In den „Fundamenta praedemonstrabilia“ der Theoria motus abstracti entwickelt Leibniz den Versuch, das Kontinuum als aus grundsätzlich unteilbaren Einheiten in einer Weise aufgebaut zu denken, die seine Kontinuität bewahrt - durch die systematische Unterscheidung der Verhältnisse von ,unum ad infinitum‘ und von ,nullius ad unum‘ versucht er hier Balance zu halten. Zwar komme ich zu dem Ergebnis, daß Leibniz' Auffassung vom Kontinuum in der Theoria motus abstracti letztlich inkohärent bleibt, gleichwohl bildet er Begriffe, die sein weiteres Bemühen, den Zugang zum (...) Unendlich-Kleinen neu zu legen, zum Mittel seiner Lösung des ,labyrinthus de compositione continui‘ gestalten. Im zweiten Teil der Arbeit konfrontiere ich die hier vorgelegte Interpretation der Position von Leibniz einer Deutung, die unlängst Philip Beeley gab. (shrink)

In der Zeit zwischen 1668 und 1671 ändert Leibniz seine Ansicht zu Bewegung und Körper von dem Standpunkt, Bewegung sei keine essentielle Eigenschaft eines Körpers, zu dem, dass Bewegung den Wesenskern eines Körpers bilde. Dieser Aufsatz will den Prozess analysieren, der diesem Wandel zu Grunde liegt. Die Theoria motus abstracþi wird dabei als vorsichtige Synthese interpretiert, die zwar den Wandel ankündigt, die aber den neuen Standpunkt noch nicht explizit vertritt. Die ausdrückliche Hinwendung zu der Position, Bewegung sei der Wesenskern eines (...) Körpers, wird als Folge davon gesehen, dass Leibniz die Existenz einer unbewegten materia prima verneint; und diese Haltung führt zu einer ausdrücklich phänomenologischen Ableitungsmethode im zweiten Entwurf des Specimen demonstrationum de natura rerum corporearum ex phaenomenis, die mit ihrer Unterscheidung zwischen dem Körper als wandelbar und dem Raum als unwandelbar zu der Schlussfolgerung, Bewegung sei der Wesenskern eines Körpers, führt. (shrink)

This paper rejoins the debate surrounding Thomas Tymockzko’s paper on the surveyability of proof, first published in the Journal of Philosophy, and makes the claim that by attending to certain broad features of modern conceptions of proof we may understand ways in which the debate surrounding the surveyability of proof has heretofore remained unduly circumscribed. Motivated by these historical reflections, I suggest a distinction between local and global surveyability which I believe has the promise to open up significant new advances (...) in the philosophy of mathematics. (shrink)

This book addresses the philosophy of Kant and the poetry of Shelley as historical starting points for a new way of thinking in the modern age. Fusing together critical philosophy and visionary poetry, Bassler develops the notion of visionary critique, or paraphysics, as a model for future philosophical endeavor. This philosophical practice is rooted in the concept of the indefinite power associated with the sublime in both Kant and Shelley’s work, to which the notion of the parafinite or indefinitely (...) large is extended in this book. (shrink)

Dieser Artikel konzentriert sich auf zwei der frühesten Schriften aus Leibniz' Pariser Zeit, die „Accessio ad Arithmeticam Infinitorum“ und die „De Minimo et Maximo. De corporibus et mentibus“ , und er beurteilt die Beziehung zwischen den in der AAI angegebenen mathematischen Ergebnissen und dem Wandel in Leibniz' Metaphysik, der in MM und in den damit in Verbindung stehenden Schriften und Briefen zum Ausdruck gebracht wird. Sowohl Leibniz' mathematische Ergebnisse als auch der Wandel seiner Haltung in der Metaphysik können als Resultat (...) einer stärkeren Verpflichtung gegenüber dem Euklidischen Axiom betrachtet werden, daß das Ganze größer ist als der Teil. Indem das Euklidische Axiom eine bedeutendere Rolle in Leibniz' Metaphysik und mathematischer Arbeit einnimmt, bewegt sich Leibniz von der Vorstellung der Zusammensetzung des Kontinuums aus unteilbaren Punkten zu einer Aufgliederung des Kontinuums in unvergleichbar kleine Teile, die in sich selbst kontinuierlich sind. Dieser Wandel führt Leibniz dazu, die Rolle der Identität und eines Kalküls von Teil und Ganzem zu betonen und sich in Richtung einer Vorstellung vom Unbestimmten als eines Unendlichen zu bewegen. (shrink)

