JOHN STUART MILL'S PHILOSOPHY TESTED. 



281 



the name Necessity, and explains it away so in- 

 geniously that he unintentionally converts it into 

 Free-Will. Again, there is no doubt that Mill 

 wished and believed himself to be a bulwark of 

 the Utilitarian Morality ; he prided himself on the 

 invention, or at least the promulgation, of the 

 name Utilitarianism ; but he expounded the doc- 

 trines of the school with such admirable candor, 

 that he converted them unconsciously into any- 

 thing rather than the doctrines of Paley and 

 Bentham. 



As regards logic, the case is much worse. 

 He affected to get rid of universal reasoning, 

 which, if accomplished, would be to get rid of 

 science and logic altogether; of course, he em- 

 ployed or implied the use of universals in almost 

 every sentence of his treatise. He overthrew the 

 syllogism on the ground of petilio principii, and 

 .then immediately set it up again as an indispen- 

 sable test of good reasoning. He defined logic as 

 the Science of Proof, and then recommended a 

 loose kind of inference from particulars to partic- 

 ulars, which he allowed was not conclusive, that 

 is, could prove nothing. Though inconclusive, 

 this loose kind of inference was really the basis 

 of conclusive reasoning. Then, again, he founded 

 induction upon the law of causation, and at the 

 same time it was his express doctrine that the law 

 of causation was learned by induction. What he 

 meant exactly by this law of causation it is im- 

 possible to say. He affirms and denies the plu- 

 rality of causes. Sometimes the sequence of 

 causation is absolutely invariable, sometimes it 

 is conditional. Generally, the law of causation is 

 spoken of as Universal, or as universal through- 

 out Nature ; yet in one passage (at the end of 

 Book III., chapter xxi.) he makes a careful 

 statement to the opposite effect, and this state- 

 ment, subversive as it is of his whole system of 

 induction, has appeared in all editions from the 

 first to the last. On such fundamental questions 

 as the meaning of propositions, the nature of a 

 class, the theory of probability, etc., he is in error 

 where he is not in direct conflict witli himself. 

 But the indictment is long enough already ; there 

 is not space in this article to complete it in detail. 

 To sum up, there is nothing in logic which he has 

 not touched, and he has touched nothing without 

 confounding it. 



To establish charges of this all-comprehen- 

 sive character will, of course, require a large 

 body of proof. It will not be sufficient to take 

 a few of Mill's statements and show that they 

 are mistaken or self-inconsistent. Any writer 

 may now and then fall into oversights, and it 



would be manifestly unfair to pick a few unfortu- 

 nate passages out of a work of considerable ex- 

 tent, and then hold them up as specimens of the 

 whole. On the other hand, in order to overthrow 

 a philosopher's system, it is not requisite to prove 

 his every statement false. If this were so, one 

 large treatise would require ten large ones to re- 

 fute it. What is necessary is to select a certain 

 number of his more prominent and peculiar doc- 

 trines, and to show that, in their treatment, 

 he is illogical. In this article I am, of course, 

 limited in space, and can apply only one test, 

 and the subject which I select for treatment is 

 Mill's doctrines concerning geometrical reason- 

 ing. 



The science of geometry is specially suited to 

 form a test of the empirical philosophy. Mill 

 certainly regarded it as a crucial instance, and 

 devoted a considerable part of his " System of 

 Logic " to proving that geometry is a strictly 

 physical science, and can be learned by direct 

 observation and induction. The particular na- 

 ture of his doctrine, or rather doctrines, on this 

 subject will be gathered as we proceed. Of 

 course, in this inquiry I must not abstain from a 

 searching or even a tedious analysis, when it is 

 requisite for the due investigation of Mill's logi- 

 cal method ; but it will rarely be found necessary 

 to go beyond elementary mathematical knowl- 

 edge, which almost all readers of the Contempo- 

 rary Review will possess. 



As a first test of Mill's philosophy, I propose 

 this simple question of fact : Are there in the 

 material universe such things as perfectly straight 

 lines ? We shall find that Mill returns to this 

 question a categorical negative answer. There 

 exist no such things as perfectly straight lines. 

 How then can geometry exist, if the things about 

 which it is conversant do not exist ? Mill's 

 ingenuity seldom fails him. Geometry, in his 

 opinion, treats not of things as they are in 

 reality, but as we suppose them to be. Though 

 straight lines do not exist, we can experiment in 

 our minds upon straight lines, as if they did ex- 

 ist. It is a peculiarity of geometrical science, 

 be thinks, thus to allow of mental experimenta- 

 tion. Moreover, these mental experiments are 

 just as good as real experiments, because we 

 know that the imaginary lines exactly resemble 

 real ones, and that we can conclude from them 

 to real ones with quite as much certainty as we 

 conclude from one real line to another. If such 

 be Mill's doctrines, we are brought into the fol- 

 lowing position : 



1. Perfectly straight lines do not really exist. 



