Probability likelihood and quantity of information in the logic of uncertain inference
Ronald Aylmer Fisher · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1934
Abstract In a previous paper H. Jeffreys put forward a method of obtaining the distribution a priori of the precision constant of a hypothetical normal distribution, by means of the principle that if three independent observations are made in succession, from a continuous distribution of any form, the probability that the third observation shall fall between the first two must be one-third (p. 48): "Two measures are made. What is the probability that the third observation will lie between them? The answer is easily seen to be one-third." This proposition, in the form in which Jeffreys states it as the foundation for his deductions, is ambiguous, and may bear one of two distinct meanings, one true and the other demonstrably false. The proposition may mean.