Newton’s Scientific and Philosophical Legacy pp 269-274 | Cite as

# Probability, Planets, and Newton’s Methodology

## Abstract

The early development of some aspects of probability was closely guided by experience, rewarding or otherwise, of games of chance. This association was fortunate so far as the origin of the ‘doctrine of chances’ in the seventeenth century was concerned; then, as now, simple games involving coins, dice or playing cards provided suitable models for understanding the relevant combinatorial arguments. But there were topics other than gambling which shared its characteristic vocabulary — ‘chance’, ‘luck’, ‘fate’, ‘coincidence’, ‘random’, etc. — and by the beginning of the eighteenth century a number of people skilled in calculating chances were finding opportunities to apply their expertise to some of these topics. John Arbuthnot’s startling memoir for the Royal Society of London on the slight, and perhaps coincidental, preponderance of births of male rather than female children is one well known example of such thinking.^{1} Another is the anonymous memoir, also published in the *Philosophical Transactions*, concerned with the credibility of testimony, where the chance of reports being false if corroborated by independent witnesses is examined. But perhaps the best example is Jakob Bernouilli’s clear and thorough account of the conditions necessary for extending the scope of the mathematical theory of chances.

## Keywords

Eighteenth Century Simple Game Planetary Orbit Planetary Motion Probabilistic Argument## Preview

Unable to display preview. Download preview PDF.

## Notes

- 1.J. Arbuthnot, “An Argument for Divine Providence taken from the constant Regularity observ’d in the Births of both Sexes”,
*Phil. Trans. Roy. Soc. London, 27*(1710), 186–90.CrossRefGoogle Scholar - 2.Anon, “A Calculation of the Credibility of Human Testimony,”
*Phil. Trans. Roy. Soc. London, 21*, (1699), 359–365.Google Scholar - 3.Jakob Bernouilli,
*Ars Conjectandi*, (Basel, 1713).Google Scholar - 4.See I. Schneider, “Why do we find the origin of a calculus of probabilities in the seventeenth century?” in J. Hintikka, D. Gruender, E. Agazzi (eds.),
*Probabilistic Thinking, Thermodynamics and the Interaction of the History and Philosophy of Science*, (Dordrecht, 1981), pp. 3–24.Google Scholar - 5.In 1691 a design argument based upon ‘contrivancies’ found in the animate world was published by John Ray in his
*Wisdom of God manifested in the Works of Creation*. Newton seems to have thought that a design argument based on inanimate features of the world was superior.Google Scholar - 6.Quoted in F.E. Manuel,
*A Portrait of Isaac Newton*, (Cambridge, Mass., 1968), p. 127. Derham’s*Astro-Theology*was first published in 1715.Google Scholar - 7.A. Dyce (ed.),
*The Works of Richard Bentley, D.D.*, (3 vols., London, 1838), v.3, p. 207.Google Scholar - 8.
*Ibid.*, 180. This is an elaboration of Newton’s argument in his first letter to Bentley. Cf. Query 31 in I. Newton,*Opticks*, (4th ed., London, 1730).Google Scholar - 9.Dyce (ed.),
*op. cit*., p. 97.Google Scholar - 10.
*Ibid*., p. 98.Google Scholar - 11.
*Ibid*., p. 100Google Scholar - 12.
*Ibid*., pp. 101–2.Google Scholar - 13.R. Descartes,
*Principles of Philosophy*, (transi. V.R. Miller and R.P. Miller, Dordrecht, 1983), pp. 98–9, 177. First published in 1644.Google Scholar - 14.“General Scholium” in I. Newton,
*Mathematical Principles of Natural Philosophy*, (revised transi. F. Cajori, University of California Press, 1934), p. 543.Google Scholar - 15.I. Newton,
*Opticks*, (Dover Publications, New York, 1952, based on 4th edition of 1730), p. 402.Google Scholar - 16.For details and discussion, see my “Planets and probability: Daniel Bernouilli on the inclinations of the planetary orbits,”
*Studies in the History and Philosophy of Science*(forthcoming).Google Scholar - 17.R. Price, prefatory letter to T. Bayes, “An Essay Towards Solving a Problem in the Doctrine of Chances,” reprinted in E.S. Pearson and M.G. Kendall (eds.),
*Studies in the History of Statistics and Probability*, vol. 1, (Griffin, London, 1970), p. 135.Google Scholar - 17a.R. Price Bayes’ essay was originally published in
*Phil. Trans., 53*, (1763), 370–418.Google Scholar