Abstract

Hilbert’s axiomatic approach to the sciences was characterized by a dynamic methodology tied to scientific and mathematical fields under investigation. In particular, it is an analytic art for choosing axioms but, at the same time, it has to include dynamically synthetic procedures and meta-theoretical reflections. Axioms have to be useful, or capture something, or help as part of explanations. The Andréka-Németi group use several formal axiomatic theories together to re-capture, predict, recover or explain the phenomena of special relativity, general relativity and classical kinematics. Their scientific methodology is close to Hilbert’s conceptions of how science should be done ideally. In this paper, we compare Formica’s reading of Hilbert’s axiomatic method to the method used by the Andréka-Németi group.