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Non-additive probabilities in the work of Bernoulli and Lambert. (English) Zbl 0392.01010

MSC:
01A45 History of mathematics in the 17th century
01A50 History of mathematics in the 18th century
60-03 History of probability theory
Biographic References:
Bernoulli, Jacob; Lambert, Johann Heinrich
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[1] Anon. (1699), A Calculation of the Credibility of Human Testimony, Phil. Trans. Roy. Soc. London, 21, 359-365.
[2] Arnauld, Antoine, & Pierre Nicole (1662), la Logique, ou l’art de penser, Paris.
[3] Bayes, Thomas (1764), An essay towards solving a problem in the doctrine of chances, Phil. Trans. Roy. Soc. London for 1763, 53, 370-418. Reprinted in Biometrika 45, 293-315 (1958), and in Pearson & Kendall, eds. · Zbl 1250.60007 · doi:10.1098/rstl.1763.0053
[4] Beran, Rudolph (1970) Upper and Lower risks and Minimax Procedures, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, pp. 1-16.
[5] Bernoulli, Daniel (1778), Dijudicatio maxime probabilis plurium observationum discrepantium atque verisimillima inductio inde formanda, Acta Acad. Petrop. for 1777, pars prior, 3-23. An English translation by G. D. Allen was published in Biometrika, 48, 1-18 (1961), and reprinted in Pearson & Kendall, eds.
[6] Bernoulli, Jacob (1713), Ars Conjectandi, Basel. Reprinted in 1968 by Culture et Civilisation, Brussels, and in 1975 in Vol. 3 of Die Werke von Jakob Bernoulli. Part IV has been translated into English by Bing Sung and issued as Technical Report No. 2 of the Department of Statistics of Harvard University (Feb. 12, 1966).
[7] Bernoulli, Jacob, Die Werke von Jakob Bernoulli, Basel. Volume 1, edited by J. O. Fleckenstein, appeared in 1969. Volume 3, edited by B. L. van der Waerden, appeared in 1975.
[8] Bernoulli, Nicolaus (1709), de Usu Artis conjectandi in jure, Basel. Reprinted in Vol. 3 of Die Werke von Jakob Bernoulli. Excerpts were published on pp. 159-170 of Vol. IV of Act. Eruditorum, Supplementa (1711).
[9] Biermann, Kurt-Reinhard, & Margot Faak (1957), G. W. Leibniz’ ?Die incerti aestimatione,? Forschungen und Fortschritte, 31, 45-50. · Zbl 0077.00708
[10] Boole, George (1854), An Investigation of the Laws of Thought on which are founded the Mathematical Theories of Logic and Probabilities, Macmillan, London. Reprinted in 1958 by Dover. · Zbl 1205.03003
[11] Brakel, J. Van (1976), Some Remarks on the Prehistory of the Concept of Statistical Probability, Archive for History of Exact Sciences, 16, 119-136. · Zbl 0358.60004 · doi:10.1007/BF00349634
[12] Byrne, Edmund F. (1968), Probability and Opinion; A Study in the Medieval Presuppositions of Post-Medieval Theories of Probability, Martinus Nijhoff, The Hague.
[13] Condorcet, Marie Jean (1785), Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Paris. Reprinted by Chelsea in 1973.
[14] Cournot, Antoine-Augustin (1843), Exposition de la théorie des chances et des probabilités, Paris. Reprinted by Edizioni Bizzari.
[15] Coutourat, Louis (1901), La Logique de Leibniz, Paris. Reprinted in 1961 by Georg Olms, Hildesheim.
[16] Craig, John (1699), Theologiae Christianae Principia Mathematica, London. The part dealing with probability was reprinted by Mouton in 1964 as Craig’s Rules of Historical Evidence, Beiheft 4 of History and Theory: Studies in the Philosophy of History.
[17] David, F. N. (1962), Games, Gods and Gambling, Griffin, London. · Zbl 0117.24603
[18] De Moivre, Abraham (1711), De Mensura Sortis, seu, de Probabilitate Eventum in Ludis a Casu Fortuito Pendentibus, Phil. Trans. Roy. Soc. London, 27, 213-264.
[19] De Moivre, Abraham (1718), The Doctrine of Chances, or a Method of Calculating the Probability of Events in Play, London.
[20] Dempster, A. P. (1966), New methods for reasoning towards posterior distributions based on sample data. Ann. Math. Statist., 37, 355-374. · Zbl 0178.54302 · doi:10.1214/aoms/1177699517
[21] Dempster, A. P. (1967), Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Statist., 38, 325-339. · Zbl 0168.17501 · doi:10.1214/aoms/1177698950
[22] Dempster, A. P. (1967a), Upper and lower probability inferences based on a sample from a finite univariate population, Biometrika, 54, 515-528.
