The point of a 'society,' as the term is here used, is that it is self-sustaining; in other words, that it is its own reason. Thus a society is more than a set of entities to which the same class-name applies: that is to say, it involves more than a merely mathematical conception of 'order.' To constitute a society, the class-name has got to apply to each member, by reason of genetic derivation from other members of that same society. The members of the society are alike because, by reason of their common character, they impose on other members of the society the conditions which lead to that likeness.
This likeness consists in the fact that (i) a certain element of 'form' is a contributory component to the individual satisfaction of each member of the society; and that (ii) the contribution by the element to the objectification of any one member of the society for prehension by other members promotes its analogous reproduction in the satisfactions of those other members. Thus a set of entities is a society (i) in virtue of a 'defining characteristic' shared by its members, and (ii) in virtue of the presence of the defining characteristic being due to the environment provided by the society itself.
For example, the life of man is a historic route of actual occasions
which in a marked degree—to be discussed more fully later—inherit from each other. That set of occasions, dating from his first acquirement of the Greek language and including all those occasions up to his loss of any adequate knowledge of that language, constitutes a society in reference to knowledge of the Greek language. Such knowledge is a common characteristic inherited from occasion to occasion along the historic route. This example has purposely been chosen for its reference to a somewhat trivial element of order, viz. knowledge of the Greek language; a more important character of order would have been that complex character in virtue of which a man is considered to be the same enduring person from birth to death. Also in this instance the members of the society are arranged in a serial order by their genetic relations. Such a society is said to possess 'personal order.'
Thus a society is, for each of its members, an environment with some element of order in it, persisting by reason of the genetic relations between its own members. Such an element of order is the order prevalent in the society.