The smallpox vaccine: the dispute between Bernoulli and d’Alembert and the calculus of probabilities

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• 作者：Camilla Colombo ; Mirko Diamanti
• 关键词：Daniel Bernoulli ; Jean Baptiste Le Rond d’Alembert ; Smallpox ; Vaccinations ; Calculus of probabilities ; Art of conjecture ; Logic ; Mathematical models
• 刊名：Lettera Matematica
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：2
• 期：4
• 页码：185-192
• 全文大小：340 KB
• 参考文献：1. Bernoulli, D.: Essai d’une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l’inoculation pour le prévenir. / Histoire et Mémoires de l’Académie des Sciences, 1760, parte 2, pp. 1-79 (1760)
  2. Daston, L (1988) Classical Probability in the Enlightenment. Princeton University Press, Princeton, NJ
  3. D’Alembert J.-B. L. R. / Opuscules mathématiques, t. II. Chez David, Paris?(1761)
  4. D’Alembert J.-B. L. R. / Mélanges de litterature, d’histoire, et de philosophie, t. V. Chatelain, Amsterdam (1767)
  5. D’Alembert, J-BLR (1821) Oeuvres de d’Alembert. A. Belin, Paris
  6. Halley, E. An Estimate of the Degrees of the Mortality of Mankind, drawn from the curious Tables of the Births and the Funerals at the City of Breslau, with an Attempt to ascertain the Price of Annuities on Lives. / Philosophical Transactions of the Royal Society of London 17: 596-10 (1693)
  7. Voltaire, F. M. A. de. / Letters on the English. Vol. XXXIV, Part 2. The Harvard Classics. P.F. Collier & Son, New York (1909-4). Retrieved from?www.bartleby.com/34/2/, 17 November 2014
  
• 刊物主题：Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Applications of Mathematics; History of Mathematical Sciences; History of Science;
• 出版者：Springer Milan
• ISSN：2281-5937

文摘

The urgent and dramatic need to introduce and promote a vaccine against smallpox, a scourge for society at the end of the 1700s, provided the occasion for a lively debate between Daniel Bernoulli and Jean Le Rond d’Alembert. This article discusses the motivations and arguments of the dispute, illustrating the probabilistic model proposed by Bernoulli to justify the greater “reasonableness-of the campaign in favour of the vaccine, and the objections raised by d’Alembert. The aim of this analysis is, beginning with a reconstruction of the contributions of the two authors, to show how the newly founded “art of conjecture-was the object of divergent interpretations, from the characterisation of its theoretical principles, such as the concept of expectation, to the question of its legitimacy in applications as a “guide to practical living-