Kant: Space

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)

Kant felsefesine karşı yapılan en yaygın eleştirilerden biri onun öznelci olduğudur. Bu eleştiriyle birlikte ayrıca Berkeleycilik suçlaması ve fenomenalist okuma karşımıza çıkmaktadır. Öznelcilik ithamına göre Kant empirik nesneleri sağlam/zihinden bağımsız bir şekilde düşün(e)mez, bu ise bilincimizin içine sıkışıp kaldığımız bir felsefeye yol açar. Berkeleycilik suçlaması ve fenomenalist okumaya göre de Kant felsefesi sadece görünüşleri bilebileceğimizi söyleyerek, bütün gerçekliği “kafanın-içinde-duran” zihinsel içeriklere indirgemiştir. Bu makalede öncelikle Kant’ın Berkeleycilik ithamına karşı kendi argümanlarını inceleyeceğiz; daha sonra fenomenalist okumanın temel varsayımlarını Van Cleve’in Kant (...) yorumunu mercek altına alarak bulacak ve eleştireceğiz. Bizim görüşümüze göre Van Cleve Kant’ı ele alırken ona iki varsayım isnat eder. Birincisine göre, Kant Kartezyen-Lockeçu temsiliyetçiliği savunur; ikincisine göre, Kantçı özne temelcidir. Bizce bu iki varsayımın Kant’a yüklenmesi haksızdır ve dolayısıyla Berkeleyci fenomenalist okuma ikna edici görünmemektedir. Kant’ın görünüş kavramı “kafanın-içinde-duran” zihinsel içerikler anlamına gelmemektedir; özne ise Kant’ın felsefesinde temelci bir pozisyon işgal etmez, dolayısıyla özne nesneyi salt bir zihinsel içerikmiş gibi taşımaz zira hem özne hem nesne Kant’ta fenomenal alana düşerler. (shrink)

This chapter discusses Kant's 1763 "possibility proof" for the existence of God. I first provide a reconstruction of the proof in its two stages, and then revisit my earlier argument according to which the being the proof delivers threatens to be a Spinozistic-panentheistic God—a being whose properties include the entire spatio-temporal universe—rather than the traditional, ontologically distinct God of biblical monotheism. I go on to evaluate some recent alternative readings that have sought to avoid this result by arguing that the (...) relevant facts about real modality can be ultimately grounded in God’s powers or thoughts – or that Kant just leaves the grounding relations mysterious. I argue that the textual and philosophical costs of each of these alternative readings are formidable. The chapter concludes with a discussion of the fate of the proof in the critical period. Some commentators think that it disappears altogether, or that it is downgraded such that it produces a mere regulative idea of God as the most real being. I suggest that the proof survives but that the mode of assent it licenses towards its conclusion changes from knowledge to a certain kind of Belief (Glaube). (shrink)

Famously, Kant describes space and time as infinite “given” magnitudes. An influential interpretative tradition reads this as a claim about phenomenological presence to the mind: in claiming that space and time are given, this reading holds, Kant means to claim that we have phenomenological access to space and time in our original intuitions of them. In this paper, I argue that we should instead understand givenness as a metaphysical notion. For Kant, space and time are ‘given’ in virtue of three (...) related facts: (i) they are necessary grounds of the existence of all other spatial and temporal possibilities; (ii) in virtue of being such grounds, they are metaphysically linked to all other represented spatiotemporal things; and (iii) as representations, space and time issue from the nature of our faculty of sensibility rather than from an arbitrary act of choice. Understanding givenness in this non-epistemological way helps us recover what is plausible in both ‘intellectualist’ and ‘anti-intellectualist’ readings of the Transcendental Aesthetic. Anti-intellectualists are correct that space and time are given in mere sensibility, but intellectualists are correct that we depend on the understanding for consciousness of space and time. (shrink)

Scholars working on Kant’s Anticipations of Perception generally attribute to him an argument that invalidly infers that objects have degrees of intensive magnitude from the premise that sensations do. I argue that this rests on an incorrect disambiguation of Kant’s use of Empfindung as referring to the mental states that are our sensings, rather than the objects that are thereby sensed. Kant’s real argument runs as follows. The difference between a representation of an empty region of space and/or time and (...) a representation of that same region as occupied by an object entails that, in addition to their extensive magnitude, objects must be represented as having a matter variable in intensive magnitude. Since it is the presence of sensation in a cognition that marks the difference between representing only the extensive magnitude of the object and the object as a whole, it is sensation that represents its intensive magnitude. (shrink)

