CRAIG, JOHN, a Scottish mathematician of the age of Newton, and one of the earliest writers on the fluxionary or differential calculus in this country. Newton no doubt had long been in possession of the principles of this calculus before his modesty allowed him to give his discoveries to the world, and he even revised one of Craig's treatises previously to publication in 1685, the year after Leibnitz had announced his discovery in the Leipsic Transactions. Residing at that time at Cambridge, similarity of pursuit had made Craig acquainted with that truly great man; and on his return to Scotland he enjoyed the intimate friendship of the accomplished Dr. Pitcairn, and of David Gregory,1 professor of mathematics in the University of Edinburgh, and afterwards Savilian professor of astronomy at Oxford. His investigations, however, with the new calculus, subjected him to the severe strictures of the distinguished John Bernoulli, but obtained for him the support of Leibnitz, whose approbation may be considered as exempt at least from that national partiality with which he himself charges Craig.2 But whatever praise may be due to Craig for his mathematical inquiries, it must be allowed that his Principia of the Christian religion, by a misapplication of the doctrine of probability to human testimony, rest on premises which lead to conclusions alike sceptical and absurd, and which, though in substance received by Hume, had been formerly refuted by Ditton, a contemporary mathematician of this country, and by Houtville and others on the Continent. If, however, it may be allowed to form an opinion of Craig's character from a letter to Dr. Cheyne,3 there may perhaps be some justice in attributing the erroneous principles of this work rather to theoretical mistake than to wrong intention. He seems ultimately to have been a Fellow of the Royal Society, and vicar of Gillingham, Dorsetshire.4
Besides several papers in the Philosophical and Leipsic Transactions, Craig's separately published writings, now chiefly interesting with reference to the progress of mathematical science, are, 1. Methodus figurarum linearum rectis et curvis quadraturis determinandi, London, 1658, 4to; 2. Tractatus Mathematicus de figurarum curvilinearum quadraturis et locis geometricis, Lond. 1693, 4to; 3. Theologia Christiana Principia Mathematica, Lond. 1699 (reprinted, with a refutation, at Leipsic, 1755); 4. De Calculo Fluentium Libri duo, quibus subjunguntur Libri duo de Optica Analytica, 1718, 4to.