Präzision versus Exaktheit: Konfligierende Ideale der angewandten mathematischen Forschung: Das Beispiel der Tragflügeltheorie

It is often supposed that mathematical argument provides a model of precision for the sciences. In contrast to this view, the present article proposes to distinguish between mathematical exactness as a (historically variable) ideal regulating the inner standards of mathematical argumentation and precision as a (historically variable) norm governing the relation between products of mathematical reasoning in scientific contexts and empirical or practical data. By discussing a major achievement in the mathematization of flight, Ludwig Prandtl's lifting line theory of wings, it is shown that exact reasoning does not necessarily lead to scientific precision, and that the achievement of precision may even require to loosen existing standards of exactness. It is argued that the main contribution of mathematical argument to generating precision in science lies in its capacity to provide sophisticated tools for the production of data, rather than in its adherence to an ideal of exactness.     

»…über Sekunden lacht man nicht« — Über die Folgen der Anwendung von Genauigkeit und Präzision in den Wissenschaften. Einführung in das Tagungsthema

Since the time of Descartes science has been influenced by the demand for precision and accuracy in research. In the 20^th century also humanities began to submit to this demand. The term precision itself has a far‐reaching and historically grown semantics. As a consequence of the attempt to answer precisely and irrefutably to scientific questions, achieved knowledge today is only valid for an increasingly narrow range.