Il principale obiettivo teoretico di questo lavoro consiste nel tentativo di verificare, attraverso un’indagine storico-genealogica e concettuale, come nella filosofia di Gilles Deleuze si assista ad un radicale mutamento del paradigma relativo alla nozione di trascendentale. Si tratta, in altre parole, di ripercorrere alcune delle tappe fondamentali che conducono il filosofo parigino a “purificare” il trascendentale da ogni riferimento ad una coscienza soggettiva egologica che si fondi in quanto principio genetico del mondo. Si riterrà utile procedere analizzando, in primo luogo, (...) il rapporto che Deleuze intrattiene con le istanze originarie del soggettivismo trascendentale kantiano, ove il trascendentale stesso, nel pensiero del filosofo tedesco, è strettamente connesso all’Io penso in quanto facoltà appercettiva dell’intelletto che incarnerebbe le condizioni di possibilità dell’esperienza. In secondo luogo, si tratterà di orientarsi nel dibattito critico che Deleuze intrattiene con la fenomenologia di Edmund Husserl, ed in particolar modo con la lettura husserliana della Critica della Ragion Pura di Kant, ove il padre fondatore dell’indirizzo fenomenologico novecentesco è colui che fa leva sullo stretto rapporto che sussiste tra il trascendentale e la coscienza. Nonostante il percorso storico, tracciato dal concetto di trascendentale, abbia inizio con l’opera di Kant, ritengo non sia possibile evitare un pur breve confronto con il ruolo che l’ego ha avuto nella formulazione cartesiana del cogito; si dovrà, per ciò stesso, considerare la particolare lettura deleuziana che riconosce nel cogito cartesiano il “luogo” in cui confluiscono tutte le facoltà del soggetto, permettendo di identificare il cogito stesso con una forma embrionale di piano di immanenza, seppur non adeguatamente radicalizzata nella misura in cui il cogito cartesiano resta saldamente ancorato al soggetto. Ritengo, tuttavia, che il più considerevole obiettivo di questa proposta d’indagine non si risolva in una ricostruzione meramente storico-genealogica. Si tratterà, al contrario, di verificare come l’importanza degli esiti raggiunti da Deleuze mediante l’opera di purificazione della nozione di trascendentale sia da individuare su due fronti: 1. La teorizzazione del concetto di campo trascendentale permette a Deleuze di disegnare una forma di temporalità non psicologica e non cronologica fondata sul paradosso secondo cui il tempo costituirebbe un’interiorità non psicologica, o per meglio dire, una dimensione autenticamente trascendentale nella quale il soggetto vive e diviene. 2. In antitesi ai proponimenti della fenomenologia husserliana, l’esito autentico del progetto di purificazione del trascendentale da ogni istanza egologica consiste nell’interruzione della correlazione a priori tra il soggetto e il mondo, nella destituzione della filosofia da ogni pregiudizio antropocentrico, e nella rideterminazione dell’umano niente più che come un effetto, o un caso, del mondo. (shrink)

In this paper I consider Tetens' reaction to Kant's Inaugural Dissertation in his two most important philosophical works, the essay “Über die allgemeine speculativische Philosophie” of 1775 and the two-volume Philosophische Versuche of 1777. In particular, I focus on Tetens’ critical discussion of Kant's account of the acquisition of concepts of space and time.

This is a defense of Kant against the allegedly neglected alternative in his formulation of transcendental idealism. What sets it apart from the contributions of others who have spoken for Kant in this regard is the construction of a general interpretive framework — a reconstruction of the one Kant provides for transcendental idealism — as opposed to the development of an ad hoc defensive strategy for refuting the charges. Hence, comprehensive clarification instead of pointed rebuttal. The difference is between focusing (...) on the text and focusing on the problem. No doubt, doing both is not only possible but also required, as the problem is supposed to be in the text, but the point is that it is not there, and further, that we need not go anywhere else to show that it is not there. Thus, the approach is constructive rather than defensive, or more accurately, constructive as well as defensive. And the construction rests on what Kant actually said rather than on what he might have meant or on what he should have said instead. (shrink)

This is the introduction to the volume Kantian Nonconceptualism (Palgrave 2016).

