Structures and Algorithms

1. Front Matter

   Pages i-x

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2. Mathematics and the Nature of Knowledge—An Introductory Essay

   • Jens Erik Fenstad

   Pages 1-11

3. Structures and Algorithms

   1. Front Matter

      Pages 13-13

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   2. The Miraculous Left Hand—On Leonardo Da Vinci and the Search for a Common Understanding of Man and Nature

      • Jens Erik Fenstad

      Pages 15-25

   3. Relationships Between the Social and the Natural Sciences

      • Jens Erik Fenstad

      Pages 27-41

   4. Changes of the Knowledge System and Their Implication for the Formative Stage of Scholars: Experiences in the Natural Sciences

      • Jens Erik Fenstad

      Pages 43-52

   5. Remarks on the Science and Technology of Language

      • Jens Erik Fenstad

      Pages 53-65

   6. How Mathematics Is Rooted in Life

      • Jens Erik Fenstad

      Pages 67-74

4. Language, Mind, and Numbers

   1. Front Matter

      Pages 75-75

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   2. Tarski, Truth, and Natural Languages

      • Jens Erik Fenstad

      Pages 77-88

   3. Formal Semantics, Geometry, and Mind

      • Jens Erik Fenstad

      Pages 89-108

   4. On What There Is—Infinitesimals and the Nature of Numbers

      • Jens Erik Fenstad

      Pages 109-134

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.

• 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

“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)

• Institute of Mathematics, University of Oslo, Oslo, Norway

  Jens Erik Fenstad

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”.

Policies and ethics