In this paper I compare two well studied approaches to topological semantics – the domain-theoretic approach, exemplified by the category of countably based equilogical spaces, Equ and Typ Two Effectivity, exemplified by the category of Baire space representations, Rep . These two categories are both locally cartesian closed extensions of countably based T0-spaces. A natural question to ask is how they are related.First, we show that Rep is equivalent to a full coreflective subcategory of Equ, consisting of (...) the so-called 0-equilogical spaces. This establishes a pair of adjoint functors between Rep and Equ. The inclusion Rep → Equ and its coreflection have many desirable properties, but they do not preserve exponentials in general. This means that the cartesian closed structures of Rep and Equ are essentially different. How ever, in a second comparison we show that Rep and Equ do share a common cartesian closed subcategory that contains all countably based-T0 spaces. Therefore, the domain-theoretic approach and TTE yield equivalent topological semantics of computation for all higher-order types over countably based T0-spaces. We consider several examples involving the natural numbers and the real numbers to demonstrate how these comparisons make it possible to transfer results from one setting to another. (shrink)

We use the theory of triposes to prove that every locale H is the set of truth values of a complete and co-complete quasi-topos into which the category of topological spaces embeds and the topos of sheaves over H reflectively embeds.

The property of admissibility of representations plays an important role in Type–2 Theory of Effectivity . TTE defines computability on sets with continuum cardinality via representations. Admissibility is known to be indispensable for guaranteeing reasonable effectivity properties of the used representations.The question arises whether every function that is computable with respect to arbritrary representations is also computable with respect to closely related admissible ones. We define three operators which transform representations into admissible ones in such a way that relative computability (...) of functions is preserved. Thus the use of admissible representations rather than of non–admissible ones does not decrease the class of relatively computable functions. (shrink)

We present a general notion of realizability encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial cartesian closed categories. We shown how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result) that the category Equ of equilogical spaces models dependent predicate logic. Moreover, we characterize when the general notion of realizability gives rise (...) to a topos, i.e., a model of impredicative intuitionistic higher-order logic. (shrink)

The Cartesian concept of nature, which has determined modern thinking until the present time, has become obsolete. It shall be shown that Hegel's objective-idealistic conception of nature discloses, in comparison to that of Descartes, new perspectives for the comprehension of nature and that this, in turn, results in possibilities of actualizing Hegel's philosophy of nature. If the argumentation concerning philosophy of nature is intended to catch up with the concrete Being-of-nature and to meet it in its concretion, then this is (...) impossible for the finite spirit in a strictly a priori sense – this is the thesis supported here which is not at all close to Hegel. As the argumentation rather has to consider the conditions of realization concerning the Being-of-nature, too, it is compelled to take up empirical elements – concerning the organism, for instance, system-theoretical aspects, physical and chemical features of the nervous system, etc. With that, on the one hand, empirical-scientific premises are assumed (e.g. the lawlikeness of nature), which on the other hand become (now close to Hegel) possibly able to be founded in the frame of a Hegelian-idealistic conception. In this sense, a double strategy of empirical-scientific concretization and objective-idealistic foundation is followed up, which represents the methodical basic principle of the developed considerations. In the course of the undertaking, the main aspects of the whole Hegelian design concerning the philosophy of nature are considered – space and time, mass and motion, force and law of nature, the organism, the pro-blem of evolution, psychic being – as well as Hegel's basic thesis concerning the philosophy of nature, that therein a tendency toward coherence and idealization manifests itself in the sense of a (categorically) gradually rising succession of nature: from the separateness of space to the ideality of sensation. In the sense of the double strategy of concretization and foundation it is shown that on the one hand possibilities of philosophical penetration concerning actual empirical-scientific results are opened, and on the other hand – in turn – a re-interpretation of Hegel's theorem on the basis of physical, evolution-theoretical and system-theoretical argumentation also becomes possible. In this mutual crossing-over and elucidation of empirical and Hegelian argumentation not only do perspectives of a new comprehension of nature become visible, but also, at the same time – as an essential consequence of this methodical principle – thoughts on the possibilities of actualizing Hegel's philosophy of nature. (shrink)

