mathematics in kant s critical philosophy studies in philosophy

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Mathematics In Kant S Critical Philosophy

Author : Lisa Shabel
ISBN : 9781135370633
Genre : Mathematics
File Size : 86. 42 MB
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First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.

Kant Studies On Mathematics In The Critical Philosophy

Author : Emily Carson
ISBN : 9781317407898
Genre : Philosophy
File Size : 20. 68 MB
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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 Critical Philosophy

Author : Gilles Deleuze
ISBN : 9780826432063
Genre : Knowledge, Theory of
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Gilles Deleuze was one of the most important and influential continental philosophers of the 20th century and this book is an essential text for the field of Kant studies.

Kant S Philosophy Of Mathematics

Author : C.J. Posy
ISBN : 9789401580465
Genre : Philosophy
File Size : 72. 81 MB
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Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come.

Kant On Proper Science

Author : Hein van den Berg
ISBN : 9789400771406
Genre : Philosophy
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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.

Research In History And Philosophy Of Mathematics

Author : Maria Zack
ISBN : 9783319645513
Genre : Mathematics
File Size : 22. 30 MB
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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.

The Oxford Handbook Of Philosophy Of Mathematics And Logic

Author : Stewart Shapiro
ISBN : 9780190287535
Genre : Mathematics
File Size : 72. 76 MB
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Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

The Post Critical Kant

Author : Bryan Hall
ISBN : 9781317624042
Genre : Philosophy
File Size : 66. 23 MB
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In this book, Bryan Wesley Hall breaks new ground in Kant scholarship, exploring the gap in Kant’s Critical philosophy in relation to his post-Critical work by turning to Kant’s final, unpublished work, the so-called Opus Postumum. Although Kant considered this project to be the "keystone" of his philosophical efforts, it has been largely neglected by scholars. Hall argues that only by understanding the Opus Postumum can we fully comprehend both Kant’s mature view as well as his Critical project. In letters from 1798, Kant claims to have discovered a "gap" in the Critical philosophy that requires effecting a "transition from the metaphysical foundations of natural science to physics"; unfortunately, Kant does not make clear exactly what this gap is or how the transition is supposed to fill the gap. To resolve these issues, Hall draws on the Opus Postumum, arguing that Kant’s transition project can solve certain perennial problems with the Critical philosophy. This volume provides a powerful alternative to all current interpretations of the Opus Postumum, arguing that Kant’s transition project is best seen as the post-Critical culmination of his Critical philosophy. Hall carefully examines the deep connections between the Opus Postumum and the view Kant develops in the Critique of Pure Reason, to suggest that properly understanding the post-Critical Kant will significantly revise our view of Kant’s Critical period.

Kant S Organicism

Author : Jennifer Mensch
ISBN : 9780226021980
Genre : Philosophy
File Size : 37. 85 MB
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Because it laid the foundation for nearly all subsequent epistemologies, Immanuel Kant’s Critique of Pure Reason has overshadowed his other interests in natural history and the life sciences, which scholars have long considered as separate from his rigorous theoretical philosophy—until now. In Kant’s Organicism, Jennifer Mensch draws a crucial link between these spheres by showing how the concept of epigenesis—a radical theory of biological formation—lies at the heart of Kant’s conception of reason. As Mensch argues, epigenesis was not simply a metaphor for Kant but centrally guided his critical philosophy, especially the relationship between reason and the categories of the understanding. Offsetting a study of Kant’s highly technical theory of cognition with a mixture of intellectual history and biography, she situates the epigenesis of reason within broader investigations into theories of generation, genealogy, and classification, and against later writers and thinkers such as Goethe and Darwin. Distilling vast amounts of research on the scientific literature of the time into a concise and readable book, Mensch offers one of the most refreshing looks not only at Kant’s famous first Critique but at the history of philosophy and the life sciences as well.

Set Theory And Its Philosophy

Author : Michael Potter
ISBN : 9780191556432
Genre : Philosophy
File Size : 39. 57 MB
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Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

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