvale, California, in Cartographic Memory: Social Movement Activism and the Production of Space is stellar. In fact, the case focused on by Herrera as an example of (...) activism producing space and creating change in the name of social justice is not the only top-quality contribution to Latinx geographies to be found in this book. Herrera’s conceptualization of “cartographic memory” builds on the intertwining of Latinx writers and historians with traditional spatial thought from the history of geography. His definition of “cartographic memory” as a “political remaking of urban geography and therefore a selective mapping” adds to the broader oeuvre of activism and space coming out in recent years (14).The geographic location for Cartographic Memory comes from the author’s long history of working in and around Fruitvale as both a volunteer and community member. As a new resident of the Oakland area, Herrera mistakenly navigated himself to Fruitvale, where he found the elements of the place clearly speaking to a cultural aesthetic of Latin-idad. Intrigued, Herrera began volunteering in the area, and learned more of the long activist history of the space. That activist history, Herrera argues, has long been under-studied, or even forgotten, in Chicano activist history, and merits recognition. Herrera’s efforts with [End Page 139] this book go a long way to gathering together that spatial history and reconstructing it for the reader through interviews and oral histories with numerous activists, extensive archival research, and ethnography focusing on the 1960s and 1970s Mexican-American activist mobilization in support of the Chicano movement.The power of the focus on Fruitvale must be recognized, as Herrera also makes space for intently peeling apart the layers of nonprofit funding, social movements, and community-building and support. The chapter, “Revolution Interrupted,” is about the funding situation of the Unity Council in Fruitvale and how the funding structure was constructed over time in the context of the political and economic opportunities of the 1960s. It speaks to how this had a profound effect on the organizers and community given the shift from grassroots to institutional funding. This chapter opens the book with a focus on the national scope of funding opportunities for organizations in the 1960s that focused on race and ethnicity. Through this lens are explored the effects of local political actions—such as the 1969 speech by San Antonio-based Mexican American Youth Organization (MAYO) leader Jose Angel Gutierrez—on funding at the federal level. Because of the perceived militancy of these remarks, the U.S. Congress became concerned, and eventually passed the 1969 Tax Reform bill, limiting the types of projects that could be funded philanthropically. This type of multi-scale understanding of Fruitvale activism is threaded throughout the entire book, from chapter 1, “Making Place,” in which Herrera summarizes activist perspectives on Fruitvale as emphasizing “not only how the neighborhood itself [produced] a geography of activism but also how it was interconnected to other places of struggle throughout the United States” (emphasis in original; 33).Herrera also navigates the interactions of race, ethnicity, and space, tracing how coalitions, influences on political efforts, and collaboration took place throughout Fruitvale and Oakland during this period. His second chapter, “The Other Minority,” identifies where Black Panther Party-related work occurred; the marketization that began to occur of a non-threatening, non-Black “Latino” identity; the effect that this had on activist efforts; and more. Importantly, in this chapter Herrera’s interviews reveal that part of the interest in these coalitions came from the clear organizational success Black activists had achieved in their [End Page 140] work, leading Mexican American activists in Oakland to pursue similar efforts. One interviewee, Herman Gallegos, a prominent activist at the time, spoke of recalling an event where Black men would gather monthly to focus on leadership. Thinking highly of them, he says that he recognized them as future “mayors, judges... [but] kept thinking... (shrink)

This essay is a conversation between two South Asian Muslim sisters both of whom are feminist academics of color, where one immigrated to the United States and the other, a decade apart, to United Kingdom. The aim of this essay is to examine the ways in which white supremacist structures influenced and molded our personal journeys as well as how our narratives are deeply entangled within broader conversations around patriarchy, neo-liberal feminism, and anti-Muslim racism.