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)
This essay explores theories of place, or lived-space, as regards the role of objectivity and the problem of relativism. As will be argued, the neglect of mathematics and geometry by the lived-space theorists, which can be traced to the influence of the early phenomenologists, principally the later Husserl and Heidegger, has been a major contributing factor in the relativist dilemma that afflicts the lived-space movement. By incorporating various geometrical concepts within the analysis of place, it is demonstrated (...) that the lived-space theorists can gain a better insight into the objective spatial relationships among individuals and within groups—and, more importantly, this appeal to mathematical content need not be construed as undermining the basic tenants of the lived-space approach. (shrink)
Hume’s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume’s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows that, working (...) within this epistemological model, we cannot attain complete certainty about the continuum but only at most about discrete quantity. Geometry, in contrast to arithmetic, cannot be a fully exact science. A number of more recent commentators have offered sympathetic interpretations of Hume’s discussion aiming to correct the older tendency to dismiss this part of the Treatise as weak and confused. Most of these commentators interpret Hume as anticipating the contemporary idea of a finite or discrete geometry. They view Hume’s conception that space is composed of simple indivisible minima as a forerunner of the conception that space is a discretely (rather than continuously) ordered set. This approach, in my view, is helpful as far as it goes, but there are several important features of Hume’s discussion that are not sufficiently appreciated. I go beyond these recent commentators by emphasizing three of Hume’s most original contributions. First, Hume’s epistemological model invokes the “confounding” of indivisible minima to explain the appearance of spatial continuity. Second, Hume’s sharp contrast between the perfect exactitude of arithmetic and the irremediable inexactitude of geometry reverses the more familiar conception of the early modern tradition in pure mathematics, according to which geometry (the science of continuous quantity) has its own standard of equality that is independent from and more exact than any corresponding standard supplied by algebra and arithmetic (the sciences of discrete quantity). Third, Hume has a developed explanation of how geometry (traditional Euclidean geometry) is nonetheless possible as an axiomatic demonstrative science possessing considerably more exactitude and certainty that the “loose judgements” of the vulgar. (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 taken as a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)
Material objects persist through time and survive change. How do they manage to do so? What are the underlying facts of persistence? Do objects persist by being "wholly present" at all moments of time at which they exist? Or do they persist by having distinct "temporal segments" confined to the corresponding times? Are objects three-dimensional entities extended in space, but not in time? Or are they four-dimensional spacetime "worms"? These are matters of intense debate, which is now driven by (...) concerns about two major issues in fundamental ontology: parthood and location. It is in this context that broadly empirical considerations are increasingly brought to bear on the debate about persistence. Persistence and Spacetime pursues this empirically based approach to the questions. Yuri Balashov begins by setting out major rival views of persistence -- endurance, perdurance, and exdurance -- in a spacetime framework and proceeds to investigate the implications of Einstein's theory of relativity for the debate about persistence. His overall conclusion -- that relativistic considerations favour four-dimensionalism over three-dimensionalism -- is hardly surprising. It is, however, anything but trivial. Contrary to a common misconception, there is no straightforward argument from relativity to four-dimensionalism. The issues involved are complex, and the debate is closely entangled with a number of other philosophical disputes, including those about the nature and ontology of time, parts and wholes, material constitution, causation and properties, and vagueness. (shrink)
This essay explores the role of God’s omnipresence in Newton’s natural philosophy, with special emphasis placed on how God is related to space. Unlike Descartes’ conception, which denies the spatiality of God, or Gassendi and Charleton’s view, which regards God as completely whole in every part of space, it is argued that Newton accepts spatial extension as a basic aspect of God’s omnipresence. The historical background to Newton’s spatial ontology assumes a large part of our investigation, but with (...) attention also focused on the details of Newton’s unique approach to these traditional Scholastic conceptions. (shrink)
