48 THE PRINCIPLES OF SCIENCE. 



class in another, or of an object in a class. It was called 

 a universal affirmative proposition, 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 propo- 

 sition. Aristotle, overlooking the importance of simple 

 identities, and indeed almost denying their existence, un- 

 fortunately founded his system upon the notion of inclusion 

 in a class, in place of identity. He regarded inference as 

 resting upon the rule that what is true of the containing 

 class is true of the contained, instead 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 a relation of identity. Mammalian animals cannot 

 be included among vertebrates unless they be identical 

 with part of the vertebrates. Cabinet Ministers are in- 

 cluded almost always in the class Members of Parlia- 

 ment, 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 

 Diatoms = species of plants. 



Cabinet Ministers = some Members of Parliament. 

 Iron = a metal. 



In ordinary language the verbs is or are express mere 

 inclusion more often than not. Men are mortals, means 

 that men form a part of the class mortal, but great con- 

 fusion exists between this sense of the verb and that in 

 which it expresses identity, as in ' The sun is the centre of 

 the planetary system/ The introduction of the indefinite 



