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Author : Daniel Sutherland
Publisher : Cambridge University Press
Page : 317 pages
File Size : 46,7 Mb
Release : 2021-10-28
Category : Mathematics
ISBN : 9781108429962
An explanation of the foundations of Kant's philosophy of mathematics and its connection to his account of human experience.
Author : Emily Carson,Lisa Shabel
Publisher : Routledge
Page : 461 pages
File Size : 44,9 Mb
Release : 2017-12-22
Category : Philosophy
ISBN : 9781317407898
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.
Author : Lisa Shabel
Publisher : Routledge
Page : 249 pages
File Size : 45,9 Mb
Release : 2017-09-25
Category : Mathematics
ISBN : 9781135370633
First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Author : Gottfried Martin
Publisher : SIU Press
Page : 240 pages
File Size : 54,9 Mb
Release : 1985
Category : Mathematics
ISBN : 0809311844
This is the only work to provide a historical account of Kant s theory of arithmetic, examining in detail the theories of both his predecessors and his successors.Until his death, Martin was the editor of "Kant-Studien "from 1954, of the general Kant index from 1964, of the Leibniz index from 1968, and coeditor of "Leibnizstudien "from 1969. This background is used to its fullest as he strives to make clear the historical milieu in which Kant s mathematical contributions developed. He uses Leibniz, Wolff, and others whose work was accomplished before Kant was born as well as Lambert, Mendelssohn, and others roughly contemporary with Kant; and when a point requires it, he refers to Gauss, Grassman, Frege, Russell, and Hilbert.In her translation Wubnig has approached the original author with an abiding respect. She makes the translation flow in English while preserving as far as possible the flavor of the original. She has added many bibliographical and biographical details to ease the following up of Martin s allusions and suggestions."
Author : Carl Posy,Ofra Rechter
Publisher : Cambridge University Press
Page : 331 pages
File Size : 44,8 Mb
Release : 2021-09-02
Category : Philosophy
ISBN : 110871708X
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.
Author : C.J. Posy
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 51,9 Mb
Release : 2013-03-09
Category : Philosophy
ISBN : 9789401580465
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.
Author : William Bragg Ewald,William Ewald
Publisher : Oxford University Press, USA
Page : 695 pages
File Size : 41,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780198505358
This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics - algebra, geometry, number theory, analysis, logic, and set theory - with narratives to show how they are linked.
Author : David Jalal Hyder
Publisher : Walter de Gruyter
Page : 239 pages
File Size : 55,5 Mb
Release : 2009
Category : Philosophy
ISBN : 9783110183917
This book offers a new interpretation of Hermann von Helmholtz's work on the epistemology of geometry. A detailed analysis of the philosophical arguments of Helmholtz's Erhaltung der Kraft shows that he took physical theories to be constrained by a regulative ideal. They must render nature "completely comprehensible", which implies that all physical magnitudes must be relations among empirically given phenomena. This conviction eventually forced Helmholtz to explain how geometry itself could be so construed. Hyder shows how Helmholtz answered this question by drawing on the theory of magnitudes developed in his research on the colour-space. He argues against the dominant interpretation of Helmholtz's work by suggesting that for the latter, it is less the inductive character of geometry that makes it empirical, and rather the regulative requirement that the system of natural science be empirically closed.
Author : Anonim
Publisher : Unknown
Page : 1340 pages
File Size : 54,6 Mb
Release : 1996
Category : Mathematics
ISBN : 019850537X
Author : Gordon G. Brittan Jr.
