Abstract
There is not the least justification for indiscriminate use of the word ‘probability’ for any statistically estimated frequency of behavior. The task of a general theory of probability can only consist of making important methods known; the establishment of generally applicable methods is nothing to strive for. We should take into account not only frequencies, but also the groupings which can be made of cases. One may try to tie a series of phenomena to the behavior of a game of chance, but so often this leads to unsatisfactory results – especially if circumstances of observation change over time. If observation of a sufficiently large number of series produces a non-normal dispersion, we should conclude that the phenomena do not behave on analogy to games of chance. That is to say, some questions about the enduring or constant circumstances of phenomena can be answered empirically.
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Notes
- 1.
Compare, for example, the experiments on coin-tosses reported by Jevons (Principles of Science, p. 208). [Jevons, W.S. (1874). The principles of science: A treatise on logic and scientific method. London: Macmillan and Co.]
- 2.
On this point, see Lexis, Zur Theorie der Massenerscheinung in der menschlichen Gesellschaft. [Lexis, W. (1877). Zur Theorie der Massenerscheinung in der menschlichen Gesellschaft. Freiburg i. B.: Fr. Wagner.]
- 3.
Compare the rules for determining a posteriori probability in Laplace, Théorie analytique des probabilités, Book 2, Chapters 1 and 6; Lacroix, Traité élémentaire du calcul des probabilités, p. 134; Meyer, Vorlesungen über Wahrscheinlichkeits-Rechnung, pp. 176 and 179, etc. Even Poisson’s much more involved theory only appears to be distinct from the simpler common theories. Basically, for them the chances assigned to individual cases are basically composed of several random judgments. The constancy of general conditions and the independence of individual cases are still assumed to be self-evident. [Laplace, P.-S. (1812). Théorie analytique des probabilités. Paris: Courcier.; Lacroix, S.-F. (1816). Traité élémentaire du calcul des probabilités. Paris: Courcier.; Meyer, A. (1879). Vorlesungen über Wahrscheinlichkeitsrechnung. Leipzig: B.G. Teuber (E. Czuber, Trans.)].
- 4.
Op. cit. Chapter 6.
- 5.
« La probabilité de la plupart des évènements simples est inconnue; en la considérant a priori elle nous paraît susceptible de toutes les valeurs comprises entre zéro et l’unité; mais si l’on a observé un résultat composé de plusieurs des ces évènements, la manière, dont ils y entrent, rend quelques unes de ces valeurs plus probables que les autres. Ainsi à mesure que le résultat observé se compose par le développement des évènements simples, leur vraie possibilité se fait de plus en plus connaître et il devient de plus en plus probable qu’elle tombe dans des limites qui, se resserrant sans cesse, finiraient par coincider, si le nombre des évènements simples devenait infini. Pour déterminer les lois, suivant lesquelles cette possibilité se découvre etc. »
- 6.
Following Lexis, it is this way of thinking according to which certain series are called ‘problematic’.
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Niall, K.K. (2023). Establishing and Justifying Probability Statements. In: Johannes von Kries: Principles of the Probability Calculus. Studies in History and Philosophy of Science, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-031-36506-5_6
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