The judgment in this category is therefore a consciousness of position, such as those mentioned above. The argument is a completion of one association by comparison with another--the expectation of similarity in groups. _Movement._ All judgments as to _change_ of position in objects come under this category. It takes at least two things arranged in a group to produce the perception of movement. If there were but one thing in our field of observation we could not say whether it moved or not, for there would be nothing which it would pass, or leave, or approach. It would appear to stand still. There is, however, more in movement than depends on mere perception. All movement is due to energy either in the observer or in the other mind acting upon his. Energy is not a generalisation of moving things, nor a property, nor a relation, though all these may be signs of energy. The most abstract idea of movement is _Motion_. It may be defined as a series of positions. _Number._ If we treat a group as a large loose object we shall perceive in it certain properties not strictly positional. Number is one of these. A group of three coins has not the same practical value as a group of six or sixty, and we are thus obliged to notice the difference and distinguish degrees of this property by names--hence Arithmetic. _Flat Space_ or space of two dimensions is another property of a group. Grouped objects have frequently intervals between them. Such intervals are negations of perception--interruptions or discontinuities of experience. But by abstraction we can reduce the objects bounding an interval to a geometrical line, and so give a sort of positive existence to the interval. Thus we talk of a hole or of darkness as if they were true objects, and measure them by standards of length. If we abstract the boundary lines from a space we get the idea 'intervalness,' which is the right name for two-dimensioned space. This abstract idea is nearly the same as abstract size. Space is interval without bounds--size is object without contents. Space and size are equally _nothing_ intrinsically or in their own right, but they have been reached by different modes of refining away the positive qualities associated with them, and this difference of origin is slightly suggested by their names. Spaces have a use in perception similar to _rests_ in music--they relieve the attention and give contrast and vigour to the next positive object. XXIV--PERSPECTION This is the first of the artificial categories. It is an ideal treatment of an associated group to facilitate a certain kind of reasoning.