=156.= This converse deduction, as regards Free Mobility, is not very difficult, and follows from the argument of Section A[162], which I will briefly recapitulate. In the first place, externality is an essentially relative conception--nothing can be external to itself. To be external to something is to be an other with some relation to that thing. Hence, when we abstract a form of externality from all material content, and study it in isolation, position will appear of necessity as purely relative--it can have no intrinsic quality, for our form consists of pure externality, and externality contains no shadow or trace of an intrinsic quality. Hence we derive our fundamental postulate, the relativity of position. From this follows the homogeneity of our form, for any quality in one position, which marked out that position from another, would be necessarily more or less intrinsic, and would contradict the pure relativity. Finally Free Mobility follows from homogeneity, for our form would not be homogeneous unless it allowed, in every part, shapes or systems of relations, which it allowed in any other part. Free Mobility, therefore, is a necessary property of every possible form of externality. =157.= In summing up the argument we have just concluded, we may exhibit it, in consequence of the two preceding paragraphs, in the form of a completed circle. Starting from the conditions of spatial measurement, we found that the comparison, required for measurement, could only be effected by superposition. But we found, further, that the result of such comparison will only be unambiguous, if spatial magnitudes and shapes are unaltered by motion in space, if, in other words, shapes do not depend upon absolute position in space. But this axiom can only be true if space is homogeneous and position merely relative. Conversely, if position is assumed to be merely relative, a change of magnitude in motion--involving as it does, the assertion of absolute position--is impossible, and our test of spatial equality is therefore adequate. But position in any form of externality must be purely relative, since externality cannot be an intrinsic property of anything. Our axiom, therefore, is _à priori_ in a double sense. It is presupposed in all spatial measurement, and it is a necessary property of any form of externality. A similar double apriority, we shall see, appears in our other necessary axioms. II. _The Axiom of Dimensions[163]._