EAN: 9783319544687

MATHEMATICS AS A TOOL GEBUNDEN

This book puts forward a new role for mathematics in the natural sciences. In the traditional
understanding  a strong viewpoint is advocated  on the one hand  according to which mathematics
is used for truthfully expressing laws of nature and thus for rendering the rational structure
of the world. In a weaker understanding  many deny that these fundamental laws are of an
essentially mathematical character  and suggest that mathematics is merely a convenient tool
for systematizing observational knowledge. The position developed in this volume combines
features of both the strong and the weak viewpoint. In accordance with the former  mathematics
is assigned an active and even shaping role in the sciences  but at the same time  employing
mathematics as a tool is taken to be independent from the possible mathematical structure of
the objects under consideration. Hence the tool perspective is contextual rather than
ontological. Furthermore  tool-use has to respect conditions like suitability  efficacy 
optimality  and others. There is a spectrum of means that will normally differ in how well they
serve particular purposes. The tool perspective underlines the inevitably provisional validity
of mathematics: any tool can be adjusted  improved  or lose its adequacy upon changing
practical conditions.

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