Kant: Studies on Mathematics in the Critical Philosophy

Author: Emily Carson,Lisa Shabel

Publisher: Routledge

ISBN: 131740789X

Category: Philosophy

Page: 280

View: 5672

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.

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: 6333

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.

The Oxford Handbook of Philosophy of Mathematics and Logic

Author: Stewart Shapiro

Publisher: OUP USA

ISBN: 0195148770

Category: Mathematics

Page: 833

View: 424

Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.

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: 3301

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.

Constantin Carathéodory

Mathematics and Politics in Turbulent Times

Author: Maria Georgiadou

Publisher: Springer Science & Business Media

ISBN: 9783540203520

Category: Mathematics

Page: 651

View: 4332

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.

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: 9442

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.

Studies in the Philosophy of Kant

Author: Lewis White Beck

Publisher: Greenwood Publishing Group


Category: Philosophy

Page: 242

View: 8127

A collection of Lewis Beck's writings on the philosophy and interpretation of Immanuel Kant.

The Cambridge Companion to Kant and Modern Philosophy

Author: Paul Guyer

Publisher: Cambridge University Press

ISBN: 1139827030

Category: Philosophy

Page: N.A

View: 8156

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: 9315

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.

Critical Approaches to Science and Philosophy

Author: Mario Bunge

Publisher: Transaction Publishers

ISBN: 9781412820707

Category: Philosophy

Page: 480

View: 2149

This collection of essays, written on four continents by scientists, philosophers and humanists, was initially presented to Karl R. Popper on his sixtieth birthday as a token of critical admiration and in recognition of his work. But the volume also stands on its own as a remarkable series of statements utilizing Popper's critical vision in the study of philosophy proper, logic, mathematics, science as method and theory, and finally to the study of society and history. What is remarkable is that Popper worked in all of these areas, not in a cursory or discursive way, but with the utmost clarity and rigor. . The core position of this volume and its contributors is that the progress of knowledge is not a linear accumulation of definitive acquisitions but a zigzagging process in which counterexamples and unfavorable evidence ruin generalizations and prompt the invention of more comprehensive and sometimes deeper generalizations, to be criticized in their turn. A critical approach to problems, procedures, and results in every field of inquiry is therefore a necessary condition for the continuance of progress. The title of this volume then is, in a sense, an homage to Popper's critical rationalism and critical empiricism. The essays are a tribute to his unceasing and uncompromising quest, not for final certainty, but for closer truth and increased clarity. Among the contributors are outstanding figures in philosophy and the exact sciences in their own right, including Herbert Feigl, R. M. Hare, J.O. Wisdom, Nicholas Rescher, David Bohm, Paul K. Feyerabend, F. A. Hayek, and Adolf Grunbaum. Social science contributions include Hans Albert on social science and moral philosophy, W. B. Gallie, on the critical philosophy of history, Pieter Geyl on "The Open Society and its Enemies, "and George H. Nadel on the philosophy of History.

Philosophical Correspondence, 1759-1799

Author: Immanuel Kant

Publisher: University of Chicago Press

ISBN: 9780226423616

Category: Philosophy

Page: 260

View: 924

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

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Author: Paolo Mancosu

Publisher: Oxford University Press on Demand

ISBN: 0195132440

Category: Drama

Page: 275

View: 7877

The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning 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 relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.

The Philosophy of Gottlob Frege

Author: Richard L. Mendelsohn

Publisher: Cambridge University Press

ISBN: 9781139444033

Category: Philosophy

Page: N.A

View: 6133

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.

Philosophy of Mathematics

An Introduction

Author: David Bostock

Publisher: John Wiley & Sons

ISBN: 1405189924

Category: Mathematics

Page: 332

View: 4646

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author?s personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals

The Blackwell Companion to Philosophy

Author: Nicholas Bunnin,Eric Tsui-James

Publisher: John Wiley & Sons

ISBN: 9780631219071

Category: Philosophy

Page: 951

View: 5201

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

Kant und die Berliner Aufklärung

Akten des IX. Internationalen Kant-Kongresses

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

Publisher: N.A


Category: Philosophy, German

Page: N.A

View: 8864