He proceeds to a generalized theory in which, at first, length is purely conventional, for comparisons at a point as well as for comparisons between different points. This generalized theory does not seem to involve the same kind of difficulties as those which have been troubling us. The following passage, for example, states the matter with great clearness (p. 226): "The relation of displacement, between point-events and the relation of 'equivalence' between displacements form part of one idea, which are only separated for convenience of mathematical manipulation. That the relation of displacement between and amounts to such-and-such a quantity conveys no absolute meaning; but that the relation of displacement between and is 'equivalent' to the relation of displacement between and is (or at any rate may be) an absolute assertion. Thus four points is the minimum number for which an assertion of absolute structural relation can be made. The ultimate elements of structure are thus four-point elements. By adopting the condition of affine geometry, I have limited the possible assertion with regard to a four-point[Pg 99] element to the statement that the four points do, or do not, form a parallelogram. The defence of affine geometry thus rests on the not implausible view that four-point elements are recognized to be differentiated from one another by a single character—viz. that they are or are not of a particular kind which is conventionally named parallelogramical. Then the analysis of the parallelogram property into a double equivalence of to and to , is merely a definition of what is meant by the equivalence of displacements."