Science is not merely a collection of facts and formulas. It is preëminently a way of dealing with experience. The word may be appropriately used as a verb: one sciences, i.e., deals with experience according to certain assumptions and with certain techniques. Science is one of two basic ways of dealing with experience. The other is art. And this word, too, may appropriately be used as a verb; one may art as well as science. The purpose of science and art is one: to render experience intelligible, i.e., to assist man to adjust himself to his environment in order that he may live. But although working toward the same goal, science and art approach it from opposite directions. Science deals with particulars in terms of universals: Uncle Tom disappears in the mass of Negro slaves. Art deals with universals in terms of particulars: the whole gamut of Negro slavery confronts us in the person of Uncle Tom. Art and science thus grasp a common experience, or reality, by opposite but inseparable poles.

It is the purpose of this paper to review the present status of discussion concerning the concept of probability. The exposition will consist of six sections: (1) A brief statement of the most important traditional views of the concept of probability: subjective and objective; (a) A brief criticism of two traditionally important conceptions: a priori probability and the Principle of Indifference; (3) A criticism of an outstanding example of the subjective theory of probability, the theory of F. P. Ramsey; (4) A criticism of the most widely known of the objective logical theories of probability, the theory of J. M. Keynes; (5) Some remarks concerning the results of the recent work of Reichenbach and von Mises with particular reference to clarification of the concept of probability; (6) A summary of the case for the frequency interpretation of probability, revealing its basic importance in the light of present evidence.

We are told that we live in a scientific world. All about us are the fruits of scientific research, and the products of scientific industry. But, in spite of this transformation of our material surroundings, scientific thought, or the scientific method as such, has had no effect upon the everyday thought and behaviour of our people. To be sure, along with the scientific gadgets a few scientific truths have been disseminated. They know the earth is round and moves about the sun; they could know that bacteria cause disease and that they are themselves descended from less articulate forms of animal life. Even when such conclusions are accepted, it is on the basis of authority with no understanding as to how they arose and on what basis they stand. For the large majority, science has merely acquired a cloak of respectability; it is a stronger magic than that of our forebears, and our modern alchemy is known as a powerful though mysterious source of pecuniary profit.

In the October 1937 number of Philosophy of Science Lindsay has made certain criticisms of the adequacy of the “operational method” of analyzing and giving meaning to the concepts of physics, documenting his criticisms chiefly from my own writings. In these criticisms he has made statements as to the method which I would by no means accept. This is not characteristic of his paper only, for I have seldom indeed seen a printed discussion of the method which I would accept as being an adequate or sometimes even fair representation of what I understand by it. It will perhaps pay therefore if I attempt to state what I conceive it to be all about, particularly since I have never attempted such a comprehensive statement and since my own ideas on the subject have been developing since I first wrote in the Logic of Modern Physics. For one reason I have hesitated to do this, for fear of seeming to subscribe to the not uncommon idea that we are dealing with some elaborate and profound new theory of the nature of knowledge or of meaning. I believe that I myself have never talked of “operationalism” or “operationism”, but I have a distaste for these grandiloquent words which imply something more philosophic and esoteric than the simple thing that I see. What we are here concerned with is an observation and description of methods which at least some physicists had already, perhaps unconsciously, adopted and found successful—the practise of the methods already existed. What I have attempted is to analyze these successful methods, not to set up a philosophical system and a theory of the properties that any method must have if it hopes to be successful. Since I was concerned with a technique already extant, my principal method of getting others to see what the technique involved has been to exhibit examples of the technique in action, rather than to attempt any exhaustive characterization of the technique itself.

In a review of my book “Wahrscheinlichkeitslehre”, Dr. Ernest Nagel has recently criticized some of my ideas on probability and induction. His review includes a good exposition of my ideas, and I have to thank him for his serious attempts to do justice to my results. He attacks, however, some very essential points of my theory. I may be allowed, therefore, to answer him as frankly and thoroughly as he attacks me.

