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)

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.

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.

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)

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)

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.