by Andrew I. Dale
© Oxford University Press 2004 All rights reserved
Craig, John (c.1663-1731), mathematician and Church of England clergyman, was the second son of James Craig (c.1632-1704), vicar of Hoddam in Dumfries, Scotland. In 1684 Craig matriculated at Edinburgh University, beginning his mathematical studies under David Gregory. In 1685 he travelled to Cambridge, where he published his first mathematical work, Methodus figurarum lineis rectis & curvis comprehensarum quadraturas determinandi. This was the first work published in England to use Leibniz's differential calculus (as opposed to Newton's fluxional calculus which was then still not in print). In 1687 Craig took his MA at Edinburgh University, and he moved to London in 1689. On 27 July 1693 he married Agnes Cleland (c.1669-1703) in the parish of St Martin-in-the-Fields; there were six children from the marriage.
Craig published two other major mathematical works, Tractatus mathematicus de figurarum curvilinearum quadraturis et locis geometricis, in 1693, and De calculo fluentium, libri duo. Quibus subjunguntur libri duo de optica analytica in 1718. In the first of these Leibniz's integral sign was used (for the first time in England), while in the second Craig used Newton's fluxional notation. In addition he published eight mathematical papers (chiefly on quadratures) in the Philosophical Transactions (1697-1710). He also contributed chapters to Cheyne's Philosophical Principles of 1715, and to Wotton's Reflections of 1694. The standard of his work was such that he was noted as a mathematician of the first order (he associated with Newton, Halley, and de Moivre), and the Acta Eruditorum of Leipzig ranked him among the originators of the calculus (after Leibniz, but before Newton). He was elected a fellow of the Royal Society on 30 November 1711.
In 1699 Craig published his Theologiae Christianae principia mathematica, a tract exhibiting the fusion of his mathematical and theological inclinations. This work has two main arguments. In the first two chapters Craig argues on probabilistic grounds that the evidence for any historical event (a) is weakened by the passage of time, the distance from the occurrence of the event, and the number of people by whom it is communicated, and (b) is strengthened by the number of witnesses and the number of independent communications. Moreover, oral and written testimony have different effects. Choosing the Newtonian fluxional calculus rather than a probabilistic one, Craig derives formulae for the calculation of the time at which the probability of an event will disappear, and applies them to the millennium. In the second part (chapters 3-6) of this tract, Craig gives a mathematical argument in support of Pascal's wager--that it is in one's self-interest to believe in God, since one who bets on believing is risking a finite happiness for a return of infinite heavenly happiness.
Later writers exhibited varying support for Craig's views. For example, David Hume ('Of miracles', Enquiry Concerning Human Understanding, 1748, chap. 10) followed Craig in supposing that the evidence for the truth of Christianity would diminish with the passage of time, while David Hartley (Observations on Man, 1749) claimed that it would increase. Commentary on the Theologiae has, however, generally been adverse. One early writer viewed it as 'scandalous and prophane' (Edwards, 86), while in the Penny Cyclopaedia (3, 1837, 136) it is seen as 'a very silly attempt to apply numerical reasoning to historical evidence'. More sympathetically, Stigler finds in Craig's 'underappreciated book' (Stigler, 879) a formula tantamount to a logistic model for posterior odds: that is, Craig's probability should be understood as the logarithm of the ratio of the probability of the historical testimony as received at the present time, given the historical hypothesis in question, to the probability of the same testimony, given the negation of that hypothesis.
All Craig's ecclesiastical career was spent in the see of Salisbury. In 1692 he was collated vicar of Potterne, Wiltshire; in 1696 he became vicar of Gillingham Major; on 2 November 1708 he was collated in addition prebend of Durnford and canon of Salisbury Cathedral; and on 28 June 1726 he was collated prebend of Gillingham, a cure formerly held by his elder brother, William (c.1657-1721).
Craig died intestate at High Holborn, London, on 11 October 1731, and was buried three days later in the churchyard of St James's, Clerkenwell, London.
ANDREW I. DALE
Sources
R. Nash, John Craige's mathematical principles of Christian theology (1991)
S. M. Stigler, 'John Craig and the probability of history: from the death of Christ to the birth of Laplace', Journal of the American Statistical Association, 81 (1986), 879-87
N. Guicciardini, The development of Newtonian calculus in Britain, 1700-1800 (1989)
J. Hutchins, The history and antiquities of the county of Dorset, 3rd edn, ed. W. Shipp and J. W. Hodson, 3 (1868)
K. Pearson, The history of statistics in the 17th and 18th centuries (1978)
Fasti Angl. (Hardy)
R. Hovenden, ed., A true register of all the christenings, mariages, and burialles in the parishe of St James, Clarkenwell, from ... 1551 (to 1754), 6, Harleian Society, register section, 20 (1894)
The penny cyclopaedia of the Society for the Diffusion of Useful Knowledge, 8 (1837), 134
J. Edwards, Some new discoveries of the uncertainty, deficiency, and corruptions of human knowledge and learning (1714)
G. Cheyne, Philosophical principles of religion: natural and revealed (1715)
W. Wotton, Reflections upon ancient and modern learning (1694)
J. L. Chester and G. J. Armytage, eds., Allegations for marriage licences issued by the bishop of London, 2, Harleian Society, 26 (1887)
Archives
Bodl. Oxf., Tanner MSS
U. Edin. L., Gregory MSS
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