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The identical figures which Euclid defined by intrinsic relations were defined by Descartes by the relations of their points to adventitious co-ordinates, the result being an absolutely different and vastly more potent way of handling curves. All our conceptions are what the Germans call denkmittel, means by which we handle facts by thinking them.
Kinds, and sameness of kind what colossally useful DENKMITTEL for finding our way among the many! The manyness might conceivably have been absolute. Experiences might have all been singulars, no one of them occurring twice. In such a world logic would have had no application; for kind and sameness of kind are logic's only instruments.
In practice, the common-sense DENKMITTEL are uniformly victorious. Everyone, however instructed, still thinks of a 'thing' in the common-sense way, as a permanent unit-subject that 'supports' its attributes interchangeably. No one stably or sincerely uses the more critical notion, of a group of sense- qualities united by a law.
From this centre the search for causal influences has spread. Hume and 'Science' together have tried to eliminate the whole notion of influence, substituting the entirely different DENKMITTEL of 'law. But law is a comparatively recent invention, and influence reigns supreme in the older realm of common sense.
They proved of such sovereign use as denkmittel that they are now a part of the very structure of our mind. We cannot play fast and loose with them. No experience can upset them. On the contrary, they apperceive every experience and assign it to its place. To what effect? That we may the better foresee the course of our experiences, communicate with one another, and steer our lives by rule.
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