V. The Self and the Relational System of the Ordinal Numbers. The Origin of Number; and the Meaning of Order
Having considered self-representation so much in the abstract, we may now approach nearer to the other illustrations of self-representative relational systems. To be sure, in beginning to do so, we shall, for the first time in this discussion, be able to state the precise logical source of the good order of the number-system, whose self-representative character, now so wearisomely illustrated, is simply due to the fact that the number-series is a purely abstract image, a bare, dried skeleton, as it were, of the relational system that must characterize an ideally completed Self. This observation, in the present form, cannot be said to be due to Hegel, although both his analysis and Fichte's account of the Self, imply a theory that apparently needs to be developed into this more modern form. But the contempt of the older Idealism for the careful analysis of mathematical forms, — its characteristic unwillingness to dwell upon the dry detail of the seemingly lifeless realm of the mathematically pure abstractions, is responsible for much of the imperfect development and relative vagueness of the idealistic Absolute. It is so easy for the philosopher to put on superior airs when he draws near to the realm of the mathematician. And Hegel, despite his laborious study of the conceptions of the Calculus, in his Logik, generally does so. The mathematician, one observes, is a mere “computer.” His barren Calcul, — what can it do for the deeper comprehension of truth? Truth is concrete. As a fact, however, these superior airs are usually the expression of an unwillingness even to spend as much time as one ought to spend over mathematical reading. And Hegel seems not to have solved the problem of the logic of mathematics. The truth is indeed concrete. But if alle Theorie is, after all, grau, and grün des Lebens Goldener Baum, the philosopher, as himself a thinker, merely shares with his colleague, the mathematician, the fate of having to deal with dead leaves and sections torn or cut from the tree of life, in his toilsome effort to make out what
