OP ARTS AND SCIENCES : NOVEMBER 13, 1867. 431 



same process when there is only a conceived increase of information. 

 Determination, for any increase of depth. Restriction, for any decrease 

 of breadth ; but more particularly without change of depth, by a sup- 

 posed decrease of information. Descent, for a decrease of breadth and 

 increase of depth, without change of information. 

 • Let us next consider the effect of the different kinds of reason- 

 ing upon the breadth, depth, and area of the two terms of the con- 

 clusion. 



In the case of deductive reasoning it would be easy to show, were it 



■ 



necessary, that there is only an increase of the extensive distinctness 

 of the major, and of the comprehensive distinctness of the minor, with- 

 out any clwinge in information. Of course, when the conclusion is 

 negative or particular, even this may not be effected. 



Induction requires more attention. Let us take the following ex- 

 ample : — 



S', S", S"', and S IV have been taken at random from among the M's ; 

 S' S", S"', and S ,v are P : 

 .-. any M is P. 



We have here, usually, an increase of information. M receives an 

 increase of depth, P of breadth. There is, however, a difference be- 

 tween these two increases. A new predicate is actually added to M ; 

 one which may, it is true, have been covertly predicated of it before, 

 but which is now actually brought to light. On the other hand, P is 

 not yet found to apply to anything but S', S", S"', and S IV , but only to 

 apply to whatever else may hereafter be found to be contained under 

 M. The induction itself does not make known any such thing. Now 

 take the following example of hypothesis : — 

 M is, for instance, P', P", P'", and P 1V ; 

 S is P', P", P"', and P ,v : 

 .-. S is all that M is. 



Here again there is an increase of information, if we suppose the 

 premises to represent the state of information before the inferences. 

 S receives an addition to its depth ; but only a potential one, since there 

 is nothing to show that the M's have any common characters besides 

 P', P", P"', and P IV . M, on the other hand, receives an actual in- 

 crease of breadth in S, although, perhaps, only a doubtful one. There 

 is, therefore, this important difference between induction and hypothe- 

 sis, that the former potentially increases the breadth of one term, and 

 actually increases the depth of another, while the latter potentially in- 



