We show that the countable axiom of choice CAC strictly implies the statements “Lindelöf metric spaces are second countable” “Lindelöf metric spaces are separable”. We also show that CAC is equivalent to the statement: “If is a Lindelöf topological space with respect to the base ℬ, then is Lindelöf”.

The nature of matter was as intriguing a question for ancient philosophers as it is for contemporary physicists, and Matter, Space, and Motion presents a fresh and illuminating account of the rich legacy of the physical theories of the Greeks from the fifth century B.C. to the late sixth century A.D.

A multidisciplinary collection which brings together cutting edge research about the cultural politics of space.

Spaces, too, have a history. And history always takes place in spaces. But what do historians mean when they use the word "spaces"? And how can spaces be historically investigated? Susanne Rau provides a survey of the history of Western concepts of space, opens up interdisciplinary approaches to the phenomenon of space in fields ranging from physics and geography to philosophy and sociology, and explains how historical spatial analysis can be methodologically and conceptually conceived and carried out in (...) practice. The case studies presented in the book come from the fields of urban history, the history of trade, and global history including the history of cartography, but its analysis is equally relevant to other fields of inquiry. This book offers the first comprehensive introduction to the theory and methodology of historical spatial analysis. (shrink)

Port Cities are historically the places for paradigm shifts, radical changes, and socio-economic transitions. In particular, the interaction zone between the port infrastructure and urban activities creates liminal spaces at the forefront of many contemporary challenges. In these liminal spaces, the port's flows, form, and function intertwine with urban contexts and conflict with the living conditions. Conceptualizing the portcityscape and harborscape as liminal space and urban thresholds leads to (re)thinking about innovative participatory methods and technologies for building community resilience (...) in port cities. Additionally, inevitable constant development in port cities requires adaptability and resilience from the waterfronts to the hinterlands and city centers. Such confrontation of port infrastructures and urbanization is socio-politically and spatially challenging, specifically in historic port cities. Therefore, as the approach to exploiting energy and human resources changes over time, the physicality of the built environment in port cities and how we (re)use the resources need to be redefined. This research investigates key socio-spatial features and challenges of port cities by examining how the port's proximity to the city requires coordination, collaboration, transparency, and community dialogue. The introduction and background literature discuss three domains and notions of port city studies, building community resiliency through participatory frameworks, and parasitic architecture. By building upon this analytical framework, the paper presents case studies developed within the research-led design studio focusing on building resilient communities in four port cities, including Amsterdam, Constanta, Alexandria, and Rio De Janeiro. This research focus on the community-enabled application of emerging technologies, innovative approaches, and co-designing and co-building participatory methods. The selected case studies introduce an integrative and multi-scalar pedagogical framework for building resilient communities in liminal spaces of port cities. (shrink)

In the book "Conceptual Spaces: the Geometry of Thought" [2000] Peter Gärdenfors proposes a new framework for cognitive science. Complementary to symbolic and subsymbolic [connectionist] descriptions, conceptual spaces are semantic structures — constructed from empirical data — representing the universe of mental states. We argue that Gärdenfors' modeling can be used in consciousness research to describe the phenomenal conscious world, its elements and their intrinsic relations. The conceptual space approach affords the construction of a universal state space of (...) human consciousness, where all possible kinds of human conscious states could be mapped. Starting from this approach, we discuss the inclusion of feelings and emotions in conceptual spaces, and their relation to perceptual and cognitive states. Current debate on integration of affect/emotion and perception/cognition allows three possible descriptive alternatives: emotion resulting from basic cognition; cognition resulting from basic emotion, and both as relatively independent functions integrated by brain mechanisms. Finding a solution for this issue is an important step in any attempt of successful modeling of natural or artificial consciousness. After making a brief review of proposals in this area, we summarize the essentials of a new model of consciousness based on neuro-astroglial interactions. (shrink)

