The story of the emergence of probability comes to an end with the publication of Ars conjectandi. In 1711, even before the book appeared in print, Abraham de Moivre published De mensura sortis, which soon was to culminate in The Doctrine of Chances, where the mathematics of probability was recognized as an independent discipline in its own right. We have only one task left: to describe certain philosophical positions that are consequent upon the events described in preceding chapters. One of these is the sceptical problem of induction, published by Hume in 1739, and the other is the problem of chance in a deterministic universe. Although the former is epistemological and the latter arises from aleatory concerns, they are no more independent than any other bifurcation in the dual concept of probability. Determinism is, however, the one to study first.

The most immediate significance of Bernoulli's limit theorem lies not in a distant potential for sound statistical inference but in making more intelligible the sheer fact of statistical stability. A curious ‘pre-Bernoullian’ paper of 1710, by John Arbuthnot, usefully illustrates this fact. Arbuthnot is now chiefly known as a satirist esteemed by his contemporaries next only to Jonathan Swift. He was also Queen Anne's doctor, a Fellow of the Royal Society, and an amateur of mathematics. In 1692 he published the first English translation of Huygens' textbook. As Todhunter says, ‘the work is preceded by a Preface written with vigour but not free from coarseness’ [1865, p. 50]. The examples are characteristic of a bawdy age.