Since my discussion of an experimental arrangement of the sciences for certain practical objectives, some comment has appeared which makes it necessary to re-emphasize certain points by a further example. There seems to be something like a desire to paralyze the hand that makes arrangements for fear that undue profound metaphysical significance may be seen in a “mere” arrangement. It is the perennial fear of the a priori, the fear of a principle being invoked because of its “self-evidence”, and then turning traitor on the actual evidence. I invoke no such principle either overtly or covertly.

To recognize the reality of the space-time structure of nature would, I think, revolutionize metaphysics. It means that we must conceive reality as history and history as having direction. It is not enough to take time seriously, we must take the order of time seriously. When we view the apparent confusion of nearby events, we may indeed be tempted to say with Heraclitus: “Time is a child playing drafts. The kingly power is a child's.” But if we take a long view we may discern order. The early Greek pioneers started philosophy on the right track. Anaximander, the real founder of Western philosophy and science, had the brilliant intuition of an order of time as regulating the cosmic process. In the one direct quotation from Anaximander we are told: “And into that from which things take their rise they pass away once more, as is meet; for they make reparation and satisfaction for their injustice according to the ordering of time.” It is because of the “ordering of time” that the universe is a self-maintaining whole. The development of the conception of the ordering of time was left to the great metaphysical genius of Heraclitus, who conceived a thought running through all things and steering through all things. There is a controlling direction of change which regulates the rhythm of exchange in nature and keeps the universe from running down. It was this emphasis upon the Word, the logos, the controlling order of change, which Heraclitus felt to be his important contribution. Change, continuous flux, is real, but there is a guiding order in change.

Like most other subjects under discussion today, the theory of nature is largely controlled by considerations of knowledge. Treatment of it is, consequently, incidental to the treatment of these other problems, and is undertaken, in the main, because they compel it. A brief catalogue of characteristic statements about nature will illustrate this. “Nature,” says one writer, “is that which we observe in perception through the senses”; and another writes, “It is not experience which is experienced, but nature—stones, plants, animals, diseases, health, temperature, electricity, and so on.” Nothing is more apparent in these sentences than the fact that it is not nature that the writers are so much concerned with, as with what it is that appears through the senses. The theory of nature, that is, is not so much guided by an analysis of the word's context and usage, as it is by the question: what is the proper object of knowledge? Consequently it is the latter question that is answered and not the question: what is nature? The reason for this is evident in the purpose of these statements and in their history; their purpose: the desire to do away with the separation between experience and nature, and to transform nature into a field familiar and accessible; and their history: the very framework against which they are directed, for they are embedded in the set-up from which they are trying to disentangle themselves. Perhaps something ought to be said to substantiate the thesis that the sentences cited are controlled by the problem of knowledge, especially since their intent seems to be to escape that problem. In any case, their history should serve to clarify them, and render a different approach to the theory of nature more significant.

When the layman reads a book or two of popularized physics and then moves solemnly forth, as occasionally happens, to expound some comprehensive doctrine purporting to be built directly out of the materials he has picked up, the type of comment which the physicist will make is plain enough in advance. But why does it so rarely occur to the physicist that others may think of his epistemologizing much what he is sure to think of their quantizing?

The following comments represent what seem to me promising lines of approach to some of the broader issues in the philosophy of logic. They are offered, it is perhaps unnecessary to say, with the intent of stimulating rather than foreclosing discussion. And if the conclusions advanced are formulated loosely and with only a crude indication of the arguments which support them, I hope that thereby they will provoke all the more the free flow of discourse which it is the object of this Conference to promote.

Is metaphysics possible? From the beginning of our present sophisticated era we have continually been compelled to ask this question. For myself I confess to a growing impatience with this and like questions. I hold with Kant that metaphysics is a Naturanlage, that should all science pass away and should we revert to barbarism, there would still be metaphysics. I am also disposed to think that should mankind develop in the opposite direction, should we become the supermen or the angels which the perfectionists of all times have envisaged, metaphysics would not only remain, but metaphysical insight would be the very life of that perfection. As Dante said, “metaphysics is the bread of angels.”

For the purposes of this paper, realism is defined as the belief that in visual perception there is a direct perception of material bodies existing in space external to the perceiver's body. Most contemporary positivists and analytical philosophers are realists in this sense. Included in this classification would be all those who argue from the character of seen relations of bodies to the uniformity view of causation; those who oppose public (extended or in space) to private experience; those who believe that one can point to facts; those who believe in the real existence of objects like extended solid tables and chairs; and those who distinguish in terms of verifiability between judgments of color and judgments of value.

