The History of Probability Theory

  • Anthony J. M. Garrett
Part of the Fundamental Theories of Physics book series (FTPH, volume 98)


An outline is given, essentially from the Bayesian point of view, of the history of probability. Because probability theory is mathematical today, histories have tended to suppose it began with the first deeply mathematical exchange, between Pascal and Fermat in the 17th century. In fact Pascal and Fermat simply led the translation of pre-existing ideas into mathematics. Special attention is paid to where these ideas came from in the prehistory of quantitative probability theory. There are acknowledged sources in philosophy but the strongest connection is with law, through the notion of the extent to which guilt is implied by evidence.

Key words

probability induction inductive logic history 


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  1. Aristotle, d. 322BC. The Art of Rhetoric. The Greek, side by side with a modern English translation, by J.H. Freese, can be found in the corresponding volume of the Loeb Classical Library, Heinemann, London, UK, 1926. Aristotle’s Rhetoric was finalised in the last thirteen years of his life in Athens, and reads like lecture notes.Google Scholar
  2. Aristotle, d. 322BC. Prior Analytics. The Greek, side by side with a modern English translation, by H. Tredennick, can be found in the corresponding volume of the Loeb Classical Library, Heinemann, London, UK, 1938.Google Scholar
  3. Arnauld, A. & Nicole, P. 1662. La Logique, ou l’Art de Penser. Charles Savreux, Paris, France. The ‘Port-Royal Logic’. English translation of the fifth edition by T.S. Baynes, second edition published by Sutherland & Knox, Edinburgh, UK, 1851.Google Scholar
  4. Augustine of Hippo, d. 430. Complete works: Patrologiae Cursus Completus (Latin series), volumes 32–46, editor J.-P. Migne, Paris, France, 1842–45. English translation by M. Dods, T. & T. Clark, Edinburgh, UK, 1871–76.Google Scholar
  5. Baldus de Ubaldis. (d. 1400) 1586. Opera (nine volumes), apud Iuntas, Venice.Google Scholar
  6. Bayes, T. 1763. An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society 53, 370–418. Reprinted in: Studies in the History of Statistics and Probability, editors E.S. Pearson & M.G. Kendall. Griffin, London, UK, 1970.CrossRefGoogle Scholar
  7. Bellhouse, D.R. 1988. Probability in the sixteenth and seventeenth centuries: an analysis of Puritan casuistry. International Statistical Review 56, 63–74.zbMATHCrossRefGoogle Scholar
  8. Bellhouse, D.R. & Franklin, J. 1997. The language of chance. International Statistical Review 65, 73–85.zbMATHCrossRefGoogle Scholar
  9. Bernoulli, J. 1713. Ars Conjectandi. Thurnisiorum, Basle, Switzerland.Google Scholar
  10. Bernstein, P.L. 1996. Against the Gods: the Remarkable Story of Risk. Wiley, New York, USA.Google Scholar
  11. Boltzmann, L. 1868. Studien über das Gleichgewicht der lebendige Kraft zwischen bewegten materiellen Punkten. Sitzungsberichte der kaiserliche Akademie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Klasse IIa 58, 517–560.Google Scholar
  12. Boole, G. 1854. An Investigation of the Laws of Thought. Macmillan, London, UK.Google Scholar
  13. Byrne, E.F. 1968. Probability and Opinion: a Study in the Medieval Presuppositions of Post-Medieval Theories of Probability. Martinus NijhofT, The Hague, Netherlands.Google Scholar
  14. Cardano, G. 1663. De Ludo Aleae. In: Opera Omnia, cura Caroli Sponii, Lyons, France, volume 1. Cardano was a popular lecturer in his time but publication is a century later. An English translation is included in Ø. Ore, Cardano, the Gambling Scholar, Princeton University Press, Princeton, New Jersey, USA, 1953.Google Scholar
