A Systemic Perspective on Cognition and Mathematics

A Systemic Perspective on Cognition and Mathematics

by Jeffrey Yi-Lin Forrest
Released February 2013
Publisher(s): CRC Press
ISBN: 9780203487327

Read it now on the O’Reilly learning platform with a 10-day free trial.

O’Reilly members get unlimited access to books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial

Book description

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.

Table of contents

  1. Front Cover
  2. Dedication
  3. Table of contents (1/2)
  4. Table of contents (2/2)
  5. Editorial board
  6. About the author
  7. Acknowledgements
  8. Preface (1/2)
  9. Preface (2/2)
  10. Part 1 - Basics
    1. Chapter 1 - Where everything starts (1/4)
    2. Chapter 1 - Where everything starts (2/4)
    3. Chapter 1 - Where everything starts (3/4)
    4. Chapter 1 - Where everything starts (4/4)
    5. Chapter 2 - Elementary properties of systemic yoyos (1/8)
    6. Chapter 2 - Elementary properties of systemic yoyos (2/8)
    7. Chapter 2 - Elementary properties of systemic yoyos (3/8)
    8. Chapter 2 - Elementary properties of systemic yoyos (4/8)
    9. Chapter 2 - Elementary properties of systemic yoyos (5/8)
    10. Chapter 2 - Elementary properties of systemic yoyos (6/8)
    11. Chapter 2 - Elementary properties of systemic yoyos (7/8)
    12. Chapter 2 - Elementary properties of systemic yoyos (8/8)
  11. Part 2 - The mind
    1. Chapter 3 - Human body as a system (1/5)
    2. Chapter 3 - Human body as a system (2/5)
    3. Chapter 3 - Human body as a system (3/5)
    4. Chapter 3 - Human body as a system (4/5)
    5. Chapter 3 - Human body as a system (5/5)
    6. Chapter 4 - The four human endowments (1/6)
    7. Chapter 4 - The four human endowments (2/6)
    8. Chapter 4 - The four human endowments (3/6)
    9. Chapter 4 - The four human endowments (4/6)
    10. Chapter 4 - The four human endowments (5/6)
    11. Chapter 4 - The four human endowments (6/6)
    12. Chapter 5 - Character and thought (1/8)
    13. Chapter 5 - Character and thought (2/8)
    14. Chapter 5 - Character and thought (3/8)
    15. Chapter 5 - Character and thought (4/8)
    16. Chapter 5 - Character and thought (5/8)
    17. Chapter 5 - Character and thought (6/8)
    18. Chapter 5 - Character and thought (7/8)
    19. Chapter 5 - Character and thought (8/8)
  12. Part 3 - Mathematics seen as a systemic flow: A case study
    1. Chapter 6 - A brief history of mathematics (1/4)
    2. Chapter 6 - A brief history of mathematics (2/4)
    3. Chapter 6 - A brief history of mathematics (3/4)
    4. Chapter 6 - A brief history of mathematics (4/4)
    5. Chapter 7 - Actual and potential infinities (1/6)
    6. Chapter 7 - Actual and potential infinities (2/6)
    7. Chapter 7 - Actual and potential infinities (3/6)
    8. Chapter 7 - Actual and potential infinities (4/6)
    9. Chapter 7 - Actual and potential infinities (5/6)
    10. Chapter 7 - Actual and potential infinities (6/6)
    11. Chapter 8 - Are actual and potential infinity the same? (1/6)
    12. Chapter 8 - Are actual and potential infinity the same? (2/6)
    13. Chapter 8 - Are actual and potential infinity the same? (3/6)
    14. Chapter 8 - Are actual and potential infinity the same? (4/6)
    15. Chapter 8 - Are actual and potential infinity the same? (5/6)
    16. Chapter 8 - Are actual and potential infinity the same? (6/6)
    17. Chapter 9 - Inconsistencies of modern mathematics (1/8)
    18. Chapter 9 - Inconsistencies of modern mathematics (2/8)
    19. Chapter 9 - Inconsistencies of modern mathematics (3/8)
    20. Chapter 9 - Inconsistencies of modern mathematics (4/8)
    21. Chapter 9 - Inconsistencies of modern mathematics (5/8)
    22. Chapter 9 - Inconsistencies of modern mathematics (6/8)
    23. Chapter 9 - Inconsistencies of modern mathematics (7/8)
    24. Chapter 9 - Inconsistencies of modern mathematics (8/8)
  13. Part 4 - Next stage of mathematics as a systemic field of thought
    1. Chapter 10 - Calculus without limit (1/11)
    2. Chapter 10 - Calculus without limit (2/11)
    3. Chapter 10 - Calculus without limit (3/11)
    4. Chapter 10 - Calculus without limit (4/11)
    5. Chapter 10 - Calculus without limit (5/11)
    6. Chapter 10 - Calculus without limit (6/11)
    7. Chapter 10 - Calculus without limit (7/11)
    8. Chapter 10 - Calculus without limit (8/11)
    9. Chapter 10 - Calculus without limit (9/11)
    10. Chapter 10 - Calculus without limit (10/11)
    11. Chapter 10 - Calculus without limit (11/11)
    12. Chapter 11 - New look at some of the historically important paradoxes (1/4)
    13. Chapter 11 - New look at some of the historically important paradoxes (2/4)
    14. Chapter 11 - New look at some of the historically important paradoxes (3/4)
    15. Chapter 11 - New look at some of the historically important paradoxes (4/4)
    16. Chapter 12 - An attempt to rebuild the system of mathematics (1/10)
    17. Chapter 12 - An attempt to rebuild the system of mathematics (2/10)
    18. Chapter 12 - An attempt to rebuild the system of mathematics (3/10)
    19. Chapter 12 - An attempt to rebuild the system of mathematics (4/10)
    20. Chapter 12 - An attempt to rebuild the system of mathematics (5/10)
    21. Chapter 12 - An attempt to rebuild the system of mathematics (6/10)
    22. Chapter 12 - An attempt to rebuild the system of mathematics (7/10)
    23. Chapter 12 - An attempt to rebuild the system of mathematics (8/10)
    24. Chapter 12 - An attempt to rebuild the system of mathematics (9/10)
    25. Chapter 12 - An attempt to rebuild the system of mathematics (10/10)
  14. Afterword - A systemic yoyomodel prediction
  15. Part 5 - Appendices: A close look at the systemic yoyo model
    1. Appendix A - Theoretical foundation of the Yoyo model (1/2)
    2. Appendix A - Theoretical foundation of the Yoyo model (2/2)
    3. Appendix B - Empirical evidence of the yoyo model (1/2)
    4. Appendix B - Empirical evidence of the yoyo model (2/2)
  16. Bibliography (1/2)
  17. Bibliography (2/2)
  18. Back Cover

Product information

  • Title: A Systemic Perspective on Cognition and Mathematics
  • Author(s): Jeffrey Yi-Lin Forrest
  • Release date: February 2013
  • Publisher(s): CRC Press
  • ISBN: 9780203487327