40 • THE PRmCIPLES OF SCIENCE. [chap 



Partial Identities. 



A second liiglily important kind of proposition is that 

 which I propose to call a partial identiti/. When we say 

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

 mammalian animals are identical with vertebrate animals, 

 bnt only that the mammalia form impart of the class verte- 

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

 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 tin- 

 whole subject mammalia ; but the attribute was said to lu 

 undistributed, because not all vertebrata were of necessit} 

 involved in the proposition. Aristotle, overlooking theim 

 portance of simple identities, and indeed almost denying 

 their existence, unfortunately founded his system upon th' 

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

 of identity. He regarded inl'erence as resting upon the ml 

 that wliat is true of the containing class is true of th 

 contained, in place of the vastly more general rule tlui 

 what IS true of a class or thing is true of the like. Thr. 

 he not only reduced logic to a fragment of its proper seb. 

 but destroyed the deep analogies which bind togeth. 

 logical and mathematical reasoning. Hence a crowd < 

 defects, difficulties and errors which will long disfigure th 

 hrst and simplest of the sciences. 



It is surely evident that the relation of inclusion rest 

 upon the relation of identity. Miunmalian animals cannu 

 be included among vertebrates unless they be identical witl; 

 part of the vertt;brates. Cabinet Ministers are included 

 almost always in the class Members of Parliament, becaus< 

 they are identical with some who sit in rarliament. We 

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

 various ways ; as for instance. 



Mammalia = part of the vertebrata. 

 l>iatomace?e = 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. iJ/e/i are mortals, means 



