Purpose – The purpose of this paper is to explain how abstract space of the State – universally and specifically within the context of Middle Eastern cities – aims to homogenise the city and eliminate any anomaly that threatens its power structure. Design/methodology/approach – Through a historical and discourse analysis of these policies and processes in the two case studies, this paper presents a contextualised reading of Lefebvre’s concept of abstract space and process of abstraction in (...) relation to the alienation of political public spaces. Findings – The paper proposes that regardless of these homogenising strategies being applied universally, they fail to respond to contextual particularities and therefore they – in a contradictory manner – may themselves produce a space of resistance and difference. Originality/value – This paper focusses on Iran, the case of Tehran and Turkey, the case of Taksim Square and Gezi Park in Istanbul. Recent policies and strategies have been proposed and implemented to reduce, alienate and possibly neutralise the impacts of urban and political protests in these cities and socio-political contexts. (shrink)

In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching space-time models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract space-time structures based on the real numbers and the integers, considering three different accessibility (...) relations between spatio-temporal points. (shrink)

Deictic pointers allow the nervous system to exploit information in a frame that is centered on the object of interest. This processing may take place in visual or haptic space, but the information processing advantages of deictic pointing can also be applied in abstract spaces, providing the basis for analogical transfer. Simulation and behavioral results illustrating this progression from embodiment to abstraction are discussed.

The present paper aims to contribute to the substantivalism versus relationalism debate and to defend general relativity (GR) against pseudoscientific attacks in a novel, especially inclusive way. This work was initially motivated by the desire to establish the incompatibility of any ether theories with accelerated cosmic expansion and inflation (motto: where would a hypothetical medium supposedly come from so fast?). The failure of this program is of interest for emergent GR concepts in high energy particle physics. However, it becomes increasingly (...) important to guard scientific results against their misrepresentation by fundamentally anti-scientific agendas. We therefore argue that although it is not known whether the perceived space-time is fundamental (rather than a condensed state or a particular membrane), in a fundamental theory, space-time must be abstract relational: fundamental space-time is the consistent spatial-temporal arrangement of events. To pursue its own goals, this work should be accessible to a wide audience: physicists, philosophers of science, those being tempted by anti-relativity theories, but also those who vigorously defend some orthodox relativity that is not actually supported by GR. It must thus be extensive in order to satisfy the different parties’ desire to have included and understood their respective positions. (shrink)

Several modern accounts of explanation acknowledge the importance of abstraction and idealization for our explanatory practice. However, once we allow a role for abstraction, questions remain. I ask whether the relation between explanations at different theoretical levels should be thought of wholly in terms of abstraction, and argue that changes of the quantities in terms of which we describe a system can lead to novel explanations that are not merely abstractions of some more detailed picture. I use the example of (...) phase transitions as described by statistical mechanics and thermodynamics to illustrate this, and to demonstrate some details of the relationship between abstraction, idealization, and novel explanation. (shrink)

Celebrated performer Giulio Caccini's life as a court musician throws light on the ways in which the soloist formulated and reformulated his/her own identity in order to fit within each of the spaces used for music. Tracing the documented performances associated with Caccini, one can map them onto a continuum of spaces from the most public to the most private. Caccini's successful passage into the more intimate spaces required him to re-form himself as the inheritor of the century-old tradition of (...) the intimate vocal improvvisatori, a stylistic and physical transformation that was, in a sense, his life's work. This performative conception of his musical work is a potent reminder of the ambiguous status of solo song at the beginning of the Seicento, perched between the abstract space of the printed score and the traditional space of the court chamber. (shrink)

L’objectif de cet article est de montrer que la réflexion engagée par Jules Vuillemin sur les structures algébriques dans les années 1960 lui permettra de dégager une conception structurale de l’abstraction, dont il tirera une compréhension nomologique de l’objectivité. Ces deux concepts seront alors convoqués bien des années plus tard pour proposer une construction de l’espace représentatif, que Vuillemin conçoit comme une réfutation de l’idéalisme matériel de Berkeley. La possibilité de retracer la genèse de nos notions spatiales et de leur (...) garantir une certaine objectivité serait ainsi rendue possible par un emprunt aux méthodes de l’algèbre moderne, conformément à l’esprit de La Philosophie de l’algèbre. (shrink)

