Forrest A Systemic Perspective on Cognition and Mathematics

Erscheinungsjahr 2013
ISBN: 978-0-203-48732-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 412 Seiten

Reihe: Communications in Cybernetics, Systems Science and Engineering

This book is devoted to the study of human thought, its systemic structure, and the historical development of mathematics both as a product of thought and as a fascinating case analysis. After demonstrating that systems research constitutes the second dimension of modern science, the monograph discusses the yoyo model, a recent ground-breaking development of systems research, which has brought forward revolutionary applications of systems research in various areas of the traditional disciplines, the first dimension of science. After the systemic structure of thought is factually revealed, mathematics, as a product of thought, is analyzed by using the age-old concepts of actual and potential infinities. In an attempt to rebuild the system of mathematics, this volume first provides a new look at some of the most important paradoxes, which have played a crucial role in the development of mathematics, in proving what these paradoxes really entail. Attention is then turned to constructing the logical foundation of two different systems of mathematics, one assuming that actual infinity is different than potential infinity, and the other that these infinities are the same. This volume will be of interest to academic researchers, students and professionals in the areas of systems science, mathematics, philosophy of mathematics, and philosophy of science.

Autoren/Hrsg.

Forrest, Jeffrey Yi-Lin

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Interdisziplinäres Wissenschaften Wissenschaften Interdisziplinär Neurowissenschaften, Kognitionswissenschaft
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

Part 1 Basics 1. Where everything starts 2. Elementary properties of systemic yoyos Part 2 The mind 3. Human body as a system 4. The four human endowments 5. Character and thought Part 3 Mathematics seen as a systemic flow: A case study 6. A brief history of mathematics 7. Actual and potential infinities 8. Are actual and potential infinity the same? 9. Inconsistencies of modern mathematics Part 4 Next stage of mathematics as a systemic field of thought 10. Calculus without limit 11. A new look at some historically important paradoxes 12. An attempt to rebuild the system of mathematics Afterword A systemic yoyo model prediction Part 5 Appendices: A close look at the systemic yoyo model Appendix A Theoretical foundation of the yoyo model Appendix B Empirical evidence of the yoyo model