The Eliminability of Masses and Forces in Newtonian Particle Mechanics: Suppes Reconsidered

Abstract

In his well known axiomatisation of classical particle mechanics (McKinsey, Sugar and Suppes [1953]; Suppes [I957]), Suppes was able to prove that masses and forces are independent primitive notions which cannot be defined on the basis of the other primitives. This result is normally taken to show that, contrary to Mach's positivist views, masses and forces are theoretical terms which cannot be eliminated in favour of observational terms. Taken at face value this conclusion seems also to provide strong support for hypothetico-deductivism as against inductivism. However it is difficult to accept Suppes's easily proved results at their philosophical face value. On the one hand (contrary to what most philosophers seem to suppose) mathematical physicists seem, in general, to have succeeded in eliminating theoretical terms in favour of more directly observational terms, in most other theories, whenever they have seriously set out to do so: for example everyone knows how to eliminate vector potentials from classical electrodynamics without loss; it is trickier in the case of quantum electrodynamics, but Mandelstam showed how to do it should we so choose; Wheeler and Feynman, following Tetrode and others, deliberately set out to eliminate even the fields from classical electrodynamics and in this they succeeded; the distinguished present-day positivist Robin Giles has published elegant formulations of classical and relativistic thermodynamics (Giles [1964]) and of quantum mechanics (Giles ['9701) in precisely defined observational languages in which the usual theoretical terms are later reintroduced by explicit definition. It would be surprising if classical mechanics proved to be an exception. On the other hand Suppes's choice of observational primitives is sufficiently idiosyncratic to invite suspicion. G. W. Mackey, in his [1963], presented in the first few pages an axiomatisation of classical particle mechanics which is very different from that of Suppes. Suppes took the position of each particle as given as a function of the time only. From this we can calculate the acceleration of each particle as a function of the time only. Mackey, on the other hand,