In undertaking a discussion of the postulates of empiricism, I am confronted by the necessity of being empirical concerning the very postulates themselves. Were those postulates directly accessible to the average mind it would hardly be necessary to enter upon an analysis the success of which seems but a remote possibility even to one who has spent years in the effort to trace the priceless ingredient of the method of experiment in the cheap madness of scientific success. How these postulates reveal themselves to more than the average mind would, of course, be very difficult for me to surmise, except by an ambitious extrapolation. It would have to be an extrapolation of the kind which telescopes a multitude of small rational steps into one swift unerring instinctive flight to the goal of goals. Yet, though genius with one intuitive glance may perceive the postulates as revelation—why not grant that there may be seers who can contemplate eternal objects unblinkingly?—it would still have to descend to mundane means to inform the average mind of its transcendental perceptions. Must not everyone indeed attend to the demands of the average mind?

I suppose it is generally agreed that the task of science is to render intelligible, or in some way account for, the objects and events of our experience. Usually we say that the job of science is to explain. While this is a satisfactory formulation for most purposes, it hides a difficulty. What is meant by “explanation”? The many interpretations of this word divide scientists and philosophers of science into sharply differentiated schools. For some “explanation” means answering the question, Why?; for others it means merely describing. For some it means finding causes; for others it means finding effects or abandoning entirely the search for causes and effects. For some it means employing quantitative methods only; for others it means supplementing or replacing quantitative methods by qualitative. For some it means interpreting or understanding; for others it means merely adjusting oneself in a practical way.

The problem of this paper is the discovery of criteria to identify conventions and the description of some of the more general properties of conventions with particular reference to scientific inquiry. Numerous specialized methodological investigations testify to the importance of conventions in inquiry, but none provide a general account of their operation. This paper aims to provide a necessary, if not sufficient, basis for such an account. The discussion falls into three parts: (I) common senses of the term ‘convention’, (II) a provisional formulation of conditions under which a certain type of behavior, which we shall call conventional, occurs, as well as a description of its characters, and (III) a brief consideration of one context of inquiry in which it appears.

From the desire to find support and confirmation for our personal sensory observations, and from the human interest in sharing our experiences with others, there emerges a basic principle of scientific method: We demand the possibility of intelligible communication and agreement concerning individuals' sensory perceptions in particular and their experiences in general. This requirement is made both for the natural and social sciences. The raw material offered for logical organization must be capable of exhibiting an inter-subjective character—such material, or protocols, must be acceptable in common to all concerned. And it must be acceptable for logical organization or systematization in some science.

If we are to accept the results of modern physics and the significance ascribed to them by eminent exponents of this most exact of all natural sciences, we are in the midst of an important transformation of our conception of the universe. The notion that the law of causality absolutely determines all events has been shaken, and if this law is not to be entirely eliminated from scientific thinking, its formulation must at least be essentially modified. In the course of this controversy the question arises as to the source of the belief that events are determined by an absolute law, that is, the origin of the assumption, which we take for granted, that each event must be the necessary effect of a cause according to an inviolable law. We must try to show how the belief in causality has arisen in the evolution of human thought.

Let us invoke philosophic license for a moment to suppose you receive the following letter:

“Dear Sir:

I am taking the liberty of calling upon you to be the judge in a dispute between me and an acquaintance who is no longer a friend. The question at issue is this: Is my creation, umbrellaology, a science? Allow me to explain this situation. For the past eighteen years, assisted by a few faithful disciples, I have been collecting materials on a subject hitherto almost wholly neglected by scientists, the umbrella. The results of my investigations to date are embodied in the nine volumes which I am sending to you under separate cover. Pending their receipt, let me describe to you briefly the nature of their contents and the method I pursued in compiling them. I began on the Island of Manhattan. Proceeding block by block, house by house, family by family and individual by individual I ascertained 1) the number of umbrellas possessed, 2) their size, 3) their weight, 4) their color. Having covered Manhattan after many years, I eventually extended the survey to the other boroughs of the City of New York, and at length completed the entire city. Thus I was ready to carry forward the work to the rest of the state and indeed the rest of the United States and the whole known world.

