Kant: Studies on Mathematics in the Critical Philosophy

Author: Emily Carson,Lisa Shabel

Publisher: Routledge

ISBN: 131740789X

Category: Philosophy

Page: 280

View: 3488

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There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason, Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason, Kant compares the Formula of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement, where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant’s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant’s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy.

Kant

Studies on Mathematics in the Critical Philosophy

Author: Emily Carson,Lisa Shabel

Publisher: N.A

ISBN: 9781138925021

Category: Philosophy

Page: 292

View: 5764

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There is a long tradition, in the history and philosophy of science, of studying Kant¿s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant¿s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason, Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason, Kant compares the Formula of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement, where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant¿s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant¿s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy.

Kant's Philosophy of Mathematics: Volume 1

The Critical Philosophy and Its Roots

Author: Carl Posy,Ofra Rechter

Publisher: Cambridge University Press

ISBN: 9781107042902

Category: Philosophy

Page: 328

View: 2710

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The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant.

Bausteine der Erkenntnistheorie

Mit einer Internationalen Bibliographie zur Kritik der reinen Vernunft

Author: Paul Natterer

Publisher: BoD – Books on Demand

ISBN: 3844876170

Category: Philosophy

Page: 356

View: 2791

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Die vorliegende Darstellung der Erkenntnistheorie ist der erste Band einer auf zehn Bände angelegten Handbuchreihe 'Edition novum studium generale', d.h.: neues Allgemeinstudium. Ein Studium generale zielt erstrangig auf eine kognitive Architektur und ein ethisches Koordinatensystem für vernetztes ganzheitliches Wissen. Neben den formalen Schlüsselqualifikationen ist dies das zweite Standbein der Persönlichkeitskompetenz. Der erste Band stellt auf der Grundlage des aktuellen Forschungsstandes die erkenntnistheoretischen Konzeptionen von Platon - Aristoteles/Aquinas - Berkeley - Kant - Fichte - Carnap vor und bietet einen Abriss zur Erkenntnistheorie der Gegenwart. In Kapitel 2 zu Platon finden Interessierte auf 100 Seiten eine systematische Darstellung und Bewertung der platonischen Theorie in Auseinandersetzung mit dem neuesten Forschungsstand. Kapitel 3 zu Aristoteles und Aquinas beinhaltet einen vollständigen Abriss der Erkenntnis- und Handlungstheorie des Aristoteles, wie ihn Leser wahrscheinlich sonst nicht in dieser Kompaktheit finden. Dasselbe gilt für die Kognitionstheorie von Thomas Aquinas. Kapitel 4 beginnt mit einer komprimierten Skizze zu John Lockes 'Essay concerning Human Understanding' und diskutiert dann ausführlich und konsequent interdisziplinär George Berkeleys 'New Theory of Vision' und dessen 'Three Dialogues'. Ein Alleinstellungsmerkmal des Buches ist eine umfassende (70 S.) Internationale Bibliographie zur Kritik der reinen Vernunft in Kapitel 5, welche die einzige, Vollständigkeit anstrebende Spezial- und Arbeitsbibliographie zum erkenntnistheoretischen Hauptwerk Kants und der modernen Philosophie überhaupt ist. Kapitel 6 orientiert über das erkenntnistheoretische Grundbuch des Deutschen Idealismus, Fichtes 'Wissenschaftslehre'; Kapitel 7 evaluiert die erkenntnistheoretische Programmschrift der Analytischen Philosophie, Carnaps 'Der Logische Aufbau der Welt'; Kapitel 8 gibt einen kompakten, aber vollständigen Einblick in die aktuelle Diskussion zur Erkenntnistheorie.

Mathematics in Kant's Critical Philosophy

Reflections on Mathematical Practice

Author: Lisa Shabel

Publisher: Psychology Press

ISBN: 9780415939553

Category: Mathematics

Page: 178

View: 8265

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First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

Research in History and Philosophy of Mathematics

The CSHPM 2016 Annual Meeting in Calgary, Alberta

Author: Maria Zack,Dirk Schlimm

Publisher: Birkhäuser

ISBN: 331964551X

Category: Mathematics

Page: 218

View: 7369

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This volume contains fourteen papers that were presented at the 2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held at the University of Calgary in Alberta, Canada. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics, this meeting also honored the life and work of the logician and philosopher of mathematics Aldo Antonelli (1962-2015). The first four papers in this book are part of that remembrance and have a philosophical focus. Included in these are a discussion of Bolzano’s objections to Kant’s philosophy of mathematics and an examination of the influence of rhetorical and poetic aesthetics on the development of symbols in the 16th and 17th Centuries. The remaining papers deal with the history of mathematics and cover such subjects as Early schemes for polar ordinates in the work of L’Hôpital, based on lessons given to him by Bernoulli A method devised by Euler for determining if a number is a sum of two squares Playfair’s Axiom and what it reveals about the history of 19th-Century mathematics education The modern library classification system for mathematical subjects An exploration of various examples of sundials throughout Paris Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

