Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F $\subseteq$ P(X) of size c, consisting of Borel sets which are not in I. Condition (M) states that there is a Borel function f: X → X with $f^{-1}[\{x\}] \not\in$ I for each x (...) ∈ X. Provided that X is a group and I is invariant, condition (D) states that there exist a Borel set B $\not\in$ I and a perfect set P $\subseteq$ X for which the family $\{B + x: x \in P\}$ is disjoint. The aim of the paper is to study whether the reverse implications in the chain (D) $\Rightarrow$ (M) $\Rightarrow$ (B) $\Rightarrow$ not-ccc can hold. We build a σ-ideal on the Cantor group witnessing (M) & ¬ (D) (Section 2). A modified version of that σ-ideal contains the whole space (Section 3). Some consistency results on deriving (M) from (B) for "nicely" defined ideals are established (Sections 4 and 5). We show that both ccc and (M) can fail (Theorems 1.3 and 5.6). Finally, some sharp versions of (M) for invariant ideals on Polish groups are investigated (Section 6). (shrink)

It is proved that--consistently--there can be no ccc closed P-sets in the remainder space ω*.

It is proved that--consistently--there can be no ccc closed P-sets in the remainder space $\omega^\ast$.

We introduce a suitable notion of eight-shaped curve in the product S × ℝ of a Suslin line S for the real line ℝ, and we prove that if S is dense in itself, then every collection of pairwise disjoint eight-shaped curves in S × ℝ is countable. This parallels a folklore result which holds for the real plane.

We investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characterisation for an algebra to carry a separable separable positive measure was suggested by Talagrand in 1980, which is that the Stone space K of the algebra satisfies that (...) its space M(K) of measures is weakly separable, equivalently that C(K) embeds into l∞. We show that there is a ZFC example of a Boolean algebra (so of a compact space) which satisfies this condition and does not support a separable strictly positive measure. However, we use this property as a tool in a proof which shows that under MA+⇁ CH every atomless ccc Boolean algebra of size < c carries a nonatomic strictly positive measure. Examples are given to show that this result does not hold in ZFC. Finally, we obtain a characterisation of Boolean algebras that carry a strictly positive nonatomic measure in terms of a chain condition, and we draw the conclusion that under MA+⇁ CH every atomless ccc Boolean algebra satisfies this stronger chain condition. (shrink)

Abstract:As a flagship program of the New Deal, the CCC was one of several federal agencies which turned to the natural and built environment to promote socio-cultural homogenization between the First and Second World War. This article investigates the CCC's role as an agent of national transformation and considers the links between the New Deal's treatment of the American landscape and its promotion of a new, more pluralistic national identity. While historians of the interwar United States are quick to note (...) the social and environmental significance of the CCC, the cultural role of this program remains largely overlooked. Specifically, relevant scholarship has neglected to address the architectural output of this program and the way it related to the New Deal's broader socio-cultural initiatives. With camps in each of the forty-eight states and overseas territories, the CCC reconfigured much of the American landscape and deployed a regionally diverse blend of vernacular architecture, all while fostering a mythologized sense of cultural heritage from coast to coast. In order to better understand both the role and rationale behind this process, this article considers several examples of CCC-produced architecture and landscape design across the greater United States. It argues that these designs were key vehicles of the unifying message that drove the New Deal and its many so-called ‘alphabet agencies’ from the depths of economic depression to a state of preparedness as the country approached the precipice of global war. This article also considers the Corps' role in the New Deal's construction of popular historical consciousness and draws attention to the frequent transregional interactions between enrollees and local populations. (shrink)

This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I (...) conclude the discussion by presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach. (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)

Learn about astronauts and space exploration.

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)

In the famous Correspondence with Clarke, which took place during the last year of Leibniz's life, Leibniz advanced several arguments purporting to refute the absolute theory of space and time that was held by Newton and his followers. The main aim of this book is to reassess Leibniz's attack on the Newtonian theory in so far as he relied on the principle of the identity of indiscernibles. The theological side of the controversy is not ignored but isolated and discussed (...) in the last three chapters, which deal with problems connected with the notions of omnipotence and omniscience. (shrink)

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

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)

Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet (...) which contains only those epistemic scenarios which are not obviously impossible. Whether something is obvious is not always a determinate matter and so the resulting picture is of an epistemic space with fuzzy boundaries. (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)

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)

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)

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)

‘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)

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)

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 volume chronicles the development of philosophical conceptions of space from early antiquity through the medieval period to the early modern era, ending with Kant. The chapters describe the interactions at different moments in history between philosophy and various other disciplines, especially geometry, optics, and natural science more generally. Central figures from the history of mathematics, science and philosophy are discussed, including Euclid, Plato, Aristotle, Proclus, Ibn al-Haytham, Nicole Oresme, Kepler, Descartes, Newton, Leibniz, Berkeley, and Kant.

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)

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)

Anthony C. Yu, Carl Buck Distinguished Professor in Humanities, Chairman, Division of East Asian Languages, University of Chicago, Divinity School, writes: "Robert Allinson's book represents tremendous thoughtfulness, originality, and erudition. Its wide-ranging and lucid discussions cover a huge terrain, from ancient metaphysics to quantum mechanics. The enlistment of certain classical Confucian concepts and themes at critical junctures to advance the book's argument also provides luminous comparison. His interpretation of the Confucian emphasis on life as social and self-preservation is both humane (...) and interesting, much as his analysis of the Mencian notion of compassion deserves our attention." This title was first published in 2002: In Space, Time and the Ethical Foundations ideas about space and time are developed, unique to the history of philosophy, that match the new physics. A well grounded metaphysics is presented which offers a safe haven between stifling scepticism and wild imagination, and an original philosophical method is demonstrated which sharply demarcates philosophy from the empirical sciences. A new foundation is laid for ethics by grounding ethics on the author's psycho-biological deduction of the emotions that offers a progressive model to replace the Freudian paradigm. An originally designed trans-cultural ethics, doubly grounded on both Eastern and Western thought, presents an antidote to the contemporary retreat into relativism. Insights from biology, psychology, evolutionary theory and ethics are brought together in a unique and fruitful synthesis. At the same time, human barbarisms such as the Holocaust are pointed to as reminders that there are just limits to compassion. This book presents a sophisticated text for metaphysics, epistemology and systematic ethics. (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 ...

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)

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)

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.

This is a pdf of a Mathematica calculation that supplements the paper "Presentist Fragmentalism and Quantum Mechanics" forthcoming in Foundations of Physics. In that paper the Born rule (or at least a progenitor) is derived from experimental conditions on the mutual observations of two fragments. In this pdf the experimental conditions are applied to Hilbert space dimensions 3, 4, and 5. It turns out each of these have a 1-dimensional solution space which, it is hoped, can be interpretated (...) as the phase. (shrink)