DEDUCTIVE REASONING. 65 



the second degree. The real forms of the propositions 

 here given are exactly those shown in the symbolic state 

 ment, but in this and many other cases it will be sufficient 

 to state them in ordinary elliptical language for sake of 

 brevity. In scientific treatises a term and its definition 

 are often both given in the same sentence, as in The 

 weight of a body in any given locality, or the force with 

 which the earth attracts it, is proportional to its mass. 

 The conjunction or in this statement gives the force of 

 equivalence to the parenthetic definition, so that the 

 propositions really are 



Weight of a body = force with which the earth at 

 tracts it. 



Weight of a body = weight, &c. proportional to its 

 mass. 



A slightly different case of inference consists in sub 

 stituting in a proposition of the form A = AB a defi 

 nition of the term B. Thus from A = AB and B = C 

 we get A = AC. For instance, we may say that Metals 

 are elements and Elements are incapable of decompo 

 sition. 



Metal = metal element. 



Element = what is incapable of decomposition. 



Hence 



Metal = metal incapable of decomposition. 

 It is almost needless to point out that the form of these 

 arguments would not suffer any real modification if some 

 of the terms happened to be negative ; indeed in the last 

 example * incapable of decomposition may be treated as 

 a negative term. Taking 



A = metal 



B = element 



C = what is capable of decomposition 

 c =~what is incapable of decomposition (p. 17); 