The question as to the existence of laws in history has frequently been discussed. A new discussion may yet be useful, since some misconceptions based on incorrect comparisons with the natural sciences have been brought forward by both advocates and opponents of historical laws. We shall try to clarify the problem by applying a few ideas familiar to physicists and astronomers to the conditions peculiar to history. Physics is the most mature of all empirical sciences as to method. In physics the law-concept has been used for three hundred years. It may be assumed, therefore, that most of the difficulties in its application to other fields have their physical counterpart and can be clarified most easily with the help of physical concepts. A few preliminary examples of historical laws will be given towards the end of the article.

The complexity of social data has been a barrier which sociology has seemingly been unable to surmount. Consequently sociology, like other social sciences, has tended to divide itself into groups advocating different emphases in approach, concerning themselves respectively with the “quantitative” or “qualitative” aspects of social data. These two camps may be seen to diverge along distinct lines, the former approaching material from what is conceived to be a “scientific” frame of reference, posing problems which—it is hoped—will be “explained” by the mathematical arrangement of materials; whereas the latter constructs questions the answer to which will make for “understanding”—ordinarily of behavior—through verbal symbolizations. Explanation usually is accomplished through the achievement of a formula—if couched in mathematical terms it is viewed as the highest order—and this group views the achievement of “understanding” a useless procedure, for—since “understanding” is not mathematically exposited—it is necessarily incapable of being validated. On the other hand, he of the group desirous to understand behavior, finds the problems posed by the “positivist” irrelevant to the larger problems in which his interest lies, and unenlightening for all of the devious steps taken to arrive at a solution; more in the manner than in the spirit of science.

The philosopher whose work best represents the type of thought and expresses the aspirations of the French writers of the eighteenth century is, beyond any doubt, Pierre Bayle (1647-1706). Not so well known as many of the others, it was he, nevertheless, who started the dialectic movement of philosophic thought which was very characteristic of that era. Furthermore, in his extensive writings, he accumulated material from which his successors could draw freely and copiously.

In theories of the mobilities of ions in gases a rather precise knowledge is required of the forces which are called into play when an ion approaches a neutral molecule; for it is by virtue of these forces that ions are deflected from their paths and that their drift along the electric force is impeded. Again, the current question whether ions, in their motion through a gas, form “clusters”, that is, whether they surround themselves by one or even more layers of neutral molecules, can be decided theoretically only on the basis of a rather precise knowledge of the interactions.

Quantum mechanics was initiated with the object of allowing only observable concepts to enter into the theory. The new mechanics has, however, inherited the old difficulty with the conservation laws involved in beta decay, and this led Pauli, about 1931, to introduce the idea of the neutrino, with the object of reconciling the facts of beta decay with the conservation laws. The neutrino, as it was proposed by Pauli and as accepted today, is a particle devoid both of mass and charge, but having a spin 1/2 and obeying the Fermi statistics. In 1934 Fermi founded his theory of beta disintegration based on the neutrino. The Fermi theory assumes that this hypothetical particle is emitted simultaneously with the disintegrating electron and carries off the excess energy, thereby reconciling the conservation laws with beta disintegration. It will be remembered that the continuous distribution in energy of the beta particles is such that, except at the maximum energy end point of the beta spectra, there is more energy available from the disintegration than is emitted in the form of beta particles.

In our discussion of rigidity, we agreed to set external differential forces equal to zero, or to correct our instruments for the effects of such forces. Let us suppose that we were in the presence of an electrostatically charged gravitational body. That is, the gravitational body (e.g. the sun) would have some electrostatic charge (as is probably the case for the sun). If we corrected our rods and clocks for the effect if any of this differential force (which would certainly be negligible in any case, so far as spatial geometry is concerned), we might then expect that the geometry of the field would be the same as when the gravitational body is uncharged. But is this the case? Not at all! And the explanation is not far to seek: the charge contributes energy to the field; but energy, by relativity theory, is equivalent to mass, and mass always modifies the gravitational potential. Hence, the geometry of the charged gravitational field (which depends on the potential) must be different from the uncharged.