This paper examines the role of Kant's theory of mathematical cognition in his phoronomy, his pure doctrine of motion. I argue that Kant's account of how we can construct the composition of motion rests on the construction of extended intervals of space and time, and the representation of the identity of the part–whole relations the construction of these intervals allow. Furthermore, the construction of instantaneous velocities and their composition also rests on the representation of extended intervals of space and (...) time, reflecting the general approach to instantaneous velocity in the eighteenth century. (shrink)

In this paper I argue for the following two related claims. First, the science of phoronomy from Kant's Metaphysical Foundations of Natural Science is grounded in the duplication of space. Second, this duplication is made possible through the self-localization of the subject, as Kant shows in the "Gegnden-Schrift". The thesis of this paper is that the self-localization transforms space into an object that can be cinematically moved and that this action sets the ground for a science of phoronomy, (...) which presupposes the existence of at least two spaces. In the end, the other endpoint of the Kantian determination of space is discussed, namely space understood as an idea of reason. (shrink)

We compare two approaches given to the parallelogram law as a fundamental notion in eighteenth century mechanics. The authors we study are Kant and d’Alembert and we use the context created by Newton’s Principia as our point of departure.

A partir do texto Metaphysische Anfansgründe der Naturwissenschaft faremos uma apresentaçãosobre estes dois conceitos fundamentais da Filosofia da Natureza, no sentido de apresentar uma crítica de acordo com a física moderna.

Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and third chapters—the (...) Dynamics and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 44.4 (2006) 559-575 MuseSearchJournalsThis JournalContents[Access article in PDF]Kant's Critical Concepts of MotionKonstantin PollokThere are two significant places in Kant's Critical corpus where he discusses the concept of motion. The first is in the Critique of Pure Reason, where in the "Deduction of the Categories" Kant writes:Motion, as an act of the subject (not as a determination of an object†), and therefore the synthesis (...) of the manifold in space, first produces the concept of succession—if we abstract from this manifold and attend solely to the act through which we determine the inner sense according to its form.In this passage Kant simply refers to the concept of motion, and the immediate context in which this reference occurs reveals little about what he means by it. In the Metaphysical Foundations of Natural Science, however, motion plays a more significant role, and, concomitantly, it is in his writings on natural science that Kant most fully expresses his thoughts on the subject. For present purposes, the most relevant passage is paragraph 15 of the Preface of the Metaphysical Foundations, where Kant says that theconcept of matter had … to be carried through all four of the indicated functions of the concepts of the understanding (in four chapters), where in each a new determination of this concept was added. The basic determination of something that is [End Page 559] to be an object of the outer senses had to be motion, because only thereby can these senses be affected. The understanding traces back all other predicates of matter belonging to its nature to this, and natural science, therefore, is either a pure or applied doctrine of motion. The metaphysical foundations of natural science are therefore to be brought under four chapters. The first considers motion as a pure quantum in accordance with its composition, without any quality of the movable, and may be called phoronomy. The second takes into consideration motion as belonging to the quality of matter, under the name of an original moving force, and is therefore called dynamics. The third considers matter with this quality as in relation to another through its own inherent motion, and therefore appears under the name of mechanics. The fourth chapter, however, determines matter's motion or rest merely in relation to the mode of representation or modality, and thus as appearance of the outer senses, and is called phenomenology. 2The first passage from the first Critique (quoted above) reveals both that the concept of motion plays a central role in Kant's epistemology and that he distinguishes clearly between motion of the object, on the one hand, and action of the subject, on the other. The two concepts of motion are quite different—the former belonging to transcendental philosophy and geometry (to "pure science" in the Kantian sense), the latter to the metaphysical and empirical investigation of nature. By contrast, the second passage from the Metaphysical Foundations shows that the conceptual apparatus Kant developed in his transcendental philosophy is also relevant for understanding the empirical concept of motion. Since all empirical concepts are based on transcendental conditions for their possibility, this connection between elements of the Critical philosophy should come as no surprise. What remains unclear, however, is the sort of connection involved, and whether in the particular case of motion there might not be a more intimate relationship between the transcendental conditions and the empirical concept than one might at first suspect.Indeed, this is a possibility that has been entertained by a number of commentators. In his investigation of Kant's metaphysics of nature, Lothar Schäfer, for example, contends that "the original perspective on the unity of the sensibility in which nature reveals itself, and which belongs to the conception of nature, results in the original perspective on motion. Therefore, the laws of nature are laws of motion …." 3 Similarly, in her book on Kant's theory of natural science, Karen Gloy argues thatin the predicable 'motion' the connection of elements of the understanding with... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.3 (2003) 421-422 [Access article in PDF] Konstantin Pollok. Kants Metaphysische Anfangsgründe der Naturwissenschaft. Ein kritischer Kommentar. Hamburg: Felix Meiner Verlag, 2001. Pp. x + 546. Cloth, € 98.00.Kant's Metaphysical Foundations of Natural Science (MFNS) was published in 1786, one year after his Groundwork of the Metaphysics of Morals, and thus also falling in the period between the two editions of the Critique (...) of Pure Reason. Long assigned a tertiary status within the corpus, the MFNShas for several reasons been the subject of renewed scholarly attention in the past two decades. Attempts to trace the origins of analytic philosophy beyond the work of the logicists and the Vienna Circle have focussed attention on neo-Kantian "scientific epistemologists" such as Helmholtz, Hertz, and their contemporaries, for whom Kant's philosophy of science formed a common point of departure. This more general concern is complemented by Kant scholars' increasing interest in his philosophies of mathematics and the sciences. Finally, there is greater appreciation of the importance of the Metaphysical Foundations for our understanding of Kant's revisions to the first Critique, for instance his emphasis in the B-edition on the necessity of external intuition to the "objective reality" of the categories.Earlier neglect of the MFNS was not merely the product of indifference to these issues, for it is an obscure book, even for Kant. In extending the transcendental metaphysics of the Critique into the domain of empirical science, Kant demands of his reader a thorough grasp of the critical philosophy. To complicate matters, the larger part of the text involves a detailed analysis of classical scientific concepts taken from the Leibnizian and Newtonian traditions. Kant often draws on his earlier writings on the natural sciences, such as the Physical Monadology, and either modifies or, in the case of pre-critical sources, inverts these to fit their new context. The book often seems to be little more than a rationalist deduction of the key concepts of Newtonian physics, at least as Kant understood them. In order to extract philosophically interesting arguments from this mixture of physical science and transcendental philosophy, one must have a firm grasp of the background in the history of science and of Kant's oeuvre as a whole. To date, there have been only two full-length studies (by Addickes and Plaass) devoted to this short work, and neither of them attempted to cover it as a whole. Konstantin Pollok's commentary of the MFNSwill therefore fill an important gap in the secondary literature. [End Page 421]Pollok's Critical Commentary, which is written in a clear anduncomplicated academic German, steers a middle course between textual analysis and criticism. The author accords each major division of the book (the Preface, Phoronomy, Dynamics, Mechanics, and Phenomenology) its own chapter, and then follows the argumentative lines of these closely. But Pollok's text does not mirror Kant's "mathematical" sub-division of the MFNSinto axioms, theses, and scholia. These are often grouped together and commented on as a single argumentative whole, which is keyed with the title of the main sub-division. The body text of the commentary consists of textual exegesis, quotations, and references to historical sources, as well as to the larger context of Kant's philosophy. The lengthy footnotes address discussions and controversies in recent secondary literature, as well as Pollok's evaluation of these. He quotes both primary and secondary sources at length, thereby freeing the reader from the bother of tracking down quotations in order to grasp what is at issue. This aid is, however, counterbalanced by his legitimate decision to quote all sources in the original language, with the exception of those available to Kant only in translation.Critical discussion is strictly confined to the conceptual context of Kant's time, in that the significance of Kant's arguments for later developments in the philosophy of science, and their status from the standpoint of such later developments are not addressed. But this decision still leaves open significant interpretative play: one can approach the... (shrink)

Die philosophische Grundhaltung des wohl letzten großen Vertreters der Systemphilosophie, Gottfried Wilhelm Leibniz (1646-1716), läßt sich nur unter Berücksichtigung seiner Auseinandersetzung mit allen wissenschaftlichen Problemen seiner Zeit rekonstruieren. Die von Ernst Cassirer zusammengestellten Hauptschriften zur Grundlegung der Philosophie bringen den universalistischen Charakter der Leibnizschen Philosophie durch die Entwicklung ihres gedanklichen Fortschriftts und das Verhältnis der einzelnen Systemglieder zur Anschauung. Inhalt: Schriften zur Logik und Methodenlehre; zur Mathematik; zur Phoronomie und Dynamik; zur geschichtlichen Stellung des Systems und zur Biologie und Entwicklungsgeschichte.

The four sections of the Metaphysische Anfangsgründe der Naturwissenschaft 1 are each introduced by a new definition of matter. For the Phoronomy it is defined as the movable in space (Ak. IV, 480); the other defini­tions presuppose this one. What is the status of the propositions ascribing existence to matter in these senses? Are the metaphysical principles of natural science as pure as the principles of pure understanding, or are they only required for experience which happens, in fact, to (...) contain matter as defined at the beginnings of the sections? (shrink)