  15. Cochrane, C.N. 1944. Christianity and Classical Culture: A Study of Thought and Action from Augustus to Augustine. Oxford University Press, Oxford, UK.Google Scholar
  16. Cox, R.T. 1946. Probability, frequency and reasonable expectation. American Journal of Physics 14, 1–13.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Crombie, A.C. 1994. Styles of Thought in the European Tradition (three volumes). Duckworth, London, UK.Google Scholar
  18. Euler, L. (d. 1783) 1923. Opera Omnia, series prima: opera mathematica, editors F. Rudio, A. Krazer & P. Stäckel, volume 7: Theory of Combinatorics and Probability (volume editor: L. du Pasquier), published for Societatis Scientiarum Naturalium Helveticae by B. Teubner, Leipzig, Germany (volume 1: 1911).Google Scholar
  19. Fermat, P. de. 1654. Correspondence with Pascal. In: Oeuvres de Fermat, editors P. Tannery & C. Henry, Gauthier-Villars, Paris, France, volume 2 (1894), pp.288–331. (The letters of Pascal are included.) English translation in Games,Gods and Gambling by F.N. David, Griffin, London, UK, 1962, pp.229–253. Also set out in Pascal (1654).Google Scholar
  20. Franklin, J. 1991. The ancient legal sources of seventeenth century probability. In: The Uses of Antiquity, editor S. Gaukroger, Kluwer, Dordrecht, Netherlands, pp.123–144 & 251.CrossRefGoogle Scholar
  21. Galilei, Galileo. 1623. II Saggiatore [The Assayer.] In: Le Opere di Galileo Galilei, edizione nazionale, editor A. Favaro, Barbèra, Florence, Italy, volume 6 (1896). The quote is on p.232, lines 11–15. English translation in: The Controversy on the Comets of 1618, editors and translators S. Drake & CD. O’Malley, University of Pennsylvania Press, Philadelphia, Pennsylvania, USA, 1960; the quote is on pp. 183–4.Google Scholar
  22. Garber, D. & Zabell, S. 1979. On the emergence of probability. Archive for History of Exact Sciences 21, 33–53.MathSciNetzbMATHCrossRefGoogle Scholar
  23. Gibbs, J.W. 1874–8. On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy of Arts and Sciences 3,108–248 & 343–524. Reprinted in: The Collected Works of J. Willard Gibbs, Longmans Green, New York, USA, 1928, volume 1.Google Scholar
  24. Gibbs, J.W. 1902. Elementary Principles in Statistical Mechanics. Yale University Press, New Haven, Connecticut, USA.zbMATHGoogle Scholar
  25. Grandy, W.T., Jr. 1987–8. Foundations of Statistical Mechanics, Volume I: Equilibrium Theory (1987), Volume II: Nonequilibrium Phenomena (1988). Reidel, Dordrecht, Netherlands.zbMATHGoogle Scholar
  26. Graunt, J. 1662. Natural and Political Observations Mentioned in a Following Index, and Made upon the Bills of Mortality. Printed by T. Roycroft for J. Martin, J. Allestry & T. Dicas, London, England. (Books were often then available from a single outlet only.) Reprinted in Natural and Political Observations Made upon the Bills of Mortality by John Graunt, editor W.F. Willcox, Johns Hopkins Press, Baltimore, Maryland, USA, 1939. The fifth and definitive edition (published by J. Martyn, London, 1676) is reprinted in The Economic Writings of Sir William Petty, volume II, editor C.H. Hull, Cambridge University Press, Cambridge, UK; reprinted by Kelley, New York, USA, 1963–4. Petty was closely involved with Graunt.Google Scholar
  27. Hacking, I. 1975. The Emergence of Probability. Cambridge University Press, Cambridge, UK.zbMATHGoogle Scholar
  28. Hume, D. 1739–40. A Treatise of Human Nature. Originally published in three volumes: volumes 1 & 2 published by John Noon, London, England, 1739; volume 3 by Thomas Longman, London, 1740. The anti-induction material occupies volume I, part III (Of knowledge and probability). The work is seldom out of print: a recent single-volume edition is published by Penguin, London, UK, 1985.Google Scholar