This paper outlines an Husserlian, phenomenological account of the first stages of the acquisition of empirical knowledge in light of some aspects of Wilfrid Sellars’ critique of the myth of the given. The account offered accords with Sellars’ in the view that epistemic status is attributed to empirical episodes holistically and within a broader normative context, but disagrees that such holism and normativity are accomplished only within the linguistic and conceptual confines of the space of reasons, and rejects the (...) limitation of the relevant normativity to the cognitive domain. Attention to the phenomenological notion of motivations in our mapping of the structure and acquisition of empirical knowledge reveals a form of weak categoriality given in experience, one outside exclusive mediation by language and concepts but also not merely causal. Section 1 outlines some basic aspects of Sellars’ account of empirical knowledge in Empiricism and the Philosophy of Mind, including a regress objection that arises due to his claim that empirical knowledge presupposes knowledge of general facts about perception. Section 2 examines Sellars’ later revisiting of the objection, via his critique of Roderick Firth, in “The Lever of Archimedes,” focusing on his analysis of the “Myth of the Categorial Given” and his use of the notion of ur-concepts. Section 3 looks at Sellars’ psychological nominalism and his rejection of the explanatory primacy of experience in light of the strict dichotomy between the space of causes and the space of reasons, and shows how Firth’s account aligns with phenomenology in its advocating for an irreducible and non-inferential role for experience. It also raises an important objection to Sellars’ account concerning the categorial givenness of causality. Section 4 turns to Husserl, arguing that his conception of motivation in the Logical Investigations and Ideas II reveals a third explanatory or logical space “between” that of causes and that of reasons. Section 5 further develops this account with regard to the explanatory role of lived experience. Section 6 revisits the regress objection to Sellars from the phenomenological standpoint developed earlier in the paper, and argues that an Husserlian account of empirical knowledge offers a viable alternative to Sellars’ that overcomes the regress objection and gives proper explanatory weight to the evidence of lived experience vis-à-vis scientific presuppositions about causality. (shrink)

In this paper, I undertake a conceptual analysis of ordinary usages of the concepts of “litter” and “pollution.” If “litter” or “pollution” applies to space debris in its various contexts, then in dealing with space debris as an ethical concern, we may more neatly apply arguments for the wrongness of litter and pollution to these new contexts. After engaging in a conceptual analysis of “litter” and “pollution,” I consider whether these concepts apply to space debris, examining three (...) contexts: (1) surface debris on Moon and Mars, (2) intentionally crashing objects into gas giants, ice giants, and stars, and (3) the pressing issue of orbital space debris. I conclude by finding that neither “litter” nor “pollution” cleanly applies to any of these three contexts. (shrink)

Spaces can make certain forms of philosophical activity more likely or more fruitful among the people who occupy them, and many public philosophers aim to promote one or another form of fruitful philosophical activity. It's helpful to distinguish four ways in which spaces can facilitate philosophical reflection and interaction: domain‐general cognitive facilitation, domain‐specific cognitive facilitation, affective facilitation, and relational facilitation. This chapter shows how philosophical spaces shape the activity of their occupants in ways of interest to public philosophers. Groups can (...) be unjustly excluded from philosophical communities for any number of reasons, but some of that exclusion is territorial. There are a number of challenges facing the would‐be designer of a philosophical space. The chapter presents three such challenges and offers some suggestions for how designers of philosophical spaces might address them. These include: the problem of rapport, the problem of urban social psychology, and the problem of the outsider. (shrink)

Le Poidevin has recently presented an argument that gives rise to a serious problem for relationist theories of space. It appeals to the simple geometrical fact that if A, B and C are three points lying in a straight line, then AB and BC together entail AC. He suggests that an ontological relationship of supervenience must be appealed to to explain this entailment. Given this thesis of supervenience, relationism is implausible. I argue that the problem that Le Poidevin raises (...) for relationism should be rejected, because the thesis of supervenience is false. The latter rests upon what Le Poidevin refers to as ‘The explanatory principle', a principle which he claims to be a natural extension of the truthmaker principle. Contrary to this, I argue that given any plausible theory of truthmaking, the explanatory principle is false. With the rejection of this principle, Le Poidevin's argument against relationism collapses. (shrink)

A classic analytic approach to biological phenomena seeks to refine definitions until classes are sufficiently homogenous to support prediction and explanation, but this approach founders on cases where a single process produces objects with similar forms but heterogeneous behaviors. I introduce object spaces as a tool to tackle this challenging diversity of biological objects in terms of causal processes with well-defined formal properties. Object spaces have three primary components: (1) a combinatorial biological process such as protein synthesis that generates objects (...) with parts that are modular, independent, and organized according to an invariant syntax; (2) a notion of “distance” that relates the objects according to rules of change over time as found in nature or useful for algorithms; (3) mapping functions defined on the space that map its objects to other spaces or apply an evaluative criterion to measure an important quality, such as parsimony or biochemical function. Once defined, an object space can be used to represent and simulate the dynamics of phenomena on multiple scales; it can also be used as a tool for predicting higher-order properties of the objects, including stitching together series of causal processes. Object spaces are the basis for a strategy of theorizing, discovery, and analysis in biology: as heuristic idealizations of biology, they help us transform inchoate, intractable problems into articulated, well-structured ones. Developing an object space is a research strategy with a long, successful history under many other names, and it offers a unifying but not overreaching approach to biological theory. (shrink)