This book charts the shape of future philosophical investigation by posing the question: "What is the Matrix?" Guided by the example of the Matrix film trilogy, the author examines issues ranging from simulation, proof and action to value, culture and mythology, offering a progressively deeper diagnosis of modern philosophical conditions. In contrast to the contemporary focus upon cognitive science and a commitment to the distinction between appearance and reality, this book helps readers to explore the argument that such abstractions are (...) inevitably displaced by a more concrete distinction between dreaming and waking, with the Matrix as the real and only world we inhabit. Researchers and scholars will find this work an engaging and enlightening examination of reality, via the medium of popular culture and film. (shrink)

New light is shed on Leibniz’s commitment to the metaphysical priority of the intensional interpretation of logic by considering the arithmetical and graphical representations of syllogistic inference that Leibniz studied. Crucial to understanding this connection is the idea that concepts can be intensionally represented in terms of properties of geometric extension, though significantly not the simple geometric property of part-whole inclusion. I go on to provide an explanation for how Leibniz could maintain the metaphysical priority of the intensional interpretation while (...) holding that logically the intensional and the extensional stand in strictly inverse relation to each other. (shrink)

In The Principles of Mathematics Revisited Jaakko Hintikka proposes nothing less than “to prepare the ground for the next revolution in the foundations of mathematics”. Hintikka’s proposal involves a rejection, inter alia, of the views that ordinary first-order logic is the basic elementary logic and that axiomatic set theory is a natural framework for theorizing about mathematics.

The second volume of Jaakko Hintikka’s selected papers brings together essays from the decade 1986–96 concerning an often tacit distinction between “two competing overall views concerning our relationship to our language”. The first of these Hintikka characterizes as the view of language as lingua universalis, a single universal medium of communication; the second view, of language as calculus ratiocinator, is not meant to indicate that language is a “mere play with symbols” but rather that language “can be re interpreted like (...) a calculus”. (shrink)