What is space? And why are questions of space important to social theory? Society, Action and Space is the first English translation of a book which has been widely recognized in Europe as a major contribution to the interface between geography and social theory. Benno Werlen focuses on the issues which are at the heart of the most important debates in human and social geography today. One of the most significant recent developments in social analysis has been the increasing interchange (...) among geographers, sociologists, anthropologists and social philosophers concerning "the spatial." This debate involves the work of Giddens, Foucault, Bourdieu, Lefebvre, Harvey, Gregory, Soja, and many others. From these new developments a whole series of new forms and empirical work, as well as theoretical innovations, have come into being. Spatial considerations are no longer confined to the realm of geography, but are now seen as fundamental to all forms of social theorizing, especially under conditions of late modernity and globalization. Society, Action and Space links discussions in the philosophy of social science with theories of action which have direct relevance to concepts of space. Benno Werlen provides a discussion of Popper's critical rationalism, and connects it to ideas drawn from phenomenology. This epistemological debate is linked with the sociological action theories of Pareto, Weber, Parsons, and Schutz. The book closes with an evaluation of how "the spatial" can be systematically integrated into action theory. Ambitious, original, and persuasive in its arguments, it raises exciting new implications for the study of space and social theory. (shrink)

Assembled here for the first time in English translation, Sigrid Weigel and Georgina Paul offer illuminating new insights into Benjamin's theory, combining impulses from post-structuralism, feminism, cultural anthropology and psychoanalysis.

‘Space does not exist fundamentally: it emerges from a more fundamental non-spatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of reality and (...) emergence in order to analyse the constitution of space by non-spatial entities. It follows that space constitution, if borne out, does not provide empirical evidence in favour of a stratified, Aristotelian in spirit, metaphysics. The view will be described in relation to two particular research programs in contemporary physics: wave function realism and loop quantum gravity. (shrink)

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical measurements. This way of thinking leads (...) to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy. (shrink)

In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and ...

Quality-space theory (QST) explains the nature of the mental qualities distinctive of perceptual states by appeal to their role in perceiving. QST is typically described in terms of the mental qualities that pertain to color. Here we apply QST to the olfactory modalities. Olfaction is in various respects more complex than vision, and so provides a useful test case for QST. To determine whether QST can deal with the challenges olfaction presents, we show how a quality space (QS) could be (...) constructed relying on olfactory perceptible properties and the olfactory mental qualities then defined by appeal to that QS of olfactory perceptible properties. We also consider how to delimit the olfactory QS from other modalities. We further apply QST to the role that experience plays in refining our olfactory discriminative abilities and the occurrence of olfactory mental qualities in non-conscious olfactory states. QST is shown to be fully applicable to and useful for understanding the complex domain of olfaction. (shrink)

In this book John Campbell shows that the general structural features of human thought can be seen as having their source in the distinctive ways in which we...

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)

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build (...) a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions can be fused into (...) one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

We live today within a system in which state and corporate power aim to render space flat, transparent, and uniform, for only then can it be truly controlled. The gaze of power and the commodity form are capable of infiltrating even the darkest of corners, and often, we invite them into our most private spaces. We do so as a matter of convenience, but also to placate ourselves and cope with the alienation inherent in our everyday lives. The resulting (...) dominant space can best be termed totalitarian. It is space stripped of uniqueness, deprived of the “spatial aura” necessary for authentic experience. In Totalitarian Space and the Destruction of Aura, Saladdin Ahmed sets out to help us grasp what has been lost before no trace remains. He draws attention to that which we might prefer not to see, but despite the bleakness of this indictment of reality, the book also offers a message of hope. Namely, it is only once we comprehend the magnitude of the threat to our spatial experience and our own complicity in sustaining this system that we can begin to resist the totalizing forces at work. (shrink)

Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure whatsoever. The (...) main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal."--P. [4] of cover. (shrink)

The aim of this book is to give an account of Einstein's work without introducing anything very technical in the way of mathematics, physics, or philosophy.

Ian Stoner has recently argued that we ought not to colonize Mars because doing so would flout our pro tanto obligation not to violate the principle of scientific conservation, and there is no countervailing considerations that render our violation of the principle permissible. While I remain agnostic on, my primary goal in this article is to challenge : there are countervailing considerations that render our violation of the principle permissible. As such, Stoner has failed to establish that we ought not (...) to colonize Mars. I close with some thoughts on what it would take to show that we do have an obligation to colonize Mars and related issues concerning the relationship between the way we discount our preferences over time and projects with long time horizons, like space colonization. (shrink)

This volume explores the multiple ways in which people experience time-space compression in varying historical and geographical circumstances.

