Structures and Algorithms: Mathematics and the Nature of Knowledge
暫譯: 結構與演算法：數學與知識的本質
Fenstad, Jens Erik
- 出版商: Springer
- 出版日期: 2018-12-25
- 售價: $4,990
- 貴賓價: 9.5 折 $4,741
- 語言: 英文
- 頁數: 134
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3030102947
- ISBN-13: 9783030102944
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相關分類:
Algorithms-data-structures
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相關主題
商品描述
This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers "see" and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author's approach is model theoretic or structural.
Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and algorithms is mathematics. But viewing "mathematics" as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what "mathematics" should actually mean.
Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2-6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind.Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author's analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book's closing chapter.
The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society.
商品描述(中文翻譯)
這本書準確地解釋了人類知識的本質。本書的關鍵概念是結構和演算法，即讀者所「看到」的內容以及他們如何利用所見之物。因此，與一些採用語法方法的科學哲學（或方法論）書籍相比，作者的方式是模型理論或結構性的方法。
正確理解後，它將當前的數學建模藝術和科學擴展到所有知識領域。結構與演算法之間的聯繫是數學。然而，將「數學」視為這種聯繫並不是讀者在學校中最有可能學到的內容；因此，本書的任務是解釋「數學」實際上應該意味著什麼。
第一章是一篇介紹性文章，對結構、演算法及其如何聯繫進行了總體分析。第二至六章提供了來自自然科學和社會科學以及知識歷史的幾個例子。接著，第七章和第八章將分析擴展到語言和心智。
結構是讀者所看到的內容。作為抽象的文化對象，它們幾乎總是可以以多種不同的方式被看見。然而，某些結構，如自然數和基本語法理論，似乎具有絕對的特性。任何基於人類文化的知識理論都必須解釋這種可能性。作者對這種文化不變性的分析，結合了進化理論和神經科學的見解，將在本書的結尾章節中呈現。
這本書將吸引研究人員、學生以及那些希望深入理解當今社會知識的非學術界人士。
作者簡介
Jens Erik Fenstad is a Professor Emeritus of Mathematics and former Pro-Rector of the University of Oslo, Norway. He was the Chairman of the Standing Committee for the Physical and Engineering Sciences of the European Science Foundation, a former President of the International Union of History and Philosophy of Science, and past Chair of the UNESCO World Commission on the Ethics of Scientific Knowledge and Technology. He is the author of several books including "General Recursion Theory," "Nonstandard Methods in Stochastic Analysis and Mathematical Physics," and "Grammar, Geometry and Brain."
作者簡介(中文翻譯)
耶恩斯·埃里克·芬斯塔德（Jens Erik Fenstad）是挪威奧斯陸大學的名譽數學教授及前副校長。他曾擔任歐洲科學基金會物理與工程科學常設委員會的主席，並曾任國際科學史與科學哲學聯合會的會長，以及聯合國教科文組織科學知識與技術倫理世界委員會的前主席。他是多本書籍的作者，包括《一般遞歸理論》（General Recursion Theory）、《隨機分析與數學物理中的非常規方法》（Nonstandard Methods in Stochastic Analysis and Mathematical Physics）以及《語法、幾何與大腦》（Grammar, Geometry and Brain）。