  29. Hume, D. 1748. An Enquiry Concerning the Human Understanding. A. Millar, London, England. The original title was Philosophical Essays Concerning Human Understanding. The anti-induction material occupies sections (essays) IV, V. The work is seldom out of print: a recent printing (of the third edition) is by Oxford University Press, Oxford, UK, 1975.Google Scholar
  30. Huygens, C. 1657. De Ratiociniis in Ludo Aleae. In: Exercitionum Mathematicorum, volume 5, editor F. van Schooten, Elsevir, Amsterdam, Netherlands, pp.521–534. The work is phrased essentially as a set of problems and answers. English translation by J. Arbuthnot, Of the Laws of Chance, or a Method of Calculation of the Hazards of Game. B. Motte (publisher) & R. Taylor (seller), London, England, 1692.Google Scholar
  31. Jaynes, E.T. 1976. Confidence intervals vs Bayesian intervals. In: Foundations of Probability Theory, Statistical Inference and Statistical Theories of Science, editors W.L. Harper & C.A. Hooker, Reidel, Dordrecht, Netherlands, pp. 175–257. Largely reprinted as chapter 9 of Jaynes (1983).CrossRefGoogle Scholar
  32. Jaynes, E.T. 1983. E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics. Synthese Library 158. Editor R.D. Rosenkrantz, Reidel, Dordrecht, Netherlands.Google Scholar
  33. Jeffreys, H. 1939. Theory of Probability. Oxford University Press, Oxford, UK. Third edition published 1961.Google Scholar
  34. John of Salisbury. 1159. Metalogicon. In: Patrologiae Cursus Completus (Latin series), volume 199, editor J.-P. Migne, Paris, France, 1855, pp.823–946. English translation by D.D. McGarry, University of California Press, Berkeley, California, USA, 1955.Google Scholar
  35. Justinian, 533. Digest (or Pandects). Constantinople, in the eastern half of the divided Roman empire. An authoritative Latin version is given side by side with an English translation by A. Watson, University of Pennsylvania Press, Philadelphia, Pennsylvania, USA, 1985. The Digest is the largest part of Justinian’s comprehensive Corpus of Civil Law.Google Scholar
  36. Kantola, I. 1994. Probability and Moral Uncertainty in Late Medieval and early Modern Times. Luther-Agricola-Society, Helsinki, Finland.Google Scholar
  37. Kassler, J. 1986. The emergence of probability reconsidered. Archives Internationales d’Histoire des Sciences 36, 17–44.MathSciNetzbMATHGoogle Scholar
  38. Keynes, J.M. 1921. A Treatise on Probability. Macmillan, London, UK.zbMATHGoogle Scholar
  39. Laplace, P.S., Marquis de. 1812. Théorie Analytique des Probabilités. Courcier, Paris, France. The third edition (Courcier, Paris, 1820) has, as introduction, the Essai Philosophique sur les Probabilités (Laplace 1814). No English translation of the Théorie has been published.Google Scholar
  40. Laplace, P.S. 1814. Essai Philosophique sur les Probabilités. Courcier, Paris, France. English translation of the sixth edition (Bachelier, Paris, 1840) by F.W. Truscott & F.L. Emory, Wiley, New York, 1902; revised translation in second edition, Wiley, New York, 1917. Reprinted by Dover publications, New York, USA, 1951.Google Scholar
  41. Leibniz, G.W. d. 1716. Oeuvres (seven volumes), editor L.A. Foucher de Careil, republished by G. Olms, Hildesheim, Germany, 1969. A definitive series of Leibniz’ works has been in progress since 1923 under the title Sämtliche Schriften und Briefen, and G. Olms of Hildesheim have republished many older collections of Leibniz’ work. There is no collection in English but the more important works have been translated individually.Google Scholar
  42. MacKay, D.J.C. 1996. Bayesian non-linear modeling for the prediction competition. In: Maximum Entropy and Bayesian Methods, Santa Barbara, California, USA, 1993, editor G.R. Heidbreder, Kluwer, Dordrecht, Netherlands, pp.221–234.Google Scholar
