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 groundbreaking 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 ageold 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
 Front Cover
 Dedication
 Table of contents (1/2)
 Table of contents (2/2)
 Editorial board
 About the author
 Acknowledgements
 Preface (1/2)
 Preface (2/2)

Part 1  Basics
 Chapter 1  Where everything starts (1/4)
 Chapter 1  Where everything starts (2/4)
 Chapter 1  Where everything starts (3/4)
 Chapter 1  Where everything starts (4/4)
 Chapter 2  Elementary properties of systemic yoyos (1/8)
 Chapter 2  Elementary properties of systemic yoyos (2/8)
 Chapter 2  Elementary properties of systemic yoyos (3/8)
 Chapter 2  Elementary properties of systemic yoyos (4/8)
 Chapter 2  Elementary properties of systemic yoyos (5/8)
 Chapter 2  Elementary properties of systemic yoyos (6/8)
 Chapter 2  Elementary properties of systemic yoyos (7/8)
 Chapter 2  Elementary properties of systemic yoyos (8/8)

Part 2  The mind
 Chapter 3  Human body as a system (1/5)
 Chapter 3  Human body as a system (2/5)
 Chapter 3  Human body as a system (3/5)
 Chapter 3  Human body as a system (4/5)
 Chapter 3  Human body as a system (5/5)
 Chapter 4  The four human endowments (1/6)
 Chapter 4  The four human endowments (2/6)
 Chapter 4  The four human endowments (3/6)
 Chapter 4  The four human endowments (4/6)
 Chapter 4  The four human endowments (5/6)
 Chapter 4  The four human endowments (6/6)
 Chapter 5  Character and thought (1/8)
 Chapter 5  Character and thought (2/8)
 Chapter 5  Character and thought (3/8)
 Chapter 5  Character and thought (4/8)
 Chapter 5  Character and thought (5/8)
 Chapter 5  Character and thought (6/8)
 Chapter 5  Character and thought (7/8)
 Chapter 5  Character and thought (8/8)

Part 3  Mathematics seen as a systemic flow: A case study
 Chapter 6  A brief history of mathematics (1/4)
 Chapter 6  A brief history of mathematics (2/4)
 Chapter 6  A brief history of mathematics (3/4)
 Chapter 6  A brief history of mathematics (4/4)
 Chapter 7  Actual and potential infinities (1/6)
 Chapter 7  Actual and potential infinities (2/6)
 Chapter 7  Actual and potential infinities (3/6)
 Chapter 7  Actual and potential infinities (4/6)
 Chapter 7  Actual and potential infinities (5/6)
 Chapter 7  Actual and potential infinities (6/6)
 Chapter 8  Are actual and potential infinity the same? (1/6)
 Chapter 8  Are actual and potential infinity the same? (2/6)
 Chapter 8  Are actual and potential infinity the same? (3/6)
 Chapter 8  Are actual and potential infinity the same? (4/6)
 Chapter 8  Are actual and potential infinity the same? (5/6)
 Chapter 8  Are actual and potential infinity the same? (6/6)
 Chapter 9  Inconsistencies of modern mathematics (1/8)
 Chapter 9  Inconsistencies of modern mathematics (2/8)
 Chapter 9  Inconsistencies of modern mathematics (3/8)
 Chapter 9  Inconsistencies of modern mathematics (4/8)
 Chapter 9  Inconsistencies of modern mathematics (5/8)
 Chapter 9  Inconsistencies of modern mathematics (6/8)
 Chapter 9  Inconsistencies of modern mathematics (7/8)
 Chapter 9  Inconsistencies of modern mathematics (8/8)

Part 4  Next stage of mathematics as a systemic field of thought
 Chapter 10  Calculus without limit (1/11)
 Chapter 10  Calculus without limit (2/11)
 Chapter 10  Calculus without limit (3/11)
 Chapter 10  Calculus without limit (4/11)
 Chapter 10  Calculus without limit (5/11)
 Chapter 10  Calculus without limit (6/11)
 Chapter 10  Calculus without limit (7/11)
 Chapter 10  Calculus without limit (8/11)
 Chapter 10  Calculus without limit (9/11)
 Chapter 10  Calculus without limit (10/11)
 Chapter 10  Calculus without limit (11/11)
 Chapter 11  New look at some of the historically important paradoxes (1/4)
 Chapter 11  New look at some of the historically important paradoxes (2/4)
 Chapter 11  New look at some of the historically important paradoxes (3/4)
 Chapter 11  New look at some of the historically important paradoxes (4/4)
 Chapter 12  An attempt to rebuild the system of mathematics (1/10)
 Chapter 12  An attempt to rebuild the system of mathematics (2/10)
 Chapter 12  An attempt to rebuild the system of mathematics (3/10)
 Chapter 12  An attempt to rebuild the system of mathematics (4/10)
 Chapter 12  An attempt to rebuild the system of mathematics (5/10)
 Chapter 12  An attempt to rebuild the system of mathematics (6/10)
 Chapter 12  An attempt to rebuild the system of mathematics (7/10)
 Chapter 12  An attempt to rebuild the system of mathematics (8/10)
 Chapter 12  An attempt to rebuild the system of mathematics (9/10)
 Chapter 12  An attempt to rebuild the system of mathematics (10/10)
 Afterword  A systemic yoyomodel prediction
 Part 5  Appendices: A close look at the systemic yoyo model
 Bibliography (1/2)
 Bibliography (2/2)
 Back Cover
Product information
 Title: A Systemic Perspective on Cognition and Mathematics
 Author(s):
 Release date: February 2013
 Publisher(s): CRC Press
 ISBN: 9780203487327
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