Excerpt from The Appeal to Immediate Experience: Philosophic Method in Bradley Whitehead and Dewey The insight and guidance of Professor John Herman Randall, Jr. have made this book possible. Rather than merely acknowledge my debt to him I would like to express my gratitude here for his unfailing kindness, his penetrating criticism of my efforts, and the help he has given me in clarifying the complex problems of this subject-matter. I wish also to acknowledge the kindness of the following (...) publishers in permitting me to quote from their publications: F. H. Bradley, Appearance and Reality, by Allen and Unwin Ltd.; J. H. Randall, Jr. and J. Buchler, Philosophy: An Introduction, by Barnes Noble, Inc.; F. H. Bradley, Appearance and Reality and Essays on Truth and Reality, by Clarendon Press, Oxford; F. J. E. Woodbridge, Nature and Mind, by Columbia University Press; R. W. Church, Bradley's Dialectic, by Cornell University Press; John Dewey, The Man and His Philosophy, by Harvard University Press; J. Dewey, Logic and Influence of Darwin on Philosophy, by Henry Holt Company; R. Kagey, F. H. Bradley's Logic, by R. Kagey; J. Dewey, Nature in Experience and Whitehead's Philosophy, by Longmans, Green & Co.; A. N. Whitehead, Symbolism, Modes of Thought, Adventures of Ideas, Process and Reality, T. M. Forsyth, English Philosophy, and J. H. Muirhead, Bradley's Place in Philosophy, by the Macmillan Company; A. N. Whitehead, The Concept of Nature-and An Equiry Concerning the Principles of Natural Knowledge, by the Macmillan Company and the Cambridge University Press; H. B. Haldane, Human Experience, by John Murray Ltd.; J. Goheen, Whitehead's Theory of Value, by Northwestern University Press; J. Dewey, Experience and Nature, by Open Court Publishing Co.; G. Santayana, Realm of Essence and Scepticism and Animal Faith, by Charles Scribner's Sons; and J. Dewey, "How is Mind to be Known?" The Objectivism-Subjectivism of Modern Philosophy," M. Gross, The Philosophy of A. N. Whitehead," and M. C. Otto, The Journal of Philosophy. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Infinitesimal Differences: Controversies between Leibniz and his ContemporariesFrançoise Monnoyeur-BroitmanUrsula Goldenbaum and Douglas Jesseph, editors. Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Berlin-New York: Walter de Gruyter, 2008. Pp. vi + 327. Cloth, $109.00.Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected (...) to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt.Many of us know and probably have used the Leibnizian formula: to calculate the area under a curve; this book considers the origin, nature, method, and metaphysics of this formula. The most fascinating question discussed in it is the fiction introduced to define the infinitesimal calculation: in his mature period, Leibniz himself referred to his calculus as “a well-founded fiction.” We learn that he gradually gave up the idea of an actual infinite in favor of describing infinitely small quantities. As a result, the quantities became fictive and finite or indefinite instead of real and infinite, and the process of calculation shifted towards mathematics rather than metaphysics.In the first essay, Richard Arthur compares the calculus of Leibniz and Newton and demonstrates how it was based for both on the development of continuously varying quantity. He also shows how the understanding of this quantity derived from the Archimedean axiom that excludes the existence of actual infinite quantity. Ursula Goldenbaum next demonstrates how Hobbes, with his conatus considered as point and instant, had a direct impact on the Leibnizian conception of continuity; to confirm her interpretation, she includes at the end of her article the “Marginalia or Leibniz comments” on Hobbes. Samuel Levey establishes a connection between the notion of the infinitesimal as a “well-founded fiction” and the law of continuity, arguing that the law of continuity, understood as an extension of Archimedes’ principle, gives a finite foundation to the infinitesimal calculation. O. Bradley Bassler discusses the idea of the differential in terms of infinitely small quantities and the use of proportions between infinitely small and finite quantities in order to measure [End Page 527] the infinitely small; here, differentials are also presented as fictions. Fritz Nagel discusses the methodological sophistication of the calculus and its opponents. His main questions concern the different grades of infinity, quantities regarded as zero, and the infinitesimal as a fiction that can be calculated. Douglas Jesseph considers the reality of the infinitesimal and the “well-founded fiction,” showing how Leibniz methodically constructs infinitesimal quantities without reality by returning to Hobbes’ notion of conatus. Hobbes is, for Jesseph, the initiator of these infinitely small quantities without existence.A second group of essays examines the connection between algebra and geometry in the calculus. Philip Beeley demonstrates how John Wallis, on the path of Cavalieri’s method of the indivisibles, found a way to transform geometric problems into sums of arithmetic sequences. Siegmund Probst expresses the different phases in the discovery of the Leibnizian method. He mentions that Leibniz coined the term ‘infinitesimal’ in 1673, and points out that he did not need the method of indivisibles to find a curve from its given arc, but only a series expansion using differences of higher order. Emily Grosholz looks at how, thanks to his algebraic and geometrical notations of curves, Leibniz could formulate the equation of his infinitesimal calculus. According to Grosholz, Leibniz exploits the ambiguity of notations in order to express the geometrical and dynamical aspect of the calculus. Herbert Breger underlines the novelty and abstract nature of Leibniz’s new method of calculation, showing how the theory of infinitesimals became an algebraic calculus independent of geometry.A final group of articles studies the relationship between the calculus and Leibniz’s physics. François Duchesneau shows how the differential and integral calculus provided a model for the integrative laws of Leibniz’s... (shrink)

