The Theory That Would Not Die

by Sharon Bertsch McGrayne

  JRSS

  Journal of the Royal Statistical Society

  OC

  Oeuvres Complètes de Laplace

  PCAS

  Proceedings of the Casualty Actuarial Society

  Part I. Enlightenment and the Anti-Bayesian Reaction

  Chapter 1. Causes in the Air

  Bayes, Joshua. Sermons and Funeral Orations. English Short Title database of 18th-century microfilms. Reels 7358 no. 08; 7324 no. 06; 7426 no. 03; and 7355 no. 08.

  Bayes, Thomas. (1731) “Divine benevolence: Or, an attempt to prove that the principal end of the divine providence and government is the happiness of his creatures.” London.

  ———. (1763) An Introduction to the Doctrine of Fluxions, and Defence of the Mathematicians against the Objections of the Author of the Analyst. Printed for J. Noon, London. The Eighteenth Century Research Publications Microfilm A 7173 reel 3774 no. 06.

  Bayes, Thomas, and Richard Price. (1763) An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F.R.S. Communicated by Mr. Price, in a letter to John Canton, A.M.F.R.S. A letter from the late Reverend Mr. Thomas Bayes, F.R.S., to John Canton, M.A. and F.R.S. Author(s): Mr. Bayes and Mr. Price. Philosophical Transactions (1683–1775) (53) 370–418. Royal Society. The original Bayes–Price article.

  Bebb, ED. (1935) Nonconformity and Social and Economic Life 1660–1800. London: Epworth Press.

  Bellhouse, David R. (2002) On some recently discovered manuscripts of Thomas Bayes. Historia Mathematica (29) 383–94.

  ———. (2007a) The Reverend Thomas Bayes, FRS: A biography to celebrate the tercentenary of his birth. Statistical Science (19:1) 3–43. With Dale (2003) the main source for Bayes’ life.

  ———. (2007b) Lord Stanhope’s papers on the Doctrine of Chances. Historia Mathematica (34) 173–86.

  Bru, Bernard. (1987) Preface in Thomas Bayes. Essai en vue de résoudre un problème de la doctrine des chances, trans. and ed., J-P Cléro. Paris.

  ———. (1988) Estimations laplaciennes. Un exemple: La recherche de la population d’un grand empire, 1785–1812. J. Soc. Stat. Paris (129) 6–45.

  Cantor, Geoffrey. (1984) Berkeley’s The Analyst revisited. Isis (75) Dec. 668–83.

  Chesterfield PDS. (1901) Letters to His Son: On the Fine Art of Becoming a Man of the World and a Gentleman. M. Walter Dunne.

  Cone, Carl B. (1952) Torchbearer of Freedom: The Influence of Richard Price on Eighteenth-Century Thought. University of Kentucky Press.

  Dale, Andrew I. (1988) On Bayes’ theorem and the inverse Bernoulli theorem. Historia Mathematica (15) 348–60.

  ———. (1991) Thomas Bayes’s work on infinite series. Historia Mathematica (18) 312–27.

  ———. (1999) A History of Inverse Probability from Thomas Bayes to Karl Pearson. 2d ed. Springer. One of the foundational works in the history of probability.

  ———. (2003) Most Honourable Remembrance: The Life and Work of Thomas Bayes. Springer. With Bellhouse, the main source for Bayes’ life.

  Daston, Lorraine. (1988) Classical Probability in the Enlightenment. Princeton University Press.

  Deming WE, ed. (1940) Facsimiles of Two Papers by Bayes, With Commentaries by W. E. Deming and E. C. Molina. Graduate School. Department of Agriculture. Washington, D.C.

  Earman, John. (1990) Bayes’ Bayesianism. Studies in History and Philosophy of Science (21) 351–70.

  ———. (2002) Bayes, Hume, Price, and miracles. In Bayes’s Theorem, ed., Richard Swinburne. 91–109.

