CRC Press A Systemic Perspective on Cognition and Mathematics (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. About the Author Dr. Jeffrey Yi-Lin Forrest, also known as Yi Lin, holds all his educational degrees (BS, MS, and PhD) in pure mathematics from Northwestern University (China) and Auburn University (USA) and had one year of postdoctoral experience in statistics at Carnegie Mellon University (USA). Currently, he is a guest and specially appointed professor in economics, finance, systems science, and mathematics at several major universities in China, including Huazhong University of Science and Technology, National University of Defense Technology, Nanjing University of Aeronautics and Astronautics, and a tenured professor of mathematics at the Pennsylvania State System of Higher Education (Slippery Rock campus). Since 1993, he has been serving as the president of the International Institute for General Systems Studies, Inc. Along with various professional endeavors he organized, Dr. Forrest has had the honor to mobilize scholars from over 80 countries representing more than 50 different scientific disciplines. Over the years, he has served on the editorial boards of 11 professional journals, including Kybernetes: The International Journal of Cybernetics, Systems and Management Sciences, Journal of Systems Science and Complexity, International Journal of General Systems, and Advances in Systems Science and Applications. And, he is the editor of the book series entitled "Systems Evaluation, Prediction and Decision-Making", and the editor of the book series “Communications in Cybernetics, Systems Science and Engineering”, both published by Taylor and Francis with the former since 2008 and the latter since 2011. Some of Dr. Forrest’s research was funded by the United Nations, the State of Pennsylvania, the National Science Foundation of China, and the German National Research Center for Information Architecture and Software Technology. Professor Jeffrey Forrest’s professional career started in 1984 when his first paper was published. His research interests are mainly in the area of systems research and applications in a wide-ranging number of disciplines of the traditional science, such as mathematical modeling, foundations of mathematics, data analysis, theory and methods of predictions of disastrous natural events, economics and finance, management science, philosophy of science, etc. As of the end of the summer of 2013, he had published over 300 research papers and over 40 monographs and edited special topic volumes by such prestigious publishers as Academic Press, Elsevier, Kluwer Academic, Springer, Taylor and Francis, Wiley, World Scientific, and others.