Physical Axiomatics

The peculiarities of physical axiom systems, by contrast to the mathematical ones, are examined. In particular, the problem of attaching a physical meaning to a formalism is handled. The main views concerning meaning—formalism, operationalism, the double language doctrine, and realism—are analyzed and arguments for realism are advanced. The realistic view is illustrated by analyzing typical physical quantities and by axiomatizing a theory—special relativistic kinematics. It is argued that all the components of a physical theory—the formalism as well as the correspondence or semantic hypotheses—contribute to sketching the meaning of the theory, and that this meaning is best found out upon displaying the basic assumptions in an axiomatic fashion. The advantages and scope of the axiomatic approach are finally discussed.