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The general logical structure of Einstein's 1905 argument1 for the introduction of photons is shown (in a rather free rendering) in the diagram overleaf. (h is Planck's constant, k Boltzmann's constant, c the velocity of light, v frequency, T temperature, E energy, S entropy, p energy density, Sentropy density, V volume, and W probability.)2 It will be observed that the premises include both fairly low-level generalisations arising rather directly from experiments and fairly high-level generalisations arising from theory, and that the argument, apart from the last step, is of a deductive character. The aim of the present paper is to show that the argument by analogy which Einstein uses to mediate the last step is as a matter of fact redundant and that his conclusion already follows deductively from what he has already established. If my argument is accepted then Einstein's introduction of photons no longer takes the form of a plausible hypothesis suggested by analogy, but can be construed as a "deduction from the phenomena" in the sense of Newton and Ampere: i.e. as the rigorous deduction of a new explanatory theory from certain empirical generalisations taken as phenomena together with certain more general theoretical assumptions whose validity is taken for granted. I hope to show in some later articles that new hypotheses in physics are commonly introduced by "deduction from the phenomena" of this general kind and that there are no fundamental logical objections against this form of argument. I start with the assertion which Einstein has arrived at by an apparently deductive argument namely

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

Professor Popperx says that Lorentz and Fitzgerald 'do not say that a rod at rest in the ether would appear contracted if measured with the rods of the moving system. (Rather, one might expect, by implication, that it would appear expanded.)' Popper then goes on to emphasise the mutual character of the Einstein contraction, and stresses that it is this mutual character of the contraction which leads to the abandonment of the ether.