Any sensation, whether produced by one or by many objects, is one, but there may be a difference in the quality of a sensation produced by one object and that of a sensation produced by more than one object.  If this difference is clear and distinct, the person assigns to each sensation the number he has associated with it.  He gives it the name two when it has the quality he has associated with that idea.  But the qualities of a sensation from which the number of objects producing it is inferred are not always clear and distinct.  The quality of the sensation must not be confused with any quality of the object.  If we had to depend entirely on the sense of touch and always remained passive and received sensations only when we were touched by something, there is no reason why we should not associate the idea of one with the sensation produced by two objects and the idea of two with that produced by one object—­assuming that we could have any idea of number under such circumstances.  The quality of a sensation from which number is inferred depends on several factors.  The number itself is determined by the attitude of the subject, but the attitude is determined largely by association.  A number of facts show this.  When a person is being experimented on, it is very easy to confuse him and make him forget how two feel and how one feels.  I have often had a subject tell me that he had forgotten and ask me to give him two distinctly that he might see how it felt.  In other words, he had forgotten how to associate his ideas and sensations.  In developing the Vexirfehler I found it much better, after sufficient training had been given, not to give two at all, for it only helped the subject to perceive the difference between two and one by contrast.  But when one was given continually he had no such means of contrast, and having associated the idea of two with a sensation he continued to do so.  The one subject with whom I did not succeed in developing the Vexirfehler to any great extent perceived the difference by comparing the sensation with one he had had some time before.  I could get him, for a few times, to answer two when only one was given, but he would soon discover the difference, and he said he did it by comparing it with a sensation which he had had some time before and which he knew was two.  By this means he was able to make correct associations when otherwise he would not have done so.  It has been discovered that when a subject is being touched part of the time with two and part of the time with one, and the time it takes him to make his judgments is being recorded, he will recognize two more quickly than he will one if there is a larger number of twos in the series than there is of ones.  I do not see how this could be if the sensation of two is any more complex than that of one.  But if both sensations are units and all the subject needs to do is to associate the sensation with an idea, then we should expect that the association he had made most frequently would be made the most quickly.