  Gillies, Donald A. (1987) Was Bayes a Bayesian? Historia Mathematica (14) 325–46.

  Haakonssen, Knud. (1996) Enlightenment and Religion: Rational Dissent in Eighteenth-Century Britain. Cambridge University Press.

  Hacking, Ian. (1990) The Taming of Chance. Cambridge University Press.

  ———. (1991) Bayes, Thomas. Biographical Dictionary of Mathematicians vol. 1, Charles Scribner’s Sons.

  Hald, Anders. (1990) A History of Probability and Statistics and Their Applications before 1750. John Wiley and Sons.

  ———. (1998) A History of Mathematical Statistics from 1750 to 1930. John Wiley and Sons. A classic.

  Hembry, Phyllis M. (1990) The English Spa 1560–1815: A Short History. Athlone Press, Fairleigh Dickinson University Press.

  Holder, Rodney D. (1998) Hume on miracles: Bayesian interpretation, multiple testimony, and the existence of God. British Journal for the Philosophy of Science (49) 49–65.

  Holland JD. (1968) An eighteenth-century pioneer Richard Price, D.D., F.R.S. (1723–1791). Notes and Records of the Royal Society of London (23) 43–64.

  Hume, David. (1748) An Enquiry Concerning Human Understanding. Widely available. Online see Project Gutenberg.

  Jacob, Margaret C. (1976) The Newtonians and the English Revolution 1689–1720. Cornell University Press.

  Jesseph DM. (1993) Berkeley’s Philosophy of Mathematics. University of Chicago Press.

  Klein, Lawrence E. (1994) Shaftesbury and the Culture of Politeness: Moral Discourse and Cultural Politics in Early Eighteenth-Century England. Cambridge University Press.

  Miller, Peter N. (1994) Defining the Common Good: Empire, Religion and Philosophy in Eighteenth Century England. Cambridge University Press.

  Owen, David. (1987) Hume versus Price on miracles and prior probabilities: Testimony and the Bayesian calculation. Philosophical Quarterly (37) 187–202.

  Price, Richard. Four Dissertations. 3d ed. (1772). Dissertation IV: On the nature of historical evidence and miracles. Google online.

  Sobel, Jordan Howard. (1987) On the evidence of testimony for miracles: A Bayesian interpretation of David Hume’s analysis. Philosophical Quarterly (37:147) 166–86.

  Stanhope G, Gooch GP. (1914) The Life of Charles Third Earl Stanhope. Longmans, Green.

  Statistical Science (2004) Issue devoted to Thomas Bayes. (19:1) Many useful articles.

  Stigler, Stephen M. (1983). Who discovered Bayes’s Theorem? American Statistician 37 290–96.

  ———. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press of Harvard University Press. A classic and the place to start for Thomas Bayes.

  ———. (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press.

  Thomas, DO. (1977) The Honest Mind: The Thought and Work of Richard Price. Clarendon Press. Thomas is the authority on Price and edited his correspondence. Thomas, DO, and Peach, WB. (–1994) Eds. The Correspondence of Richard Price, vols 1-3. Duke University Press.

  Watts, Michael R. (1978) The Dissenters vols. 1 and 2. Clarendon Press.

  Chapter 2. The Man Who Did Everything

  Albrecht, Peter. (1998) What do you think of smallpox inoculations? A crucial question in the eighteenth century, not only for physicians. In The Skeptical Tradition around 1800, eds., J. van der Zande, RH Popkin. Dordrecht, Kluwer Academic Publishers. 283–96.

  Arago, F. (1875) Laplace: Eulogy before the French Academy. Trans. Baden Powell. Smithsonian Institution. Annual report 1874 in Congressional Papers for 43rd Congress. Washington, D.C., 129–68.

  Arbuthnot J. (1711) An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes. Philos. Trans. Roy. Soc., Lond. (27) 186–90.

