Philosophy of Mathematics

An Introduction to a World of Proofs and Pictures

Author: James Robert Brown

Publisher: Routledge

ISBN:

Category: Philosophy

Page: 232

View: 510

Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

An Introduction to the Philosophy of Science

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN:

Category: Science

Page: 336

View: 354

Stimulating, thought-provoking text by one of the 20th century's most creative philosophers makes accessible such topics as probability, measurement and quantitative language, causality and determinism, theoretical laws and concepts, more.

Perspectives on Mathematical Practices

Bringing Together Philosophy of Mathematics, Sociology of Mathematics, and Mathematics Education

Author: Bart van Kerkhove

Publisher: Springer Science & Business Media

ISBN:

Category: Science

Page: 242

View: 738

In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

18 Unconventional Essays on the Nature of Mathematics

Author: Reuben Hersh

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 326

View: 338

Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines

Platonism, Naturalism, and Mathematical Knowledge

Author: James Robert Brown

Publisher: Routledge

ISBN:

Category: Philosophy

Page: 182

View: 548

This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.

Handbook of International Research in Mathematics Education

Author: Lyn D. English

Publisher: Routledge

ISBN:

Category: Education

Page: 944

View: 206

This book brings together mathematics education research that makes a difference in both theory and practice - research that anticipates problems and needed knowledge before they become impediments to progress.

Routledge History of Philosophy Volume IX

Philosophy of the English-Speaking World in the Twentieth Century 1: Science, Logic and Mathematics

Author: S. G. Shanker

Publisher: Routledge

ISBN:

Category: Philosophy

Page: 504

View: 251

Volume 9 of the Routledge History of Philosophy surveys ten key topics in the philosophy of science, logic and mathematics in the twentieth century. Each of the essays is written by one of the world's leading experts in that field. Among the topics covered are the philosophy of logic, of mathematics and of Gottlob Frege; Ludwig Wittgenstein's Tractatus; a survey of logical positivism; the philosophy of physics and of science; probability theory, cybernetics and an essay on the mechanist/vitalist debates. The volume also contains a helpful chronology to the major scientific and philosophical events in the twentieth century. It also provides an extensive glossary of technical terms in the notes on major figures in these fields.

A Logical Journey

From Gödel to Philosophy

Author: Hao Wang

Publisher: MIT Press

ISBN:

Category: Philosophy

Page: 408

View: 784

Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.

Why Is There Philosophy of Mathematics At All?

Author: Ian Hacking

Publisher: Cambridge University Press

ISBN:

Category: Science

Page: 212

View: 713

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.