SOURCE: "Einstein's Conception of Science," in Albert Einstein: Philosopher-Scientist, revised edition, edited by Paul Arthur Schlipp, The Library of Living Philosophers, 1970, pp. 387-408.

[Northrop was an American author and educator who specialized in the fields of law, science, philosophy, and economics. In the following essay, originally published in 1949, he argues that understanding Einstein's views of the scientific method requires a well-honed "epistemological philosophy."]

Albert Einstein is as remarkable for his conception of scientific method as he is for his achievements by means of that method. It might be supposed that these two talents would always go together. An examination, however, of statements upon scientific method by truly distinguished scientists indicates that this is far from being the case. Nor is the reason difficult to understand. The scientist who is making new discoveries must have his attention continuously upon the subject matter of his science. His methods are present, but he must have them so incorporated in his habits that he operates according to them without having to give any conscious attention to them. He is like the truly natural athlete, who performs spontaneously, but who often cannot teach others how he does it. Albert Einstein, however, is an exception to this frequently illustrated rule. He has given as much attention consciously and technically to the method of science as he has given to the theoretical foundations of physics to which he has applied scientific method.

Moreover, his analysis of scientific method has taken him beyond empirical logic into epistemology. In fact, his technical epoch-making contributions to theoretical physics owe their discovery and success in considerable part to the more careful attention which he has given, as compared with his predecessors, to the epistemological relation of the scientist as knower to the subject matter of physics as known. It happens, therefore, that to understand Albert Einstein's conception of scientific method is to have a very complete and precisely analyzed epistemological philosophy—an epistemological philosophy, moreover, which, while influenced by positivism on the one hand and ancient Greek and Kantian formal thinking on the other, departs nonetheless rather radically from both and steers a course of its own, checked at every point by actual methodological practices of scientists. The result is an epistemology which has fitted itself to an expert understanding and analysis of scientific method rather than an epistemology, such as Kantianism or positivism, which has come to science with certain epistemological premises and prescriptions and tried to fit scientific procedure to these prescriptions.

In this connection, Albert Einstein himself gives us very important advice. At the very beginning of a paper "On the Method of Theoretical Physics" he writes, "If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds." Obviously this is excellent advice, and, as we shall see, Einstein has followed it, illustrating all his statements about scientific method and epistemology by specific illustrations from technical scientific theories and the technical scientific methods which they entail in their formulation, discovery and verification.

Nonetheless, his words as thus stated might easily mislead one who has not read everything which Albert Einstein has written on scientific method. One might suppose that, when he talks about fixing one's attention on the deeds of physicists, he means by "deeds" the denotatively given operations and experiments performed in a laboratory; in other words, one might suppose that he means something identical with P. W. Bridgman's operationalism.

Actually, however, Albert Einstein's meaning is almost the reverse of this, as the very next sentence in the aforementioned paper clearly indicates: "To him who is a discoverer in this field, the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities."

What Einstein means here is that the full meaning of verified mathematical physics is only given in part empirically in sense awareness or in denotatively given operations or experiments, and hence involves also meanings which only the imagination can envisage and which only deductively formulated, systematic, mathematical constructions, intellectually conceived rather than merely sensuously immediate, can clearly designate. But because these deductively formulated constructions, as the scientist becomes more at home with them, so capture his imagination as to appear both "necessary and natural," and also because their deductive consequences become empirically confirmed, the tendency of the scientist is to think that they are merely denotative, empirically "given realities," rather than empirically unobservable, purely imaginatively or intellectually known, theoretically designated factors, related in very complicated ways to the purely empirically given.

This counsel by Albert Einstein is something which philosophers especially need to take seriously. If one approaches epistemology by itself, simple answers to epistemological questions often seem very satisfactory. It is obviously much more simple to affirm that all meanings in science come down to purely empirically given, positivistically immediate, denotative particulars than to hold that the source of scientific meanings is much more complicated than this. Consequently, if some philosopher, especially one with a position in a physics department, holds this simple-minded theory and asserts that this is the scientific epistemology, he can fool most philosophers, even those who are experts in epistemology. There is only one cure for this, and this cure is an examination of the technical theories of the physical sciences, their technical concepts, the specific scientific methods used actually by the scientist who introduced the concepts, and the attendant specification of the epistemological relations joining the meanings of the concepts as specified by the deductively formulated theory to meanings denotatively exhibited in empirical experience. Albert Einstein has the competence to construct such an epistemology, and he happens to have directed his attention seriously and technically to this end.

