It is possible that many will declare, as being nonsensical, any attempt to introduce number-concepts[AJ] into an animal's mind, because the necessary motor basis is lacking. We will not, just at this point, stop to discuss whether or not it was not possible to develop number-concepts from purely auditory or visual representations. It is evident, however, that Mr. von Osten believed that a motor basis of some sort was essential. In the case of man this basis is found in the enunciation of the number names (or in the manipulation of the fingers). Mr. von Osten seemed to think that he was justified in assuming that, even in the case of the horse, some form of inner articulation of the word-sounds was possible;--at the same time, in so doing, he did not blink at the psychological difficulty of this hypothesis. The tapping of the foot was to be regarded merely as the expression of the process of inner counting, but not as the motor basis of the process. For this latter purpose tapping would be quite inadequate, for the number complexes which arise in the summation process of counting, could not be differentiated by mere tapping with the foot, any more than a child could learn to count by employing only one finger. Mr. von Osten evidently imagined the process was somewhat like this: Whenever Hans was about to count 5, he would enunciate inwardly the numbers from 1 to 5, and would accompany each word with a tap of the foot. Since, furthermore, wooden pins and balls could be used--as in the case of children--for giving visual content in learning the significance of the number-terms, it seemed as if all the conditions necessary for the formation of number-concepts were supplied. However, the most essential thing had to be presupposed, viz.: that the horse virtually possessed the general power of forming concepts,[AK] and that all that had been lacking was the suitable conditions for its development. Mr. von Osten held tenaciously to this conviction, and it was this conviction that was the basis for the infinite patience with which the tests had been pursued. [Footnote AJ: The author intends to take up the problem of counting, so-called, on the part of animals and of the principle involved, in another work soon to be forthcoming.]