This book aims to provide scientists and engineers, and those interested in scientific issues, with a concise account of how the nature of scientific knowledge evolved from antiquity to a seemingly final form in the Twentieth Century that now strongly limits the knowledge that people would like to gain in the Twenty-first Century. Some might think that such issues are only of interest to specialists in epistemology (the theory of knowledge); however, today's major scientific and engineering problems-in biology, medicine, environmental science, etc.-involve enormous complexity, and it is precisely this complexity that runs up against the limits of what is scientifically knowable. To understand the issue, one must appreciate the radical break with antiquity that occurred with the birth of modern science in the Seventeenth Century, the problems of knowledge and truth engendered by modern science, and the evolution of scientific thinking through the Twentieth Century. The book concludes by considering the impact of scientific uncertainty on the translation of scientific knowledge into means to alter the course of Nature- that is, the effect of uncertainty in engineering. It proposes a course of action based on integrating existing partial knowledge with limited data to arrive at an optimal operation on some system, where optimality is conditioned on the uncertainty regarding the system. As for a new scientific epistemology in which valid knowledge can be defined, that awaits the bold efforts of fertile minds enriched with the mathematical, scientific, and philosophic education required for such a quest.