  43. de Moivre, A, 1718. The Doctrine of Chances, or a Method of Calculating the Probability of Events in Play. W. Pearson, London, England. Second edition published by Woodfall, London, England, 1738; third edition by Millar, London, UK, 1756; successive editions were greatly expanded. The second edition was reprinted by Cass, London, UK, 1967, and the third edition by Chelsea publishing, New York, USA, 1967.Google Scholar
  44. de Moivre, A. 1725. Annuities on Lives. Printed by W. P[earson], sold by F. Fayram, London, England.Google Scholar
  45. Montmort, P.R. de, 1708. Essay d’Analyse sur les Jeux de Hazard. J. Quillau, Paris, France. Second edition, much expanded, published by Quillau, Paris, 1713.Google Scholar
  46. von Neumann, J. & Morgenstern, O. 1944. Theory of Games and Economic Behaviour. Princeton University Press, Princeton, New Jersey, USA.Google Scholar
  47. Pascal, B. 1654. Correspondence with Fermat. In: Blaise Pascal, Oeuvres Complètes, volume 2, editor J. Mesnard, published by de Brouwer, Bruges, Belgium and Paris, France, 1970, pp.1132–1158 (volume 1:1964). (The letters of Fermat are included.) English translation in Games, Gods and Gambling by F.N. David, Griffin, London, UK, 1962, pp.229–253. Also set out in Fermat (1654).Google Scholar
  48. Patey, D.L. 1984. Probability and Literary Form: Philosophic Theory and Literary Practice in the Augustan Age. Cambridge University Press, Cambridge, UK.Google Scholar
  49. Rabinovitch, N.L. 1973. Probability and Statistical Inference in Ancient and Medieval Jewish Literature. University of Toronto Press, Toronto, Canada.zbMATHGoogle Scholar
  50. Robertson, B. & Vignaux, G.A. 1995. Interpreting Evidence: Evaluating Forensic Science in the Courtroom. Wiley, Chichester, UK.Google Scholar
  51. Sambursky, S. 1956. On the possible and the probable in ancient Greece. Osiris 12, 35–48.CrossRefGoogle Scholar
  52. Shannon, CE. 1948. A mathematical theory of communication. Bell System Technical Journal 27, 379–423 & 623–659. Reprinted in: The Mathematical Theory of Communication, editors C.E. Shannon h W.W. Weaver, University of Illinois Press, Urbana, Illinois, USA, 1949.MathSciNetzbMATHGoogle Scholar
  53. Sheynin, O.B. 1974. On the prehistory of the theory of probability. Archive for the History of Exact Sciences 12, 97–141.MathSciNetzbMATHCrossRefGoogle Scholar
  54. Stigler, S.M. 1986. The History of Statistics: the Measurement of Uncertainty before 1900. Belknap Press of Harvard University Press, Cambridge, Massachusetts, USA.zbMATHGoogle Scholar
  55. Thomas [of] Aquinas. 1265–74. Summa Theologiae. Multi-volume Latin with modern English translation, Eyre & Spottiswode, London, UK; II-II q. 70 is in volume 38, published 1975.Google Scholar
  56. Todhunter, I. 1865. A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace. Macmillan, London, UK.Google Scholar
  57. Tribus, M. 1969. Rational Descriptions, Decisions and Designs. Pergamon Press, New York, USA.Google Scholar
  58. Venn, J. 1866. The Logic of Chance. Macmillan, London, UK.Google Scholar
  59. Wald, A. 1950. Statistical Decision Functions. Wiley, New York, USA.zbMATHGoogle Scholar
  60. de Witt, J. 1671. Waerdye van Lyf-renten naer Proportie van Los-renten [Value of Life Annuities in Proportion to Redeemable Rents.] J. Scheltus, s’GravenHage, Netherlands. Reprinted in Feest-gave van het Wiskundig Genootschap te Amsterdam, published by J. Enschedé, Haarlem, Netherlands, 1879. Translated in: R.G. Darnwell, A Sketch of the Life and Times of John de Witt, Grandpensionary of Holland, to which is added his Treatise on Life Annuities, New York, USA, 1856.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Anthony J. M. Garrett
    • 1
  1. 1.CambridgeUK

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