Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’. And he rests these upon consistently opposite grounds. In the Antinomy we are told that (...) we can have no intuitive grasp of an infinite space, and in the Aesthetic he says that our grasp of infinite space is precisely intuitive. (shrink)

Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’ (A25/B39). And he rests these upon consistently opposite grounds. In the Antinomy we are told (...) that we can have no intuitive grasp of an infinite space, and in the Aesthetic he says that our grasp of infinite space is precisely intuitive. (shrink)

This chapter contains sections titled: * Brief History * How We Talk * Science and Infinity * Religion and Infinity * Concluding Remarks * Notes * References * Further Reading.

The significance of absolute space and absolute motion in the Critical philosophy is clarified by analysis of relevant passages in Kant's Metaphysical Foundations of Natural Science. Newton's absolute space is rejected in favor of absolute space conceived of as an idea of reason serving to unify the infinity of possible relative kinematic spaces. On the other hand, something like newton's concept of absolute motion (e.g., in the case of rotation) is accepted by Kant under the heading (...) of real - as opposed to illusory - motion. (shrink)

The genesis of space and time is investigated within the rotational-monadic paradigm. It is established that the essence of the phenomenon of space is revealed through the dialectical synthesis of its two aspects — ideal and material, where the material aspect is represented by the metaphysical construct of protomonad. It is shown that basic physical distinctions such as motion, mass, gravitation find a meaningful hermeneutic through the material aspect of space, which has a purely discrete structure, while (...) the contradiction about finitude — infinity is resolved by juxtaposing metaphysical and ontic spaces, where the Universe is represented as an “egg”. The analysis of temporality is preceded by remarks on the relational and substantive concepts of time, consideration of the discreteness-continuity dilemma, and criticism of the absolutization of discreteness in the temporality representation. It is argued that discreteness and continuity are combined dialectical oppositions through which the temporal reality is actualized, where continuity is hidden from observation in the metaphysical world and discreteness is manifested explicitly in the physical world. Three dimensions of time — Present, Past and Future — are discussed, as a result of which it is stated that in the primary way time is found as an attribute of consciousness and only in the secondary way it correlates with phenomenological reality. New differentiations of time are revealed: interval Present, embracing as a universum other moduses of the Present, and two- component time in the form of cyclic and linear components which allow us to make a justified positive conclusion about the existence of transcendental subjectivity, being the basis of absolute temporality. (shrink)

Kant's theory of transcendental ideas can be conceived as a sort of model theory for an empirical first-order object theory. The main features of Kant's theory of transcendental ideas (especially its antinomies and their solutions) can be recognized, in a modified way, in a religious discourse as exemplified in the dialogue of Jesus and the Samaritan woman (John 4). In this way, what is by Kant meant merely as regulative ideas obtains a sort of objective reality and becomes a religiously (...) founded metaphysics. A metaphysical theory of religious dialogue is formalized on the basis of an extended justification logic of evidence and wish agents. (shrink)

Draft for presentation at the 14th International Kant-Congress, September 2024. -/- Abstract: Kant claims we intuit infinite space. There’s a problem: Kant thinks full awareness of infinite space requires synthesis—the act of putting representations together and comprehending them as one. But our ability to synthesize is finite. Tobias Rosefeldt has argued in a recent paper that Kant’s notion of decomposing synthesis offers a solution. This talk criticizes Rosefeldt’s approach. First, Rosefeldt is committed to nonconceptual yet determinate awareness of (...) (potentially) infinite space, but I argue that such awareness is (1) prima facie implausible, as well as contravened by textual evidence from Kant’s (2a) definitions of ‘infinity’ and (2b) account of geometrical construction. Second, scrutiny of how Kant thinks awareness of potential infinity is afforded by geometrical construction (e.g., extending a line segment ad indefinitum) indicates no essential role for decomposing synthesis. Familiar synthesis from parts to wholes is sufficient. (shrink)

Philosophers, theologians, physicists, and psychologists join their efforts to reflect on the crucial issues of limit and infinity, time and eternity, empty space and material space. The volume offers an invaluable contribution to some of the most important issues of our times: questions on God and consciousness are discussed in parallel with quantum theory, black holes, the inflationary universe, the Big Bang, and string theory, from different perspectives and angles, ranging from neuroscience to AI.

