Abstract
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
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
Baldus de Ubaldis. (d. 1400) 1586. Opera (nine volumes), apud Iuntas, Venice.
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.
Bellhouse, D.R. 1988. Probability in the sixteenth and seventeenth centuries: an analysis of Puritan casuistry. International Statistical Review 56, 63–74.
Bellhouse, D.R. & Franklin, J. 1997. The language of chance. International Statistical Review 65, 73–85.
Bernoulli, J. 1713. Ars Conjectandi. Thurnisiorum, Basle, Switzerland.
Bernstein, P.L. 1996. Against the Gods: the Remarkable Story of Risk. Wiley, New York, USA.
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.
Boole, G. 1854. An Investigation of the Laws of Thought. Macmillan, London, UK.
Byrne, E.F. 1968. Probability and Opinion: a Study in the Medieval Presuppositions of Post-Medieval Theories of Probability. Martinus NijhofT, The Hague, Netherlands.
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.
Cochrane, C.N. 1944. Christianity and Classical Culture: A Study of Thought and Action from Augustus to Augustine. Oxford University Press, Oxford, UK.
Cox, R.T. 1946. Probability, frequency and reasonable expectation. American Journal of Physics 14, 1–13.
Crombie, A.C. 1994. Styles of Thought in the European Tradition (three volumes). Duckworth, London, UK.
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).
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).
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.
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.
Garber, D. & Zabell, S. 1979. On the emergence of probability. Archive for History of Exact Sciences 21, 33–53.
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.
Gibbs, J.W. 1902. Elementary Principles in Statistical Mechanics. Yale University Press, New Haven, Connecticut, USA.
Grandy, W.T., Jr. 1987–8. Foundations of Statistical Mechanics, Volume I: Equilibrium Theory (1987), Volume II: Nonequilibrium Phenomena (1988). Reidel, Dordrecht, Netherlands.
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.
Hacking, I. 1975. The Emergence of Probability. Cambridge University Press, Cambridge, UK.
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.
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.
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.
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).
Jaynes, E.T. 1983. E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics. Synthese Library 158. Editor R.D. Rosenkrantz, Reidel, Dordrecht, Netherlands.
Jeffreys, H. 1939. Theory of Probability. Oxford University Press, Oxford, UK. Third edition published 1961.
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.
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.
Kantola, I. 1994. Probability and Moral Uncertainty in Late Medieval and early Modern Times. Luther-Agricola-Society, Helsinki, Finland.
Kassler, J. 1986. The emergence of probability reconsidered. Archives Internationales d’Histoire des Sciences 36, 17–44.
Keynes, J.M. 1921. A Treatise on Probability. Macmillan, London, UK.
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.
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.
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.
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.
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.
de Moivre, A. 1725. Annuities on Lives. Printed by W. P[earson], sold by F. Fayram, London, England.
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.
von Neumann, J. & Morgenstern, O. 1944. Theory of Games and Economic Behaviour. Princeton University Press, Princeton, New Jersey, USA.
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).
Patey, D.L. 1984. Probability and Literary Form: Philosophic Theory and Literary Practice in the Augustan Age. Cambridge University Press, Cambridge, UK.
Rabinovitch, N.L. 1973. Probability and Statistical Inference in Ancient and Medieval Jewish Literature. University of Toronto Press, Toronto, Canada.
Robertson, B. & Vignaux, G.A. 1995. Interpreting Evidence: Evaluating Forensic Science in the Courtroom. Wiley, Chichester, UK.
Sambursky, S. 1956. On the possible and the probable in ancient Greece. Osiris 12, 35–48.
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.
Sheynin, O.B. 1974. On the prehistory of the theory of probability. Archive for the History of Exact Sciences 12, 97–141.
Stigler, S.M. 1986. The History of Statistics: the Measurement of Uncertainty before 1900. Belknap Press of Harvard University Press, Cambridge, Massachusetts, USA.
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.
Todhunter, I. 1865. A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace. Macmillan, London, UK.
Tribus, M. 1969. Rational Descriptions, Decisions and Designs. Pergamon Press, New York, USA.
Venn, J. 1866. The Logic of Chance. Macmillan, London, UK.
Wald, A. 1950. Statistical Decision Functions. Wiley, New York, USA.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Garrett, A.J.M. (1998). The History of Probability Theory. In: Erickson, G.J., Rychert, J.T., Smith, C.R. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 98. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5028-6_18
Download citation
DOI: https://doi.org/10.1007/978-94-011-5028-6_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6111-7
Online ISBN: 978-94-011-5028-6
eBook Packages: Springer Book Archive