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Updated: May 10, 2025
The claim assumes that character of absoluteness, that apparent infinity, and incommensurability with all other considerations, which constitute the distinction between the feeling of right and wrong and that of ordinary expediency and inexpediency.
But it is true that lacking the perception of the uniqueness of every individual, his incommensurability with others, and consequently not recognizing that a society might change and yet be stable, his doctrine of limited powers and classes came in net effect to the idea of the subordination of individuality.
But, indeed, human nature being as it is, there would inevitably arise, and have always arisen, many cases of strain and friction in marriage relations. As Chesterton says, a man and a woman are, in the nature of the case, incompatible; and that underlying incommensurability of viewpoint easily results in clash where a deep-rooted affection and a habit of self-control are absent.
The claim assumes that character of absoluteness, that apparent infinity, and incommensurability with all other considerations, which constitute the distinction between the feeling of right and wrong, and that of ordinary expediency and inexpediency. Having presented his own analysis of the sentiment of Justice, the author proceeds to examine the intuitive theory.
In an original thinker, in one who really thinks and does not merely argue, to call a thing supernatural, or spiritual, or intelligible is to declare that it is no thing at all, no existence actual or possible, but a value, a term of thought, a merely ideal principle; and the more its reality in such a sense is insisted on the more its incommensurability with brute existence is asserted.
We exclude from deliberation things Eternal, like the Kosmos, or the incommensurability of the side and the diagonal of a square; also things mutable, that are regulated by necessity, by nature, or by chance; things out of our power; also final ends of action, for we deliberate only about the means to ends. The deliberative process is compared to the investigation of a geometrical problem.
Hence what the Eleatic dialectic illustrates is a case of incommensurability; the radical inability of analysis to end a certain task; our powerlessness to explain the fact of the transit, if we apply to it such and such modes of numerical decomposition or recomposition, which are valid only for space; the impossibility of conceiving becoming as susceptible of being cut up into arbitrary segments, and afterwards reconstructed by summing of terms according to some law or other; in short, it is the nature of movement, which is without division, number, or concept.
But the speculation we have hinted at, if it gives no explanation, at least supplies a framework for many questions which attract us, and do so even from the point of view of religion: for instance the collective, diffuse, and almost divisible nature of consciousness in the lower stages, its increasing and ever more strict centralisation, the natural relationship of the psychical in man to the psychical in general, and yet its incommensurability and superiority to all the world.
Aristotle mentions an ancient proof of the incommensurability of the diagonal with the side by a reductio ad absurdum showing that, if the diagonal were commensurable with the side, it would follow that one and the same number is both odd and even. This proof was doubtless Pythagorean. A word should be added about the Pythagorean astronomy.
The solar year, the lunar month, and the day were the units, and it is owing to their incommensurability that we find so many calendars proposed and in use at different times. The only object to be attained by comparing the chronologies of ancient races is to fix the actual dates of observations recorded, and this is not a part of a history of astronomy.
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