Many people believe that we have responsibility towards the distant future, but exactly how far this responsibility reaches and how we can find a reasonable ethical foundation for it has not been answered in any definitive manner. Future people have no power over us, they form no part of our moral community and it is unclear how we can represent them in a possible original position. All these problems can be circumvented when you take an impersonal decision criterion like maximizing (...) total or average utility. Such a sum-ranking criterion is neutral with respect to distance in time or space: my utility, my neighbour's and that of our descendants all carry the same weight. This makes future people an integral part of present decisions. Time-neutrality was defended by, among others, Sidgwick, Pigou and Ramsey. (shrink)

The article proposes an interpretation of Kant’s notions of form of, and formal intuition of space to explain and justify the claim that representing space as object requires a synthesis. This involves identifying the transcendental conditions of the analytic unity of consciousness of this formal intuition and distinguishing between it and its content. On this reading which builds upon recent proposals, footnote B160–1n. involves no revision of the Transcendental Aesthetic: space is essentially characterized by non-conceptual features. The (...) article also addresses worries about the infinite magnitude and the unicity of space, by considering the characteristics and requirements of geometric constructions. (shrink)

In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes (...) that we always imagine an earlier time in which God might have created the world if he had wanted, but insists that this imaginary earlier existence of the world is not connected to its actual duration in the way that the indefinite extension of space is connected to the actual extension of the world. This paper considers whether Descartes’s metaphysics can sustain this asymmetrical attitude towards infinite space vs. time. I first consider Descartes’s relation to the ‘imaginary’ space/time tradition that extended from the late scholastics through Gassendi and More. I next examine carefully Descartes’s main argument for the indefinite extension of space and explain why it does not apply to time. Most crucially, since duration is merely conceptually distinct from enduring substance, the end or beginning of the world entails the end or beginning of real time. In contrast, extension does not depend on any enduring substance besides itself. (shrink)

I argue that Kant's claim in the “Transcendental Aesthetic” of the Critique of Pure Reason that space and time are immediately given in intuition as infinite magnitudes is undercut by his general theory of mathematical knowledge. On this general theory, pure intuition does not give objects of any determinate magnitude at all, but only forms of possible objects. Specifically, what pure intuition itself yields is the recognition that any determinate space or time is part of a larger one, (...) but it requires an inference of reason to go from that to the claim that space and time are infinite. I further argue that this result is consistent with Kant's claim in the second-edition “Transcendental Deduction” that the unity of space and time are the products of synthesis, but also means that the unity of space and time as objects cannot be used a premise in the Deduction but can only be regarded as a conclusion of the deduction and the following “System of Principles.”. (shrink)

Comments on Fullerton's paper, 'The doctrine of space and time' (1901). Fullerton adapts both Kantian and Berkelian doctrine of space, but his view on space is dominated more by the Berkelian views. His views on time are the same as that on space. His comparative study on animals has been criticized since it is claimed that animals are living wholes and abstracting certain parts have little value for fundamental comparison. The concepts of infinity and infinite (...) divisibility are considered important. However, he misses the real import of infinity by recognizing the possibility of infinite divisibility and ignores the distinction between being infinitely divisible and infinitely divided. The world according to him is not given directly by intuition and consciousness can only represent it. (shrink)

This introduction to the roles infinity plays in metaphysics includes discussion of the nature of infinity itself; infinite space and time, both in extent and in divisibility; infinite regresses; and a list of some other topics in metaphysics where infinity plays a significant role.

The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds (...) to set-theory or intuitionist approach to the foundation of mathematics and to Peano or Heyting arithmetic. Quantum mechanics can be reformulated in terms of information introducing the concept and quantity of quantum information. A qubit can be equivalently interpreted as that generalization of “bit” where the choice is among an infinite set or series of alternatives. The complex Hilbert space can be represented as both series of qubits and value of quantum information. The complex Hilbert space is that generalization of Peano arithmetic where any natural number is substituted by a qubit. “Negation”, “choice”, and “infinity” can be inherently linked to each other both in the foundation of mathematics and quantum mechanics by the meditation of “information” and “quantum information”. (shrink)

