I. THE PROBLEM STATED

Physics is said to be an empirical science, based upon observation and experiment. It is supposed to be verifiable, i.e. capable of calculating beforehand results subsequently confirmed by observation and experiment. What can we learn by observation and experiment? Nothing, so far as physics is concerned, except immediate data of sense: certain patches of colour, sounds, tastes, smells, etc., with certain spatio-temporal relations. The supposed contents of the physical world are _prima facie_ very different from these: molecules have no colour, atoms make no noise, electrons have no taste, and corpuscles do not even smell. If such objects are to be verified, it must be solely through their relation to sense-data: they must have some kind of correlation with sense-data, and must be verifiable through their correlation _alone_. But how is the correlation itself ascertained? A correlation can only be ascertained empirically by the correlated objects being constantly _found_ together. But in our case, only one term of the correlation, namely, the sensible term, is ever _found_: the other term seems essentially incapable of being found. Therefore, it would seem, the correlation with objects of sense, by which physics was to be verified, is itself utterly and for ever unverifiable. There are two ways of avoiding this result. (1) We may say that we know some principle _a priori_, without the need of empirical verification, e.g. that our sense-data have _causes_ other than themselves, and that something can be known about these causes by inference from their effects. This way has been often adopted by philosophers. It may be necessary to adopt this way to some extent, but in so far as it is adopted physics ceases to be empirical or based upon experiment and observation alone. Therefore this way is to be avoided as much as possible. (2) We may succeed in actually defining the objects of physics as functions of sense-data. Just in so far as physics leads to expectations, this _must_ be possible, since we can only _expect_ what can be experienced. And in so far as the physical state of affairs is inferred from sense-data, it must be capable of expression as a function of sense-data. The problem of accomplishing this expression leads to much interesting logico-mathematical work. In physics as commonly set forth, sense-data appear as functions of physical objects: when such-and-such waves impinge upon the eye, we see such-and-such colours, and so on. But the waves are in fact inferred from the colours, not vice versa. Physics cannot be regarded as validly based upon empirical data until the waves have been expressed as functions of the colours and other sense-data. Thus if physics is to be verifiable we are faced with the following problem: Physics exhibits sense-data as functions of physical objects, but verification is only possible if physical objects can be exhibited as functions of sense-data. We have therefore to solve the equations giving sense-data in terms of physical objects, so as to make them instead give physical objects in terms of sense-data.