Considerations on probability: from games of chance to modern science
Keywords:History of probability, Definitions of Probability, P. S. Laplace, B. De Finetti
AbstractThe article sets out a number of considerations on the distinction between variability and uncertainty over the centuries. Games of chance have always been useful random experiments which through combinatorial calculation have opened the way to probability theory and to the interpretation of modern science through statistical laws. The article also looks briefly at the stormy nineteenth-century debate concerning the definitions of probability which went over the same grounds – sometimes without any historical awareness – as the debate which arose at the very beginnings of probability theory, when the great probability theorists were open to every possible meaning of the term.
L. BOLTZMANN (1905). Populare Schriften. Barth, Leipzig.
M. BUNGE (1981). Four concepts of probability. Appl. Math. Modell., 5.
R. CARNAP (1950). Logical Foundation of Probability. Chicago.
F.N. DAVID (1962). Games, God and Gambling. C. Griffin & Co, London.
B. DE FINETTI (1931). Sul signicato soggettivo della probabilit a. English translation in Probabilità e induzione. Scritti scelti a cura di P. Monari e D. Cocchi in Statistica, LII, Supplemento al n.3, Clueb, Bologna, 1992.
C. GINI (1911). Considerations on a posteriori probability. English translation in Statistica e induzione, Scritti scelti a cura di P. Monari e D. Cocchi in Statistica, LII, Supplemento al n.1, Clueb, Bologna, 2001.
C. GINI (1964). The inductive applications of probability theory. English translation in Statistica e induzione, Scritti scelti a cura di P. Monari e D. Cocchi in Statistica, LII, Supplemento al n.1, Clueb, Bologna, 2001.
I. HACKING (1975). The Emergence of Probability. Cambridge University Press.
C. G. HEMPEL (1952). Fundamentals of Concept Formation in Empirical Science. Chicago Universit Press.
C. G. HEMPEL (1966). Philosophy of Natural Science. Englewood Cliffs, N.J., Prentice-Hall.
P. S. LAPLACE (1814). Essai philosophique sur les probabilits. Gautier-Villard,Paris. D. V. Lindley (1987), The probability approach to the treatment of uncertainty in Artificial Intelligence and expert System, Stat. Sciences, 21.
P. MONARI (2005). The concept of measure, from Plato to modern statistics. Art of living or intellectual principle?. Statistica, LXV, 3.
P. MONARI (2014). The semantic role of variability in the developmente of statistical thought. In Statistical Methods and Applications from Historical Perspective, Springer, Heidelberg.
J. PIAGET (1947). The Psychology of Intelligence. Routledge and Kegan Paul, 1951. First published as La psychologie de l’intelligence, 1947.
J. PIAGET (1955). The Growth of Logical Thinking from Childhood to Adolescence. New York, Basic Books, 1958. First published as De la logique de l’enfant à la logique de l’adolescent , 1955.
S. D. POISSON (1837). Recherches sur la probabilit des jugements en matire civile, prcdes des rgles gnrales du calcul des probabilits. Bachelier, Paris.
K. POPPER (1934). The Logic of Scientific Discovery. Routledge. First English Ed., Hutchinson, 1959. First published as Logik Der Forschung in Wien, Springer, 1934.
T. M. PORTER (1986). The rise of statistical thinking 1820-1900. Princeton Un. Press.
L. J. SAVAGE (1954). The foundation of statistics. Wiley, New York.
I. SCARDOVI (1982). The idea of chance in the statistical intuition of natural variability. Genus, 38, 3-4.
I. SCARDOVI (1988). Ambiguous uses of probability. In E. Agazzi (Ed.) Probability in the Science, Kluwer Academic Publisher, Dordrecht, 51-66.
D. J. SPIEGELHALTER, R. COWELL (1992). . Learning in Probabilistic expert systems, in J.M.Bernardo e al. (eds)Bayesian Statistics 4, Oxford University Press.
S. M. STIGLER (1986). The History of Statistics: the measurement of uncertainty before 1900. Harvard University Press, Cambridge, Mass.
J. VON NEUMANN, O. MORGENSTERN (1944). Theory of Games and economic behaviour, Princeton Univ. Press.