It is to be understood that the philosopher is not the one to query the procedures and the working hypotheses of the physicist. These arise from grappling with technical problems which have arisen historically in his science; and the philosopher seldom has the technical competence to get the concrete feel of the situation and to realize, to the full, the meaning of what is being proposed.

This is in no sense an attack on the theory of relativity but, instead, an attempt to clarify some points about its epistemology and ontology. It is quite probable that the queries I have had in mind are products of the past. But I observe enough uncertainty in writings here and there to justify a brief discussion.

Discarding both ether and Newtonian Space either as entities or as frames for light, we have left the problem of relating the behavior of light to physical bodies, such as the proverbial rods.

There is a famous character in one of Oscar Wilde's plays who knew the price of everything and the value of nothing. An economist wonders uneasily if the reference is not to him. The word “value” occurs in economic writings with high frequency, the frequency of meanings being almost as great as the frequency of occurrence. It has been the occasions of long and bitter disputes, some on the semantic level, some more substantive. What I want to accomplish in this paper is a relatively humble task—to examine some of the concepts and related systems in economics which seem to be relevant to the general problem of value, and to see how far and in what directions they might be safely generalized. I do not claim that economics, even when generalized to the full, gives us a complete theory of value. Many of the most important and most difficult questions in value theory cannot be answered within the framework which I shall set up. But economics can, I hope, provide something of a foundation on which to build, or at least a launching platform from which to send off our philosophical rockets.

Russell's book on Leibniz appeared in 1900. That it is important, because of its subject and because of its author, hardly needs to be argued. An examination of it, or of parts of it, after more than half a century is therefore in order. Yet the title I chose indicates only part of my intent. The other part is to examine certain ideas, irrespective of what either Leibniz or Russell thought and of what the latter thought about the thoughts of the former. The title best suited to this part is Individuals, Natures, Relations, and Change. The mixed form of presentation, analytic and quasihistorical, has very great advantages. For the nature of the philosophical enterprise is such that an analyst is lost without some grasp or, at least, some image of “structural history.” The danger is that only very few, if any, are masters of two trades; in this case, logical analysis and historical scholarship. I, for one, make no pretense whatsoever of being a scholar. Naturally, I have read in Leibniz; and I did not skip or take lightly anything in the letters to Arnauld and Clarke; but I have by far not read everything that is available. Reading about Leibniz, aside from Russell, of which I did but little, I found Latta and, particularly, Joseph sometimes helpful. More often, though, I felt that the former's Hegelianism and the latter's Aristotelianism had got between them and their subject.

We have undertaken to discuss the nature of mathematical systems, the way in which they are discovered, and the uses to which they are put in the empirical sciences. The empirical sciences employ mathematical systems in framing final formulations, but adopt mathematical techniques long before reaching that stage. It is a prerequisite that the mathematics they employ has been developed separately and within its own domain. We shall return to the relation between mathematics and the empirical sciences before we are done, but in the meanwhile we shall be constrained to begin by discussing the situation in mathematics in isolation from any empirical considerations.

Whether or not history is, or could be, or ought to be a science, depends in part upon how the words “science” and “history” are to be used. But if one of the criteria of a science is an ability to provide explanations of large numbers of events by means of a small number of general laws, it then becomes in part a question of whether or not history does, or can, provide explanations of this sort for the phenomena which concern it. It is common knowledge that history, at the present time, displays no obvious instance of such an explanation; and I shall try to argue that, though the phenomena with which history deals could conceivably be explained in a “scientific” manner, it is not the office of history to provide such explanations, nor does its lack of explanations in any way diminish either the effectiveness or importance of history. So if my conclusions here suggest that history is not a science, and could not be one, they also suggest that it ought not to be one, but that it is a special and irreducible activity of the human spirit, with a function and justification of its own.

The following reflections are submitted in awareness of an unfortunate situation which currently finds both psychologists and philosophers concerned with the search after criteria for assessing human conduct, yet with either profession suspicious of the contributions to be expected from the other. The objections frequently entertained against psychologizing philosophers are only matched by those entertained against philosophizing psychologists. Yet, if the worst is said, it still remains true that much psychological work, devoted to problems of mental health, maturity or neurosis, makes contact with moral issues. It also is true that such contact has so far not been fruitful to the point of encouraging psychologists or philosophers to expect new illumination from each other. Unless it be groundless, in principle, to look towards psychological findings as potentially relevant for moral theory or vice versa, it would seem that the only cure for poor relations between the two disciplines are better ones rather than none at all. At any rate, it is on the assumption that more successful relations are possible that I shall now comment upon what appears to be both a most influential and unsuccessful attempt by one psychologist to solve an ethical problem. I shall take my departure from B. F. Skinner's recent Science and Human Behavior,∗ especially from his chapters on value and the survival concept.

Admirers of Whitehead who know him best have suggested that Wordsworth had possibly a greater influence upon him than anyone except Plato. Nowhere apparently has Whitehead admitted such an influence, as he has that of Plato and Locke and that of William James, Bergson, and Alexander among traditional and contemporary philosophers But he had a predilection for poetry, and attributes to the great poets philosophical importance. They capture uniquely, he says, “a fragrance of experience”; and “… express deep intuitions of mankind penetrating into what is universal in concrete fact.” As observers of nature both Wordsworth and Whitehead ascribed to animate and inanimate life a degree of feeling or satisfaction in the course of being and becoming. Like the poet, Whitehead must have found “joy in widest commonalty spread.” The multiplication table, he noted at one time, “… is no good to the realist. It shuts him up with Plato's ideas out of space and out of time” when “… like Wordsworth and the rest of us he wants to hear the throstle sing.”