Are contemporary soldiers exploited by the state and society that they defend? More specifically, have America's professional service members disproportionately carried the moral weight of America's war-fighting decisions since the inception of an all-volunteer force? In this volume, Michael J. Robillard and Bradley J. Strawser, who have both served in the military, examine the question of whether and how American soldiers have been exploited in this way. Robillard and Strawser offer an original normative theory of 'moral exploitation'--the notion that (...) persons or groups can be wrongfully exploited by being made to shoulder an excessive amount of moral weight. They make the case that this exploitation accurately describes the relationship between the United States and the members of its military, and offer a thorough and in-depth analysis of some of the exploitative and misleading elements of present-day military recruitment, the moral burdens soldiers often bear, and the stifling effect that a 'Thank You for Your Service' and 'I support the troops' culture has had on serious public engagement about America's ongoing wars. Robillard and Strawser offer a piercing critique of the pernicious divide between military members and the civilians who direct them. They conclude by arguing for several normative and prudential prescriptions to help close this ever-widening fissure between the U.S. and its military, and within the U.S. itself. In so doing, their work gives a much needed and urgent voice to America's soldiers, the other 1%. (shrink)

We explore the finite model theory of the characterisation theorems for modal and guarded fragments of first-order logic over transition systems and relational structures of width two. A new construction of locally acyclic bisimilar covers provides a useful analogue of the well known tree-like unravellings that can be used for the purposes of finite model theory. Together with various other finitary bisimulation respecting model transformations, and Ehrenfeucht–Fraïssé game arguments, these covers allow us to upgrade finite approximations for full bisimulation equivalence (...) towards approximations for elementary equivalence. These techniques are used to prove several ramifications of the van Benthem–Rosen characterisation theorem of basic modal logic for refinements of ordinary bisimulation equivalence, both in the sense of classical and of finite model theory. (shrink)

Excerpt from The Appeal to Immediate Experience: Philosophic Method in Bradley Whitehead and Dewey The insight and guidance of Professor John Herman Randall, Jr. have made this book possible. Rather than merely acknowledge my debt to him I would like to express my gratitude here for his unfailing kindness, his penetrating criticism of my efforts, and the help he has given me in clarifying the complex problems of this subject-matter. I wish also to acknowledge the kindness of the following (...) publishers in permitting me to quote from their publications: F. H. Bradley, Appearance and Reality, by Allen and Unwin Ltd.; J. H. Randall, Jr. and J. Buchler, Philosophy: An Introduction, by Barnes Noble, Inc.; F. H. Bradley, Appearance and Reality and Essays on Truth and Reality, by Clarendon Press, Oxford; F. J. E. Woodbridge, Nature and Mind, by Columbia University Press; R. W. Church, Bradley's Dialectic, by Cornell University Press; John Dewey, The Man and His Philosophy, by Harvard University Press; J. Dewey, Logic and Influence of Darwin on Philosophy, by Henry Holt Company; R. Kagey, F. H. Bradley's Logic, by R. Kagey; J. Dewey, Nature in Experience and Whitehead's Philosophy, by Longmans, Green & Co.; A. N. Whitehead, Symbolism, Modes of Thought, Adventures of Ideas, Process and Reality, T. M. Forsyth, English Philosophy, and J. H. Muirhead, Bradley's Place in Philosophy, by the Macmillan Company; A. N. Whitehead, The Concept of Nature-and An Equiry Concerning the Principles of Natural Knowledge, by the Macmillan Company and the Cambridge University Press; H. B. Haldane, Human Experience, by John Murray Ltd.; J. Goheen, Whitehead's Theory of Value, by Northwestern University Press; J. Dewey, Experience and Nature, by Open Court Publishing Co.; G. Santayana, Realm of Essence and Scepticism and Animal Faith, by Charles Scribner's Sons; and J. Dewey, "How is Mind to be Known?" The Objectivism-Subjectivism of Modern Philosophy," M. Gross, The Philosophy of A. N. Whitehead," and M. C. Otto, The Journal of Philosophy. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

First: there is ample precedent for what I am doing. Socrates, for example, examined the religious beliefs of his contemporaries-- especially the belief that we ought to do what the gods command--and showed them to be both ill-founded and conceptually confused. I wish to follow in his footsteps though not to share in his fate. A glass of wine, not of poison, would be my preferred reward.

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.