This paper examines connections between concepts of space and extension on the one hand and immaterial spirits on the other, specifically the immanentist concept of spirits as present in rerum natura. Those holding an immanentist concept, such as Thomas Aquinas, typically understood spirits non-dimensionally as present by essence and power; and that concept was historically linked to holenmerism, the doctrine that the spirit is whole in every part. Yet as Aristotelian ideas about extension were challenged and an actual, infinite, (...) dimensional space readmitted, a dimensionalist concept of spirit became possible—that asserted by the mature Henry More, as he repudiated holenmerism. Despite More’s intentions, his dimensionalist concept opens the door to materialism, for supposing that spirits have parts outside parts implies that those parts could in principle be mapped onto the parts of divisible bodies. The specter of materialism broadens our interest in More’s unconventional ideas, for the question of whether other early modern thinkers, including Isaac Newton, followed More becomes a question of whether they too unwittingly helped usher in materialism. This paper shows that More’s attack upon holenmerism fails. He illegitimately injects his dimensionalist concept of spirit into the doctrine, failing to recognize it as a consequence of the non-dimensionalist concept of spirit, which in itself secures indivisibility. The interpretive consequence for Newton is that there is no prima facie reason to suppose that the charitable interpretation takes him to deny holenmerism. (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 first edition of his book on the completeness of Kant’s table of judgments, Klaus Reich shortly indicates that the B-version of the metaphysical exposition of space in the Critique of pure reason is structured following the inverse order of the table of categories. In this paper, I develop Reich’s claim and provide further evidence for it. My argumentation is as follows: Through analysis of our actually given representation of space as some kind of object (the formal (...) intuition of space in general), the metaphysical exposition will show that this representation is secondary to space considered as an original, undetermined and as such unrepresentable intuitive manifold. Now, following Kant, the representation of any kind of object involves diversity, synthesis and unity. In the case of our representation of space as formal intuition, this involves, firstly, a manifold a priori, i.e. space as pure form, delivered by the transcendental Aesthetic, secondly, a figurative, productive synthesis of that manifold, and, thirdly, the unity provided by the categories. Analysing our given representation of space – the task of the metaphysical exposition – amounts to dismantling its unity and determine its characteristics with respect to the categories. (shrink)
Storrs McCall presents an original philosophical theory of the nature of the universe based on a striking new model of its space-time structure. He shows how his model illuminates a broad range of subjects, including causation, probability, quantum mechanics, identity, and free will, and argues that the fact that the model throws light on such a large number of problems constitutes strong evidence that the universe is as the model portrays it.
Life, but not as we know it -- Still life in nearly present time -- Driving and the city -- Movement-space -- Afterwords -- From born to made -- Spatialities of feeling -- But malice aforethought -- Turbulent passions.
Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features of this contraction are (...) not the same as would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)
Kant argued that the perceptual representations of space and time were templates for the perceived spatiotemporal ordering of objects, and common to all modalities. His idea is that these perceptual representations were specific to no modality, but prior to all—they are pre-modal, so to speak. In this paper, it is argued that active perception—purposeful interactive exploration of the environment by the senses—demands premodal representations of time and space.
Here are two ways space might be (not the only two): (1) Space is “pointy”. Every finite region has infinitely many infinitesimal, indivisible parts, called points. Points are zero-dimensional atoms of space. In addition to points, there are other kinds of “thin” boundary regions, like surfaces of spheres. Some regions include their boundaries—the closed regions—others exclude them—the open regions—and others include some bits of boundary and exclude others. Moreover, space includes unextended regions whose size is zero. (...) (2) Space is “gunky”.1 Every region contains still smaller regions—there are no spatial atoms. Every region is “thick”—there are no boundary regions. Every region is extended. Pointy theories of space and space-time—such as Euclidean space or Minkowski space—are the kind that figure in modern physics. A rival tradition, most famously associated in the last century with A. N. Whitehead, instead embraces gunk.2 On the Whiteheadian view, points, curves and surfaces are not parts of space, but rather abstractions from the true regions. Three different motivations push philosophers toward gunky space. The first is that the physical space (or space-time) of our universe might be gunky. We posit spatial reasons to explain what goes on with physical objects; thus the main reason.. (shrink)
One of the most compelling questions still unanswered in neuroscience is how consciousness arises. In this article, we examine visual processing, the parietal lobe, and contralateral neglect syndrome as a window into consciousness and how the brain functions as the mind and we introduce a mechanism for the processing of visual information and its role in consciousness. We propose that consciousness arises from integration of information from throughout the body and brain by the thalamus and that the thalamus reimages visual (...) and other sensory information from throughout the cortex in a default three-dimensional space in the mind. We further suggest that the thalamus generates a dynamic default three-dimensional space by integrating processed information from corticothalamic feedback loops, creating an infrastructure that may form the basis of our consciousness. Further experimental evidence is needed to examine and support this hypothesis, the role of the thalamus, and to further elucidate the mechanism of consciousness. (shrink)