Theoretical physics is a deductive discipline which presupposes the validity and applicability of certain other disciplines. Among these are logic, algebra, analysis, and geometry. Before relativity, Euclidean geometry was the only one thought to be important for physical space. These disciplines correlate well with experience, and, in the course of time, a priori validity came to be ascribed to them. To Kant, for example, the universe could not possibly be based on any geometry other than Euclid's. The discovery of non-Euclidean geometries by Bolyai and Lobatchevsky, its systematic extension by Riemann, and the critical scrutiny of foundations by Mach and Poincaré shook the “self-evident truth” of Euclidean geometry as applied to the world of physics. The death knell of the a priori truth of any geometry was supplied by Einstein. He showed that a wider body of experience was coordinated by a Riemannian geometry than by Euclidean. He traced the success of Euclidian geometry back to the existence of so-called rigid bodies, in terms of which operations can be associated with numbers which correlate well with numbers associated in a purely mathematical way with mathematical constructs put in correspondence with these bodies. For the physicist, then, the geometry of the real world is now a physical theory whose “truth” like that of all physical theory, is measured by its degree of success in coordinating experience.

The concept of simultaneity, and the associated problems of synchronization of moving clocks and establishment of a universal time scale, were given little or no attention prior to the twentieth century. In 1905, however, Einstein analyzed the concept of simultaneity on the basis of two principal postulates:

1. (1) Absolute velocity is meaningless (relativity postulate),

2. (2) The velocity of light in a vacuum is the same for all unaccelerated observers.

During the past half-century the patterns of publication in science have undergone radical change. A vast increment has occurred in the amount of scientific writing. And scientific findings are increasingly being disseminated through “non-traditional” publishing media such as mimeographing and microfilming. These two interrelated trends have had some notable effects upon science. 1. With the rapid increase in the number of publications the problem of maintaining continuity in science has become acute; the traditional scientific social structure seems quite incapable of accomplishing this vital task. 2. An extensive organization is developing which seeks to provide the desired continuity, but its very existence poses dilemmas for the traditional scientific order. 3. Moreover, the changing publication patterns seem to be intensifying the “schisms” between the theoretician and the specialized researcher. 4. They are also challenging the older standards for evaluating scientists. We thus hypothesize that the volume and form of communication is a significant variable inducing modifications in the scientific social system. This theoretical orientation has in part been suggested by Harold Innis (7) who, however, was concerned with broader systems—i.e., civilizations. The following analysis should point up some little-considered problems inherent in the research process.

What strikes one first about two recent books in philosophy of science is that they seem to be polar opposites in all important respects. Bridgman, of course, typifies the hard-headed and skeptical physical scientist, whose interest in the broad “philosophic” questions of scientific methodology stems largely from current problems in theoretical physics, but he is, nevertheless, very much concerned to extend the salutary effects of operational analysis to other intellectual disciplines. Jung, on the other hand, not only is a psychiatrist—and therefore professionally committed to a certain gullibility about mental phenomena—but he also is deeply convinced of the importance for science of such subjects as astrology and alchemy; and Pauli, although a distinguished physicist in his own right, has clearly been influenced by Jung's conception of archetypal ideas in the collective unconscious.

In the course of his researches in electromagnetism and the kinetic theory of gases, James Clerk Maxwell gave some thought to the nature of science itself. His observations in this field are of interest today not only because they are his, but because they are still instructive. Maxwell's views are to be found in the many asides with which he enlivened his scientific papers and treatises and in the various articles and reviews which he prepared for more popular consumption. The topics discussed bear on his own contributions to physics; they include the logic of dynamical explanation, the method of physical analogy, and the perennial question of action at a distance versus contiguity. In the present essay, I wish to discuss Maxwell's views on dynamical explanation.

Following an initial section, in which the relation of materialism to positivism (including operationalism) and agnosticism is discussed, and the latter views criticized, a formal definition of dialectical materialism is given. Materialism is contrasted to idealism and dualism. Dialectics is contrasted to metaphysics. Some additional assumptions, usually included in dialectics, such as the interpenetrating character of the levels of science, and rationalism, are listed. In a section devoted to the relation between matter and spirit, the foundations of materialist ethics are laid by stating the humanist axiom of purpose. In the last section, historical materialism is defined, and some reasons for the occasional entanglement of scientific, philosophical, and political controversies are discussed.

Current discussions of science—both popular and philosophical—often represent the development of science in our civilization as a gradual process of purification from superstitious, religious, and metaphysical elements. This purification is usually presumed to be complete by now—although there may be occasional lapses on the part of individual scientists. That science has changed in character over the centuries is a truism; that it has increasingly loosened ancient ties with magic, religion, and speculative philosophy is an easily substantiated historical thesis. This much admitted, however, an interesting question remains over for discussion: is science by its very nature independent of philosophy? This question has only as much meaning as its two key words (“science” and “philosophy”). According to one common view, “science” would signify some cumulative heritage of methods, principles, and results, while “philosophy” would signify a certain tradition of writings in which the later constantly refer to the earlier, but which otherwise exhibit no discernible uniformity of methods, principles, or results. On this view, then, science is essentially monistic while philosophy is essentially pluralistic.

In Executive Order No. 10521, March 17, 1954, President Eisenhower stated: “…only a small fraction of the Federal Funds is being used to stimulate and support the vital basic research which makes possible our practical scientific progress. I believe strongly that this Nation must extend its support of research in basic science.”

I yield to no one in my admiration for and appreciation of what the scientists have accomplished in the last few centuries as well as back in the days of the Greeks. Nonetheless there are certain questions that perennially recur. One might readily say that scientists have not yet reached the proper answers, but judging from what they have already accomplished satisfactory answers will be forthcoming in the revolving years. That is too facile a reply. On some things we want real answers now. To put off fairly adequate explanations until some future limbo is wholly unsatisfactory.