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity using a geometrical approach, emphasizing intrinsic (...) space-time structure rather than coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics. (shrink)

There is an apparent tension in Shepherd’s accounts of space and time. Firstly, Shepherd explicitly claims that we know that the space and time of the unperceived world exist because they cause our phenomenal experience of them. Secondly, Shepherd emphasizes that empty space and time do not have the power to effect any change in the world. My proposal is that for Shepherd time has exactly one causal power: to provide for the continued existence of self-same or (...) changing objects. Because Shepherd takes causation to be a relation whereby two objects combine to form a third, their effect, whenever we perceive a continually existing object, since time is a proper part of such objects, our perception of time is caused by time itself. Likewise, space’s causal power is to provide for the possibility of the motion or rest of objects, and so when we perceive objects with space as a proper part, we come into causal contact with space. (shrink)

In this paper recognition is taken to be a question of social ontology, regarding the very constitution of the social space of interaction. I concentrate on the question of whether certain aspects of the theory of recognition can be translated into the terms of a socio-ontological paradigm: to do so, I make reference to some conceptual tools derived from John Searle's social ontology and Robert Brandom's normative pragmatics. My strategy consists in showing that recognitive phenomena cannot be isolated at (...) the level of human interaction, and are, rather, in part proper to animal interaction as well. Furthermore, it is argued that recognitive powers are constitutive powers more basic than deontic ones and play a role much broader than the one they in fact assume in Searle and in Brandom. (shrink)

This chapter contains sections titled: Endnotes.

The overreliance on verbal models and theories in psychology has been criticized for hindering the development of reliable research programs (Harris, 1976; Yarkoni, 2020). We demonstrate how the conceptual space framework can be used to formalize verbal theories and improve their precision and testability. In the framework, scientific concepts are represented by means of geometric objects. As a case study, we present a formalization of an existing three-dimensional theory of emotion which was developed with a spatial metaphor in mind. (...) Wundt posits that the range of human emotion can be represented along three axes of basic emotions (pleasure/displeasure, excitement/inhibition, tension/relaxation), just as color vision can be represented using three basic colors. We use dimensions to represent basic emotions, points to represent emotional states, and regions to represent broader emotional concepts. We then compare our formalization to an existing structuralist formalization of Wundt’s theory. Further, we discuss the empirical predictions that our formalization generates, such as comparisons of similarity and intensity. We conclude by demonstrating how the tools developed in the conceptual space framework can be used to formulate a theory of emotion based on empirical observation. (shrink)

‘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)

Hardly any other problem has been discussed more than that of the status of time in modem physics. This is only natural since there are not many other more important problems in philosophy of science and in philosophy in general. There are also few other areas where controversies as well as confusion were more frequent. This is true not only of popular and semi-popular expositions of the Minkowski concept of space-time but also of a number of its philosophical interpretations. (...) Generally we do not find anything of this kind in the writings of physicists, at least as long as they confine themselves to strictly mathematical and physical expositions; but when they sometimes venture beyond a strictly mathematical approach, they often do not escape certain unconscious or semi-conscious prejudices which are contrary not only to the spirit but sometimes even to the letter of relativity. The true significance of the relativistic fusion of space and time can be understood only when we contrast it with its classical counterpart, i.e., with what may be called the Newtonian space-time. Only on such a contrasting background will the revolutionary meaning of the new concept clearly stand out. (shrink)

The Web initially emerged as an “antidote” to accumulated scientific knowledge, since it enables global representation and communication at a minimum cost. Its gigantic scale and interdependence allow us our ability to find relevant information and develop trustworthy contexts. It is time for science to compensate by providing an epistemological “antidote” to Web issues. Philosophy should be in the front line by forming the salient questions and analysis. We need a theory about Web being that will bridge philosophical thinking and (...) engineering. This chapter analyzes existence and spatiotemporality in the Web and how it transforms the traditional actualities. The resulting issues concern the self‐determination of a being and the way in which the Web could be a free and open platform for innovation and participation. (shrink)

Learn about astronauts and space exploration.

