Book Description
An explanation of the foundations of Kant's philosophy of mathematics and its connection to his account of human experience.
Author : Daniel Sutherland
Publisher : Cambridge University Press
Page : 317 pages
File Size : 31,1 MB
Release : 2021-10-28
Category : Mathematics
ISBN : 1108429963
An explanation of the foundations of Kant's philosophy of mathematics and its connection to his account of human experience.
Author : Daniel Sutherland
Publisher : Cambridge University Press
Page : 318 pages
File Size : 10,16 MB
Release : 2021-10-28
Category : Philosophy
ISBN : 1108660045
Kant's Mathematical World aims to transform our understanding of Kant's philosophy of mathematics and his account of the mathematical character of the world. Daniel Sutherland reconstructs Kant's project of explaining both mathematical cognition and our cognition of the world in terms of our most basic cognitive capacities. He situates Kant in a long mathematical tradition with roots in Euclid's Elements, and thereby recovers the very different way of thinking about mathematics which existed prior to its 'arithmetization' in the nineteenth century. He shows that Kant thought of mathematics as a science of magnitudes and their measurement, and all objects of experience as extensive magnitudes whose real properties have intensive magnitudes, thus tying mathematics directly to the world. His book will appeal to anyone interested in Kant's critical philosophy -- either his account of the world of experience, or his philosophy of mathematics, or how the two inform each other.
Author : Lisa Shabel
Publisher : Routledge
Page : 249 pages
File Size : 37,22 MB
Release : 2017-09-25
Category : Mathematics
ISBN : 113537063X
First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Author : Øystein Linnebo
Publisher : Princeton University Press
Page : 214 pages
File Size : 36,97 MB
Release : 2020-03-24
Category : Mathematics
ISBN : 069120229X
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
Author : C J Posy
Publisher : Springer
Page : 392 pages
File Size : 36,98 MB
Release : 2014-01-15
Category :
ISBN : 9789401580472
Author : John McDowell
Publisher : Harvard University Press
Page : 298 pages
File Size : 34,6 MB
Release : 2013-09-02
Category : Philosophy
ISBN : 0674725808
This is a decisive volume that seeks to heal the divisions in contemporary philosophy.
Author : Michael Roubach
Publisher : Continuum
Page : 168 pages
File Size : 40,53 MB
Release : 2008-04-15
Category : Mathematics
ISBN :
An important new monograph analysing the connections between mathematics and ontology in Heidegger's thought.
Author : Ian Hacking
Publisher : Cambridge University Press
Page : 307 pages
File Size : 42,41 MB
Release : 2014-01-30
Category : Science
ISBN : 1107729823
This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.
Author : Stewart Shapiro
Publisher : OUP USA
Page : 850 pages
File Size : 44,41 MB
Release : 2005-02-10
Category : Mathematics
ISBN : 0195148770
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.
Author : Michael Friedman
Publisher : Harvard University Press
Page : 396 pages
File Size : 32,28 MB
Release : 1992
Category : History
ISBN : 9780674500358
Kant sought throughout his life to provide a philosophy adequate to the sciences of his time--especially Euclidean geometry and Newtonian physics. In this new book, Michael Friedman argues that Kant's continuing efforts to find a metaphysics that could provide a foundation for the sciences is of the utmost importance in understanding the development of his philosophical thought from its earliest beginnings in the thesis of 1747, through the Critique of Pure Reason, to his last unpublished writings in the Opus postumum. Previous commentators on Kant have typically minimized these efforts because the sciences in question have since been outmoded. Friedman argues that, on the contrary, Kant's philosophy is shaped by extraordinarily deep insight into the foundations of the exact sciences as he found them, and that this represents one of the greatest strengths of his philosophy. Friedman examines Kant's engagement with geometry, arithmetic and algebra, the foundations of mechanics, and the law of gravitation in Part One. He then devotes Part Two to the Opus postumum, showing how Kant's need to come to terms with developments in the physics of heat and in chemistry formed a primary motive for his projected Transition from the Metaphysical Foundations of Natural Science to Physics. Kant and the Exact Sciences is a book of high scholarly achievement, argued with impressive power. It represents a great advance in our understanding of Kant's philosophy of science.