Many philosophic arguments concerned with infinite series depend on the mutual inconsistency of statements of the following five forms: (1) something exists which has R to something; (2) R is asymmetric; (3) R is transitive; (4) for any x which has R to something, there is something which has R to x; (5) only finitely many things are related by R. Such arguments are suspect if the two-place relation R in question involves any conceptual vagueness or inexactness. Traditional sorites arguments (...) show that a statement of form (4) can fail to be true even though it has no clear counter-example. Conceptual vagueness allows a finite series not to have any definite first member. I consider the speculative possibilities that there have been only finitely many non-overlapping hours although there has been no first hour and that space and time are only finitely divisible even though there are no smallest spatial or temporal intervals. (shrink)

I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely (...) complex, the spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition. (shrink)

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

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the (...) nature of part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason. (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)

This introduction to one of the liveliest and most popular fields in philosophy is written specifically for a beginning readership with no background in philosophy or science. Step-by-step analyses of the key arguments are provided and the philosophical heart of the issues is revealed without recourse to jargon, maths, or logical formulas. The book introduces Einstein's revolutionary ideas in a clear and simple way, along with the concepts and arguments of philosophers, both ancient and modern that have proved of lasting (...) value. Specifically, the theories of the ancient Greek philosophers, Zeno, Euclid and Parmenides are considered alongside the ideas of Newton, Leibniz and Kant as well as the giants of twentieth-century physics, Einstein and Lorentz. The problems at the heart of the philosophy of space and time, such as change, motion, infinity, shape, and inflation, are examined and the seismic impact made by relativity theory and quantum theory is assessed in the light of the latest research. The writing is lucid and entertaining, allowing a beginning readership to grasp some difficult concepts while offering the more experienced reader a succinct and illuminating presentation of the state of the debate. "Space, Time and Einstein" shows the reader the excitement of scientific discovery and the beauty of theory in the search for answers to these fundamental questions. (shrink)

The paper is devoted to the reconstruction of some stage of the proces leading to the emergence in modern science the concept of Infinite „Euclidean” space to geometry of the Elements in late antiquity and the Middle Ages. Some historical medieval sources and views concerning Archytas, Cleomedes, Proclus, Simplicius, Aganis, al-Nayrizi and the Arabs, Boetius, Gerard of Cremona, Albertus Magnus et al., are described analyzed and compared. The small changes in the understanding of geometry in the Elements during the (...) ages are reconstructed up to the first explicit use of the concept of infinity in geometry by Nicole Oresme. (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)

In this introduction, we explain our choice to approach the topic of space from a cosmological perspective, that is, by studying the conceptions of space that were implicitly or explicitly entailed by ancient, medieval and early modern representations of the cosmos, and the role that imagination played in those conceptions. We compare our approach with those of Alexandre Koyré and Edward Grant, and we present the two important issues this book intends to shed light on, namely the continuity (...) and discontinuity between ancient, medieval, and early modern conceptions of space and the cosmos; and the role that metaphysical, cosmological, and theological considerations played in the elaboration of new theories of space in the course of history. This chapter also presents the main, recurring themes of this book: the relation between place and space; the notion of imaginary spaces; the role played by thought experiments in discussions concerning the nature of space and the structure of the cosmos; the impact of the condemnation of 1277 on subsequent theories of space; and the relation between God’s immensity and the infinity of space. (shrink)

Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination (...) of three central figures in the period: Locke, Descartes, and Leibniz. (shrink)

It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to (...) prefer various topological properties over others. In particular, I favor the adoption of multiply connected universe models on grounds of (i) simplicity, (ii) Machian considerations, and (iii) explanatory power. We are able to appeal to such grounds because multiply connected topologies open up the possibility of finite universe models (consistent with our best data), which in turn avoid thorny issues concerning the postulation of an actually infinite universe. (shrink)

In his Pensées, Blaise Pascal gives vivid voice to both the wonder and anxiety that many early modern thinkers felt towards infinity. Contemplating our place between the infinite expanse of space and the infinite divisibility of matter, Pascal writes.