Philosophie und Wissenschaft / Philosophy and Science

[Print + Online]

Author: Jürgen Stolzenberg,Fred Rush

Publisher: Walter de Gruyter

ISBN: 3110222868

Category: Philosophy

Page: 320

View: 6737

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The contributions to volume 8 of the Internationales Jahrbuch des Deutschen Idealismus/International Yearbook of German Idealism pursue from various perspectives the multifarious relations of German Idealism to the natural sciences and mathematics. The concepts of nature and of the basis for mathematics develop complexly in German philosophy after Kant. At issue are: the foundation of mathematics; the relation of freedom to nature; the significance of philosophy to emerging research in biology, chemistry, and physics, and reconsideration of the thought of Leibniz and Spinoza. Contributors: Gideon Freudenthal, Michael Friedman, Hans-Peter Neumann, Wolfgang Neuser, Konstantin Pollok, Sebastian Rand, Pirmin Stekeler-Weithofer, Thomas Sturm, Lars-Thade Ulrichs, Eric Watkins, John Zammito, Paul Ziche, Rachel Zuckert

Constantin Carathéodory

Mathematics and Politics in Turbulent Times

Author: Maria Georgiadou

Publisher: Springer Science & Business Media

ISBN: 9783540203520

Category: Mathematics

Page: 651

View: 2251

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Constantin Carathéodory - Mathematics and Politics in Turbulent Times is the biography of a mathematician, born in Berlin in 1873, who became famous during his life time, but has hitherto been ignored by historians for half a century since his death in 1950, in Munich. In a thought-provoking approach, Maria Georgiadou devotes to Constantin Carathéodory all the attention such a personality deserves. With breathtaking detail and the appropriate scrutiny she elucidates his oeuvre, life and turbulent political and historical surroundings. A descendant of the the Greek élite of Constantinople, Carathéodory graduated from the military school of Brussels, became engineer at the Assiout dam in Egypt and finally dedicated a life of effort to mathematics and education. He studied and embarked on an international academic career, haunted by wars, catastrophes and personal tragedies. Over the last years of his life, he stayed in Munich despite World War II, an ambiguous decision upon which the author sheds unprecedented light. Carathéodory's most significant mathematical contributions were to the calculus of variations, the theory of point set measure and the theory of functions of a real variable, pde's, also to complex function theory. The interdisciplinary nature of the text allows easy access for both scholars and readers with a general interest in mathematics, politics and history. The thoroughness of the author’s research and evaluations is certain to leave everyone impressed and more knowledgeable.

The Cambridge Companion to Kant and Modern Philosophy

Author: Paul Guyer

Publisher: Cambridge University Press

ISBN: 1139827030

Category: Philosophy

Page: N.A

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The philosophy of Immanuel Kant is the watershed of modern thought, which irrevocably changed the landscape of the field and prepared the way for all the significant philosophical movements of the nineteenth and twentieth centuries. This 2006 volume, which complements The Cambridge Companion to Kant, covers every aspect of Kant's philosophy, with a particular focus on his moral and political philosophy. It also provides detailed coverage of Kant's historical context and of the enormous impact and influence that his work has had on the subsequent history of philosophy. The bibliography also offers extensive and organized coverage of both classical and recent books on Kant. This volume thus provides the broadest and deepest introduction currently available on Kant and his place in modern philosophy, making accessible the philosophical enterprise of Kant to those coming to his work for the first time.

Intuition and the Axiomatic Method

Author: Emily Carson,Renate Huber

Publisher: Springer Science & Business Media

ISBN: 9781402040399

Category: Philosophy

Page: 324

View: 5034

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Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Author: Paolo Mancosu

Publisher: Oxford University Press

ISBN: 9780195359152

Category: Mathematics

Page: 288

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The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.

Philosophical Correspondence, 1759-1799

Author: Immanuel Kant

Publisher: University of Chicago Press

ISBN: 9780226423616

Category: Philosophy

Page: 260

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Drawn from the Prussian Academy edition of Kant's collected works, these letters make it possible to trace the development of Kant's thought from his earliest worries about the topics discussed in the Critique of Pure Reason to his attempts in later life to meet the objections of his critics and erstwhile disciples. "Perhaps the major value of these writings is their demonstration of Kant's own attitude towards his philosophical works."—Paul Arthur Schilpp, Saturday Review

The Philosophy of Gottlob Frege

Author: Richard L. Mendelsohn

Publisher: Cambridge University Press

ISBN: 9781139444033

Category: Philosophy

Page: N.A

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This analysis of Frege's views on language and metaphysics in On Sense and Reference, arguably one of the most important philosophical essays of the past hundred years, provides a thorough introduction to the function/argument analysis and applies Frege's technique to the central notions of predication, identity, existence and truth. Of particular interest is the analysis of the Paradox of Identity and a discussion of three solutions: the little-known Begriffsschrift solution, the sense/reference solution, and Russell's 'On Denoting' solution. Russell's views wend their way through the work, serving as a foil to Frege. Appendices give the proofs of the first 68 propositions of Begriffsschrift in modern notation. This book will be of interest to students and professionals in philosophy and linguistics.

