430 PROCEEDINGS OF THE AMERICAN ACADEMY 



It may be the case that either or both of these increases does not 

 take place. If P is a negative term, it may have no depth, and there- 

 fore adds nothing. to the depth of S. If S is a particular term, it may 

 have no breadth, and then adds nothing to the breadth of P. This 

 latter case often occurs in metaphysics, and, on account of not-P as well 

 as P being predicated of S, gives rise to an appearance of contradiction 

 where there really is none ; for, as a contradiction consists in giving to 

 contradictory terms some breadth in common, it follows that, if the com- 

 mon subject of which they are predicated has no real breadth, there is 

 only a verbal, and not a real contradiction. It is not really contradic- 

 tory, for example, to say that a boundary is both within and without 

 what it bounds. There is also another important case in which we 

 may learn that " S is P," without thereby adding to the depth of S or 

 the breadth of P. This is when, in the very same act by which we 

 learn that S is P, we also learn that P was covertly contained in the 

 previous depth of S, and that consequently S was a part of the previous 

 breadth of P. In this case, P gains in extensive distinctness and S in 

 comprehensive distinctness. 



We are now in condition to examine Vorlander's objection to the 

 inverse proportionality of extension and comprehension. He requires 

 us to think away from an object all its qualities, but not, of course, by 

 thinking it to be without those qualities, that is, by denying those 

 qualities of it in thought. How then ? Only by supposing ourselves 

 to be ignorant whether it has qualities or not, that is, by diminishino- 

 the supposed information ; in which case, as we have seen, the depth 

 can be diminished without increasing the breadth. In the same man- 

 ner we can suppose ourselves to be ignorant whether any American 

 but one exists, and so diminish the breadth without increasing the 

 depth. 



It is only by confusing a movement which is accompanied with a 

 change of information with one which is not so, that people can con- 

 found generalization, induction, and abstraction. Generalization is an 

 increase of breadth and a decrease of depth, without change of infor- 

 mation. Induction is a certain increase of breadth without a change 

 of depth, by an increase of believed information. Abstraction is a 

 decrease of depth without any change of breadth, by a decrease of con- 

 ceived information. Specification is commonly used (I should say 

 unfortunately) for an increase of depth without any change of breadth, 

 by an increase of asserted information. Supposition is used for the 