  Baker, Keith Michael. (1975) Condorcet: From Natural Philosophy to Social Mathematics. University of Chicago Press.

  Biot, JB. (1850) Une anecdote relative à M. Laplace. Journal Des Savants 65–71.

  Buffon. (1774) A Monsieur de la Place. Journal Officiel May 24, 1879, p. 4262; and Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences (88) 1879, 1019. I am indebted to Roger Hahn for this letter.

  Bugge T, Crosland M. (1969) Science in France in the Revolutionary Era. Society for the History of Technology and MIT Press.

  Clark W, Golinski J, Schaffer S. (1999) The Sciences in Enlightened Europe. University of Chicago Press.

  Condo
rcet, Jean-Antoine-Nicolas de Caritat, B. Bru, P. Crépel (1994) Condorcet, Arithmétique politique Textes rares ou inédits (1767–1789). Presses Universitaires de France.

  Crosland, Maurice P. (1967) The Society of Arcueil; A View of French Science at the Time of Napoleon I. Harvard University Press.

  Dale, Andrew I. (1995) Pierre-Simon Laplace: Philosophical Essay on Probabilities. Trans. and notes by Dale. Springer-Verlag.

  ———. (1999) A History of Inverse Probability from Thomas Bayes to Karl Pearson. 2d ed. Springer. One of the foundational works in the history of probability.

  Daston, Lorraine. (1979) D’Alembert’s critique of probability theory. Historia Mathematica (6) 259–79.

  Dhombres, Jean. (1989) Books: reshaping science. In Revolution in Print: The Press in France 1775–1800, eds., R Darnton, D Roche. University of California Press. 177–202.

  Doel, Ronald E. (1990) Theories and origins in planetary physics. Isis (90) 563–68.

  Dreyer JLF, ed. (1912) The Scientific Papers of Sir William Herschel, vol. I. London: Royal Society and Royal Astronomical Society.

  Dunnington, G. Waldo. Carl Friedrich Gauss: Titan of Science. Exposition Press, 1955.

  Duveen DI, Hahn R. (1957) Laplace’s succession to Bézout’s post of examinateur des élèves de l’artillerie. Isis (48) 416–27.

  Duveen DI, Hahn R (1958) Deux Lettres de Laplace à Lavoisier. Revue d’histoire des Sciences et de leurs Applications (11:4) 337–42.

  Fourier, Joseph. (1830) Historical Eulogy of the M. le Marquis de Laplace. Trans. RW Haskins. Buffalo; and (1831) Eloge historique de M. le marquis de Laplace, prononcé . . . le 15 juin 1829, MASIF (10) lxxxi-cii.

  Fox, Robert. (1974) The rise and fall of Laplacian Physics. Historical Studies in the Physical Sciences (4) 89–136.

  ———. (1987) La professionalisation: un concept pour l’historien de la science française au XIXe siècle. History and Technology (4) 413–22.

  Gillispie, Charles C. (1972) Probability and politics: Laplace, Condorcet, and Turgot. Proceedings of the American Philosphical Society (116) 1–20.

  ———. (1978) Laplace, Pierre-Simon, Marquis De. Dictionary of Scientific Biography, Supplement I, Vol. XV. Charles Scribner’s Sons.

  ———. (1979) Mémoires inedits ou anonymes de Laplace. Revue d’Histoire des Sciences et de Leurs Applications (32) 223–80.

  ———. (2004) Science and Polity in France: The End of the Old Regime. And Science and Polity in France: The Revolutionary and Napoleonic Years. Princeton University Press.

  Gillispie, CC, with Robert Fox and Ivor Grattan-Guinness. (1997) Pierre-Simon Laplace 1749–1827: A Life in Exact Science. Princeton University Press.

  Greenberg, John. (1986) Mathematical physics in eighteenth-century France. Isis (77) 59–78.

  Grimaux, Édouard. (1888) Lavoisier 1743–1794. Alcan, Paris.

