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In the title of this paper I speak of the "mathematical overdetermination of physics", and the reader is fully entitled not to know what I mean by this. Right at the beginning of this paper it may be of some help to compare its subject with the related though different so-called theoretical overdetermination of a corpus of empirical data. Just as an empirical theory often exhibits an unnecessarily rich structure when compared with the observational data to be explained by it so the mathematics introduced to formulate a physical theory frequently brings a wealth of structure into play that cannot be matched by the physical elements of that theory. In both cases we find ourselves deluded in our expectation that in order to reformulate a certain corpus of statements by submitting it to logical analysis there be only two things to be taken into consideration: 1) the concepts characteristic for the corpus in question, and 2) the logical expressions binding together those concepts. I say we are deluded in expecting this because in both cases of overdetermination the truth seems to be that a third component has to be considered. In the case to be dealt with in the following this phenomenon has found its expression already long ago in Galileo's saying that "the book of nature is written in the language of mathematics." Let me illustrate the situation by two examples: empirical laws and electrodynamics.

DOI: 10.1007/978-3-642-78808-6_12

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