Johannes von Kries: Principles of the Probability Calculus

This book provides an English translation of the work Principles of the Probability Calculus published in 1886 by Johannes von Kries, which discusses the range theory of probability. It offers a novel account of the foundations of probability, an account which was familiar to Keynes, Kneale, Weber, Reichenbach, and von Mises. This account dispenses with the principle of indifference in probability, and it introduces the method of arbitrary functions. Confusions in the history of probability are pinpointed, and a novel theory is developed in which probability is neither entirely subjective nor objective. The book develops what is known as the range theory or Spielraum theory in detail, in a narrative way using few formulas. Von Kries applies range theory to Boltzmann’s theory of the statistical behaviour of gases, and to several applications in medical statistics. Many uses of probability are found wanting; very often they are found not to admit any expression of probability in numbers at all. The book will be of first interest to philosophers of science and historians interested in the foundations of probability. It is also of general interest to anyone who applies statistics everyday in such fields as econometrics, psychology, or medicine.

Keith K. Niall is the Editor and Translator of the Springer book: Erwin Schrödinger’s Color Theory (ISBN: 978-3-319-64619-0), as well as the Editor of the Springer book Vision and Displays for Military and Security Applications (ISBN: 978-1-4419-1722-5), which was subsequently translated for the National Defense Industry Press in Beijing (ISBN: 978-7-118-09146-5). Earlier he translated an 1882 article by Johannes von Kries on psychophysics: ‘Über die Messung intensiver Grössen und über das sogenannte psychophysische Gesetz.’ He was a Defence Scientist with Defence Research & Development Canada (DRDC Toronto), serving as an Exchange Scientist to the Air Force Research Laboratory (Mesa, Arizona), and as First Secretary within the Canadian Defence Liaison Staff (Washington) at the Canadian Embassy to the USA. He received his Ph.D. from McGill University in 1988, and pursued postdoctoral studies at Queen’s University (Kingston, Ontario) and the Defence and Civil Institute of Environmental Medicine. He has written on topics of the application of projective geometry to problems of visual form perception, on concerns with the phenomenon known as the mental rotation effect, on the perception of distance with night vision devices, and on a flexible micromirror display for high-resolution display projection.