On Probability (1925-1949)

"Hypothesis, however, is an inference based on knowledge which is insufficient to prove its high probability." (Frederick L Barry, "The Scientific Habit of Thought", 1927) 

"The rational concept of probability, which is the only basis of probability calculus, applies only to problems in which either the same event repeats itself again and again, or a great number of uniform elements are involved at the same time. Using the language of physics, we may say that in order to apply the theory of probability we must have a practically unlimited sequence of uniform observations." (Richard von Mises, "Probability, Statistics and Truth", 1928)

"There can be no unique probability attached to any event or behaviour: we can only speak of ‘probability in the light of certain given information’, and the probability alters according to the extent of the information." (Sir Arthur S Eddington, "The Nature of the Physical World", 1928)

"With fuller knowledge we should sweep away the references to probability and substitute the exact facts." (Sir Arthur S Eddington, "The Nature of the Physical World", 1928)

"Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means." (Bertrand Russell, 1929)

"Thought interferes with the probability of events, and, in the long run therefore, with entropy." (David L Watson, 1930)

"When an observation is made on any atomic system that has been prepared in a given way and is thus in a given state, the result will not in general be determinate, i.e. if the experiment is repeated several times under identical conditions several different results may be obtained. If the experiment is repeated a large number of times it will be found that each particular result will be obtained a definite fraction of the total number of times, so that one can say there is a definite probability of its being obtained any time that the experiment is performed. This probability the theory enables one to calculate." (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)

"The theory of probability as a mathematical discipline can and should be developed from axioms in exactly the same way as geometry and algebra." (Andrey Kolmogorov, "Foundations of the Theory of Probability", 1933)

"Statistics is a scientific discipline concerned with collection, analysis, and interpretation of data obtained from observation or experiment. The subject has a coherent structure based on the theory of Probability and includes many different procedures which contribute to research and development throughout the whole of Science and Technology." (Egon Pearson, 1936)

"Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations. " (Richard von Mises, "Probability, Statistics, and Truth", 1939)

"The fundamental difference between engineering with and without statistics boils down to the difference between the use of a scientific method based upon the concept of laws of nature that do not allow for chance or uncertainty and a scientific method based upon the concepts of laws of probability as an attribute of nature." (Walter A Shewhart, 1940)

"Events with a sufficiently small probability never occur, or at least we must act, in all circumstances, as if they were impossible." (Félix E Borel, "Probabilities and Life", 1943)

"Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation." (Emile Borel, "Probabilities and Life", 1943)

"The conception of chance enters in the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception that causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation." (Max Born, 1949)