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.     

Die Entwicklung der Sozialgeschichte der modernen Mathematik und Naturwissenschaft und die Frage nach dem sozialen Raum zwischen Disziplin und Wissenschaftler

The use of the concept of social history of science is sketched in the Anglo‐American and the German discussions from the mid 1970s up to recent work. By presenting a ‘social map’ of a selected scientific community it is argued that between the categories of discipline and single scientist there exists a wide ‘social space’ of groups within which science is pursued. In adopting a milieu theoretic approach an ecology of science is proposed as a suitable extension of the social history of science.     

Disziplinerneuerung und Universitätsreform: Das Ius publicum Romano Germanicum

What caused the reforms which permitted the universities in the Holy Roman Empire to become leading places of scientific communication and mental orientation for centuries? In most cases, outside influences - pressures from governments, princes, scholars, councillors, consistories, or, as we would say today, state and churches - were decisive. But some reforms were the consequences of paradigm-changes within the universities themselves. Such shifts were less likely to originate with faculties concerned with medicine or the natural sciences than with those which were concerned directly with the political community or human societies. This changed only in the nineteenth century, which cannot be dealt with here.