In this article I intend to show the strict relation between the notions of “second nature” and “recognition”. To do so I begin with a problem (circularity) proper to the theory of Hegelian and post- Hegelian Anerkennung. The solution strategy I propose is signifi cant also in terms of bringing into focus the problems connected with a notion of “space of reasons” that stems from the Hegelian concept of “Spirit”. I thus broach the notion of “second nature” as a (...) bridgeconcept that can play a key role both for a renewal of the theory of Anerkennung and for a rethinking of the “space of reasons” within the debate between Robert Brandom and John McDowell. Against this background I illustrate the novelties introduced by the dialectical conception of the relation between fi rst and second nature developed by Hegel and the contribution this idea can make to a revisited theory of recognition as a phenomenon articulated on two levels. I then return to the question of the space of reasons to show the contribution the renewed conception of recognition as second nature makes to the definition of its intrinsic sociality as something that is not in principle opposed to a sense of naturalness. (shrink)
b>: The problem of how physical systems, such as brains, come to represent themselves as subjects in an objective world is addressed. I develop an account of the requirements for this ability that draws on and refines work in a philosophical tradition that runs from Kant through Peter Strawson to Gareth Evans. The basic idea is that the ability to represent oneself as a subject in a world whose existence is independent of oneself involves the ability to represent space, (...) and in particular, to represent oneself as one object among others in an objective spatial realm. In parallel, I provide an account of how this ability, and the mechanisms that support it, are realized neurobiologically. This aspect of the article draws on, and refines, work done in the neurobiology and psychology of egocentric and allocentric spatial representation. (shrink)
This article analyses the way in which websites of conservation foundations organise the affective investments of viewers in animals by the use of webcams. Against a background of—often overly—general speculation on the influence of electronic media on our engagement with the world, it focuses on one particular practice where this issue is at stake. Phenomenological investigation is supplemented with ethnographic observation of user practice. It is argued that conservation websites provide caring spaces in two interrelated ways: by providing affective spaces (...) where users’ feelings are evoked, articulated and organised; and by opening up ethical space where the beauty of animals appears as an incentive to care. As an alternative to thinking of on- and off-line places as clearly delineated and of bodies and technologies as separate entities, the analysis focuses on trajectories of engagement that cut through these in various directions. In actual acts of looking and being affected, users, animals, places and technologies are intimately entwined. The article further suggests how focussing on trajectories of involvement can be developed to evaluate various websites and their user activity in relationship to clearly defined goals, e.g. conservation goals. (shrink)
Newton had a fivefold argument that true motion must be motion in absolute space, not relative to matter. Like Newton, Kant holds that bodies have true motions. Unlike him, though, Kant takes all motion to be relative to matter, not to space itself. Thus, he must respond to Newton’s argument above. I reconstruct here Kant’s answer in detail. I prove that Kant addresses just one part of Newton’s case, namely, his “argument from the effects” of rotation. And, to (...) show that rotation is relative to matter, Kant changes the meaning of ‘relative motion.’ However, that change puts Kant’s doctrine in deep tension with Newton’s science. Based on my construal, I correct earlier readings of Kant by John Earman and Martin Carrier. And, I argue that we need to revise Michael Friedman’s influential view of Kant. Kant’s struggle, I conclude, illustrate the difficulties that early modern relationists faced as they turned down Newtonian absolute space ; and it typifies their selective engagement with Newton’s case for it. (shrink)
In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss (...) some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)
Space and time are the most fundamental features of our experience of the world, and yet they are also the most perplexing. Does time really flow, or is that simply an illusion? Did time have a beginning? What does it mean to say that time has a direction? Does space have boundaries, or is it infinite? Is change really possible? Could space and time exist in the absence of any objects or events? What, in the end, are (...)space and time? Do they really exist, or are they simply the constructions of our minds? Robin Le Poidevin provides a clear, witty, and stimulating introduction to these deep questions and many other mind-boggling puzzles and paradoxes. He gives a vivid sense of the difficulties raised by our ordinary ideas about space and time, but he also gives us the basis to think about these problems independently, avoiding large amounts of jargon and technicality. His book is an invitation to think philosophically rather than a sustained argument for particular conclusions, but Le Poidevin does advance and defend a number of controversial views. He argues, for example, that time does not actually flow, that it is possible for space and time to be both finite and yet be without boundaries, and that causation is the key to an understanding of one of the deepest mysteries of time: its direction. Drawing on a variety of vivid examples from science, history, and literature, Travels in Four Dimensions brings to life some of the most profound questions imaginable. (shrink)