This book presents an innovative analysis of the role of imagination as a central concept in both literary and art criticism. Dee Reynolds brings this approach to bear on works by Rimbaud, Mallarme;, Kandinsky, and Mondrian. It allows her to redefine the relationship between Symbolism and abstract art, and to contribute new methodological perspectives to comparative studies of poetry and painting. The late nineteenth and early twentieth century was a crucial period in the emergence of new modes of representation, (...) and is currently at the forefront of critical enquiry. This is the first book to examine Symbolism and abstraction in this way, and the first to treat these poets and painters together. It is an original contribution to interdisciplinary scholarship in art history, literary history, and comparative aesthetics. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized functions (...) to solve nonlinear problems on Hilbert spaces. (shrink)

We study computability of the abstract linear Cauchy problem equation image)where A is a linear operator, possibly unbounded, on a Banach space X. We give necessary and sufficient conditions for A such that the solution operator K: x ↦ u of the problem is computable. For studying computability we use the representation approach to computable analysis developed by Weihrauch and others. This approach is consistent with the model used by Pour-El/Richards.

Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive critical assessment (...) of the problems raised by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

PREFACE: - BY his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. The achievement consists essentially in this Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circumstances for example, distance will make it appear smaller and dimmer. We make allowance for this (...) almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the observer has hitherto been too crude a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer and only an amorphous combination of the two is left inherent in the external world. When space and time are relegated to their proper source the observer the world of nature which remains appears strangely unfamiliar but it is in reality simplified, and the underlying unity of the principal phenomena is now clearly revealed. The deductions from this new outlook have, with one doubtful exception, been confirmed when tested by experiment. It is my aim to give an account of this work without intro ducing anything very technical in the way of mathematics, physics, or philosophy. The new view of space and time, so opposed to our habits of thought, must in any case demand unusual mental exercise. The results appear strange and the incongruity is not without a humorous side. For the first nine chapters the task is one of interpreting a clear-cut theory, accepted in all its essentials by a large and growing school of physicists although perhaps not everyone would accept the authors views of its meaning. Chapters x and xi deal with very recent advances, with regard to which opinion is more fluid. As for the last chapter, containing the authors specula tions on the meaning of nature, since it touches on the rudiments of a philosophical system, it is perhaps too sanguine to hope that it can ever be other than controversial. A non-mathematical presentation has necessary limitations and the reader who wishes to learn how certain exact result follow from Einsteins, or even Newtons, law of gravitation m bound to seek the reasons in a mathematical treatise. But thj limitation of range is perhaps less serious than the limitation of intrinsic truth. There is a relativity of truth, as there is a relativity of space. For is and IS-NOT though with Rule and Line And UP-AND-DOWK without, I could define, Alas It is not so simple. We abstract from the phenomena that which is peculiar to the position and motion of the observer but can we abstract that which is peculiar to the limited imagina tion of the human brain We think we can, but only in the symbolism of mathematics. As the language of a poet rings with a truth that eludes the clumsy explanations of his commentators, so the geometry of relativity in its perfect harmony expresses a truth of form and type in nature, which my bowdlerised version misses. But the mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with familiar images. The mathematician, who handles x so lightly, may fairly be asked to state, not indeed the in scrutable meaning of a in nature, but the meaning which x conveys to him. Although primarily designed for readers without technical knowledge of the subject, it is hoped that the book may also appeal to those who have gone into the subject more deeply. A few notes have been added in the Appendix mainly to bridge the gap between this and more mathematical treatises, and to indicate the points of contact between the argument in the text and the parallel analytical investigation. It is impossible adequately to express my debt to con temporary literature and discussion... (shrink)

Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the non-unitary collapse processes are interpreted as isometric functional transformations. Several experiments are analyzed in the new context.

Modern cosmology treats space and time, or rather space-time, as concrete particulars. The General Theory of Relativity combines the distribution of matter and energy with the curvature of space-time. Here space-time appears as a concrete entity which affects matter and energy and is affected by the things in it. I question the idea that space-time is a concrete existing entity which both substantivalism and reductive relationism maintain. Instead I propose an alternative view, which may be (...) called non-reductive relationism, by arguing that space and time are abstract entities based on extension and changes. (shrink)

