Proof and other dilemmas : mathematics and philosophy / edited by Bonnie Gold and Roger A. Simons.

Format:

Book

Contributor:

Gold, Bonnie, 1948- editor.

Simons, Roger A., editor.

Series:

MAA spectrum.

Spectrum series

Language:

English

Subjects (All):

Mathematics--Philosophy.

Mathematics.

Proof theory.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (xxxii, 346 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Proof & Other Dilemmas

Place of Publication:

Washington : Mathematical Association of America, 2008.

Language Note:

English

Summary:

Has the advent of computers changed the nature of mathematical knowledge? Should it? Is the importance of proof decreasing? Is there an empirical aspect to mathematics after all? To what extent is mathematics socially constructed? Is mathematics the "science of patterns?" Recently emerging questions like these are discussed in this book along with some recent thinking about classical questions. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philosophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made (in the article itself, or in its introduction) to issues relevant to the teaching of mathematics.

Contents:

Proof and how it is changing. Proof : its nature and significance / Michael Detlefsen

Implications of experimental mathematics for the philosophy of mathematics / Jonathan Borwein

On the roles of proof in mathematics / Joseph Auslander

Social constructivist views of mathematics. When is a problem solved? / Philip J. Davis

Mathematical practice as a scientific problem / Reuben Hersh

Mathematical domains : social constructs? / Julian Cole

The nature of mathematical objects and mathematical knowledge. The existence of mathematical objects / Charles Chihara

Mathematical objects / Stewart Shapiro

Mathematical platonism / Mark Balaguer

The nature of mathematical objects / Øystein Linnebo

When is one thing equal to some other thing? / Barry Mazur

The nature of mathematics and its applications. Extreme science : mathematics as the science of relations as such / R.S.D. Thomas

What is mathematics? A pedagogical answer to a philosophical question / Guershon Harel

What will count as mathematics in 2100? / Keith Devlin

Mathematics applied : the case of addition / Mark Steiner

Probability : a philosophical overview / Alan Hájek.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references.

Description based on print version record.

ISBN:

1-61444-505-2

OCLC:

923220456