How do engineers respond to ethical dilemmas that occur in practice? How do they view their individual and collective responsibilities? How do they make decisions before all the facts are in? Using the space shuttle programme as the framework, this book examines the role of ethical decision making in the practice of engineering. In particular, the book considers the design and development of the main engines of the space shuttle as a paradigm for how individual engineers perceive, articulate, (...) and resolve ethical dilemmas in a large, complex organisation. A series of in-depth case studies show engineers at work on various stages of the project as they balance budgets, deadlines and risks. By documenting the historical development of a single system, the book provides a unique opportunity to explore the complex interactions between political, organisational and technical pressures and engineering and management decisions. (shrink)
This paper investigates the question of, and the degree to which, Newton’s theory of space constitutes a third-way between the traditional substantivalist and relationist ontologies, i.e., that Newton judged that space is neither a type of substance/entity nor purely a relation among such substances. A non-substantivalist reading of Newton has been famously defended by Howard Stein, among others; but, as will be demonstrated, these claims are problematic on various grounds, especially as regards Newton’s alleged rejection of the traditional (...) substance/accident dichotomy concerning space. Nevertheless, our analysis of the metaphysical foundations of Newton’s spatial theory will strive to uncover its unique and innovative characteristics, most notably, the distinctive role that Newton’s “immaterialist” spatial ontology plays in his dynamics. (shrink)
What is consciousness? Some philosophers have contended that ‘qualia’, or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being comprised of ‘occasions of experience’. To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to terms with the physics of space-time -- as is described by Einstein's general theory of relativity -- and its relation to the fundamental theory (...) of matter -- as described by quantum theory. This leads us to employ a new physics of objective reduction: OR which appeals to a form of ‘quantum gravity’ to provide a useful description of fundamental processes at the quantum/classical borderline . Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific ‘objective’ criterion is reached; the coherent system then self-reduces . We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness. OR is taken as an instantaneous event -- the climax of a self-organizing process in fundamental space-time -- and a candidate for a conscious Whitehead-like ‘occasion’ of experience. How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate an OR process with the requisite characteristics to be occurring in cytoskeletal microtubules within the brain's neurons. (shrink)
This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means of (...) mereology and Whitehead-like connection structures. We list and briefly analyze axioms for mereological structures, as well as those for connection structures. We argue that mereology is a good tool to model so called spatial relations. We also try to justify our choice of axioms for connection relation. Finally, we briefly discuss two theories: Grzegorczyk’s point-free topology and Tarski’s geometry of solids. (shrink)
Trendelenburg argued that Kant's arguments in support of transcendental idealism ignored the possibility that space and time are both ideal and real. Recently, Graham Bird has claimed that Trendelenburg (unlike his contemporary Kuno Fischer) misrepresented Kant, confusing two senses of . I defend Trendelenburg's : the ideas of space and time, as a priori and necessary, are ideal, but this does not exclude their validity in the noumenal realm. This undermines transcendental idealism. Bird's attempt to show that the (...) Analytic considers, but rejects, the alternative fails: an epistemological reading makes Kant accept the alternative, while an ontological reading makes him incoherent. As I demonstrate, Trendelenburg acknowledged the ambiguity of , focusing on the transcendental, not the empirical sense. Unlike Fischer, Bird denies Kant's commitment to things-in-themselves in favour of a descriptivist, non-ontological reading of transcendental idealism as an inventory of . But neither Bird's descriptivism, nor Fischer's commitment to things-in-themselves, answers Trendelenburg's sceptical worry about transcendental idealism. (shrink)
Frank Arntzenius presents a series of radical new ideas about the structure of space and time. 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. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one's peril! (shrink)
Previous research has linked the concept of number and other ordinal series to space via a spatially oriented mental number line. In addition, it has been shown that in visual scene recognition and production, speakers of a language with a left-to-right orthography respond faster to and tend to draw images in which the agent of an action is located to the left of the patient. In this study, we aim to bridge these two lines of research by employing a (...) novel method that measures the spatial bias produced by transitive sentences that use a wide variety of abstract and concrete verbs. Across four experiments, participants read sentences and then responded to probe words appearing on either the left or right sides of the screen. Probe words consisted of agents, patients, other words in the sentence, or newly encountered words. We found consistent lateral biases to responding to agents and patients, which appears to be independent of order of mention in the sentence but which does reflect a correspondence between position in the sentence and role in the causal sequence of the action. Our results also show that this spatial bias is driven by the use of the hands in two different ways: The left hand shows a greater sensitivity to the spatial effect than the right hand, and vocal responses produce no spatial effect. (shrink)
