DEDUCTIVE REASONING. 63 



the ancient Greek ^aX/co? is our copper, tlien it must be 

 the French cuivre, the German kupfer, the Latin cuprum, 

 because fc these are words, in one sense at least, equivalent 

 to copper. Whenever we can give two definitions or 

 expressions for the same term, the formula applies ; thus 

 Senior defined wealth as ' whatever is transferable, limited 

 in supply, and productive of pleasure or preventive of 

 pain ;' it is also equivalent to ' whatever has value in 

 exchange -' hence obviously 4 Whatever has value in ex- 

 change' = ' Whatever is transferable, limited in supply, and 

 productive of pleasure or preventive of pain/ Two ex- 

 pressions for the same term are often given in the same 

 sentence, and their equivalency implied. Thus Thomson 

 and Tait say c , ' The naturalist may be content to know 

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

 that which k 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. 



For the term * matter' in either of these identities we 

 may substitute its equivalent given in the other definition. 

 Elsewhere they often employ sentences of the form exem- 

 plified'in the following d ; ' The integral curvature, or whole 

 change of direction of an arc of a plane curve, is the angle 

 through which the tangent has turned as we pass from 

 one extremity to the other.' This sentence is certainly of 

 the form 



The integral curvature = the whole change of direction, 

 &c. = the angle through which the tangent has 

 turned, &c. 



Disguised cases of the same kind of inference occur 

 throughout all sciences, and a remarkable instance is 

 found in algebraic geometry. Mathematicians readily 



c 'Treatise on Natural Philosophy,' vol. i. p. 161. 

 d Ibid. vol. i. p. 6. 