concepts are defined as concepts that cannot be experienced directly through the sensorimotor modalities. Explaining our understanding of such concepts poses a challenge to neurocognitive models of knowledge. One account of how these concepts come to be represented is that sensorimotor representations of grounded experiences are reactivated in a way that is constitutive of the abstract concept. In the present experiment, we investigated how sensorimotor information might constitute GOD-related concepts, and whether a person’s self-reported religiosity modulated this grounding. To (...) do so, we manipulated both the state of the body and the state of stimuli in two tasks that required conceptual categorization of abstract words. Linear Mixed Effects model fitting procedures were used to determine which manipulated factors best predicted response latency and accuracy in both tasks. We successfully replicated previous research demonstrating faster categorization of GOD-related words when they were presented at the top of the screen. Importantly, results demonstrated that the kneeling posture manipulation enhanced this effect, as did religiosity, as participants who scored higher in religiosity showed a greater effect of the posture manipulation on the speed with which word categorization occurred when those words were presented in the higher visuospatial presentation condition. Overall, we interpreted our findings to suggest that directly manipulating sensorimotor information can facilitate the categorization of abstract concepts, supporting the notion that this information in part constitutes the representation of abstract concepts. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main (...) reason for producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

Hume's discussion of the idea of space in his Treatise on Human Nature is fundamental to an understanding of his treatment of such central issues as the existence of external objects, the unity of the self, the relation between certainty and belief, and abstract ideas. Marina Frasca-Spada's rich and original study examines this difficult part of Hume's philosophical writings and connects it to eighteenth-century works in natural philosophy, mathematics and literature. Focusing on Hume's discussions of the infinite divisibility (...) of extension, the origin of the idea of space, geometry, and the notion of a vacuum, she shows that the central questions of Hume's 'science of human nature' - what does the 'science of human nature' reveal about the mind and its operations? what is experience? - underlie all of these discussions. Her analysis points the way to a reassessment of the central current interpretative problems in Hume studies. (shrink)

In finite type arithmetic, the real numbers are represented by rapidly converging Cauchy sequences of rational numbers. Ulrich Kohlenbach introduced abstract types for certain structures such as metric spaces, normed spaces, Hilbert spaces, etc. With these types, the elements of the spaces are given directly, not through the mediation of a representation. However, these abstract spaces presuppose the real numbers. In this paper, we show how to set up an abstract type for the real numbers. The appropriateness (...) of our construction works in tandem with the bounded functional interpretation. (shrink)

Most research on metaphors that construe time as motion (motion metaphors of time) has focused on the question of whether it is the times or the person experiencing them (ego) that moves. This paper focuses on the equally important distinction between metaphors that locate times relative to ego (the ego-based metaphors Moving Ego and Moving Time) and a metaphor that locates times relative to other times (sequence is relative position on a path). Rather than a single abstract target domain (...) TIME, these two kinds of temporal metaphor metaphorize different kinds of temporal concept—perspective-specific vs. perspective-neutral temporal concepts. Recognition of this distinction enhances the explanatory potential of conceptual metaphor theory (Lakoff and Johnson 1980). An example involves the interaction of deixis and the temporal reference crosslinguistically of vocabulary with the spatial meanings in-front and behind. More generally, this approach refines our ability to describe the temporal concepts involved in motion metaphors of time. Such temporal concepts are present not only in the target domains, but also in the source domains of motion metaphors of time, where we find space-to-time metonymy, which may play a role in motivating the metaphors. In order to distinguish such metonymy from metaphor, we need to characterize metaphor as a mapping across frames rather than domains. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Space, Place and Capitalism: The Literary Geographies of “The Unknown Industrial Prisoner” by Brett HeinoDavid McLaughlinSpace, Place and Capitalism: The Literary Geographies of “The Unknown Industrial Prisoner” BY BRETT HEINO Singapore: Palgrave Macmillan, 2021I would not be the first to describe Brett Heino’s new book as timely. Its publication in 2021 coincided with the fiftieth anniversary of the first publication of David Ireland’s The Unknown Industrial (...) Prisoner (1971). This experimental novel, centered on a “kaleidoscopic vision” of its characters and their lives, tells the story of a group of workers at the Puroil refinery in a fictionalized part of Sydney. In Heino’s own words, this project emerged from a desire to write about industrialization and representation in Australian fiction. Working primarily as a legal scholar and historian, this work represents his first foray into literary geography.At the heart of Heino’s argument is a question: What does literature know about space? In his pursuit of a spatially-directed reading of The Unknown Industrial Prisoner, Heino eschews work in literary geography that cultural geographers might recognize— particularly the writings of Sheila Hones, the doyenne of an emerging interdiscipline of literary geography, whose practitioners work at the interstices between literary studies and geography. Heino criticizes this interdisciplinary literary geography as being too focused on establishing the “sovereignty” or “imperialism” of fictional space at the expense of recognizing the [End Page 132] role of literature in the world. Arguably, such a stance is a misreading of the thinking within literary geography that “reading literature is essentially an experimental process in which the categorical distinction between the frames of ‘fact’ and ‘fiction’ become blurred,”1 and where the “ontological distinction between literary and non- literary spaces” is undermined.2 Neither of these statements supposes that reading literature is a practice by which the world falls away and nothing remains but the book. Instead, following Doreen Massey’s idea that space is a complicated process of events and happenings, literary geographers in this mold argue that fiction is a part of life as it happens, and reading is a constitutive practice in the co- production of space.In its place, Heino emphasizes a form of literary geographical thinking that understands literature’s role as being separate from, but intimately connected to, the actual world. His theoretical framework is multi-layered, borrowing from Marxist literary scholars, including Terry Eagleton and Fredric Jameson, and Marxist geographers, including Henri Lefebvre. In essence, however, it can be expressed neatly in the following quotation from geocritic Bertrand Westphal:Fiction does not reproduce the real, but actualises new virtualities that had remained unformulated, and then goes on to interact with the real according to the hypertextual logic of interfaces... fiction detects possibilities buried in the folds of the real, knowing that these folds have not been temporised.3I think that Heino’s rejection of what he characterizes as poststructural literary geography, of the kind represented in his analysis of Sheila Hones’s work, misses some opportunities. First, there are similarities between his conception of literary geography and those he leaves aside— not least, their shared acceptance of the productive tension that sits between literature as text and world as practical, non- representational, and exceeding narrative. Secondly, the shared aim of both approaches is to understand how “representation ‘takes place’ and precisely how texts are part of what happens.”4 This is particularly powerful in the light of Heino’s aim to understand the development and contents of literary texts in materialist terms. Despite these areas [End Page 133] of convergence, Heino’s argument that literary geography’s potential to analyze class and political structures remains untapped is well founded. This is where Heino’s contribution is at its strongest.Heino’s work is at its most convincing when he discusses the realities of “abstract space” that both permeate the spaces of The Unknown Industrial Prisoner and structure the very fabric of latter- twentieth century Australia. Running through both Heino’s critique and Ireland’s novel is an understanding “that the inherent drive of capital is towards the creation of a fragmented, homogenised and hierarchised space within which it can produce and... (shrink)

