JOHN STUART MILL'S PHILOSOPHY TESTED. 



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JOHN STUART MILL'S PHILOSOPHY TESTED. 



By W. STANLEY JEVONS, F. E. S. 



II. 



IN the previous article on John Stuart Mill's 

 " Philosophy," I made the strange assertion 

 that Mill's mind was essentially illogical. To those 

 who have long looked upon him as their guide, 

 philosopher, and friend, such a statement must 

 of course have seemed incredible and absurd, 

 and it will require a great body of evidence to 

 convince them that there is any ground for the 

 assertion. My first test of his logicalness was 

 derived from his writings on geometrical science. 

 I showed, by carefully authenticated extracts, 

 that Mill had put forth views which necessarily 

 imply the existence of perfectly straight lines ; 

 yet he had at the same time distinctly denied the 

 existence of such lines. It was pointed out that 

 he emphatically promised to use names always as 

 the names of things, not as the names of our 

 ideas of things ; yet, as straight lines in his opin- 

 ion do not exist, the name straight line is either 

 the name of "just nothing at all," as James 

 Mill would have said, or else it is the name of our 

 ideas of what they are. It is by experimenting 

 on these ideal straight lines in the mind that we 

 learn the axioms and theorems of geometry ac- 

 cording to Mill ; nevertheless Mill had denounced, 

 as the cardinal error of philosophy, the handling 

 ideas instead of things, and had, indeed, in the 

 earlier editions of the " System of Logic," as- 

 serted that not a single truth ever had been ar- 

 rived at by this method, except truths of psy- 

 chology. Mill asserted that we might experi- 

 ment on lines in the mind by prolonging them to 

 any required distance ; but these lines according 

 to Mill's own statements must have thickness, 

 and on minute inquiry it was found impossible to 

 attach any definite meaning at all to the prolon- 

 gation of a thick line. Finally, it .was pointed 

 out that, when Mill incidentally speaks of an im- 

 portant mathematical theorem concerning the 

 ratio of the diameter and circumference of the 

 circle, he abandons his empirical philosophy pro 

 tempore, and speaks of the ratio in question as 

 being discovered by a long train of difficult rea- 

 soning. 



Such is the summary of the first small install- 

 ment of my evidence. On some future occasion 

 I shall return to the subject of geometrical rea- 

 soning, which is far from being exhausted. It 



will then be proved that, on the question whether 

 geometry is an inductive or a deductive science, 

 Mill held opinions of every phase ; in one part 

 of his writings geometry is strictly inductive ; in 

 another part it is improperly called inductive ; 

 elsewhere it is set up as the type of a deductive 

 science, and anon it becomes a matter of direct 

 observation and experiment ; presently Mill dis- 

 covers, unexpectedly, that there is no difference 

 at all between an inductive and a deductive sci- 

 ence — the true distinction is between a deductive 

 and an experimental science. But Mill charac- 

 teristically overlooks the fact that, if the differ- 

 ence lies between a deductive and an experimental 

 science, and not between a deductive and an in- 

 ductive science, then a similar line of difference 

 must be drawn between an inductive and an 

 experimental science, although Mill's inductive 

 methods are the Four Experimental Methods. 



But the origin of our geometrical knowledge 

 is a very slippery subject, as I before allowed. 

 It would not be fair to condemn Mill for the 

 troubles in which he involved himself in regard 

 to such a subject if there were no other counts 

 proved against him. Certainly he selected geom- 

 etry as a critical test of the truth of his empiri- 

 cal philosophy, but he may have erred in judg- 

 ment in choosing so trying a test. Let us, there- 

 fore, leave geometry for the present, and select 

 for treatment in this second article a much 

 broader and simpler question — one which lies at 

 the basis of the philosophy of logic and knowl- 

 edge. We will endeavor to gain a firm compre- 

 hension of Mill's doctrine concerning the nature 

 and importance of the relation of Resemblance. 

 This question touches the very nature of knowl- 

 edge itself. Now, critics who are considered to 

 be quite competent to judge have declared that 

 Mill's logic is peculiarly distinguished by the 

 thorough analysis which it presents of the cogni- 

 tive and reasoning processes. Mill has not re- 

 stricted himself to the empty forms and methods 

 of argument, but has pushed his inquiry, as they 

 think, boldly into the psychology and philosophy 

 of reasoning. In the " System of Logic," then, 

 we shall find it clearly decided whether resem- 

 blance is. or is not, the fundamental relation with 

 which reasoning is concerned. It was the doc- 



