While probability theory is generally thought of as a branch of mathematics, its foundations are purely philosophic, and Richard von Mises, in his great work Probability, Statistics, and Truth, developed the correct, objective, or "frequency" theory of probability.
what the fraction means is this: if the die is not loaded, and if it is thrown a very large number of times, it will tend asymptotically to come up as a two one-sixth of the time. And the only way you can really make sure that the die is not loaded, i.e., that the two-spot will come up one-sixth of the time is to make the very large number of throws.
Hence, it is scientifically meaningless to say that the "probability of Jerry Ford being elected in 1976 is three-eighths," since elections are not homogeneous events repeated a large number of times. And yet a large amount of modern social science and of its mathematizing rests on this faulty view of probability theory.
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