It is valuable also that Albert Einstein is a theoretical rather than an experimental physicist. The experimental physicist's business is to perform denotatively given operations. This tends to cause him to have his attention upon, and consequently to emphasize, the purely empirical, positivistically immediate side of scientific theory. It tends also to cause him to want to reduce all other meanings in science to such purely empirical, positivistically immediate operational meanings. The theoretical physicist, on the other hand, tends to approach science from the standpoint of its basic theoretical problems, as these problems are defined either by the points of difference between major theories in different parts of the science or by points of difference between the deductions from a single systematic scientific theory and propositions incompatible with these deductions, which are nonetheless called for by the experimental evidence. Thus the experimental physicist who writes on the methodology, epistemology and theory of physics tends naturally to reduce imaginatively constructed, systematically and deductively formulated scientific meanings to positivistically immediate, purely denotatively given meanings. The theoretical physicist, on the other hand, tends to see that the problems of physics are only theoretically formulatable, since facts cannot contradict each other; only the theoretically prescribed conceptualizations of the facts can contradict one another.

Albert Einstein has seen that in scientific knowledge there are two components, the one given empirically with positivistic, denotative immediacy, the other given imaginatively and theoretically and of a character quite different from the empirically immediate. In the aforementioned paper Albert Einstein makes this point unequivocally clear. After telling us to watch what physicists do, he writes as follows: "Let us now cast an eye over the development of the theoretical system, paying special attention to the relations between the content of the theory and the totality of empirical fact. We are concerned with the eternal antithesis between the two inseparable components of our knowledge, the empirical and the rational.…" Upon this epistemological point Albert Einstein, notwithstanding all his other major departures from Kant, is a Kantian and a Greek empirical rationalist, rather than a Humean British positivistic empiricist. Albert Einstein, at a formative period in his intellectual life, did not study Immanual Kant's Critique of Pure Reason to no avail.

Furthermore, in the sentence immediately following the aforementioned quotation Einstein continues:

We reverence ancient Greece as the cradle of western science. Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every one of its deduced propositions was absolutely indubitable—I refer to Euclid's geometry. This admirable triumph of reasoning gave the human intellect the necessary confidence in itself for its subsequent achievements. If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.

There is, to be sure, the empirical, positivistically immediate, denotatively known component in scientific knowledge also. This Einstein immediately proceeds to designate:

But before mankind could be ripe for a science which takes in the whole of reality, a second fundamental truth was needed, which only became common property among philosophers with the advent of Kepler and Galileo. Pure logical thinking cannot yield us any knowledge of the empirical world; all knowledge of reality starts from experience and ends in it. Propositions arrived at by purely logical means are completely empty as regards reality. Because Galileo saw this, and particularly because he drummed it into the scientific world, he is the father of modern physics—indeed, of modern science altogether.

In short, there must be both the postulationally designated, deductively formulated theoretic component and the inductively given, denotative, empirical component in scientific knowledge.

It might be thought from the last quotation, if nothing more by Einstein were read, that, because "knowledge of reality starts from experience and ends in it," what happens in between, as given theoretically and formulated deductively, reduces to the empirical component and hence adds to the conception of "reality" nothing of its own. The sentence, to the effect that "Propositions arrived at by purely logical means are completely empty as regards reality" might seem to suggest this. The point of the latter statement, however, is that logical implications are always carried through with expressions which contain variables; thus in themselves they designate nothing empirical. But logical deductions proceed from expressions containing variables which are postulates, or what Albert Einstein terms "axioms." And these axioms express a systematic relatedness. Consequently, when one finds empirically, by the method of Galileo, the inductive factors which function as material constants for the variables in the postulates of the deductive system, then to this inductively given material there is contributed a systematic relatedness which pure empiricism and induction alone do not exhibit. Thus the theoretically known systematic factor, between the experience with which scientific method begins and that with which it ends, contributes something of its own to what Einstein terms the scientific "knowledge of reality." Hence, Einstein concludes: "We have thus assigned to pure reason and experience their places in a theoretical system of physics. The structure of the system is the work of reason; the empirical contents and their mutual relations must find their representation in the conclusions of the theory."

Furthermore, Albert Einstein makes it clear that it is the rationalistic, deductively formulated, structural component which is the basic thing in mathematical physics and the empirical component which is derived. This was implicit in the last sentence just quoted, when it affirmed that "the empirical contents and their mutual relations must find their representation in the conclusions of the theory." They do not find their representation in the postulates or axiomatic basis of the deductively formulated theory.

Not only do the basic concepts and postulates of theoretical physics fail to reduce to purely nominalistic, denotatively given meanings, but they cannot be derived from the empirical, or what we have elsewhere [The Meeting of East and West] termed the aesthetic, component in scientific knowledge by any logical means whatever; neither the logical method of formal implication nor the more Aristotelian or Whiteheadian method of extensive abstraction. Upon these points Einstein is unequivocal.