  Grimsley, Ronald. (1963) Jean d’Alembert 1717–83. Clarendon Press.

  Guerlac, Henry. (1976) Chemistry as a branch of physics: Laplace’s collaboration with Lavoisier. Historical Studies in the Physical Sciences (7) 193–276.

  Hahn, Roger. (1955) Laplace’s religious views. Archives Internationals d’Histoire des Sciences (8) 38–40.

  ———. (1967a) Laplace as a Newtonian Scientist. William A. Clark Memorial Library 1967.

  ———. (1967b) Laplace’s first formulation of scientific determinism in 1773. Nadbitka. Actes du XIe Congrès International d’Histoire des Sciences. (2) 167–171.

  ———. (1969) Élite scientifique et democratie politique dans la France révolutionnaire. Dix-Huitième Siècle (1) 252–73.

  ———. (1976) Scientific careers in eighteenth-century France. In The Emergence of Science in Western Europe, ed., Maurice Crossland. New York: Science History Publications.

  ———. (1981) Laplace and the vanishing role of God in the physical universe. In The Analytic Spirit, ed., Harry Woolf. Cornell University Press. 85–95.

  ———. (1987a) Changing patterns for the support of scientists from Louis XIV to Napoleon. History and Technology (4) 401–11.

  ———. (1987b) Laplace and Boscovich. Proceedings of the Bicentennial Commemoration of R. G. Boscovich, eds., M. Bossi, P. Tucci. Milan.

  ———. (1989) The triumph of scientific activity: From Louis XVI to Napoleon. Proceedings of the Annual Meeting of the Western Society for French History (16) 204–11.

  ———. (1990) The Laplacean view of calculation. In The Quantifying Spirit in the 18th Century, eds., T Frängsmyr, HL Heilbron, RE Rider. University of California Press. 363–80.

  ———. (1994) Le role de Laplace à l’École Polytechnique. In La Formation polytechnicienne, 1794–1994, eds., B. Belhoste, A. Dahan and A. Picon. Seyssel.

  ———. (1995) Lavoisier et ses collaborateurs: Une Équipe au Travail. In Il y a 200 Ans Lavoisier, ed., C. Demeulenaere-Douyère, Paris: Technique et Documentation Lavoisier. 55–63.

  ———. (2005) Pierre Simon Laplace, 1749–1827: A Determined Scientist. Harvard University Press; (2004) Le Système du Monde: Pierre Simon Laplace, Un Itinéraire dans la Science. Trans. Patrick Hersant. Éditions Gallimard. These are the same book, the original in English, the translation in French. These books are my primary sources for Laplace’s life.

  Hald, Anders. (1998) A History of Mathematical Statistics from 1750 to 1930. John Wiley and Sons. A classic.

  Hankins, Thomas L. (1970) Jean d’Alembert: Science and the Enlightenment. Oxford University Press.

  ———. (1985) Science and the Enlightenment. Cambridge University Press.

  Harte, Henry H. (1830) On the System of the World. English translation of Laplace’s Exposition du système du monde. Dublin University Press.

  Heilbron HL. (1990) Introductory essay and The measure of enlightenment. In The Quantifying Spirit in the 18th Century, eds., T Frängsmyr, HL Heilbron, RE Rider. University of California Press. 1–24, 207–41.

  Herivel, John. (1975) Joseph Fourier: The Man and the Physicist. Clarendon Press.

  Holmes, Frederick Lawrence. (1961) Antoine Lavoisier—The Next Crucial Year; or, the Sources of His Quantitative Method in Chemistry. Cornell University Press.

  Koda H, Bolton A. (2006) Dangerous Liaisons: Fashion and Furniture in the Eighteenth Century. Metropolitan Museum of Art and Yale University Press.

