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THE POPULAR SCIENCE MONTHLY.— SUPPLEMENT. 



suits of the experiment to a general law founded 

 upon it. This confusion of ideas has led him ' 

 to the astounding and absurd statement that two 

 instances of any phenomenon, treated in strict 

 accordance with the Method of Difference, are 

 sufficient to give with certainty a general law. 

 But, on the present occasion, I treat of the man- 

 ner in which these methods are set up. We must 

 inquire what is the warrant for their validity, and 

 it will be my duty to prove that in this point 

 Mill has fallen into a complete circulus in pro- 

 bando. These methods are the only means of 

 proving the connection of cause ami effect; yet 

 the methods depend for their validity upon our 

 assurance of the certainty and universality of 

 that connection — that is, upon the universal law 

 of causation. 



To students of Mill's logic it is so familiarly 

 known that he bases induction upon the notion 

 of causation, that it may seem superfluous to 

 prove the position. I must, nevertheless, refer 

 to the chapter treating " Of the Law of Univer- 

 sal Causation," 4 where he speaks of " the notion 

 of Cause being the root of the whole theory of 

 Induction." Observe the comprehensive force 

 of the expression, "the whole theory." Else- 

 where, 3 the " universal fact " of the uniform 

 course of Nature is parenthetically described as 

 " our warrant for all inference from experience," 

 again an unlimited and most comprehensive re- 

 mark. The fourth paragraph of the same chnp- 

 ter commences thus: "Whatever be the most 

 proper mode of expressing it, the proposition 

 that the course of Nature is uniform, is the fun- 

 damental principle, or general axiom of Induc- 

 tion." It is true that Mill sometimes distinguish- 

 es between the Uniformity of Nature and the Law 

 of Causation, and gets into perplexities which I 

 have not space to unravel here. It will, there- 

 fore, be better to refer to a later chapter, 4 where 

 Mill places the matter beyond doubt, saying : 



" As -we recognized in the commencement, and 

 have been enabled to see more clearly in the prog- 

 ress of the investigation, the basis of all these logi- 

 cal operations is the law of causation. The valid- 

 ity of all the Inductive Methods depends on the 

 assumption that every event, or the beginning of 



1 Book m., chapter x., section 2, third and fifth 

 paragraphs. Also chapter xxi., first paragraph. 



8 Chapter v., beginning of second section. As al- 

 most all the quotations in this article are taken from 

 the. third book of the "System of Logic," it will be 

 unnecessary again to cite the number of the book, 

 which, unless otherwise specified, will always be the 

 third bonk, treating "Of Induction." 



3 Chapter iii., beginning of third paragraph. 



4 Chapter xxi., first paragraph. 



every phenomenon, must have some cause ; some 

 antecedent, on the existence of which it is inva- 

 riably and unconditionally consequent. In the 

 Method of Agreement this is obvious ; that meth- 

 od avowedly proceeding on the supposition that 

 we have found the true cause as soon as we have 

 negatived every other. The assertion is equally 

 true of the Method of Difference. The method 

 authorizes us to infer a general law from two in- 

 stances : l one, in which A exists together with a 

 multitude of other circumstances, and B follows ; 

 another, in which, A being removed, and all other 

 circumstances remaining the same, B is prevented. 

 What, however, does this prove ? It proves that 

 B, in the particular instance, cannot have had any 

 other cause than A ; but to conclude from this that 

 A was the cause, or that A will on other occasions 

 be followed by B, is only allowable on the assump- 

 tion that B must have some cause ; that, among its 

 antecedents in any single instance in which it oc- 

 curs, there must be one which has the capacity of 

 producing it at other times. This being admitted, 

 it is seen that in the case in question that antece- 

 dent can be no other than A ; but that, if it be no 

 other than A, it must be A, is not proved, by these 

 instances at least, but taken for granted. There 

 is no need to spend time in proving that the same 

 thing is true of the other Inductive Methods. The 

 universality of the law of causation is assumed in 

 them all." 



It would be easy to show that this passage is 

 in substance all wrong and unscientific. The idea 

 that we must assume each phenomenon to have 

 one antecedent, and only one, which has the ca- 

 pacity of producing it at (all ?) other times, is 

 quite inconsistent with the scientific idea of cau- 

 sation, as well as with Mill's own statements in 

 other places. It is to a conjunction of causes, 

 joined to all kinds of negative conditions — that 

 is to say, the absence of counteracting causes — 

 that the production of an effect is due ; and this 

 fact alone is enough to disperse Mill's extraordi- 

 nary assertion that two instances can prove a 

 general law. But the point with which we are 

 concerned now is the complete dependence of 

 the Inductive Methods on the Law of Causation ; 

 not merely the occasional truth of that law, but 

 its universality is assumed in all the methods. 



The four great pillars of Mill's logical edifice 

 rest, then, upon the universal law of causation. 

 Upon what does this law rest ? An ancient sys- 

 tem of cosmogony represented the world as rest- 

 ing on an elephant, and the elephant on a tor- 

 toise ; we want something to correspond to the 

 tortoise. Now, it is quite certain that Mill would 



1 This is the absurd statement alluded to on the 

 preceding page. 



