相關主題
商品描述
What kind of objects does mathematics investigate, and in what sense do these objects exist? Why are we justified in considering mathematical statements as part of our knowledge, and how can they be validated?
A philosophy of mathematics seeks to answer such questions. In this introduction, we present the major positions in the philosophy of mathematics and formulate their core ideas into clear, accessible theses. Readers will learn which philosophers developed each position and the historical context in which they emerged. Drawing on fundamental intuitions and scientific findings, one can argue for or against these theses - such arguments form the second focus of this book.
The book aims to encourage readers to reflect on the philosophy of mathematics, to develop their own stance, and to learn how to argue for it. This book is a translation of the original German 2nd edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.
A philosophy of mathematics seeks to answer such questions. In this introduction, we present the major positions in the philosophy of mathematics and formulate their core ideas into clear, accessible theses. Readers will learn which philosophers developed each position and the historical context in which they emerged. Drawing on fundamental intuitions and scientific findings, one can argue for or against these theses - such arguments form the second focus of this book.
The book aims to encourage readers to reflect on the philosophy of mathematics, to develop their own stance, and to learn how to argue for it. This book is a translation of the original German 2nd edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.
商品描述(中文翻譯)
數學研究什麼樣的對象，這些對象在什麼意義上存在？為什麼我們有理由將數學陳述視為我們知識的一部分，這些陳述又如何得到驗證？數學哲學旨在回答這些問題。在本書的介紹中，我們呈現數學哲學中的主要立場，並將其核心思想整理成清晰、易於理解的論點。讀者將了解哪些哲學家發展了每個立場，以及它們出現的歷史背景。基於基本的直覺和科學發現，可以對這些論點進行辯論——這些辯論構成了本書的第二個重點。本書旨在鼓勵讀者反思數學哲學，發展自己的立場，並學習如何為其辯護。
本書是原德文第二版的翻譯。翻譯工作是借助人工智慧機器翻譯工具完成的。隨後進行的人類修訂主要針對內容，因此本書的風格可能與傳統翻譯有所不同。
作者簡介
Jörg Neunhäuserer earned his doctorate in mathematics at Freie Universität Berlin. He has published numerous articles in academic journals and has taught mathematics lectures in various bachelor's and master's programs at the universities of Berlin, Brunswick, Clausthal, Dresden, Hanover, Göttingen and Lüneburg. His German-language books on Mathematical Concepts and Beautiful Theorems of Mathematics are also available from Springer Spektrum.
作者簡介(中文翻譯)
約爾格·諾因豪瑟在柏林自由大學獲得數學博士學位。他在學術期刊上發表了許多文章，並在柏林、布倫瑞克、克勞斯塔爾、德累斯頓、漢諾威、哥廷根和呂訥堡的多個學士和碩士課程中教授數學課程。他的德語書籍《數學概念與數學之美的定理》也可從Springer Spektrum獲得。
