Philosophy of Mathematics(Princeton Foundations of Contemporary Philosophy)

数学哲学(普林斯顿当代哲学基础系列)

基本信息

Author：Øystein Linnebo

Format：Paperback | 216 pages

Dimensions：140 x 216 x 15.24mm | 272.16g

Publication date：24 Mar 2020

Publisher：Princeton University Press

Language：English

ISBN10：069120229X

ISBN13：9780691202297

页面参数仅供参考，具体以实物为准

书籍简介

一位杰出的思想家对数学哲学进行的详尽而根本的介绍

数学是一种精确和客观的模型，但它似乎与经验科学不同，因为它似乎提供了关于数字、集合和函数的非物理现实的非经验知识。数学的这两个方面如何调和？这本简明的书提供了一个系统的，可接受的介绍领域，试图回答“数学哲学”这个问题。Oystein Linnebo，在这一主题上的世界领先学者之一，介绍了该领域的所有经典方法以及更专业的问题，包括数学直觉，潜在无穷大，和寻找新的数学公理。复杂但清楚和平易近人，这是一个必要的书为所有的学生和老师的哲学和数学。

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. Oystein 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.

作者简介

Øystein Linnebo是奥斯陆大学的哲学教授。他是《细物体:抽象主义的叙述》的作者，也是《多与一:哲学研究》的合著者(与Salvatore Florio合著)。

Øystein Linnebo is professor of philosophy at the University of Oslo. He is the author of Thin Objects: An Abstractionist Account and the coauthor (with Salvatore Florio) of The Many and the One: A Philosophical Study.

目录

Acknowledgments vii

Introduction l

Chapter 1 Mathematics as a Philosophical Challenge 4

Chapter 2 Frege's Logicism 21

Chapter 3 Formalism and Deductivism 38

Chapter 4 Hilbert's Program 56

Chapter 5 Intuitionism 73

Chapter 6 Empiricism about Mathematics 88

Chapter 7 Nominalism 101

Chapter 8 Mathematical Intuition 116

Chapter 9 Abstraction Reconsidered 126

Chapter 10 The Iterative Conception of Sets 139

Chapter 11 Structuralism 154

Chapter 12 The Quest for New Axioms 170

Concluding Remarks 183

Bibliography 189

Index 199