Leibniz’s main thesis regarding the nature of space is that space is relational. This means that space is not an independent object or existent in itself, but rather a set of relations between objects existing at the same time. The reality of space, therefore, is derived from objects and their relations. For Leibniz and his successors, this view of space was intimately connected with the understanding of the composite nature of material objects. The nature of the relation between space and (...) matter was crucial to the conceptualization of both space and matter. In this paper, I discuss Leibniz’s account of relational space and examine its novel elaborations by two of his successors, namely, the young Immanuel Kant and the Croat natural philosopher Roger Boscovich. Kant’s and Boscovich’s studies of Leibniz’s account lead them to original versions of the relational view of space. Thus, Leibniz’s relational space proved to be a philosophically fruitful notion, as it yielded bold and intriguing attempts to decipher the nature of space and was a key part in innovative scientific ideas. (shrink)

This essay examines the relationship between monads and space in Kant’s early pre-critical work, with special attention devoted to the question of ubeity, a Scholastic doctrine that Leibniz describes as “ways of being somewhere”. By focusing attention on this concept, evidence will be put forward that supports the claim, held by various scholars, that the monad-space relationship in Kant is closer to Leibniz’ original conception than the hypotheses typically offered by the later Leibniz-Wolff school. In addition, Kant’s monadology, in conjunction (...) with God’s role, also helps to shed light on further aspects of his system that are broadly Leibnizian, such as monadic activity and the unity of space. (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 this article it is shown that a careful analysis of Kant 's Gedanken von der wahren Schätzung der lebendigen Kräfte und Beurtheilung der Beweise leads to a conclusion that does not match the usually accepted interpretation of Kant 's reasoning in 1747, according to which the young Kant supposedly establishes a relationship between the tridimensionality of space and Newton's law of gravitation. Indeed, it is argued that this text does not yield a satisfactory explanation of space dimensionality, and actually (...) restricts itself to justifying the tridimensionality of extension. (shrink)

I argue that Kant’s distinction between the cognitive roles of sensibility and understanding raises a question concerning the conditions necessary for objective representation. I distinguish two opposing interpretive positions—viz. Intellectualism and Sensibilism. According to Intellectualism all objective representation depends, at least in part, on the unifying synthetic activity of the mind. In contrast, Sensibilism argues that at least some forms of objective representation, specifically intuitions, do not require synthesis. I argue that there are deep reasons for thinking that Intellectualism is (...) incompatible with Kant's view as expressed in the Transcendental Aesthetic. We can better see how Kant’s arguments in the first Critique may be integrated, I suggest, by examining his notion of the 'unity' [Einheit] of a representation. I articulate two distinct ways in which a representation may possess unity and claim that we can use these notions to integrate Kant’s arguments in the Aesthetic and the Transcendental Deduction without compromising the core claims of either Sensibilism or Intellectualism—that intuition is a form of objective representation independent of synthesis, and that the kind of objective representations that ground scientific knowledge of the world require synthesis by the categories. (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.

Mit dem Terminus 'ursprünglicher Raum' wird der Raum bezeichnet, der Kant innerhalb der transzendentalen Ästhetik als reine subjektive Form der Anschauung des äußeren Sinnes bestimmt. Man könnte ihn auch den 'ästhetischen Raum' nennen. Auf jeden Fall muss er vom (proto-)geometrischen Raum unterschieden werden, da letzterer eine Einheit voraussetzt die auf einer Synthesis beruht, und dadurch – weil bei Kant alle Synthesis unter den Kategorien steht – weniger ursprünglich zum Anschauungsvermögen gehört. Es ist diese Unterscheidung zwischen dem ursprünglichen Raum, der „Form (...) der Anschauung“ ist, und dem (proto-)geometrischen Raum, der „formale Anschauung“ ist, auf die Kant in einer bekannten Fußnote im §26 der transzendentalen Deduktion der B-Auflage anspielt. -/- Die Bedeutung der Unterscheidung zwischen (proto-)geometrischem und ursprünglichem Raum liegt unter anderem darin, dass sie stipuliert, dass das ursprüngliche Wesen des Raumes vor und unabhängig von dem erreichbar ist, was durch jedwede Mathematik der Ausdehnung von ihm ausgesagt wird. Das bedeutet nun aber nicht, dass diese Unterscheidung uns zwingt, anzunehmen, dass das ursprüngliche Wesen des Raumes auch von uns erreichbar ist. Und nehmen wir mal an, dass wir tatsächlich über eine Art Zugang zu diesem Wesen verfügen, dann noch stellt sich überdies die Frage, ob ein solcher Zugang sich innerhalb der Sphäre der Erkenntnis befindet, mit anderen Worten: ob das ursprüngliche Wesen des Raumes vom Philosophen auch wirklich erkannt – das heißt: in Erkenntnisurteile gefasst und ausgedrückt – werden kann. (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 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)

