40 THE PRINCIPLES OF SCIENCE. [CHAP. 



Partial Identities. 



A second highly important kind of proposition is that 

 which I propose to call a partial identity. When we say 

 that "All mammalia are vertebrata," we do not mean that 

 mammalian animals are identical with vertebrate animals, 

 but only that the mammalia form a part of the class verte- 

 brata. Such a proposition was regarded in the old logic as 

 asserting the inclusion of one class in another, or of an 

 object in a class. It was called a universal affirmative pro- 

 position, because the attribute vertebrate was affirmed of the 

 whole subject mammalia ; but the attribute was said to be 

 undistributed, because not all vertebrata were of necessity 

 involved in the proposition. Aristotle, overlooking the im- 

 portance of simple identities, and indeed almost denying 

 their existence, unfortunately founded his system upon the 

 notion of inclusion in a class, instead of adopting the basis 

 of identity. He regarded inference as resting upon the rule 

 that what is true of the containing class is true of the 

 contained, in place of the vastly more general rule that 

 what is true of a class or thing is true of the like. Thus 

 he not only reduced logic to a fragment of its proper self, 

 but destroyed the deep analogies which bind together 

 logical and mathematical reasoning. Hence a crowd of 

 defects, difficulties and errors which will long disfigure the 

 first and simplest of the sciences. 



It is surely evident that the relation of inclusion rests 

 upon the relation of identity. Mammalian animals cannot 

 be included among vertebrates unless the}' be identical with 

 part of the vertebrates. Cabinet Ministers are included 

 almost always in the class Members of Parliament, because 

 they are identical with some who sit in Parliament. We 

 may indicate this identity with a part of the larger class in 

 various ways ; as for instance, 



Mammalia = part of the vertebrata. 



Diatomacea3 = a class of plants. 



Cabinet Ministers = some members of Parliament. 



Iron = a metal. 



In ordinary language the verbs is and are express mere 

 inclusion more often than not. Men are mortals, means 



