Functions and Shapes in the Light of the International System of Units
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Famously, Galilei made the ontological claim that the book of nature is written in the language of mathematics. Probably, if only implicitly, most contemporary natural scientists share his view. This paper, in contradistinction, argues that nature is only partly written in the language of mathematics; partly, it is written in the language of functions and partly in a very simple purely qualitative language, too. During the argumentation, three more specific but in themselves interesting theses are put forward: first (in Section 3), there are more shapes than real numbers; second (in Section 4), the metrological notion ‘amount of substance’ can profitably be exchanged for ‘number of entities’; third (in Section 5), prototypical concepts will always be scientifically important.
KeywordsQuantities Functions Shapes SI system
This work was done under the auspices of the Wolfgang Paul Program of the Alexander von Humboldt Foundation, the Network of Excellence in Semantic Interoperability and Data Mining in Biomedicine of the European Union, and the project Forms of Life sponsored by the Volkswagen Foundation.
The ideas were first presented in a symposium on the philosophy of biology in Buffalo, NY (USA), October, 2006. In July 2007, I presented them at my home research institute, IFOMIS, Saarland University (Germany). Here is a list of persons that I would like to thank for useful comments on either of these occasions: James Beebe, Michelle Carnell, Randall Dipert, Pierre Grenon, Boris Hennig, Barry Smith, and Neil Williams. For comments on a later written version I thank Giovanni Camardi, Jean Gayon, Frédéric Trembaly, Inge-Bert Täljedal, and Marcel Weber; for comments on my thoughts about the impossibility of quantifying shapes, I would like to thank Brandon Bennett; and for kindly answering a couple of questions around the mole and the SI, I thank René Dybkaer. It is quite necessary to add: the author alone is responsible for the views now publicly put forward.
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