If this be the case, it may be possible and even necessary for reflection at some stage to transcend this distinction. At least, there can be no reason except an arbitrary one for taking this first step of reflection to be a finality. And there would be the same justification for a second step that would transcend this dualism, as for the initial step out of which the distinction arose; provided, it should be found that the initial distinction does not supply an adequate basis for a rational interpretation of the world that can be taken as final. Now, it is precisely because the dualistic distinction of the sciences does fail in this regard, that a further demand for a reflective transformation of the data arises. Let us bear in mind that the data of the sciences are not the simple facts of observation, but rather those facts transformed by an act of reflection by virtue of which they become phenomena distinguished from a more fundamental nature on which they depend and which itself is not open to observation. The real data of science are found only when the world of observation has been thus transformed by an act of reflection. If then at some stage in our effort to interpret our world it should become clear that the sciences of phenomena, whatever value their results may possess, are not giving us an interpretation in terms that can be taken as final, and that in order to ground such an interpretation a further transformation of our data becomes necessary, I do not see why any of the sciences should feel that they have cause to demur. In truth, it is out of just such a situation as this that the metaphysical interpretation arises (as I propose very briefly here to show), a situation that supplies a genuine demand in the light of which the effort of metaphysics to understand its world seems to possess as high a claim to legitimacy as that of the sciences of phenomena. Let us take our stand with the plain man or the child, within the world of unmodified observation. The things of observation, in this world, are the realities, and at first we may suppose have undergone little reflective transformation. The first reflective effort to change this world in any way will, no doubt, be an effort to _number_ or _count_ the things that present themselves to observation, and out of this effort will arise the transformation of the world that results from considering it under the concepts and categories of number. In short, to mathematical reflection of this simple sort, the things of observation will resolve themselves into a plurality of countable things, which the numbering reflection becoming explicit in its ordinal and cardinal moments will translate into a system that will be regarded as a whole made up of the sum of its parts. The very first step, then, in the reflective transformation of things resolves them into a dual system, the world conceived as a cardinal whole that is made up of its ordinal parts, and exactly equal to them.