Kant on Proper Science

Biology in the Critical Philosophy and the Opus postumum

Author: Hein van den Berg

Publisher: Springer Science & Business Media

ISBN: 9400771401

Category: Philosophy

Page: 283

View: 8739

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This book provides a novel treatment of Immanuel Kant’s views on proper natural science and biology. The status of biology in Kant’s system of science is often taken to be problematic. By analyzing Kant’s philosophy of biology in relation to his conception of proper science, the present book determines Kant’s views on the scientific status of biology. Combining a broad ideengeschichtlich approach with a detailed historical reconstruction of philosophical and scientific texts, the book establishes important interconnections between Kant’s philosophy of science, his views on biology, and his reception of late 18th century biological theories. It discusses Kant’s views on science and biology as articulated in his published writings and in the Opus postumum. The book shows that although biology is a non-mathematical science and the relation between biology and other natural sciences is not specified, Kant did allow for the possibility of providing scientific explanations in biology and assigned biology a specific domain of investigation.

Kant und die Berliner Aufklärung

Akten des IX. Internationalen Kant-Kongresses

Author: Volker Gerhardt,Rolf-Peter Horstmann,Ralph Schumacher

Publisher: N.A

ISBN: N.A

Category: Philosophy, German

Page: N.A

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The Blackwell Companion to Philosophy

Author: Nicholas Bunnin,Eric Tsui-James

Publisher: John Wiley & Sons

ISBN: 9780631219071

Category: Philosophy

Page: 951

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An introduction to philosophy looks at key issues, figures, and movements in the field.

Kant and the Reach of Reason

Studies in Kant's Theory of Rational Systematization

Author: Nicholas Rescher

Publisher: Cambridge University Press

ISBN: 9780521667913

Category: Philosophy

Page: 258

View: 5902

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The essays collected in this volume have a strong thematic and interpretative unity. Their underlying concern is with the overall nature of Kant's philosophical system, and thus with his deepest intentions and basic commitments. The book falls into three parts. The first three essays deal with Kant's approach to things in themselves and with the realm of noumenal causality. The second part considers Kant's approach to the methodology of rational inquiry, and, in particular, his views on cognitive systematization and the limits of philosophizing itself. The third section focuses on the role played by the categorical imperative in both the theoretical and practical philosophy. The aim throughout, one that many Kant scholars and students will find provocative, is to show that in an important sense Kant is prepared to assert the primacy of practical over theoretical philosophy.

Japanese Studies in the Philosophy of Science

Author: F.G. Nagasaka

Publisher: Springer Science & Business Media

ISBN: 940115175X

Category: Science

Page: 202

View: 4082

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The splendid achievements of Japanese mathematics and natural sciences during the second half of our 20th century have been a revival, a Renaissance, of the practical sciences developed along with the turn toward Western thinking in the late 19th century. The equally admirable results of Japanese philosophers (and historians) of science in our time followed upon a period less congenial to Western interests in the philosophical questions linked to modern science; and this reluctance to confront the epistemology, not even the humane significance, of the sciences went along with devotion to other Western trends. Thus, with the 'new' Japan of the Meiji restoration of 1868, and the early introduction of Western philosophy in the subsequent decade by Nishi Amane, a period of intellectual attraction to utilitarian, positivist, evolutionary, even materialist outlooks was soon replaced by devotion to scholarly work on Kant and Hegel, on ethical and general philosophical idealism. These studies often could emulate the critical spirit (the philosopher Onishe Hajime, praised for his own critical independence, was known as the Japanese Kant) but the neo Kantian and neo-Hegelian developments were not much affected by either empirical sciences or theoretical speculations about Nature. The pre-eminent philosopher of Japan ofthe first half of our century was Nishida Kitaro, with a pioneering treatise A Study of the Good, who, with his leading student Tanabe Hajime, formed the 'Kyoto School' of pre-war philosophy.

Kants Ontologie der raumzeitlichen Wirklichkeit

Versuch einer anti-realistischen Interpretation der Kritik der reinen Vernunft

Author: Kiyoshi Chiba

Publisher: Walter de Gruyter

ISBN: 9783110280685

Category: Philosophy

Page: 427

View: 3523

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Originally presented as the author's thesis--Bonn, 2010.