Russian abstract: В данном сборнике статей раскрывается формирование структурно-онтологического представления о таком явлении, как городское пространство. Наряду с соответствующей концептуализацией, также представлено и объяснено определение городского сообщества. Обоснована логика классификации городских сообществ. А также проанализированы факторы, обуславливающие их устойчивость. -/- English abstract: This collection of articles reveals the formation of a structural-ontological concept of such a phenomenon as urban space. Along with relevant conceptualization, the definition of an urban community is also presented and explained. The logic of (...) classification of urban communities is substantiated. And also analyzed the factors that determine their stability. (shrink)

Philosophers have often claimed that general ideas or representations have their origin in abstraction, but it remains unclear exactly what abstraction as a psychological process consists in. We argue that the Lockean aspiration of using abstraction to explain the origins of all general representations cannot work and that at least some general representations have to be innate. We then offer an explicit framework for understanding abstraction, one that treats abstraction as a computational process that operates over an innate quality (...) class='Hi'>space of fine-grained general representations. We argue that this framework has important philosophical implications for the nativism-empiricism dispute, for questions about the acquisition of unstructured representations, and for questions about the relation between human and animal minds. (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)

Many critics have pointed to the failures of modernist urban design, which include its obliteration of thriving neighborhoods, isolation of functions and production of alienating spaces hostile to the human form. Less focus has been placed on defining the source of the modernists’ errors. This essay argues that these errors were in part due to neglect of the nature of fully embodied experience, a neglect manifested in an overwhelmingly visual disposition in embodiment. The author argues that a visual disposition is (...) implicated in the occlusion of place by the modern concept of abstract space. This concept of space and the visual disposition that is implicated in it undergird the utopianism and veneration for abstract forms that characterized the project of modernist urban design. The author concludes by suggesting that the basis for a humanizing urbanism should be the solicitation of all the senses in synesthetic interaction. This phenomenological critique can help us to see precisely where modernist urban design went wrong; it can also help lead us out of the false dichotomy between alienating modernism and orthodox traditionalism by establishing a basis for successful urban environments in embodiment rather than in any rigidly determined formula for urban design. (shrink)

