294 ELEMENTS OF SCIENCE 



are animals " may be converted thus : Some animals are 

 men. 



A particular negative proposition (0) can only be 

 converted by a threefold process which consists in 



(1) changing the copula from negative to affirmative; 



(2) inverting the terms; and (3) changing the subject 

 into the term contradictory to it. Thus, e.g., the 

 proposition : 



" Some animals are not apes," may be changed by 



(1) Change of copula, " Some animals are apes." 



(2) Inversion of terms, "Apes are some animals." 



(3) Changing subject into its ) "Not apes are some 



contradictory, / animals." 



The third part of logic concerns reasoning, which may 

 be either inductive or deductive. Inductive reasoning 

 has been and will again be referred to.* 



" Deductive reasoning," or ratiocination, consists in 

 the discovery of the relation of one thing to another, by 

 means of the relations they each bear to some third 

 thing. This is effected through the juxtaposition of 

 two propositions in such a manner that a third proposi- 

 tion is seen to follow necessarily from them. The 

 essence of the process (and perception) exists in the 

 word therefore, which expresses the " inference" and 

 that its truth is a necessary consequence of what has 

 been before laid down the third proposition being 

 certainly and necessarily true, if the two preceding 

 propositions are themselves true. 



These three propositions must not contain more than 

 three terms. Each of the first two of the three pro- 



"* See ante, p. 260, and post, p. 309. 



