This also was indicated by collective, indefinite names, and sometimes by onomatopœia. Eventually this was done by abstract prefixes or suffixes. Three steps in the development of declension are known. In the first there are no distinctive forms for the cases, in the second an excessive number of casual forms express relations between ideas, and in the third the number of cases is limited to those of essential relations. Where case was externally determined the development followed the order of perception, the subject, the object, and the determination of the object being shown respectively by the nominative, the accusative, and the dative and genetive cases. The emotional elements are the points of departure in internal determination of cases. The subject or the object was indicated by accent or syntactical position. Wundt considers emotional emphasis the source of the distinction of cases. All cases internally determined are dependent on psychological associations, except that of the subject. Originally the verb had no temporally distinct character, since consciousness presents objects and their qualities on the same temporal plane with states of consciousness. Thought later eliminated the time index from all but the states of consciousness. Finally a verb came to be the expression of the thought or will of the subject. A perception of action in objective form probably originated in an emotional state. The third person which denotes objects of thought is, like metaphysical "substance," a projection into the world of objects of an invariable substratum of the changing states of consciousness. In this sense things are the "third persons," since they express the durable element of our objective representations. Voice, mode, and tense evolved in the order given. Tense is a late development. Primitive man related events as present. Then, as now, each spoke what might be called his own dialect, having expressions peculiar to himself. For that reason the psychology of language is a chapter of social psychology. Its materials are furnished by common elements, through values of words accepted in accordance with social agreement.
From a philosophical point of view the most brilliant results of mathematical logic are the exact theories of infinity and continuity. In infinite collections, for example, the assemblage of finite integers, we can establish a one-to-one correspondence between the entire class and a proper part. Thus, the cardinal number of an infinite class is the same as the cardinal number of a certain part of the class. The traditional contradiction in the concept of infinity resulted from the assumption that all members obey complete induction. Closely allied to the problems about infinity are those concerning continuity, and their solution is obtained by the same method. The paradoxes of Zeno and the difficulties encountered in the analysis of space, time and motion are completely removed by the modern theory of continuity. According to this the continuum consists of an infinite number of distinct elements. It is true that these elements cannot be obtained by continual division but it does not
