On Probability (1950-1974)

"It is never possible to predict a physical occurrence with unlimited precision." (Max Planck, "The Meaning of Causality in Physics", 1953)

"The epistemological value of probability theory is based on the fact that chance phenomena, considered collectively and on a grand scale, create non-random regularity." (Andrey Kolmogorov, "Limit Distributions for Sums of Independent Random Variables", 1954)

"Just as in applied statistics the crux of a problem is often the devising of some method of sampling that avoids bias, our problem is that of finding a probability assignment which avoids bias, while agreeing with whatever information is given. The great advance provided by information theory lies in the discovery that there is a unique, unambiguous criterion for the 'amount of uncertainty' represented by a discrete probability distribution, which agrees with our intuitive notions that a broad distribution represents more uncertainty than does a sharply peaked one, and satisfies all other conditions which make it reasonable." (Edwin T Jaynes, "Information Theory and Statistical Mechanics" I, 1956)

"Starting from statistical observations and applying to them a clear and precise concept of probability it is possible to arrive at conclusions which are just as reliable and ‘truth-full’ and quite as practically useful as those obtained in any other exact science." (Richard von Mises, "Probability, Statistics, and Truth" 2nd Ed., 1957)

"Probability is a mathematical discipline with aims akin to those, for example, of geometry or analytical mechanics. In each field we must carefully distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, (c) the applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation." (William Feller, "An Introduction to Probability Theory and Its Applications", 1957)

"Everybody has some idea of the meaning of the term 'probability' but there is no agreement among scientists on a precise definition of the term for the purpose of scientific methodology. It is sufficient for our purpose, however, if the concept is interpreted in terms of relative frequency, or more simply, how many times a particular event is likely to occur in a large population." (Alfred R Ilersic, "Statistics", 1959)

"The mathematician, the statistician, and the philosopher do different things with a theory of probability. The mathematician develops its formal consequences, the statistician applies the work of the mathematician and the philosopher describes in general terms what this application consists in. The mathematician develops symbolic tools without worrying overmuch what the tools are for; the statistician uses them; the philosopher talks about them. Each does his job better if he knows something about the work of the other two." (Irvin J Good, "Kinds of Probability", Science Vol. 129, 1959)

"The practical power of a statistical test is the product of its’ statistical power and the probability of use." (John W Tukey, A Quick, "Compact, Two Sample Test to Duckworth’s Specifications", 1959)

"In its efforts to learn as much as possible about nature, modem physics has found that certain things can never be ‘known’ with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities." (Richard P Feynman, "The Feynman Lectures on Physics", 1964)

"The probability concept used in probability theory has exactly the same structure as have the fundamental concepts in any field in which mathematical analysis is applied to describe and represent reality." (Richard von Mises, "Mathematical Theory of Probability and Statistics", 1964)

"After all, without the experiment - either a real one or a mathematical model - there would be no reason for a theory of probability." (Thornton C Fry, "Probability and Its Engineering Uses", 1965)

"The statistician has no magic touch by which he may come in at the stage of tabulation and make something of nothing. Neither will his advice, however wise in the early stages of a study, ensure successful execution and conclusion. Many a study, launched on the ways of elegant statistical design, later boggled in execution, ends up with results to which the theory of probability can contribute little." (W Edwards Deming, "Principles of Professional Statistical Practice", Annals of Mathematical Statistics, 36(6), 1965)

"[I]n probability theory we are faced with situations in which our intuition or some physical experiments we have carried out suggest certain results. Intuition and experience lead us to an assignment of probabilities to events. As far as the mathematics is concerned, any assignment of probabilities will do, subject to the rules of mathematical consistency." (Robert Ash, "Basic probability theory", 1970)

"Probability theory, for us, is not so much a part of mathematics as a part of logic, inductive logic, really. It provides a consistent framework for reasoning about statements whose correctness or incorrectness cannot be deduced from the hypothesis. The information available is sufficient only to make the inferences 'plausible' to a greater or lesser extent." (Ralph Baierlein, "Atoms and Information Theory: An Introduction to Statistical Mechanics", 1971)

"[...] we will adopt the broad view and will take 'probability', to be a quantitative relation, between a hypothesis and an inference, corresponding to the degree of rational belief in the correctness of the inference, given the hypothesis. The hypothesis is the information we possess, or assume for the sake of argument. The inference is a statement that, to a greater or lesser extent, is justified by the hypothesis. Thus 'the probability' of an inference, given a hypothesis, is the degree of rational belief in the correctness of the inference, given the hypothesis." (Ralph Baierlein, "Atoms and Information Theory: An Introduction to Statistical Mechanics", 1971)

"The relevant question is not whether ANOVA assumptions are met exactly, but rather whether the plausible violations of the assumptions have serious consequences on the validity of probability statements based on the standard assumptions." (Gene V Glass et al, "Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance", Review of Educational Research Vol. 42 (3), 1972)

"Since small differences in probability cannot be appreciated by the human mind, there seems little point in being excessively precise about uncertainty." (George E P Box & G C Tiao, "Bayesian inference in statistical analysis", 1973)