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large is intimately related to the infinitely small. Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest (...) upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. (shrink)

Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the (...) border between them. A special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or “observer”, or “user” to infinity implied by Henkin’s proposition as the only consistent ones as to infinity. (shrink)

This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through (...) Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic. (shrink)

We informally discuss some recent results on the incompleteness of formal systems. These theorems, which are of great importance to contemporary mathematical epistemology, are proved using a variety of conceptual tools provably stronger than those of finitary axiomatisations. Those tools require no mathematical ontology, but rather constitute particularly concrete human constructions and acts of comprehending infinity and space rooted in different forms of knowledge. We shall also discuss, albeit very briefly, the mathematical intelligence both of God and of (...) computers. We hope in this manner to help the reader overcome formalist reductionism, while avoiding naive Platonist ontologies, typical symptoms of Godelitis which affected many in the last seventy years. (shrink)

When it first appeared, this lucid exposition embodied the author's most advanced thinking on such topics as the finitude or infinity of the universe in space, the age of the universe, theories of "continuous creation", the rival claims made for the use of "ordinary" and "special deductive" methods in cosmological inquiry, and the meaning and importance of theory-construction in scientific cosmology. All currently relevant subject matter has been retained here; this edition also incorporates many revisions and an entirely (...) new chapter that explores the feasibility of reconciling the scientific and theological views of the origin of the universe. (shrink)

This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through (...) Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic. (shrink)

Manifest in this writing experiment is a proposition that traversing theoretical dispositions as a new infinity (nod to Deleuze, 1994) brings our attention to the qualification of vibrancy, or as D...

The aim of this paper is not only to deal with the concept of infinity, but also to develop some considerations about the epistemological status of cosmology. These problems are connected because from an epistemological point of view, cosmology, meant as the study of the universe as a whole, is not merely a physical (or empirical) science. On the contrary it has an unavoidable metaphysical character which can be found in questions like “why is there this universe (or a (...) universe at all)?”. As a consequence, questions concerning the infinity of the universe in space and time can correctly arise only taking into account this metaphysical character of cosmology. Accordingly, in the following paper it will be shown that two different concepts of physical infinity of the universe (the relativistic one and the inflationary one) rely on two different ways of solution of a metaphysical problem. The difference between these concepts cannot be analysed using the classical distinctions between actual/potential infinity or numerable/continuum infinity, but the introduction of a new “modal” distinction will be necessary. Finally, it will be illustrated the role of a philosophical concept of infinity of the universe. (shrink)

Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is (...) strictly smaller than an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. (shrink)

Catherine Keller's Cloud of the Impossible knits together process theology and relational ontology with quantum mechanics. In quantum physics, she finds a new resource for undoing the architecture of classical metaphysics and its location of autonomous human subjects as the primary gears of ethical agency. Keller swarms theology with the quantum perspective, focusing in particular on the phenomenon of quantum entanglement, by which quantum particles are found to remain influential over each other long after they have been physically separated—what Albert (...) Einstein and his collaborators recklessly dismissed as “spooky action at a distance.” This spooky action, Keller suggests, reroutes process thought—classically concerned with flux—to a new concern with intransigence—particularly the intransigence of the ethical relationship. Attending to the ethical urgency of the Other, she leaves process theology in a position of susceptibility to the moral imperative posed by the marginalized, the victimized, and the oppressed. This essay argues that although the ontological work of Keller's book productively integrates quantum physics into process theology, the ethical dimension of relationality is left cold in the quantum field. This is because, contra the ethical framework of contemporary deconstruction, which, following Emmanuel Levinas, sees ethical relationships as emerging out of a dynamic of infinite distance, moral connection has nothing to do with the remote reaches of the quantum scale or the macro-scale limits of space—nothing to do with “infinity” at all. Ethics emerges out of a much messier landscape—the evolved dynamic of fleshy, finite, material bodies. Rather than seeing ethical labor as a matter of physics, my contention is that interdisciplinary undertakings like Cloud of the Impossible are ethical disciplinary practices, re-acquainting us with the non-sovereignty of the self in order to open up new habits of relating rather than spotlighting ethical imperatives. (shrink)

Contemporary psychiatry faces serious challenges because it has failed to incorporate accumulated knowledge from basic neuroscience, neurophilosophy, and brain–mind relation studies. As a consequence, it has limited explanatory power, and effective treatment options are hard to come by. A new conceptual framework for understanding mental health based on underlying neurobiological spatial-temporal mechanisms of mental disorders (already gained by the experimental studies) is beginning to emerge.

