METAPHYSICS AND THE OTHER SCIENCES 245 



a term which is really concrete. Thus when we say red, blue, green, 

 are different kinds of color, surely what we mean is different kinds of 

 colored surface. Qua colored, they are not different; I mean just as 

 much and no more when I say "a red thing is colored," or "has 

 color," as when I say " a green thing is colored." If Mill were right, the 

 proposition "red is a color" ought to mean exactly the same as "red 

 is red." Or, to put it in another way, it would become impossible to 

 form in thought any concept of a single class of colored things. 



But need we infer because abstract terms are singular that there- 

 fore they have no intension and are mere meaningless marks? Com- 

 monly as this inference is made, it seems to me clearly mistaken. It 

 seems, in fact, to rest upon the vague and ill-defined principle that 

 an attribute can have no attributes of its own. That it is false is 

 shown, I think, by the simple reflection that scientific definitions 

 are one and all statements as to the meaning of abstract names of 

 attributes and relations. For example, the definition of a circle is 

 a statement as to the meaning of circularity, the legal definition of 

 responsible persons a statement as to the meaning of the abstraction 

 "responsibility," and so on. (We only evade the point if we argue 

 that abstract terms when used as the subjects of propositions are 

 really being employed concretely. For "cruelty is odious," for 

 instance, does not merely mean that cruel acts are odious acts, 

 but that they are odious because they are cruel.) In fact, the doc- 

 trine that abstract terms have no intension would seem, if thought 

 out, to lead to the view that there are only classes of individuals, but 

 no classes of classes. Thus to say "cruel acts are odious because 

 cruel " implies, not only that I can form the concept of a class of cruel 

 acts, but also that of classes of odious acts of which the class of cruel 

 acts in its turn is a member. And to admit as much as this is to admit 

 that the class of cruel acts, considered as a member of the class of odious 

 acts, shares the common predicate of odiousness with the other classes 

 of acts composing the higher class. Hence the true account of abstract 

 terms seems to me to be that we have in them another limiting case, 

 a case in which the extension and the intension are coincident. Inci- 

 dentally, by illustrating the ambiguity of the principle that attributes 

 have no attributes of their own, our discussion seems to indicate the 

 advantage of taking the purely extensional view as opposed to the 

 predicative view of the import of propositions as the basis of an ele- 

 mentary treatment of logical doctrine. 



