enowning
Sunday, July 09, 2006
 
Here's the final bit from What is a Thing?, B. Kant's Manner of Asking About the Thing, I. The Historical Basis on Which Kant's Critique of Pure Reason Rests, 5. The Modern Mathematical Science of Nature and the Origin of a Critique of Pure Reason, e. The Essence of the Mathematical Project (Galileo's Experiment with Free Fall).
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 things themselves. Up to this hour such questions have been open. Their questionability is concealed by the results and the progress of scientific work. One of these burning questions concerns the justification and limits of mathematical formalism in contrast to the demand for an immediate return to intuitively given nature (anschaulich gegebene Natur).

If we have grasped some of what has been said up till now, then it is understandable that the question cannot be decided by way of an either/or, either formalism or immediate intuitive determination of things; for the nature and direction of the mathematical project participate in deciding their possible relation to the intuitively experienced and vice versa. Behind this question concerning the relation of mathematical formalism to the intuition of nature stands the fundamental question of the justification and limits of the mathematical in general, within a fundamental position we take toward what is, as a whole. But, in this regard the delineation of the mathematical has gained an importance for us.

P. 94-95
That's the end of the chapter on the essence of the mathematical project. The next chapter goes into the metaphysics of the mathematical, how the relevant bits of Aristotle were interpreted by Scholasticism, and the Cartesian method. This book is terrific at expanding on the scientific background for the treatment of time in Being and Time; e.g. section 69. I hope to get around to typing in a bit on Galileo from Der Zeitbegriff in der Geschichtswissenschaft (1915) and then how Glazebrook ties them all together in her book.
 
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