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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.