Authors:
- Presents a collection of essays on what exists and how the readers know it exists
- Offers revealing insights into the general nature of human knowledge
- Includes structures and algorithms, which are essential tools for understanding what the readers “see” and how they make use of what they see
- Uses a proper understanding of mathematics to serve as the link between understanding what readers see and making use of it
Part of the book series: Logic, Argumentation & Reasoning (LARI, volume 15)
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Table of contents (9 chapters)
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Front Matter
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Structures and Algorithms
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Front Matter
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Language, Mind, and Numbers
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Front Matter
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About this book
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, Chapters7 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.
Keywords
- Structures Algorithms
- Nature Knowledge
- Nature Numbers
- Universal Grammar
- Grammar Brain
- Knowledge Culture
- Knowledge Nature Culture
- Knowledge Grammar Culture
- Fenstad European Science Foundation
- Fenstad History and Philosophy of Science
- Fenstad World Commission
- Fenstad General Recursion Theory
- Social Natural Sciences
- Knowledge System Scholars
- Theory of Knowledge
- Structure Culture
- Evolutionary Thinking Neuroscience
- Modeltheoretic Philosophy
Reviews
Authors and Affiliations
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Institute of Mathematics, University of Oslo, Oslo, Norway
Jens Erik Fenstad
About the author
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”.
Bibliographic Information
Book Title: Structures and Algorithms
Book Subtitle: Mathematics and the Nature of Knowledge
Authors: Jens Erik Fenstad
Series Title: Logic, Argumentation & Reasoning
DOI: https://doi.org/10.1007/978-3-319-72974-9
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-72973-2Published: 19 March 2018
Softcover ISBN: 978-3-030-10294-4Published: 25 December 2018
eBook ISBN: 978-3-319-72974-9Published: 10 March 2018
Series ISSN: 2214-9120
Series E-ISSN: 2214-9139
Edition Number: 1
Number of Pages: X, 134
Number of Illustrations: 7 b/w illustrations
Topics: Epistemology, Mathematical Logic and Foundations, Mathematical Logic and Formal Languages, Philosophy of Mathematics, Philosophy of Language