[23] Dempster, A. P. (1968), Upper and lower probabilities generated by a random closed interval, Ann. Math. Statist., 39, 957-966. · Zbl 0251.62010 · doi:10.1214/aoms/1177698328
[24] Dempster, A. P. (1968a), A generalization of Bayesian inference (with discussion), J. Roy. Statist. Soc. Ser. B, 30, 205-247. · Zbl 0169.21301
[25] Dempster, A. P. (1968b), Probability (Chapter 2 of The Theory of Statistical Inference: A Critical Analysis). Research Report S-3, Department of Statistics, Harvard University, September 27, 1968.
[26] Dempster, A. P. (1969), Upper and lower probability inferences for families of hypotheses with monotone density ratios, Ann. Math. Statist., 40, 953-969. · Zbl 0211.50204 · doi:10.1214/aoms/1177697600
[27] Dempster, A. P. (1974), Discussion of a paper by A. W. F. Edwards, pp. 57-58 of Memoirs No. 1 of the Dept. of Theoretical Statistics, Aarhus; Barndorff-Nielsen, Blaesild & Schou, eds.
[28] Diderot, Denis, et al. (1765), Encyclopédie, ou Dictionnaire raisonné des sciences, des arts et des métiers, Paris.
[29] Eisenring, M. E. (1942), Johann Heinrich Lambert und die wissenschaftliche Philosophie der Gegenwart, Zürich.
[30] Fermat, Pierre de, Oeuvres, ed. by P. Tannery & C. Henry, Paris, 4 vols., 1891-1922.
[31] Fine, Terry (1973), Theories of Probability, Academic Press. · Zbl 0275.60006
[32] Fontenelle, Bernard (1706), Eloge de Jacques Bernoulli, Histoire de l’Académie royale des sciences, Volume for 1705, pp. 148-149.
[33] Giles, Robin (1976), A Logic for Subjective Belief, in Harper & Hooker, eds., Vol. I, pp. 41-72. · Zbl 0323.02043
[34] Good, I. J. (1962), The Measure of a Non-measurable Set, in Logic, Methology and Philosophy of Science (edited by Ernest Nagel, Patrick Suppes & Alfred Tarski), pp. 319-329, Stanford University Press. · Zbl 0192.02104
[35] Granger, Thomas (1620), Divine Logike, London.
[36] Hacking, Ian (1975), The Emergence of Probability, Cambridge University Press, London. · Zbl 0311.01004
[37] Hailperin, Theodore (1976), Boole’s Logic and Probability, North-Holland, Amsterdam. · Zbl 0352.02002
[38] Harper, W. L., & Hooker, C. A., eds. (1976), Foundatións of Probability Theory, Statistical Inference, and Statistical Theories of Science, Reidel, Dordrecht. · Zbl 0311.00019
[39] Henny, Julian (1975), Niklaus und Johann Bernoullis Forschungen auf dem Gebiet der Wahrscheinlichkeitsrechnung in ihrem Briefwechsel mit Pierre Rémond de Montmort, pp. 457-507 of Vol. 3 of Die Werke von Jakob Bernoulli.
[40] Hofmann, Joseph E. (1974), Leibniz in Paris 1672-1676; His Growth to Mathematical Maturity, Cambridge University Press. · Zbl 0281.01004
[41] Huber, Peter (1973), The use of Choquet capacities in statistics, Bulletin of the International Statistical Institute, Vol. XLV, Book 4, pp. 181-188.
[42] Huygens, Christiaan, Oeuvres complètes, The Hague, 22 vols., 1888-1950.
[43] Huygens, Christiaan (1657), De ratiociniis in aleae ludo, in Exercitionum Mathematicorum, ed. F. van Schooten, Amsterdam. Incorporated into Part I of Bernoulli’s Ars Conjectandi. The original Dutch version, published in 1660, is in Vol. XIV of the Oeuvres complètes.
[44] Kendall, M. G. (1951), The beginnings of a probability calculus, Biometrika, 43, 1-14. Reprinted in Pearson & Kendall, eds. · Zbl 0070.36101
[45] Kohli, Karl, & B. L. van der Waerden (1975), Bewertung von Leibrenten, pp. 515-539 of Vol. 3 of Die Werke von Jakob Bernoulli.
[46] Kohli, Karl (1975a), Zur Publikationsgeschichte der Ars Conjectandi, pp. 391-401 of Vol. 3 of Die Werke von Jakob Bernoulli.
[47] Kohli, Karl (1975b), Spieldauer: Von Jakob Bernoullis Lösung der fünften Aufgabe von Huygens bis zu den Arbeiten von de Moivre, pp. 403-455 of Vol. 3 of Die Werke von Jakob Bernoulli.
[48] Kohli, Karl (1975c), Aus dem Briefwechsel zwischen Leibniz und Jakob Bernoulli, pp. 509-513 of Vol. 3 of Die Werke von Jakob Bernoulli.
