ON THE STATISTICAL VIEW OF NATURP:. 509 



in appalling niystei}.' 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 



' In spite of the encomium on 

 the theory of jtrobabilities ((uoted 

 in vol. i. J), l'2-i, Sir John Herschel 

 gave onl}' a quahfied adherence to 

 one of its principal applications 

 (see ' Brit. Ah.soc. Rep.,' vol. i. p. 

 16.")). The two foremo.st adverse 

 critics of the theory were Augu.ste 

 Comte in France and John Stuart 

 Mill in England. In the second 

 volume of the ' Philosophic Posi- 

 tive ' (Ist ed., 1835, p. 371) the 

 former explains why he omitted 

 to deal with so im])ortant a sub- 

 ject in his mathematical ])hiloso]ihy. 

 " Le calcul de.s probabilit<Ss ne me 

 .semble avoir 6t6 rcellement, pour 

 ses illustres iuventeurs, qu'un te.\te 

 commode h, d'ingunieux et difficiles 

 problcmes numeriques, qui n'en con- 

 servent pas moins toute leur valeur 

 abstraite, comme les theories ana- 

 lytiques dont il a etc ensuite I'occa- 

 sion, ou, si Ton veut, I'origine. 

 Quant li la conception philoso- 

 jjhique 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 

 I'application ovidemment illusoire 

 qu'on a souvent tent<5 d'en faire 

 au pretendu perfectionnment des 

 .sciences sociales : ces essais, neces- 

 sairement chimuriques, seront car- 

 acteriscs dans la dernicre 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 

 nomlire de gcomctres a rendre 

 positives les etudes sociales d'aprcs 

 une subordination chim(?rique ^ 

 I'illusoire thdorie mathematique 

 des chances. . . . (^uehiue gros- 

 siere que soit dvidemment une 

 telle illusion, elle etait neanmoins 



essentiellement excusable, quand 

 I'esprit eminemment philosojjhique 

 de I'illustre Jaccjues Bernoulli 

 con(;ut, le premier, cette pensee 

 g(5n(5rale, dont la production, h. une 

 telle dpoque, constituait reellement 

 le prt-cieux et irrecusable symptome 

 du besoin premature pour ce temps, 

 mais ()ui n'y pouvait ctre dprouvd 

 nieme ainsi (jue par une intelligence 

 vraiment sujidrieure. " John Stuart 

 Mill, in the .second volume of his 

 ' Logic,' has devoted a whole chapter 

 to the sul)ject, 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 

 increa.sing use to which the methods 

 for the correction of error have 

 been put in manv' branches of 

 science have convinced mathema- 

 ticians of its apjilicability. 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 his 

 ' Essay on Probabilities ' (London, 



