ON THE STATISTICAL VIEW OF NATURE. 569 



in appalling mystery. 1 There is, however, no doubt that 

 the Theory of Probability increasingly pervades scientific 

 as well as statistical work in our age, and that in the 



1 In spite of the encomium on 

 the theory of probabilities quoted 

 in vol. i. p. 123, Sir John Herschel 

 gave only a qualified adherence to 

 one of its principal applications 

 (see ' Brit. Assoc. Rep.,' vol. i. p. 

 165). The two foremost adverse 

 critics of the theory were Auguste 

 Comte in France and John Stuart 

 Mill in England. In the second 

 volume of the ' Philosophic Posi- 

 tive' (1st ed., 1835, p. 371) the 

 former explains why he omitted 

 to deal with so important a subject 

 in his mathematical philosophy. 

 " Le calcul des probabilites ne me 

 semble avoir etc reellement, pour 

 ses illustres inventeurs, qu'un texte 

 commode a d'ingenieux et difficiles 

 problemes numeViques,qui n'en con- 

 servent pas moins toute leur valeur 

 abstraite, comme les theories ana- 

 lytiques dont il a etc ensuite 1'oc- 

 casion, ou, si 1'on veut, 1'origine. 

 Quant a la conception philoso- 

 phique sur laquelle repose une telle 

 doctrine, je la crois radicalement 

 fausse et susceptible de conduire 

 aux plus absurdes consequences. 

 Je ne parle pas seulement de 

 1'application eVidemment illusoire 

 qu'on a souvent tente d'en faire 

 au pretendu perfectionnement des 

 sciences sociales : ces essais, neces- 

 sairement chimeriques, seront car- 

 acterises dans la derniere partie de 

 cet ouvrage " : and in the fourth 

 volume (1839, p. 512), "La seule 

 aberration de ce genre . . . c'est 

 la vaine pretention d'un grand 

 nombre de geometres a rendre 

 positives les etudes sociales d'apres 

 une subordination chimeVique a 

 1'illusoire theorie mathematique 

 des chances. . . . Quelque gros- 

 siere que soit evidemment une 

 telle illusion, elle i-tait neanmoins 



essentiellement excusable, quand 

 1'esprit emineniment philosophique 

 de 1'illustre Jacques Bernoulli 

 con9ut, le premier, cette pensee 

 generale, dont la production, a une 

 telle epoque, constituait reellement 

 le precieux et irrecusable symptome 

 du besoiii premature^ pour ce temps, 

 mais qui n'y pouvait etre eprouve 

 meme ainsi que par une intelligence 

 vraiment supeVieure." John Stuart 

 Mill, in the second volume of his 

 ' Logic,' has devoted a whole chapter 

 to the subject, in which he corrects 

 a statement made by him in the 

 first edition of his book, attributing 

 a "fundamental fallacy" to the 

 arguments of Laplace and other 

 mathematicians, but nevertheless 

 takes an unfavourable view of the 

 usefulness of the calculus. In 

 more recent times the subject has 

 been exhaustively treated from a 

 logical point of view by Mr John 

 Venn in his work, ' The Logic of 

 Chance '(3rd ed., London, 1888), 

 and by Stanley Jevons in ' The 

 Principles of Science ' (vol. i. ch. x.) 

 The doubts with which Mill, and 

 still more Comte, regarded the 

 subject, seem to have been dis- 

 pelled in works on Logic ; and the 

 increasing use to which the methods 

 for the correction of error have 

 been put in many branches of 

 science have convinced mathema- 

 ticians of its .applicability. The 

 ninth edition of the ' Ency. Brit. ' 

 contains an excellent article on 

 "Probabilities" by M. W. Crofton. 

 Among the clearest and safest 

 guides in this intricate subject 

 must be counted the late Prof. 

 Augustus de Morgan, whose pro- 

 found treatise in the ' Ency. 

 Metrop.' (vol. ii.), as well as hi 

 ' Essay on Probabilities ' (London, 



