Издательство CRC Press, 2013, -434 pp.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.Part 1 Basics
Where everything starts
Elementary properties of systemic yoyos
Part 2 The mind
Human body as a system
The four human endowments
Character and thought
Part 3 Mathematics seen as a systemic flow: A case study
A brief history of mathematics
Actual and potential infinities
Are actual and potential infinity the same?
Inconsistencies of modern mathematics
Part 4 Next stage of mathematics as a systemic field of thought
Calculus without limit
New look at some historically important paradoxes
An attempt to rebuild the system of mathematics
A systemic yoyo model prediction
Appendices: A close look at the systemic yoyo model
A Theoretical foundation of the yoyo model
B Empirical evidence of the yoyo model