  Laplace, Pierre Simon. (1878–1912) Oeuvres Complètes de Laplace.14 vols. National Bibliothèque de la France. Available online. In some cases, two dates are given; the first is the year when Laplace read his paper to the academy, the second when it was published. We are indebted to Charles C. Gillispie for rationalizing Laplace’s publication dates.

  ———. (1773) Recherches: 1° sur l’intégration des equations différentielles aux différences finies, and sur leur usage dans la théorie des hazards; 2° Sur le principe de la gravitation universelle, and sur les inégalités séculaires des planètes qui en dependent. (February 10, 1773) OC (8) 69–197, 198–275.

  ———. (1774a) Mémoire sur la probabilité des causes par les événements. OC (8) 27–69. This is Laplace’s discovery of inverse probability, his first version of what is now known as Bayes’ rule. For the English translation with modern mathematical notation, see Stigler (1986).

  ———. (1774b) Mémoire sur les suites récurro-récurrentes et sur leurs usages dans la théorie des hazards. OC (8) 5–24.

  ———. (1776) Sur le principe de la gravitation universelle et sur les inégalités séculaires des planets qui en dependent. OC (8) 201–78.

  ———. (1778/81) Mémoire sur les Probabilités. OC (9) 383–485.

  ———. (1782/1785) Mémoire sur les approximations des formules qui sont functions de très grands nombres. OC (10) 209–294.

  ———. (1783/1786) Mémoire sur les approximations des formulas qui sont functions de très grands nombre (suite). OC (10) 295–338.

  ———. (1783/1786) Sur les naissances, les mariages, et les morts à Paris, depuis 1771 jusqu’en 1784, et dans
toute l’étendue de la France, pendant les années 1781 et 1782. OC (11) 35–49.

  ———. (1787/1788) Sur l’équation séculaire de la lune.” OC (11) 243–71.

  ———. (1788) Théorie de Jupiter et de Saturne. OC (11) 95–207 and (Suite) 211–39.

  ———. (1800) Séances des Écoles Normales, receuillies par des Sténographes, et revues par les Professeurs, nouvelle édition, tome sixième, Paris: l’Primerie du Cercle-Social.

  ———. (1815/1818) Sur l’Application du calcul des probabilities à la philosophie naturelle. OC (13) 98–116.

  ———. (1818) Troisième Supplément, Application de calcul des probabilités aux opérations géodésiques. OC (7) 531–80.

  ———. (1826/1829) Mémoire sur les deux grandes inégalités de Jupiter et de Saturne. OC (13) 313–33.

  Lind, Vera. (1998) Skepticism and the discourse about suicide in the eighteenth century. In The Skeptical Tradition around 1700, eds., J van der Zande, RH Popkin. Kluwer Academic Publishers. 296–313.

  Lindberg DC, Numbers RL, eds. (1986) God and Nature: Historical Essays on the Encounter between Christianity and Science. University of California Press.

  ———. (2003) When Science and Christianity Meet. University of Chicago Press.

  Luna, Frederick A. de. (1991) The Dean Street style of revolution: J.-P. Brissot, jeune philosophe. French Historical Studies (17:1) 159–90.

  Maréchal, Pierre Sylvain. (VIII) Dictionnaire des athées anciens et modernes. Paris. 231–32.

  Marmottan, Paul. (1897). Lettres de Madame de Laplace à Élisa Napoléon, princesse de Lucques et de Piombino. Paris.

  Mazzotti, Massimo. (1998) The geometers of God: Mathematics and reaction in the Kingdom of Naples. Isis (89) 674–701.

  Numbers, Ronald L. (1977) Creation by Natural Law: Laplace’s Nebular Hypothesis in American Thought. University of Washington Press.

  Orieux, Jean. (1974) Talleyrand: The Art of Survival. Alfred A. Knopf. A classic about Laplace’s era.

  Outram, Dorinda. (1983) The ordeal of vocation: The Paris Academy of Sciences and the Terror, 1793–95. History of Science (21) 251–73.