Kant's Mathematical World

Kant's Mathematical World
Author: Daniel Sutherland
Publisher: Cambridge University Press
Total Pages: 317
Release: 2021-10-28
Genre: Mathematics
ISBN: 1108429963

An explanation of the foundations of Kant's philosophy of mathematics and its connection to his account of human experience.

Kant's Mathematical World

Kant's Mathematical World
Author: Daniel Sutherland
Publisher: Cambridge University Press
Total Pages: 318
Release: 2021-10-28
Genre: 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.

Mathematics in Kant's Critical Philosophy

Mathematics in Kant's Critical Philosophy
Author: Lisa Shabel
Publisher: Routledge
Total Pages: 249
Release: 2017-09-25
Genre: Mathematics
ISBN: 113537063X

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

Philosophy of Mathematics

Philosophy of Mathematics
Author: Øystein Linnebo
Publisher: Princeton University Press
Total Pages: 214
Release: 2020-03-24
Genre: 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.

Philosophy of Mathematics

Philosophy of Mathematics
Author: James Robert Brown
Publisher: Psychology Press
Total Pages: 181
Release: 1999
Genre: Mathematics
ISBN: 0415122759

Philosophy of Mathematicsis clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.

Kant and the Exact Sciences

Kant and the Exact Sciences
Author: Michael Friedman
Publisher: Harvard University Press
Total Pages: 396
Release: 1992
Genre: 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.

Having the World in View

Having the World in View
Author: John McDowell
Publisher: Harvard University Press
Total Pages: 298
Release: 2013-09-02
Genre: Philosophy
ISBN: 0674725808

This is a decisive volume that seeks to heal the divisions in contemporary philosophy.

Why Is There Philosophy of Mathematics At All?

Why Is There Philosophy of Mathematics At All?
Author: Ian Hacking
Publisher: Cambridge University Press
Total Pages: 307
Release: 2014-01-30
Genre: 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.

Being and Number in Heidegger's Thought

Being and Number in Heidegger's Thought
Author: Michael Roubach
Publisher: Continuum
Total Pages: 168
Release: 2008-04-15
Genre: Mathematics
ISBN:

An important new monograph analysing the connections between mathematics and ontology in Heidegger's thought.