There is a growing body of scholarship that is addressing the ethics, in particular, the bioethics of space travel and colonisation. Naturally, a variety of perspectives concerning the ethical issues and moral permissibility of different technological strategies for confronting the rigours of space travel and colonisation have emerged in the debate. Approaches ranging from genetically enhancing human astronauts to modifying the environments of planets to make them hospitable have been proposed as methods. This paper takes a look at a critique (...) of human bioenhancement proposed by Mirko Garasic who argues that the bioenhancement of human astronauts is not only functional but necessary and thus morally permissible. However, he further claims that the bioethical arguments proposed for the context of space do not apply to the context of Earth. This paper forwards three arguments for how Garasic’s views are philosophically dubious: (1) when he examines our responsibility towards future generations he refers to a moral principle (which we will call the principle of mere survival) which, besides being vague, is not morally acceptable; (2) the idea that human bioenhancement is not natural is not only debatable but morally irrelevant; and (3) it is not true that the situations that may arise in space travel cannot occur on Earth. We conclude that not only is the (bio)enhancement of humans on Earth permissible but perhaps even necessary in certain circumstances. (shrink)

INTRODUCTION In Einstein's theory of gravitation matter and its dynamical interaction are based on the notion of an intrinsic geometric structure of the space -time continuum. The ideal aspiration, the ultimate aim, of the theory is not more and ...

The essays in Rhetorical Spaces grow out of Lorraine Code's ongoing commitment to engaging philosophical issues as they figure in people's everyday lives. The arguements in this book are informed at once by the moral-political implications of how knowledge is produced and circulated and by issues of gendered subjectivity. In their critical dimension, these lucid essays engage with the incapacity of the philosophical mainstream's dominant epistemologies to offer regulative principles that guide people in the epistemic projects that figure centrally (...) in their lives. In its constructive dimension, Rhetorical Spaces focuses on developing productive, case-by-case analyses of knowing other people in situations where social-political inequalities create asymmetrical patterns of epistemic power and privilege. Framing all of the essays is the conception of rhetorical spaces which shows that prevailing intellectual-political climates can work to enhance or to thwart possibilities of establishing cognitive authority for the members of a society who belong to groups other than the dominant ones. Finally, bridging the gap between theory and practice, Lorraine Code shows how the issue of reconfiguring structures of authority and expertise are not just matters of individual responsibility, but require a radical restructuring of the communities and social orders in which people know and act. (shrink)

In this paper I argue that empty space can be heard. This position contrasts with the generally held view that the only things that can be heard are sounds, their properties, echoes, and perhaps sound sources. Specifically, I suggest that when sounds reverberate in enclosed environments we auditorily represent the volume of space surrounding us. Clearly, we can learn the approximate size of an enclosed space through hearing a sound reverberate within it, and so any account that denies that we (...) hear empty space must instead show how beliefs about volumes of space can be derived indirectly from what is heard. That is, if space is not auditorily represented when we hear sounds reverberate, what is? I consider whether hearing reverberation can be thought of as hearing a distinct sound, hearing echoes, or hearing a property of a sound. I argue that experiences of reverberation cannot be reduced to the perception of any of these types and that therefore empty space is represented in auditory perceptual content. In the final section I outline two ways in which space might be represented. (shrink)

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

This paper provides a method for characterizing space events using the framework of conceptual spaces. We focus specifically on estimating and ranking the likelihood of collisions between space objects. The objective is to design an approach for anticipatory decision support for space operators who can take preventive actions on the basis of assessments of relative risk. To make this possible our approach draws on the fusion of both hard and soft data within a single decision support framework. Contextual data (...) is also taken into account, for example data about space weather effects, by drawing on the Space Domain Ontologies, a large system of ontologies designed to support all aspects of space situational awareness. The framework is coupled with a mathematical programming scheme that frames a mathematically optimal approach for decision support, providing a quantitative basis for ranking potential for collision across multiple satellite pairs. The goal is to provide the broadest possible information foundation for critical assessments of collision likelihood. (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)

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)

This paper argues that all of the standard theories about the divisions of space and time can benefit from, and may need to rely on, parsimony considerations. More specifically, whether spacetime is discrete, gunky or pointy, there are wildly unparsimonious rivals to standard accounts that need to be resisted by proponents of those accounts, and only parsimony considerations offer a natural way of doing that resisting. Furthermore, quantitative parsimony considerations appear to be needed in many of these cases.