magnitudes, I see no reason why Renouvier's objection need longer hold. The countless may still be the determinate. As such, it might appear as the socially verifiable, i.e., as the external fact.
V.
We have now considered the definite place and dimensions and numbers of the objects of the external world. A similar condition applies to the real movements of these objects. What appears more axiomatic than the statement that whatever moves must change its place in some definite direction and upon some definite path ? Yet, this apparent axiom actually does not hold for the world of the inner life, if one takes account of all the classes of sensations of movement, as these occur in our experience. In the inner world we can find cases where objects appear to move, and yet do not appear to move in any definable path, and even while they thus appear to move, do not seem to change their place. The after-images of movement offer numerous instances of experiences of this paradoxical type. Look for a while fixedly at a rapidly moving strip or band, drawn athwart the field of vision, and seen in clear relief, or at a revolving disk, marked with a broad spiral line. Then look away at resting objects. You will see an after-image of the portion of the field of vision where the objective movement was recently pictured. This after-image will itself show a shadowy movement in a reverse direction. In consequence, portions of the resting objects in the new field of vision will seem to be in a dimly visible motion, recti-linear or circular, as the case may be. Yet, strange to say, this subjective motion, at the very moment when it is seen, is also seen as not altering or disturbing the structure of the objective field of vision or the relations of its apparently moving and resting parts. In the objective field of vision, since nothing really moves, no space relations of objects are changing. But meanwhile you seem to see, despite this changelessness, a very obvious sort of movement going on. Thus, in the now altered field of vision, you may see, for
