The Axiomatic Method in Physics

Abstract

The axiomatic approach has seldom been tried in physics, partly because the term ‘axiomatic’ is still widely mistaken for ‘self-evident’ or for ‘a priori’, partly because physical theories are often regarded as mere data processing devices in no need of logical organization, and partly because of a fear of rigor and clarity. As a result, between Newton’s naive axiomatization of point mechanics (1687) and the birth of modern axiomatics (Hilbert, 1899), no significant effort in the logical organization of physical thought seems to have been made. Even though mathematical logic, metamathematics, and semantics have vigorously developed during our century, only a few essays in physical axiomatics have been influenced by these developments ’ namely those of Hilbert (1912, 1913 and 1914) for phenomenological radiation theory, McKinsey et al. (1953) for classical particle mechanics, Noll (1959) for classical continuum mechanics, Streater and Wightman (1964) for quantum field theory, and Edelen (1962) for general classical field theory. Most other attempts have failed to pinpoint and characterize the basic (undefined) concepts or to give a sufficient set of postulates entailing the typical theorems of the theory concerned. In particular, the works of Carathéodory (1909) for thermostatics, and von Neumann (1932) for quantum mechanics, fall short of the requirements of modern axiomatics. In short, physical axiomatics is having a protracted infancy. It would therefore be unfair to judge it by its fruits.

Adapted from Bunge (1967d).