Different observers have found that subjects sometimes describe a sensation as ‘more than one, but less than two.’  I had a subject who habitually described this feeling as ‘one and a half.’  This does not mean that he has one and a half sensations.  That is obviously impossible.  It must mean that the sensation seems just as much like two as it does like one, and he therefore describes it as half way between.  If we could discover any law governing this feeling of half-way-between-ness, that might well indicate the threshold.  But such feelings are not common.  Sensations which seem between one and two usually call forth the answer ‘doubtful,’ and have a negative rather than a positive character.  This negative character cannot be due to the stimulus; it must be due to the fluctuating attitudes of the subject.  However, if the doubtful cases could be classed with the ‘more than one but less than two’ cases and a law be found governing them, we might have a threshold mark.  But such a law has not been formulated, and if it had been an analysis of the ‘doubtful’ cases would invalidate it.  For, since we cannot have half of a sensation or half of a place as we might have half of an area, the subject regards each stimulation as produced by one or by two points as the case may be.  Occasionally he is stimulated in such a way that he can regard the object as two or as one with equal ease.  In order to describe this feeling he is likely to use one or the other of the methods just mentioned.

We might say that when the sum of conditions is such that the subject perceives two points, the points are above the threshold, and when the subject perceives one point when two are given they are below the threshold.  This might answer the purpose very well if it were not for the Vexirfehler.  According to this definition, when the Vexirfehler appears we should have to say that one point is above the threshold for twoness, which is a queer contradiction, to say the least.  It follows that all of the elaborate and painstaking experiments to determine a threshold are useless.  That is, the threshold determinations do not lead us beyond the determinations themselves.

In order to explain the fact that a person sometimes fails to distinguish between one point and two points near together, it has been suggested that the sensations fuse.  This, I suppose, means either that the peripheral processes coalesce and go to the center as a single neural process, or that the process produced by each stimulus goes separately to the brain and there the two set up a single activity.  Somewhat definite ‘sensory circles,’ even, were once believed in.