In a promising working note to the Visible and Invisible, Merleau-Ponty proposes that we understand Being according to topological space – relations of proximity, distance, and envelopment – and move away from an image of Being based on homogeneous, inert Euclidean space. With reference to treatments of cross-sensory perception, color-blindness, and the concept of quale or qualia, I seek to rehearse this shift from Euclidean to topological Being by illustrating how modern science confines color itself to a Euclidean (...) model of color space. I discuss “being as Object” in Merleau-Ponty’s later work before showing how color, and indeed all perception, is reduced to being as Object in the form of “quale”. Next, I address discussions in Merleau-Ponty’s work and contemporary research to illustrate how synesthesia and so-called color-blindness are rendered abnormal by this objectified being of color. Merleau-Ponty’s reading of synesthesia follows directly from his rejection of quale, and his use of color perception serves as a rejection of solipsism. With appeal to his proposed topological model of Being, I conclude by recognizing the problematic nature of synesthesia and color-blindness as being ontological, not psychological.Dans une note de travail, à mon sens décisive, du Visible et l’Invisible, Merleau-Ponty propose que l’on comprenne l’Être à partir de l’espace topologique – relations de proximité, distance et enveloppement – allant à l’encontre d’une l’image de l’Être fondée sur un espace euclidien homogène et inerte. En faisant référence aux traitements de la perception synesthésique, au daltonisme et au concept de quale ou qualia, j’essayerai de décrire ce passage de l’Être euclidien à l’Être topologique en montrant que la science moderne finit par confiner la couleur dans un modèle euclidien d’espace-couleur. J’examinerai « l’Être-objet » dans les derniers écrits de Merleau-Ponty avant de montrer comment la couleur, et plus en général la perception, est réduite à être comme un Objet dans la forme d’un « quale ». Ensuite, en examinant les analyses merleau-pontiennes et les recherches contemporaines, je montrerai comment la synesthésie et le daltonisme sont donc considérés comme anormaux à partir de cette objectivation de la couleur. La lecture que Merleau-Ponty donne de la synesthésie est la conséquence directe de son refus du quale, et l’utilisation qu’il fait de la perception des couleurs sert comme un refus du solipsisme. En faisant appel au modèle topologique de l’Être qu’il propose, je conclurai en constatant que la nature problématique de la synesthésie et du daltonisme est ontologique et non pas psychologique.In una nota di lavoro al Visibile e l’invisibile, Merleau-Ponty propone di comprendere l’Essere a partire da uno spazio topologico – secondo le relazioni di prossimità, distanza e avvolgimento – e abbandona l’immagine di un Essere fondato su uno spazio omogeneo, inerte, euclideo. Facendo riferimento ai trattamenti per le percezioni sinestetiche, al daltonismo e al concetto di quale o qualia, si cercherà di provare questo passaggio da un Essere euclideo a uno topologico, illustrando quanto la scienza moderna tenda a ridurre il concetto stesso di colore a un modello euclideo di spazio-colore. Si esaminerà l’“Essere-oggetto” degli ultimi lavori di Merleau-Ponty, mostrando come il colore, e in realtà la percezione tout court, vengano ridotti a oggetto nella forma di “quale”. Infine, si esaminerà l’opera merleau-pontiana e la ricerca contemporanea al fine di illustrare quanto la sinestesia e il daltonismo siano resi anormali da questa oggettivazione dell’essere del colore. L’interpretazione merleau-pontiana della sinestesia deriva proprio dal suo rifiuto del quale, e il suo uso della percezione del colore funge da rifiuto del solipsismo. Ricorrendo al modello topologico di Essere elaborato da Merleau-Ponty, si conclude riconoscendo che il problema della sinestesia e del daltonismo è, a tutti gli effetti, ontologico e non psicologico. (shrink)

The application of the general theory of relativity to the cosmological plane has led to a significant change in traditional notions on the space-time structure of the universe. This has been expressed in a new formulation and solution of cosmological problems such as that of a single world space and time, the problem of selection of a cosmological model for description of the universe, and the problem of the infinity of the universe.