94

WHAT IS A THING?

project. The founding of analytical geometry by Descartes, the founding of the infinitesimal calculus by Newton, the simultaneous founding of the differential calculus by Leibniz--all these novelties, this mathematical in a narrower sense, first became possible and, above all, necessary, on the grounds of the basically mathematical character of the thinking.

We would certainly fall into great error if we were to think that with this characterization of the reversal from ancient to modern natural science and with this sharpened essential outline of the mathematical we had already gained a picture of the actual science itself.

What we have been able to cite is only the fundamental outline along which there unfoldes the entire richness of posing questions and experiments, establishing of laws and disclosing of new districts of what is. Within this fundamental mathematical position the questions about the nature of space and time, motion and force, body and matter remain open. These questions now receive a new sharpness; for instance, the question of whether motion is sufficently formulated by the designation "change of location." Regarding the concept of force, the question arises whether it is sufficient to represent force only as cause that is effective only from the outside. Concerning the basic laws of motion, the law of inertia, the question arises whether this law is not to be subordinated under a more general one, i.e., the law of the conservation of energy which is now determined in accordance with its *expenditure* and *consumption*, as *work*--a name for new basic representations which now enter into the study of nature and betray a notable accord with economics, with the "calculation" of success. All this develops within and according to the fundamental mathematical position. What remains questionable in all this is a closer determination of the relation of the mathematical in the sense of mathematics to the intuitive direct perceptual experience (*zur anschaulichen Erfahrung*) of the given things and to these