들뢰즈(와 과타리)에 따르면 공간은 추상적, 등질적, 선험적 조건으로 이해되지 않는다. 공간은 실제로 혼합되어 존재할지라도, 경향성의 차이에 따라 매끈한 공간과 홈 파인 공간으로 분류되어야 한다. 홈 파인 공간에서는 모든 것이 기존 규칙에 따라 조직된다. 반면 매끈한 공간에서는 가장 조직화된 것조차도 가능성을 향해 해방될 수 있다. 장기의 공간은 홈 파인 공간이며, 바둑의 공간은 매끈한 공간이다. E. 라로슈의 연구에 따르면, 노모스의 의미도 호메로스 시대와 고전기 시대에 서로 달랐다. 호메로스 시대에 노모스는 매끈한 공간에서 ‘분배하기’를 뜻한 반면, 고전기에는 홈 파인 공간에서 ‘배당하기’를 뜻했다. 전쟁기계의 임무는 (...) 매끈한 공간을 만드는 일이다. 따라서 전쟁기계의 역할은 예술가나 실험가의 역할과 같다고 할 수 있다. (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 ...

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)

The overreliance on verbal models and theories in psychology has been criticized for hindering the development of reliable research programs (Harris, 1976; Yarkoni, 2020). We demonstrate how the conceptual space framework can be used to formalize verbal theories and improve their precision and testability. In the framework, scientific concepts are represented by means of geometric objects. As a case study, we present a formalization of an existing three-dimensional theory of emotion which was developed with a spatial metaphor in mind. (...) Wundt posits that the range of human emotion can be represented along three axes of basic emotions (pleasure/displeasure, excitement/inhibition, tension/relaxation), just as color vision can be represented using three basic colors. We use dimensions to represent basic emotions, points to represent emotional states, and regions to represent broader emotional concepts. We then compare our formalization to an existing structuralist formalization of Wundt’s theory. Further, we discuss the empirical predictions that our formalization generates, such as comparisons of similarity and intensity. We conclude by demonstrating how the tools developed in the conceptual space framework can be used to formulate a theory of emotion based on empirical observation. (shrink)

Video game spaces have vastly expanded the built environment, offering new worlds to explore and inhabit. Like buildings, cities, and gardens before them, these virtual environments express meaning and communicate ideas and affects through the spatial experiences they afford. Drawing on the emerging field of embodied cognition, this book explores the dynamic interplay between mind, body, and environment that sits at the heart of spatial communication. To capture the wide diversity of forms that spatial expression can take, the book builds (...) a comparative analysis of twelve video games across four types of space, spanning ones designed for exploration and inhabitation, kinetic enjoyment, enacting a situated role, and enhancing perception. Together, these diverse virtual environments suggest the many ways that video games enhance and extend our embodied lives."--Publisher's website. (shrink)

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)

This book is a ricochet against mainstream physics. It sprang out of the idea that outer symmetries of space-time are the same as inner symmetries of matter. In other words, the standard model of physics is a space-time group. This book is about structures and phenomena that are lying hidden underneath the surface of space-time. It begins with a few biographic events, Majoranas legacy, the philosophy of Gerhard Frey and some related anthropological topics which have to do (...) with high energy physics. It continues with a reconstruction of the theorem by Banach and Tarski in Minkowski space. We are making acquaintance with the standard model as a property of space-time. So we are challenging quite unusual actions such as penetration of quarks by a probe. We propose to apply a penetrating function D. Then, measure and basis are connected with the axiom of choice. (shrink)

In this compendium of essays, some of the world's leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader. Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, yet holistic, (...) independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of space and time, computer scientists theoretically and practically try to optimize the space-time complexities in storing and retrieving data/information. The list is never-ending. Linguists, logicians, artists, evolutionary biologists, geographers et cetera, all are trying to weave a web of understanding around the same duo. However, our endeavour into a world of such endless imagination is restrained by intellectual dilemmas such as: Can humans comprehend everything? Are there any limits? Can finite thought fathom infinity? We have sought far and wide among the best minds to furnish articles that provide an overview of the above topics. We hope that, through this journey, a symphony of patterns and tapestry of intuitions will emerge, providing the reader with insights into the questions: What is Space? What is Time? Chapter [15] of this book is available open access under a CC BY 4.0 license. (shrink)