On the Alleged Incommensurability of Newtonian and Relativistic Mass

In separate 1962 publications, Feyerabend and Kuhn introduced the concept of the incommensurability of scientific theories, using as an example (among others) Newtonian mechanics and the special theory of relativity. They suggested, in particular, that the two theories employed incommensurable concepts of mass. Feyerabend took this incommensurability as a fatal objection to a kind of conceptual conservatism that he found in contemporaneous accounts of scientific explanation and reduction, which demanded that older theories were explained by or absorbed into newer theories as special cases. In contrast, I develop here a unified technical framework for particle kinematics and collision mechanics that includes the Newtonian and relativistic versions as particular cases. The mass concept plays the same functional role for each model of the framework, and there is appropriate continuity between their realizations, as I prove that within this framework, certain Newtonian collision models are limits of relativistic collision models. Yet I argue that while one can understand in retrospect why Feyerabend and Kuhn were wrong about their specific claim about the concept of mass, one can still uphold Feyerabend’s insights about the inadequacies of views of scientific progress adhering to conceptual conservatism.