Philosophy of Mathematics(Princeton Foundations of Contemporary Philosophy)

數學哲學(普林斯頓當代哲學基礎系列)

基本信息

Author：?ystein 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

頁面參數僅供參考，具體以實物為準

書籍簡介

一位傑出的思想家對數學哲學進行的詳盡而根本的介紹

數學是一種精確和客觀的模型，但它似乎與經驗科學不同，因為它似乎提供了關於數字、集合和函數的非物理現實的非經驗知識。數學的這兩個方面如何調和？這本簡明的書提供了一個系統的，可接受的介紹領域，試圖回答“數學哲學”這個問題。Oystein Linnebo，在這一主題上的*學者之一，介紹了該領域的所有經典方法以及更專業的問題，包括數學直覺，潛在無窮大，和尋找新的數學公理。複雜但清楚和平易近人，這是一個必要的書為所有的學生和老師的哲學和數學。

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.

作者簡介

?ystein Linnebo是奧斯陸大學的哲學教授。他是《細物體:抽象主義的敍述》的作者，也是《多與一:哲學研究》的合著者(與Salvatore Florio合著)。

?ystein 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.

目錄

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