JUST as a world-conqueror of ancient times, as he halts for a day in the midst of his victorious career, might long to see the boundaries of the vast territories he has subjugated more clearly defined, so that here he may levy tribute of some nation hitherto exempt, or that there he may discern some natural barrier that cannot be overcome by his horsemen, and which constitutes the true limit of his power, in like manner it will not be out of place, if Natural Science, the world-conqueror of our times, resting as on a festive occasion from her labor, should strive to define the true boundaries of her immense domain. And this undertaking I hold to be all the more legitimate, because I believe there exist two widely-diffused errors with regard to the limits of natural science, and because I think it possible that from the study of such a question, despite its apparent triviality, some advantage might be derived even by those who do not at all share in the errors of which I speak.
Hence I propose to investigate the limits of natural science; and first I must say what natural science is.
Natural science—or, more definitely, knowledge of the physical world with the aid of and in the sense of theoretical natural science—means the reduction of all change in the physical world to movements of atoms produced independently of time by their central forces; or, in other words, natural science is the resolution of natural processes into the mechanics of atoms. It is a fact of psychological experience that, where such a resolution is practicable, our desire of tracing things back to their causes is provisionally satisfied. The propositions of mechanics are mathematically presentable, and have in themselves the same apodictic certainty as the propositions of mathematics. As the changes of the physical world are reduced to a constant sum of potential and kinetic energy, which is inseparable from a constant quantity of matter, there remains in these changes themselves nothing further that needs explanation.
What Kant says in the introduction to his "Metaphysical Elements of Natural Science," viz., "that "in each special natural science the amount of science, properly so called, is equal to the amount of mathematics it contains"—must, therefore, be further narrowed down, and instead of mathematics we must read atomic mechanics. Plainly this
- An Address delivered at the Forty-fifth Congress of German Naturalists and Physicians at Leipsic.