The one point of philosophical interest about this doctrine appears alike in the scheme of the "Categories" in the presence of a category of "substance," and in the list of "Predicaments" in the sharp distinction drawn between "definition" and "proprium." From a logical point of view it does not appear why _any_ proprium, _any_ character belonging to all the members of a class and to them alone, should not be taken as defining the class. Why should it be assumed that there is only _one_ predicate, viz. _man_, which precisely answers the question, "What is Socrates?" Why should it not be equally correct to answer, "a Greek," or "a philosopher"? The explanation is that Aristotle takes it for granted that not all the distinctions we can make between "kinds" of things are arbitrary and subjective. Nature herself has made certain hard and fast divisions between kinds which it is the business of our thought to recognise and follow. Thus according to Aristotle there is a real gulf, a genuine difference in kind, between the horse and the ass, and this is illustrated by the fact that the mule, the offspring of a horse and an ass, is not capable of reproduction. It is thus a sort of imperfect being, a kind of "monster" existing _contra naturam_. Such differences as we find when we compare _e.g._ Egyptians with Greeks do not amount to a difference in "kind." To say that Socrates is a man tells me what Socrates is, because the statement places Socrates in the real kind to which he actually belongs; to say that he is wise, or old, or a philosopher merely tells me some of his attributes. It follows from this belief in "real" or "natural" kinds that the problem of definition acquires an enormous importance for science. We, who are accustomed to regard the whole business of classification as a matter of making a grouping of our materials such as is most pertinent to the special question we have in hand, tend to look upon any predicate which belongs universally and exclusively to the members of a group, as a sufficient basis for a possible definition of the group. Hence we are prone to take the "nominalist" view of definition, _i.e._ to look upon a definition as no more than a declaration of the sense which we intend henceforward to put on a word or other symbol. And consequently we readily admit that there may be as many definitions of a class as it has different propria. But in a philosophy like that of Aristotle, in which it is held that a true classification must not only be formally satisfactory, but must also conform to the actual lines of cleavage which Nature has established between kind and kind, the task of classificatory science becomes much more difficult. Science is called on to supply not merely a definition but _the_ definition of the classes it considers, _the_ definition which faithfully reflects the "lines of cleavage" in Nature. This is why the Aristotelian view is that a true