El capítulo introduce al debate sobre la naturaleza del espacio entre Leibniz y Clarke/Newton y a la posición que adopta Kant más tarde. En particular, se exponen los dos principales argumentos de Leibniz, basados en los Principios de Razón Suficiente e Identidad de Indiscernibles, en favor del relacionismo así como algunas respuestas de Clarke/Newton. También se presenta el argumento basado en la orientación del espacio que propuso Kant en 1768 para refutar el relacionismo de Leibniz. Se concluye con una breve (...) exposición del idealismo trascendental de Kant en su Primera Crítica. (shrink)

David Hyder.The Determinate World: Kant and Helmholtz on the Physical Meaning of Geometry. viii + 229 pp., bibl., index. Berlin/New York: Walter de Gruyter, 2009.

Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set of determinately oriented, constructed (...) geometrical spaces is a proper subset of metaphysical space, thus, metaphysical space is infinite. Kant's paradoxical doctrine of metaphysical space is necessary to reconcile his empiricism with his transcendental idealism. (shrink)

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)

In Van Cleve's "Problems from Kant," it is suggested that his interpretation of Kant's metaphysics resolves the problem of "The Neglected Alternative"--the worry that Kant failed to consider that space and time, while perhaps necessary for sensible intuition, could also be objectively real in-themselves. However, it is far from clear how Van Cleve is supposed to have solved this objection. This paper examines why Van Cleve might have thought the problem resolved on his view, and argues that there is no (...) reason to think the problem has in fact been resolved. (shrink)

This paper examines the young Kant’s claim that all motion is relative, and argues that it is the core of a metaphysical dynamics of impact inspired by Leibniz and Wolff. I start with some background to Kant’s early dynamics, and show that he rejects Newton’s absolute space as a foundation for it. Then I reconstruct the exact meaning of Kant’s relativity, and the model of impact he wants it to support. I detail (in Section II and III) his polemic engagement (...) with Wolffian predecessors, and how he grounds collisions in a priori dynamics. I conclude that, for the young Kant, the philosophical problematic of Newton’s science takes a back seat to an agenda set by the Leibniz-Wolff tradition of rationalist dynamics. This results matters, because Kant’s views on motion survive well into the 1780s. In addition, his doctrine attests to the richness of early modern views of the relativity of motion. (shrink)

By transcendental aesthetic, Kant means “the science of all principles of a priori sensibility” (A 21/B 35). These, he argues, are the laws that properly direct our judgments of taste (B 35 – 36 fn.), i.e. our aesthetic judgments as we ordinarily understand that notion in the context of contemporary art. Thus the first part of the Critique of Pure Reason, entitled the Transcendental Aesthetic, enumerates the necessary presuppositions of, among other things, our ability to make empirical judgments about particular (...) works of art. These presuppositions are sensible rather than intellectual because on Kant’s view, all intellection that considers objects of any kind, whether abstract or concrete, must at base connect to actual, material objects with which we come into direct contact; and this we can do only through sensibility (A 19/B 33). Thus the following discussion explores what Kant claims must be true of us in order to make the sorts of aesthetic judgments we make, rather than any particular class or quality of aesthetic judgments itself. On Kant’s view, what must be true of us in order to make aesthetic judgments is not different from what must be true of us in order to make any other kind of judgment about empirical objects. (shrink)

A look at the dynamical concept of space and space-generating processes to be found in Kant, J.F. Herbart and the mathematician Bernhard Riemann's philosophical writings.

This paper examines Helmholtz's attempt to use empirical psychology to refute certain of Kant's epistemological positions. Particularly, Helmholtz believed that his work in the psychology of visual perception showed Kant's doctrine of the a priori character of spatial intuition to be in error. Some of Helmholtz's arguments are effective, but this effectiveness derives from his arguments to show the possibility of obtaining evidence that the structure of physical space is non-Euclidean, and these arguments do not depend on his theory of (...) vision. Helmholtz's general attempt to provide an empirical account of the "inferences" of perception is regarded as a failure. (shrink)