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Mathematics as a Tool - Tracing New Roles of Mathematics in the Sciences (Hardcover, 1st ed. 2017)
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Mathematics as a Tool - Tracing New Roles of Mathematics in the Sciences (Hardcover, 1st ed. 2017)
Series: Boston Studies in the Philosophy and History of Science, 327
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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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