The concept of causality as it appears in a specific scientific theory involves two factors: (1) the relation of necessary connection between the states of a system at different times, and (2) the definition of state at a given time.

Professor Schiller's question, “Must philosophers disagree?” can be answered in the negative if a technique can be worked out whereby it becomes possible to answer the question, “What are they talking about?” It is the aim of the ensuing remarks to provide at least the outline of such a technique and to illustrate its possible effectiveness in the specific context of controversies about the nature of time. That philosophers may continue to disagree in spite of the suggestions offered is, of course, to be expected in view of the long history of failures which compromise positions have encountered. The fate of the conciliator usually has been to receive the contempt of the embattled polemicists, and the fate of his peacemaking, to be construed as just another theory. Of course, this is in most cases the ulterior motive for his pretended altruism in assuming the rôle of arbitrator. Yet there are theories and theories. A position like that of Hume on the question of causality may reasonably be opposed to that of Leibniz but not in the same sense as to that of Kant. For the latter does attempt to provide a bridge between rationalism and empiricism and to do justice to the valid claims of each. The theory of time here proposed immodestly attempts a rapprochement among the multitudinous doctrines of time by setting forth one more doctrine.

This paper attempts to explore some of the implications of the distinction between having or enjoying and knowing, between “experiencing” and science, for these implications have not always been adequately realized by those for whom the distinction is fundamental.

Recent advances in quantum physics have led to a renewal of interest in the problem of human freedom and in the wider problem of indeterminism. It is important to recognize, however, that if every denial of determinism is to be called indeterminism, the latter term covers a wide range of logically distinguishable positions. We should perhaps speak in the plural number of indeterminisms rather than of indeterminism. For determinism may be defined, simply, as the doctrine that every event has a cause; or we may add that the effect is always uniquely determined; or that when the effect is complex it can always be exhaustively analyzed into components each of which is the effect of a component of the cause; or that every cause directly or indirectly includes the entire universe. And in the case of each of these, or of still other interpretations of determinism, the denial would be a form of indeterminism.

The pervasive contrast in modern life between the certainties of science and technology, on the one hand, and the uncertainties of human goals and policies, on the other, is the objective source of a fundamental conflict in theory. It is now widely held that facts are rather definitely verifiable, but that values are unverifiable; though other students assume that values are also verifiable in some significant sense and degree.

Mr. E. J. Nelson, in “The Inductive Argument for an External World,” treats of fundamental topics with erudition and urbanity, but his essay remains inconclusive, I believe, with respect to its purpose of discrediting the argument. He agrees with Mr. Savery, Mr. Pratt, and me, as against the positivists, that the question of the existence of an external world is meaningful (249) and indeed of paramount importance for both metaphysics and logic. But he argues against us that it cannot be inductively established by its supposed power of “saving the appearances.” He is not sure that any induction is valid; but even if other inductions are valid, he thinks this one can not be (240, 245, 247), for the following reasons. (1) By the multiplicative axiom of probability-theory, evidence for a hypothesis can only multiply its antecedent probability, and can increase the probability only when the latter is finite, while the hypothesis of an external world has and can have no finite antecedent probability (241, 245). (2) By the same axiom, even granted an antecedent probability for the hypothesis itself, no experience can act as evidence to increase the probability of a hypothesis except in so far as the hypothesis implies, makes probable, or “explains” the evidence, and this the hypothesis of an external world cannot do (244, 245, 247).

There are some indications that the philosophy of science is reaching the age of discretion. Now, as I understand it, the age of discretion is characterized by self-examination. Youth is a period of blundering enthusiasm. But maturity demands the sobering influence of principles, perspectives and techniques. The adult must put away childish things. This does not demand the elimination of spontaneity and imagination, but it does require their chastening according to the principles of propriety. It seems time to ask ourselves whether the philosophy of science ought to be allowed henceforth just to grow, like Topsy, or whether a serious attempt ought not to be made to determine its nature and task.