“This book collects eight essays … . there is much to be learnt from this collection for the reader who is prepared to make the effort to interrogate Fenstad’s thoughts … provided him with a deep appreciation of the role of mathematical modeling in the development of scientific knowledge. … As for who the interested reader might be, I see four potential candidates: well-educated lay people … philosophers of mathematics and philosophers of science … .” (Julian C. Cole, Philosophia Mathematica, July 9, 2022)

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.
Les mer
1.Preface.- 2.Introduction.- 3.Mathematics and the nature of knowledge – an introductory essay.- 4.The miraculous left hand – Leonardo and the nature of knowledge.- 5.Relationships between the social and natural sciences.- 6.Changes in the knowledge system and their implications for the formative stage of scholars.- 7.Remarks on the science and technology of language.- 8.How mathematics is rooted in life.- 9.Tarski, truth and natural languages.- 10.Formal semantics, geometry and mind.- 11.Discours, Interaction and Communication.- 12.On what there is – infinitesimals and the nature of numbers.
Les mer
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.
Les mer
“This book collects eight essays … . there is much to be learnt from this collection for the reader who is prepared to make the effort to interrogate Fenstad’s thoughts … provided him with a deep appreciation of the role of mathematical modeling in the development of scientific knowledge. … As for who the interested reader might be, I see four potential candidates: well-educated lay people … philosophers of mathematics and philosophers of science … .” (Julian C. Cole, Philosophia Mathematica, July 9, 2022)
Les mer
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
Les mer

Produktdetaljer

ISBN
9783319729732
Publisert
2018-03-19
Utgiver
Vendor
Springer International Publishing AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet

Forfatter

Biographical note

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”.