52 THE PRINCIPLES OF SCIENCE. [CRAP. 



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 identity, but may be equally well effected in pro- 

 positions asserting difference or 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 regard to the equi- 

 valence of words this form of inference must be constantly 

 employed. If the ancient Greek %aXo5 is our copper, then 

 it must be the French cuivre, the German kupfcr, the Latin 

 cuprum, because these are words, in one sense at least, 

 equivalent to copper. Whenever we can give two defini- 

 tions or expressions for the same term, the formula applies ; 

 thus Senior defined wealth as " All those things, and those 

 things only, which are transferable, are limited in supply, 

 and are directly or indirectly productive of pleasure or 

 preventive of pain." Wealth is also equivalent to " things 

 which have value in exchange ; " hence obviously, " things 

 which have value in exchange = all those things, and those 

 things only, which are transferable, &c." Two expressions 

 for the same term are often given in the same sentence, and 

 their equivalence implied. Thus Thomson and Tait say, 1 

 "The naturalist may be content to know matter as that 

 which can be perceived by the senses, or as that which 

 can be acted upon by or can exert force." I take this to 

 mean 



Matter = what can be perceived by the senses ; 



Matter = what can be acted upon by or can exert 

 force. 



1 Treatise on Natural Philosophy, vol. i. p. 161. 