Kant’s text on Kästner, which for the first time appears in an integral English translation in this same issue of Kantian Review in which this article appears, is important for our understanding of Kant’s conception of space. The key point is Kant’s insistence on a clear distinction between metaphysical and geometric space. The first is a given infinite, while the second is a potential infinite. Fichant’s translation into French of this text in the 1990s (Fichant 1997) came at (...) a time when Béatrice Longuenesse’s magnum opus on CPR (Longuenesse 1998a) had just established itself as a serious alternative approach to the dominant interpretative strands in the analytic tradition. A key feature of Longuenesse’s work is its claim that space is, in effect, a product of the faculty of productive imagination, and therefore, given that according to Kant the productiveimagination is an effect of the understanding on sensibility (B151–2), a product of the faculty of understanding (Longuenesse 1998a: 219, 222–3). The stress Kant puts in the article on Kästner upon the independence of a notion of space from any conceptualization such as occurs in geometry certainly provided ammunition for an ‘anti- conceptualist’ backlash. In French Kant scholarship, this was led by Fichant’s translation of Kant’s reply to Kästner, as well as a paper underlining its importance for an understanding of Kant on space (Fichant 1997). Replies followed from Longuenesse (1998b, 2005), and from philosophers upholding the stronger conceptualist stance of Marburg neo-Kantianism (Dufour 2003). In English-speaking Kant scholarship, a related discussion has been taking place about the sense to be given to Kant’s claim that constructions in spatial intuition are required to derive geometric truths. A key text in this debate is Friedman (1992). Friedman claims that Kant’s requirement is, in effect, a consequence of the limitations of the monadic logic he used. Friedman (1992: 63–4) points out that, while Kant thought he needed to carry out iterative constructions to construct new points as part of a geometric proof, existential quantifiers in the setting of a polyadic logic could have been used instead, had such a logic been available to Kant. For Friedman, this shows that Kant’s view of geometry as synthetic was conditioned by the limits of the logic at his disposal. Friedman’s reading of the Metaphysical Exposition (1992: 68–70) has it that it is only because of its role in grounding geometry that the representation of space must be an a priori intuition. Carson (1997: 495–7) takes up this point and shows that the infinity of space described by Kant in the Metaphysical Exposition is not that of infinite iteration, but of an infinite given space, and that it therefore is irreducible to logic. In so doing, she is upholding an emphasis upon the phenomenological character of space first made by Parsons (1992: 72), which parallels the anti-conceptualist thrust of Fichant’s position. Partly in response to Carson, Friedman revised his position (Friedman 2000, 2003, 2012) leading to some convergence with Carson’s position, eventually abandoning in effect the fully conceptualist take upon space which he still held in 2000, as we shall see below, while other authors reinforced the need to take the phenomenological notion of space seriously (e.g. Kjosavik 2009). It is noteworthy that Kant’s response to Kästner is discussed by Friedman in the last of those three papers, and indeed its key distinction between metaphysical space that is a given infinite and space as the topic of geometry is what is at the heart of this particular debate around the importance of the phenomenology of space. (shrink)
Although the “Transcendental Aesthetic” is the briefest part of the first Critique, it has garnered a lion's share of discussion. This fact reflects the important implications that Kant drew from his arguments there. He used the arguments concerning space and time to display examples of synthetic a priori cognition, to secure his division between intuitions and concepts, and to support transcendental idealism. Earlier, in the years around 1770, Kant's investigations into space and time had facilitated his turn toward (...) “critical” philosophy. Prior to that time, Kant's main interests in space and time pertained to physics and metaphysics. As he entered the critical period, he delved into the cognitive basis of our experience of space (and time), and drew his conclusions about their ideality. Kant's doctrines of space and time provoked extensive response in his own time and throughout the nineteenth century. These responses variously concerned the metaphysics, physics, epistemology, psychology, and geometry of space. Throughout the nineteenth century, philosophers, physiologists, and psychologists sought to extend or to refute Kant's theories of space. By the last decades of the nineteenth century, many had rightly concluded that the existence of non-Euclidean geometry as a candidate description of physical space refuted Kant's full doctrine of space - though some have hoped that his position might be saved by restricting it to “visual space.”. (shrink)
Bede Rundle presents a philosophical investigation of the nature and reality of time and space, by means of analysis of the concepts involved. He discusses anti-realism, time travel, temporal parts, geometry, convention, and infinity, and more general issues concerning identity, objectivity, causation, facts, and verifiability.
