Philosophy of Mathematics / / Øystein Linnebo.

• Superior document: Title is part of eBook package: De Gruyter PUP eBook-Package Pilot Project 2017
• VerfasserIn: Linnebo, Øystein,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2017]; ©2017
• Year of Publication: 2017
• Language: English
• Series: Princeton Foundations of Contemporary Philosophy ; 15
• Physical Description: 1 online resource

A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholarsMathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but 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 yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics.Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field.Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.

Table of Contents

Frontmatter -- Contents -- Acknowledgments -- Introduction -- Chapter One. Mathematics as a Philosophical Challenge -- Chapter Two. Frege's Logicism -- Chapter Three. Formalism and Deductivism -- Chapter Four. Hilbert's Program -- Chapter Five. Intuitionism -- Chapter Six. Empiricism about Mathematics -- Chapter Seven. Nominalism -- Chapter Eight. Mathematical Intuition -- Chapter Nine. Abstraction Reconsidered -- Chapter Ten. The Iterative Conception of Sets -- Chapter Eleven. Structuralism -- Chapter Twelve. The Quest for New Axioms -- Concluding Remarks -- Bibliography -- Index