THE FOUR EXPERIMENTAL METHODS. 



259 



all have in common the circumstance 

 A, and (as far as can be observed) no 

 other circumstance, the Method of 

 Agreement, so far, bears testimony 

 to a connection between A and a. 

 In order to convert this evidence of 

 connection into proof of causation by 

 the direct Method of Difference, we 

 ought to be able, in some one of these 

 instances, as, for example, A B C, to 

 leave out A, and observe whether by 

 doing so a is prevented. Now suj)- 

 posing (what is often the case) that 

 we are not able to try this decisive 

 experiment, yet, provided we can by 

 any means discover what would be 

 its result if we could try it, the ad- 

 vantage will be the same. Suppose, 

 then, that as we previously examined 

 a variety of instances in which a oc- 

 curred, and found them to agree in 

 containing A, so we now observe a 

 variety of instances in which a does 

 not occur, and find them agree in not 

 containing A ; which establishes, by 

 the Method of Agreement, the same 

 connection between the absence of A 

 and the absence of a, which was before 

 established between their presence. 

 As, then, it had been shown that 

 whenever A is present a is present, 

 so it being now shown that when A 

 is taken away a is removed along 

 with it, we have by the one proposi- 

 tion A B C, a 6 c, by the other B C, 

 b c, the positive and negative in- 

 stances which the Method of Differ- 

 ence requires. 



This method may be called the 

 Indirect Method of Difference, or 

 the Joint Method of Agreement and 

 Difference, and consists in a double 

 employment of the Method of Agree- 

 ment, each proof being independent 

 of the other, and corroborating it. 

 But it is not equivalent to a pioof by 

 the direct Method of Difference. For 

 the requisitions of the Method of Dif- 

 ference are not satisfied unless we 

 can be quite sure either that the in- 

 stances affirmative of a agree in no 

 antecedent whatever but A, or that 

 the instances negative of a agree in 

 potbing but the nefication of A, Now 



if it were possible, which it never is, 

 to have this assurance, we should not 

 need the joint method ; for either of 

 the two sets of instances separately 

 would then be sufficient to prove 

 causation. This indirect method, 

 therefore, can only be regarded as a 

 great extension and improvement of 

 the Method of Agreement, but not 

 as participating in the more cogent 

 nature of the Method of Difference. 

 The following may be stated as its 

 canon : — 



Third Canon. 

 If two or more instances in which 

 the phenomenon occurs have only one 

 circumstance in common, while two or 

 more instances in which it does not 

 occur have nothing in common save the 

 absence of that circumstance, the cir- 

 cumstance in which alone the two sets 

 of instances differ is the effect, or the 

 cause, or an indispensable part of the 

 cause, of the phenomenon. 



We shall presently see that the Joint 

 Method of Agreement and Difference 

 constitutes, in another respect not yet 

 adverted to, an improvement upon 

 the common Method of Agreement, 

 namely, in being unaffected by a 

 characteristic imperfection of that 

 method, the nature of which still 

 remains to be pointed out. But as 

 we cannot enter into this exposition 

 without introducing a new element 

 of complexity into this long and in- 

 tricate discussion, I shall postpone it 

 to a subsequent chapter, and shall at 

 once proceed to a statement of two 

 other methods, which will complete 

 the enumeration of the means which 

 mankind possess for exploring the laws 

 of nature by specific observation and 

 experience. 



§ 5. The first of these has been 

 aptly denominated the Method of Re- 

 sidues. Its principle is very simple. 

 Subducting from any given pheno- 

 menon all the portions which, by 

 virtue of preceding inductions, can 

 be assigned to known causes, the re- 

 maii^der will be the effect of the 