I take up Kant's remarks about a " transcendental deduction" of the "concepts of space and time". I argue for the need to make a clearer assessment of the philosophical resources of the Aesthetic in order to account for this transcendental deduction. Special attention needs to be given to the fact that the central task of the Aesthetic is simply the "exposition" of these concepts. The Metaphysical Exposition reflects upon facts about our usage to reveal our commitment to the (...) idea that these concepts refer to pure intuitions. But the legitimacy of these concepts still hangs in the balance: these concepts may turn out to refer to nothing real at all. The subsequent Transcendental Exposition addresses this issue. The objective validity of the concepts of space and time, and hence their transcendental deduction, hinges on careful treatment of this last point. (shrink)
This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of (...) Newton’s own spatial hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors. (shrink)
This paper, which has both a historical and a polemical aspect, investigates the view, dominant throughout the eighteenth and nineteenth centuries, that the sense of sight is, originally, not phenomenally three-dimensional in character, and that we must come to interpret its properly two-dimensional data by reference to the sense of 'touch'. The principal argument for this claim, due to Berkeley, is examined and found wanting. The supposedly confirming findings concerning 'Molyneux subjects' are also investigated and are shown to be either (...) irrelevant or disconfirming. Recent investigations on infant and neonatal perception are discussed and are also found to be disconfirming. An innatist version of the theory is then considered and is shown to be undermined by the largely 'Gibsonian' character of early space-perception. Finally three recent arguments in favour of the theory - two from psychologists, one from a philosopher - are considered and answered. (shrink)
This paper aims to show that many criticisms of McDowell’s naturalism of second nature are based on what I call ‘the orthodox interpretation’ of McDowell’s naturalism. The orthodox interpretation is, however, a misinterpretation, which results from the fact that the phrase ‘the space of reasons’ is used equivocally by McDowell in Mind and World. Failing to distinguish two senses of ‘the space of reasons’, I argue that the orthodox interpretation renders McDowell’s naturalism inconsistent with McDowell’s Hegelian thesis that (...) the conceptual is unbounded. My interpretation saves McDowell from being inconsistent. However, the upshot of my interpretation is that what is really at work in McDowell’s diagnosis of the dualism between nature and reason is the Hegelian thesis, not the naturalism of second nature. (shrink)
To determine the role Latino community gardens play in community development, open space, and civic agriculture, we conducted interviews with 32 community gardeners from 20 gardens, and with staff from 11 community gardening support non-profit organizations and government agencies. We also conducted observations in the gardens, and reviewed documents written by the gardeners and staff from 13 support organizations and agencies. In addition to being sites for production of conventional and ethnic vegetables and herbs, the gardens host numerous social, (...) educational, and cultural events, including neighborhood and church gatherings, holiday parties, children’s activities, school tours, concerts, health fairs, and voter registration drives. In some cases, the gardens also serve to promote community activism. The primary concern of gardeners is to secure land tenure in the face of pressures to develop the garden sites for housing. The support organizations and agencies provide help with land tenure, as well as with advocacy, organization, and horticultural practices. Although the role of the Latino gardens in community development appears to be more important than their role in open space or agricultural production, the gardens can also be viewed as unique “participatory landscapes” that combine aspects of all three movements, as well as provide a connection between immigrants and their cultural heritage. (shrink)
I argue that there are no physical singularities in space–time. Singular space–time models do not belong to the ontology of the world, because of a simple reason: they are concepts, defective solutions of Einstein’s field equations. I discuss the actual implication of the so-called singularity theorems. In remarking the confusion and fog that emerge from the reification of singularities I hope to contribute to a better understanding of the possibilities and limits of the theory of general relativity.
