Experimenting theory: The proofs of Kirchhoff's radiation law before and after Planck

The role of experimental thinking and action in theorizing is investigated using an example from classical theory. The history of Kirchhoff's law exhibits both the development of the views on radiation and the evolution of the content as well as the assumed foundational roots of this law. Planck's search for the correct justification of his radiation formula is placed into the context of the contemporary debate over his prerequisite. It is then asked what the analysis of the variety of approaches, arguments, and ontological claims that can be found in radiation theory can reveal to us concerning the conceptual framework that was available in Planck's researches. Next, the different forms of reasoning applied in proving a physical law will be exemplified, which range from procedures that are closely abstracted from experimental action like those found with Kirchhoff or Helmholtz, to a purely mathematical approach-as that of Hilbert-which is void of any experimental notion or object. This discussion shall finally both locate Planck's specific method and elucidate the great difficulties the establisment of a truly non-experimental, i.e., mathematical, theory in physics met before a new generation of quantum physics appeared.