Art and Abstract Objects presents a lively philosophical exchange between the philosophy of art and the core areas of philosophy. The standard way of thinking about non-repeatable (single-instance) artworks such as paintings, drawings, and non-cast sculpture is that they are concrete (i.e., material, causally efficacious, located in space and time). Da Vinci's Mona Lisa is currently located in Paris. Richard Serra's Tilted Arc is 73 tonnes of solid steel. Johannes Vermeer's The Concert was stolen in 1990 and remains (...) missing. Michaelangelo's David was attacked with a hammer in 1991. By contrast, the standard way of thinking about repeatable (multiple-instance) artworks such as novels, poems, plays, operas, films, symphonies is that they must be abstract (i.e., immaterial, causally inert, outside space-time): consider the current location of Melville's Moby Dick, the weight of Yeats' "Sailing to Byzantium", or how one might go about stealing Puccini's La Boheme or vandalizing Mozart's Piano Concerto No. 9. Although novels, poems, and symphonies may appear radically unlike stock abstract objects such as numbers, sets, and propositions, most philosophers of art think that for the basic intuitions, practices, and conventions surrounding such works to be preserved, repeatable artworks must be abstracta. -/- This volume examines how philosophical enquiry into art might itself productively inform or be productively informed by enquiry into abstracta taking place within not just metaphysics but also the philosophy of mathematics, epistemology, philosophy of science, and philosophy of mind and language. While the contributors chiefly focus on the relationship between philosophy of art and contemporary metaphysics with respect to the overlap issue of abstracta, they provide a methodological blueprint from which scholars working both within and beyond philosophy of art can begin building responsible, mutually informative, and productive relationships between their respective fields. (shrink)

ABSTRACT This article takes up questions regarding the interrelation of the given and the undetermined in Augustine’s understanding of the self. As a critical point, it argues that debate regarding the Augustinian self has been marked by an emphasis on given structures that has constricted conceptions of human becoming. This emphasis emerges by way of competing narratives of discovery: Augustine is presented as a discoverer either of a constitutive space of the self, or of a determinative temporality. It (...) results in accounts of formation that occlude the spiritual significance of the full sweep of Christ’s history, from incarnation through ascension. As a constructive point, this article argues that Augustine positions himself to develop a Christological vision of Christian becoming, rooted in attention to all aspects of Christ’s life and work, by understanding space and time not as structures that fix the bounds of human becoming, but rather as realities that take on different forms in accordance with differing modes of love. (shrink)

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its (...) angles and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

This essay develops on the aesthetic dimensions of decolonial thought in the work of Rodolfo Kusch and Enrique Dussel, who both point us to non-objectifying modes of thinking and being. Beyond a strictly epistemological approach, decolonial critique ought to offer an account of bodies, spaces, and movements that are the very condition of thought—that is to say, the condition of a mode of thinking otherwise, beyond the dominant colonial paradigm. This account of aesthetics involves the spacing and temporalizing of bodies (...) as they live and move through the world, or what Alejandro Vallega calls living-thinking. The spacing-temporalizing of life points us also to the rhythm of life—life as movement, flow, and spacing. Turning to resistant epistemologies alongside the work of Omar Rivera, I consider how these epistemologies go beyond disembodied and abstracted ways of knowing as they sidestep the subject/object divide and engage sensuous and embodied dimensions of thinking, aesthetic experiences, diverse geographies, and histories. In closing, I argue that decolonial aesthetics also points us to a critique of the coloniality of space. Moving beyond a cartographic grid that attempts to capture subjects and spaces in advance on its coordinate plane, decolonial aesthetics opens onto the richness of embodied and cosmic spaces. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces (...) was used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

Abstract.Russell Stannard distinguishes between objective time as measured in theoretical physics and subjective time, or time as experienced by human beings in normal consciousness. Because objective time, or four‐dimensional space‐time for the physicist, does not change but exists all at once, Stannard argues that this is presumably how God views time from eternity which is beyond time. We human beings are limited to experiencing the moments of time successively and thus cannot know the future as already existing in (...) the same way that God does. I argue that Stannard is basically correct in his theological assumptions about God's understanding of time but that his explanation would be more persuasive within the context of a neo‐Whiteheadian metaphysics. The key points in that metaphysics are (1) that creation is contained within the structured field of activity proper to the three divine persons of the Christian doctrine of the Trinity and (2) that the spontaneous decisions of creatures are continually ordered and reordered into an ever‐expanding totality already known in its fullness by the divine persons. (shrink)

