an ordered aggregate, of which the elements have become disembodied into mere concepts of position in a series, devoid of all perceptual content.
A given attribute is “simple” (or one-dimensional) if all its degrees can be uniquely determined by their correlation with members of a single series of natural numbers, “complex” (or n-dimensional) if members of more than one (that is n) series of natural numbers are required for the unique determination of an element which possesses this attribute; a one-dimensional relation gives rise to a one-dimensional aggregate or continuum (according as it comprises a finite or an infinite and continuous number of degrees) and an n-dimensional relation similarly to an n-dimensional aggregate or continuum.
26. If, within the world of our perceptions, we try to order parts of our perceptual data under any ordinal characteristic arbitrarily chosen from among those which we immediately apprehend, we find that we can order (that is, correlate with one or more series of natural numbers) under this characteristic a determinate part of the totality of events into which the mind divides its Experience; but we can as a general rule expect that in a given Experience we shall always be able to find events which remain outside the ordering, that is, outside the system of co-ordinates which we have chosen. The requirement of simplicity and uniformity, upon which a satisfactory physical description of a phenomenon is based, would be disregarded to a considerable extent, if we arbitrarily took as the basis of our description any one of the characteristics immediately apprehended: instead of one, uniform description we should obtain a whole series of descriptions, each one of which would only describe the Experience partially; and we should never know how much of the Experience still remained to be described, since we could not be certain that we should not eventually succeed in discovering events distinguished by an attribute which could not be reduced to the one we had selected. In order to satisfy that requirement we must find an ordering relation—an ordinal characteristic—which could be predicated as existing between any and all parts of Experience, and which could therefore serve as an ordering principle for all events. The discovery of such a relation will be attempted in the following section; meanwhile we will postulate its existence in Experience and call it a formative relation. A formative relation is thus an ordering principle which can subsist between any and all parts of Experience whatever; the “Form” of a given aggregate of events will then be the sum of relations of which
