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Updated: May 29, 2025
Later in this book there will be occasion to introduce a concept of number in tune with our qualitative world-outlook. What led Mayer to look upon number as an expression of existing spiritual associations in nature will then become clear.
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For this successful union of Bacon's experimental induction with the mathematical deduction of Descartes, this combination of the analytic and the synthetic methods, which was shown in the demand for, and the establishment of, mathematically formulated natural laws, presupposes that nature is deprived of all inner life and all qualitative distinctions, that all that exists is compounded of uniformly acting parts, and that all that takes place is conceived as motion.
Even when we have established it as a fact that all phenomena are linked together in a chain of causes we are still far from having discovered how things actually come to pass. Every qualitative effect and change is entirely hidden from us as far as the cause of its coming about and its real and inner nature are concerned.
For the physicist, accustomed to a purely quantitative observation of nature, it is difficult to comprehend that Mayer could have arrived at the thought of a constant quantitative relation between the various manifestations of natural energy, without deriving from it the conviction of their qualitative indentity i.e., without concluding from the existence of the mechanical heat equivalent that heat is itself nothing else than a certain form of spatial movement.
The only qualitative distinction they seemed to recognize was between 'cold' and 'warm' colours. In some way this colour seemed to him to be related to black. In order to rouse his artist friends and to stimulate their reflexions, he liked to indulge in paradoxes, as when he asserted that blue was not a colour at all. He found, however, as time went on, that in this way he came no nearer his goal.
According to the testimony of history as well as according to analysis, and notwithstanding the anomalies caused by the antagonism of economic principles, intelligence differs in men, not by power, clearness, or reach, but, in the first place, by specialty, or, in the language of the schools, by qualitative determination, and, in the second place, by exercise and education.
Perceived fact, then, combines meaning and present bare sensation to form a whole with a qualitative flavour which is itself always unique, but which lends itself to abstraction in so far as the bare sensations, past and present, which go to produce it, would, as matter in isolation, be repetitions.
They are not; and this qualitative difference is indicated by the terms higher and lower, as the quantitative difference was by greater and less. But differences of rank are more slippery matters than difference of amount, and easily lend themselves to arbitrary and capricious treatment. In ordinary speech we are apt to employ the words high and low as mere signs of approval or disapproval.
In English we may class as novels works like "Kenilworth," "The Newcomes," "The Last of the Mohicans," "The Rise of Silas Lapham"; and we may class as novelettes works like "Daisy Miller," "The Treasure of Franchard," "The Light that Failed." The distinction is quantitative but not qualitative.
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