because, as we conceive, there is always another between. So the postulate: Between any two there is a third, is the working postulate of our process of comprehending things through our successive discriminations. And this is the process upon which all scientific description of given facts depends.
Now the definition of between suggested by Mr. Kempe’s papers has quite freed us from the need of limiting the application of this postulate to the extended world, or to the numerical and quantitative aspects of things. The points on a line, as conceived by the geometer, the series of rational fractions arranged in order as greater and less, and the series of the real numbers, all indeed illustrate our postulate.[1] They are conceptual systems of objects especially wrought out by the mathematician in such wise as to conform to the postulate. And every homogeneous system of measurable and continuous quantities (masses, distances, durations, forces, temperatures, etc.) is conceived by our exact science as also to illustrate this postulate. Yet the formation of series has application to qualities as well as to quantities, — in fact, to whatever we can undertake to discriminate. Hence there is no obvious limit to the variety of objects that we can undertake to deal with in this way. We can compare colors and shades as well as points and magnitudes. Europe and America, compared geographically, or socially, or politically, lead us to attempt the formation of series of
- ↑ All these systems are so ordered that no term is conceived to have a next neighbor. Yet the process whereby we reach the conception of each is always a Well-Ordered Process, in which each of our own acts leads to the next one.