[49] Koopman, Bernard O. (1940), The Bases of Probability, Bulletin of the American Mathematical Society, Vol. 46, pp. 763-774. · Zbl 0024.05002 · doi:10.1090/S0002-9904-1940-07294-5
[50] Kyburg, Henry E. (1961), Probability and the Logic of Rational Belief, Wesleyan University Press, Middletown.
[51] Lambert, Johann Heinrich (1764) Neues Organon, oder Gedanken über die Erforschung und Bezeichnung des Wahren und dessen Unterscheidung Von Irrtum und Schein, Leipzig. Reprinted in 1965 by Olms of Hildesheim as the first two volumes of Lambert’s Philosophische Schriften.
[52] Laplace, P.S. (1774), Mémoire sur la probabilité des causes par évènements. Mém. Acad. Sci. Sav. Etranger 6, 621-656, Oeuvres complètes 8, 27-65.
[53] Laplace, Pierre Simon (1814), Théorie analytique des probabilités, 2nd edition, Paris.
[54] Laplace, Pierre Simon, Oeuvres complètes, Paris, 14 vols., 1878-1912.
[55] Leibniz, Gottfried Wilhelm (1669), De conditionibus, Leipzig. Reprinted by Dutens, Vol. IV, Part III, pp. 148ff.
[56] Leibniz, Gottfried Wilhelm, Opera Omnia, L. Dutens, ed., Geneva, 6 vols., 1768.
[57] Leibniz, Gottfried Wilhelm, Mathematische Schriften, ed. C.I. Gerhardt, Halle, 7 vols., 1849-63.
[58] Lewis, Geneviève (1952), Lettres de Leibniz à Arnauld, Paris.
[59] Locke, John (1690), An Essay Concerning Human Understanding, London.
[60] Locke, John (1936), An Early Draft of Locke’s Essay, R.I. Aaron & J. Gibb, eds., Oxford.
[61] Montmort, Pierre Rémond de (1708), Essay d’analyse sur les jeux de hazard, Paris. · Zbl 0476.60001
[62] Ore, Oystein (1953), Cardano, the Gambling Scholar, Princeton University Press. Includes Gould’s translation of Cardano’s de Ludo Aleae.
[63] Pearson, E.S., & M.G. Kendall, eds. (1970), Studies in the History of Statistics and Probability, Hafner, Darien. · Zbl 0206.17902
[64] Poisson, Siméon-Denis (1837), Recherches sur la probabilité des jugements en matière criminelle et en matière civile, précédées des règles générales du calcul des probabilités, Paris.
[65] Prevost, Pierre, & Simon Lhuilier (1800), Mémoire sur l’application du Calcul des probabilités à la valeur du témoignage, Mémoires de l’Académie Royal des Sciences et Belles Lettres à Berlin, Volume for 1797, 120-152.
[66] Ravier, Emile (1937), Bibliographie des Oeuvres de Leibniz, Paris. · JFM 63.0808.02
[67] Renyi, Alfred (1973), Letters on Probability, Wayne State University Press. · Zbl 0269.62011
[68] Saurin, Joseph (?) (1706), Eloge de Jacques Bernoulli, Journal des Sçavans, Tome 34, Part I, pp. 126-139.
[69] Schneider, Ivo (1968), Der Mathematiker Abraham de Moivre (1667-1754), Archive for History of Exact Sciences, 5, 258-300. · Zbl 0172.00601 · doi:10.1007/BF00411630
[70] Shafer, Glenn (1976), A Mathematical Theory of Evidence, Princeton University Press. · Zbl 0359.62002
[71] Shafer, Glenn (1976a), Review of Ian Hacking’s The Emergence of Probability, in Journal of the American Statistical Association, 71, 519-521. · doi:10.2307/2285346
[72] Shafer, Glenn (1976b), A Theory of Statistical Evidence, in Harper & Hooker eds., Vol. II, pp. 365-436. · Zbl 0326.62009
[73] Sheynin, O.B. (1971), J. H. Lambert’s Work on Probability, Archive for History of Exact Sciences, 7, 244-256. · Zbl 0263.01017 · doi:10.1007/BF00357218
[74] Smith, C.A.B. (1961), Consistency in statistical inference and decision (with discussion), J. Roy. Statist. Soc. Ser. B, 23, 1-25. · Zbl 0124.09603
[75] Smith, C.A.B. (1965), Personal probability and statistical analysis (with discussion), J. Roy. Statist. Soc. Ser. A, 128, 469-499. · doi:10.2307/2343466
[76] Stigler, Stephen M. (1975), Napoleonic Statistics: The Work of Laplace, Biometrika, 62, pp. 503-517. · Zbl 0315.01004
[77] Suppes, Patrick (1974), The measurement of belief, J. Roy. Statist. Soc. Ser. B, 36, 160-175. · Zbl 0287.60007
[78] Todhunter, Isaac (1865), A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace, Cambridge. Reprinted in 1949 by Chelsea. · JFM 06.0041.03
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