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the (...) representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor. (shrink)
In the philosophy of perception, direct realism has come into vogue. Philosophical authors assert and assume that what their readers want, and what anyone should want, is some form of direct realism. There are disagreements over precisely what form this direct realism should take. The majority of positions in favor now offer a direct realism in which objects and their material or physical properties constitute the contents of perception, either because we have an immediate or intuitive acquaintance with those objects (...) and properties, or because our perceptual states have informational content that represents the properties of those objects (and which is not itself an object of perception and has no specifically subjective aspect). This paper considers various forms of perceptual realism, including, for purposes of comparison, the largely abandoned indirect or representative realism. After surveying the variety of perceptual realisms and considering their various commitments, I introduce some considerations concerning the phenomenology of visual space that cause trouble for most forms of direct realism. These considerations pertain to the perception of objects in the distance and, secondarily, to the perception of shapes at a slant. I argue that one of the lesser known varieties of perceptual realism, critical direct realism, can meet the challenges offered by the facts of spatial perception. (shrink)
This essay offers an interpretation of Descartes’ treatment of the concepts of place and space in the Principles of Philosophy. On the basis of that interpretation, I argue that his understanding and application of the concept of space supports a pluralist interpretation of Descartes on extended substance. I survey the Scholastic evolution of issues in the Aristotelian theory of place and clarify elements of Descartes’ appropriation and transformation thereof: the relationship between internal and external place, the precise content (...) of the claim that space and body are really identical, and the way we conceptually distinguish space from body. Descartes applies his concept of space in ways that illuminate the metaphysical structure of extension. In particular, he uses the concept to specify the degree to which finite parts of matter are independent of each other. I argue that for Descartes, conceiving extension as indivisible is an artifact of conceiving it as a space. That is, pace the monistic reading of Cartesian extended substance, regarding extension as indivisible is an artifact of conceiving it in a way more removed from its real nature. (shrink)
I argue that Leibniz's treatment of void or empty space in the appendix to his fourth letter to Clarke conflicts with the way he elsewhere treats (metaphysical) evil, insofar as he allows that God has created a world with the one kind of privation (evil), while insisting that God would not have created a world with the other kind of privation (void). I consider three respects in which the moral case might be thought to differ relevantly from the physical (...) one, and argue that none of them succeed in removing the inconsistency. Rather than denying the existence of void, Leibniz should have been led by his treatment of evil to realize that the arguments he deploys in this appendix are dubious, and that the principles to which he appeals do not rule out empty space any more than they rule out evil, darkness, cold, or any other privations. (shrink)
The moral obligation to support space exploration follows from our obligations to protect the environment and to survive as a species. It can be justified through three related arguments: one supporting space exploration as necessary for acquiring resources, and two illustrating the need for space technology in order to combat extraterrestrial threats such as meteorite impacts. Three sorts of objections have been raised against this obligation. The first are objections alleging that supporting space exploration is impractical. (...) The second is the widely held notion that space exploration and environmentalism are at odds with one another. Finally, there are two objections to using space resources that Robert Sparrow has raised on the topic of terraforming. The obligation to support space exploration can be defended in at least three ways: (1) the "argument from resources," that space exploration is useful for amplifying our available resources; (2) the "argument from asteroids," that space exploration is necessary for protecting the environment and its inhabitants from extraterrestrial threats such as meteorite impacts; and (3) the "argument from solar burnout," that we are obligated to pursue interstellar colonization in order to ensure long-term human survival. (shrink)
Consciousness lacks extension and other spatial properties. But how can this be, if it arises from matter in space? The paper argues that this conundrum can only be solved by recognizing that our current conception of space is fundamentally inadequate. However, no other conception is available to us.
The ontology of Bohmian mechanics includes both the universal wave function and particles. Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated—replaced by a set of single-particle pilot-wave fields (...) living in ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields which influence the particles’ motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the program of trying to replace the configuration space wave function with a set of fields in ordinary physical space. (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)
Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130: 78-94,2006). In particular, we show that subjectivestate-space models (henceforth HMS structures) can be (...) embedded within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse. (shrink)
I argue that space has three dimensions, and quantum mechanics does not show otherwise. Specifically, I argue that the mathematical wave function of quantum mechanics corresponds to a property that an N-particle system has in three-dimensional space.