The growing body of research on temporal and spatial experience lacks a comprehensive theoretical approach. Drawing on Giddens’ framework, we present time-space distanciation as a construct for theorizing the relations between culture, time, and space. TSD in a culture may be understood as the extent to which time and space are abstracted as separate dimensions and activities are extended and organized across time and space. After providing a historical account of its development, we outline a multi-level (...) conceptualization of TSD supported by research on cultural differences in the experience of time and space. We impact this conceptualization by examining two ethnographic case studies. We conclude by highlighting future research directions. TSD is an integrative, interdisciplinary, multi level construct with the potential to guide the burgeoning social science of time and space. (shrink)

Isaac Newton founded classical mechanics on the view that space is something distinct from body and that time is something that passes uniformly without regard to whatever happens in the world. For this reason he spoke of absolute space and absolute time, so as to distinguish these entities from the various ways by which we measure them (which he called relative spaces and relative times). From antiquity into the eighteenth century, contrary views which denied that space and (...) time are real entities maintained that the world is necessarily a material plenum. Concerning space, they held that the idea of empty space is a conceptual impossibility. Space is nothing but an abstraction we use to compare different arrangements of the bodies constituting the plenum. Concerning time, they insisted, there can be no lapse of time without change occurring somewhere. Time is merely a measure of the cycles of change within the world. (shrink)

When entering an environment, animals – including humans – tend to consult their memories to determine what they know about the place. This information is useful to determine: is this place safe? And what happens next? In this chapter, we argue on both empirical and conceptual grounds that memory is largely organized by space. Spatial relations determine what is recalled and which experiences are combined in generalizations. Time does not play an analogous role. We show that space and (...) time in memory are thus deeply asymmetrical. We conclude with a consequence of our view: spatial organization entails a basic form of abstraction in a way temporal organization does not, and so the spatial organization of memory reveals that memory involves generalization from the very beginning. (shrink)

This book addresses the social, functional and symbolic dimensions of urban space in today’s world. The twelve essays range from a conceptual framing of the issues to case descriptions, rich with illustrations. Together they provide a thorough exploration of the nature and significance of social space and particular aspects of its distribution in today’s urban spaces and the various factors that are competing for it. -/- The book addresses a topic that is intrinsically interdisciplinary. Questions of space (...) are examined from a rich variety of perspectives from urban planning to political philosophy, shedding some light on this shadowy process. Some of the issues addressed include the dichotomies of public and private space, rights and duties regarding the use of space, and conflicts over its allocation. Well-reasoned and lively discussions are offered from the perspective of basic values and rights. The recognition of the specifics of (minority community) identity as an institutional policy is raised in opposition to “abstract distributive accounts of justice” – economic pressures by developers and would-be gentrifiers. (shrink)

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence (...) each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed. (shrink)

What is consciousness? Where is it? What happens to our consciousness when we die? We associate consciousness with our material brain yet no one has found it there, or anywhere else. Within a framework of established science, however, the author outlines a compelling new way to think about consciousness and its workings. This first revised edition of Between Space describes our material world construed of tiny bits of space and time ("quantized space"). Each of these bits exist, (...) as only they can, within a field of non-space; an abstract reality outside of space and time... but not outside of Nature. Non-space is a reality of awareness, meanings, concepts, and ideas of every sort, while space-time is a reality of distinct objects such as your brain. The author describes in detail how self-awareness and your mind are the result of interaction between the two realms by means of Simultaneity and quantum Observation. While this little book contains scientific descriptions and speculations, it's written in common language so that it can be enjoyed by most of us who have little or no background in science or math; about a hundred pages plus many appendices and illustrations. (shrink)

Questions concerning the epistemological status of computer science are, in this paper, answered from the point of view of the formal verification framework. State space reduction techniques adopted to simplify computational models in model checking are analysed in terms of Aristotelian abstractions and Galilean idealizations characterizing the inquiry of empirical systems. Methodological considerations drawn here are employed to argue in favour of the scientific understanding of computer science as a discipline. Specifically, reduced models gained by Dataion are acknowledged as (...) Aristotelian abstractions that include only data which are sufficient to examine the interested executions. The present study highlights how the need to maximize incompatible properties is at the basis of both Abstraction Refinement, the process of generating a cascade of computational models to achieve a balance between simplicity and informativeness, and the Multiple Model Idealization approach in biology. Finally, fairness constraints, imposed to computational models to allow fair behaviours only, are defined as ceteris paribus conditions under which temporal formulas, formalizing software requirements, acquire the status of law-like statements about the software systems executions. (shrink)