Publisher : Princeton University Press
Page : 229 pages
File Size : 41,8 Mb
Release : 2015-03-08
Category : Science
ISBN : 9781400867486
While interest in Kant's philosophy has increased in recent years, very little of it has focused on his theory of science. This book gives a general account of that theory, of its motives and implications, and of the way it brought forth a new conception of the nature of philosophical thought. To reconstruct Kant's theory of science, the author identifies unifying themes of his philosophy of mathematics and philosophy of physics, both undergirded by his distinctive logical doctrines, and shows how they come together to form a relatively consistent system of ideas. A new analysis of the structure of central arguments in the Critique of Pure Reason and the Prolegomena draws on recent developments in logic and the philosophy of science. Professor Brittan's unified account of the philosophies of mathematics and physics explores the nature of Kant's commitment to Euclidean geometry and Newtonian mechanics as well as providing an integrated reading of the Critique of Pure Reason and the Metaphysical Foundations of Natural Science. Contemporary ideas help both to illuminate Kant's position and to show how that position, in turn, illuminates contemporary problems in the philosophy of science. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : A T Winterbourne
Publisher : Theschoolbook.com
Page : 0 pages
File Size : 46,7 Mb
Release : 2007
Category : Mathematics
ISBN : 184549198X
"The Ideal and the Real should prove valuable to two particular sets of readers: (i) those with an interest in Kant and little or no background in the philosophy of mathematics, or (ii) those with an interest in the philosophy of mathematics and little or no background in Kant...The book contains much that is suggestive which should promote further discussion...(and) offers more than a simple examination of Kant's philosophy of mathematics. Of particular interest is his suggestion that Newton's thought experiments have been changed and idealized by commentators." R.R.Wojtowicz, (Canadian Philosophical Review) This book argues that Kant's theory of space, time and mathematics has contemporary significance principally because of its roots in the ideas of construction and schematism. These concepts are analysed in the light of the central Kantian distinction between the ideal and the empirically real. A reassessment of Newton's arguments for absolute space is followed by an examination of Leibniz's theory of space, time and continuity. The metaphysical frameworks of these theories are presented as essential precursors of Kant's critical programme. The ideas of construction and schematism illuminate all aspects of Kant's philosophy of mathematics, and have important implications for understanding both the task and the achievement of the critical philosophy. Through an analysis of these concepts, the role of intuition, and in particular the argument from incongruent counterparts, is given added significance. "While he intends The Ideal and the Real as a limited commentary on space, time, and mathematical construction, it also brings the reader into contact with a whole series of problems treated by Kant in the First Critique and the Prolegomena....While the discussion of Newton displays a sensitivity to the complexity of Newton's position, Winterbourne's own exposition develops clearly....(and) advances with such sensitivity both to primary and secondary sources that one could hardly find a better summary of the issues surrounding the Leibniz-Clarke controversy....The discussion of incongruent counterparts provides the most interesting part of the monograph....Winterbourne avoids technical jargon and obscure explanation in an admirable way...(and) gives us one of the best treatments of the Schematism available. Kantian scholars would do well to take note of Winterbourne's conclusions." John Treloar, (The Modern Schoolman) "One of the main strengths of Winterbourne's book is his treatment of Kant's philosophy of mathematics....and (it) offers an interesting overview of the ideas of Leibniz and Newton..." Grant West (Isis)
Author : Michael Potter
Publisher : Oxford University Press
Page : 316 pages
File Size : 53,9 Mb
Release : 2000-03-16
Category : Mathematics
ISBN : 9780198250418
How do we account for the truth of arithmetic? And if it does not depend for its truth on the way the world is, what constrains the world to conform to arithmetic? Reason's Nearest Kin is a critical examination of the astonishing progress made towards answering these questions from the late nineteenth to the mid-twentieth century. In the space of fifty years Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, and Carnap developed accounts of the content of arithmeticthat were brilliantly original both technically and philosophically. Michael Potter's innovative study presents them all as finding that content in various aspects of the complex linkage between experience, language, thought, and the world. Potter's reading places them all in Kant's shadow since it was hisattempt to ground arithmetic in the spatio-temporal structure of reality that they were reacting against; but it places us in Gödel's shadow since his incompleteness theorems supply us with a measure of the richness of the content they were trying to explain. This stimulating reassessment of some of the classic texts in the philosophy of mathematics reveals many unexpected connections and illuminating comparisons, and offers a wealth of ideas for future work in the subject.
Author : Giacomo Maria Virone
Publisher : LED Edizioni Universitarie
Page : 257 pages
File Size : 49,5 Mb
Release : 2012
Category : Philosophy
ISBN : 8879165992
Author : Emily Carson
Publisher : Unknown
Page : 128 pages
File Size : 53,7 Mb
Release : 2017
Category : Electronic books
ISBN : 1315684012
"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. "--Provided by publisher.
Author : Daniel Smyth
Publisher : Cambridge University Press
Page : 275 pages
File Size : 47,7 Mb
Release : 2024-02-29
Category : Philosophy
ISBN : 9781009330329
In this book Daniel Smyth offers a comprehensive overview of Immanuel Kant's conception of intuition in all its species – divine, receptive, sensible, and human. Kant considers sense perception a paradigm of intuition, yet claims that we can represent infinities in intuition, despite the finitude of sense perception. Smyth examines this heterodox combination of commitments and argues that the various features Kant ascribes to intuition are meant to remedy specific cognitive shortcomings that arise from the discursivity of our intellect Intuition acting as the intellect's cognitive partner to make knowledge possible. He reconstructs Kant's conception of intuition and its role in his philosophy of mind, epistemology, and philosophy of mathematics, and shows that Kant's conception of sensibility is as innovative and revolutionary as his much-debated theory of the understanding.
