62 THE PRINCIPLES OF SCIENCE. 



of the general rule of inference. We have two propo- 

 sitions, A = B and B = C, and we may for a moment con- 

 sider the second one as affirming a truth concerning B 

 while the former one informs us that B is identical with 

 A ; hence by substitution we may affirm the same truth 

 of A. It happens in this particular form that the truth 

 affirmed is identity to C, and we might, if we had preferred, 

 have considered the substitution as made by means of the 

 second identity in the first. Having two identities we 

 have a choice of the mode in which we will make the 

 substitution, though the result is exactly the same in 

 either case. 



Now compare the three following formulae 



(1) A = B = C hence A^C 



(2) A = B-C hence A-C 



(3) A B ^ C, no inference. 



In the second formula we have an identity and a differ- 

 ence, and we are able to infer a difference ; in the third 

 we have two differences and are unable to make any 

 inference at all. Because A and C both differ from B, we 

 cannot tell whether they will or will not differ from each 

 other. The flowers and leaves of a plant may both differ 

 in colour from the earth in which the plant grows, and 

 yet they may differ from each other ; in other cases the 

 leaves and stem may both differ from the soil and yet agree 

 with each other. Where we have difference only we can 

 make no inference ; where we have identity we can infer. 

 This fact gives great countenance to my assertion that 

 inference proceeds always through an identity, but may 

 be indifferently effected in a difference or an identity. 



Deferring a more complete discussion of this point, I 

 will only mention now that arguments from double 

 identity occur very frequently, and are usually taken 

 for granted owing to their extreme simplicity. In the 

 equivalency of words it must be constantly employed. If 



