§ 3. Further questions.—It may cost more or less effort to discern an unlikeliness. The difficulty is greatest when the unlikeliness is very small. Now it has been maintained that what we really estimate when we suppose ourselves to be estimating degrees of unlikeliness, is the degree of difficulty which we find in perceiving unlikeliness at all; the greater the difficulty, the less the unlikeliness. A simple consideration shows that this is untrue. The lower grades of unlikeliness are specially difficult to distinguish; and, as the unlikeliness is increased in degree, it becomes more easily discernible. But this holds only up to a certain point. When the unlikeliness is sufficiently great it is discernible without appreciable difficulty, and after this further increase does not make it appreciably easier to perceive. We must therefore conclude that our judgment of unlikeliness depends primarily on the actual unlikeliness, and not on the ease or difficulty of detecting it. At the same time, the ease or difficulty of detecting an unlikeliness may more or less affect our judgment of its amount. It may thus be a source of error, and may to some extent explain apparent deviations from Weber's law.

Here a question of some importance arises. It is often assumed without discussion that all least perceptible degrees of unlikeliness between the same kinds of sensible qualities are equal. Now this is by no means selfevident. It is indeed not selfevident that degrees of unlikeliness which are just discernible, are therefore equally discernible, that is to say, discernible with equal ease. Even if they are all discernible with equa ease, it does not follow that they are themselves equal. The appeal in the last instance must be to actual comparison. A valid reason for assuming them to be equal is that they appear equal. Another reason is that they occur under the conditions of Weber's law, which holds in general for equal degrees of unlikeness.

A stimulus must reach a certain degree of intensity before it can produce any discernible sensation at all. The question arises whether it produces any sensation before it produces a discernible sensation. Proceeding on the general analogy of the results we have reached in discussing Weber's law we must assume that in all probability it does. We have here a special case of the general relation of stimulus to sensation. Within limits, the sensation varies as the stimulus is increased, without the variation becoming perceptible. It is most natural to bring the case of a stimulus, which is not yet intense enough to produce a discernible sensation at all, under the same principle. It is still more improbable that sensations which escape notice merely because our attention is otherwise occupied have no existence as psychical facts. Thus, from our present point of view, we can reinforce the argument of Bk. II., ch. i., § 2 Sensory Elements.