He tells us that the deductively formulated theoretic component in scientific knowledge is a "free invention(s) of the human intellect.…"He adds,

Newton, the first creator of a comprehensive, workable system of theoretical physics, still believed that the basic concepts and laws of his system could be derived from experience. This is no doubt the meaning of his saying, hypotheses non fingo … the tremendous practical success of his doctrines may well have prevented him and the physicists of the eighteenth and nineteenth centuries from recognising the fictitious character of the foundations of his system. The natural philosophers of those days were, on the contrary, most of them possessed with the idea that the fundamental concepts and postulates of physics were not in the logical sense free inventions of the human mind but could be deduced from experience by 'abstraction'—that is to say by logical means. A clear recognition of the erroneousness of this notion really only came with the general theory of relativity, which showed that one could take account of a wider range of empirical facts, and that too in a more satisfactory and complete manner, on a foundation quite different from the Newtonian. But quite apart from the question of the superiority of one or the other, the fictitious character of fundamental principles is perfectly evident from the fact that we can point to two essentially different principles, both of which correspond with experience to a large extent; this proves at the same time that every attempt at a logical deduction of the basic concepts and postulates of mechanics from elementary experiences is doomed to failure.

He adds that the "axiomatic basis of theoretical physics cannot be abstracted from experience but must be freely invented, … Experience may suggest the appropriate mathematical concepts, but they most certainly cannot be deduced from it." In short, the method taking one from empirically given experience to the systematic factor in scientific knowledge designated by the postulates of deductively formulated scientific theory is not that of either extensive abstraction or formal implication.

But neither is it that of any explicitly formulatable scientific method grounded in probability rather than deductive certainty. It is precisely at this point, notwithstanding his agreement with the positivists' emphasis upon empirical verification, that Albert Einstein, along with Max Planck, becomes so uneasy about positivism. The way from the empirical data to the postulates of deductively formulated physical science is a frightfully difficult one. Here, rather than anywhere else, the scientist's genius exhibits itself. The way is so difficult that no methods whatever must be barred; no sources of meaning whatever, imaginative, theoretical, of whatever kind, are to be excluded. It appears that nature covers up her basic secrets; she does not wear her heart upon her sleeve. Thus only by the freest play of the imagination, both the intuitive imagination and the non-intuitive, formal, theoretical imagination, can the basic concepts and postulates of natural science be discovered. In fact, Einstein writes, with respect to the discovery of "the principles which are to serve as the starting point…" of the theoretical physicist's deductive system, that "there is no method capable of being learnt and systematically applied so that it leads to the goal."

In a paper on "The Problem of Space, Ether, and the Field of Physics," Albert Einstein adds that the "hypotheses with which it [theoretical physics] starts becomes steadily more abstract and remote from experience," the greater the number of empirical facts the logical deduction from the basic postulates includes. Consequently, the "theoretical scientist is compelled in an increasing degree to be guided by purely mathematical, formal considerations in his search for a theory, because the physical experience of the experimentor cannot lift him into the regions of highest abstraction. The predominantly inductive methods appropriate to the youth of science are giving place to tentative deduction." Consequently, instead of hampering the theoretical physicist by epistemological prohibitions concerning the kind of meanings and their source permitted in his basic concepts, Albert Einstein writes that the "theorist who undertakes such a labour should not be carped at as 'fanciful'; on the contrary, he should be encouraged to give free reign to his fancy, for there is no other way to the goal." He adds: "This plea was needed …; it is the line of thought which has led from the special to the general theory of relativity and thence to its latest off-shoot, the unitary field theory."

But if Einstein's dictum that the "axiomatic basis of theoretical physics cannot be abstracted from experience but must be freely invented" entails the rejection on the one hand of the positivistic, purely empirical, Humean philosophy, which would reduce all scientific meanings to nominalistic particulars, and also, on the other hand, of the Aristotelian and Whiteheadian epistemology, which, while admitting universal or nontemporal invariant meanings, would nonetheless insist upon deriving them from empirical immediacy by the method of extensive abstraction, it equally rejects the Kantian epistemological thesis that the postulated, deductively formulated systematic relatedness of scientific knowledge is a categorical a priori. The more systematic relatedness of space and time in scientific knowledge is as tentative, even though not given purely empirically, as is the empirical content which may be observed and correlated with factors within the space-time relatedness. This is what Albert Einstein means when he speaks of the method of theoretical physics as the method of "tentative deduction."

There is, for Albert Einstein, as for Kant, spatio-temporal relatedness in scientific knowledge, which is not to be identified with sensed relatedness. But this systematic relatedness is not a universal and necessary presupposition of any possible empirical experience. It has to be discovered by a free play of the formal, mathematical, intellectual imagination, and it has to be tested by a long sequence of deductive implications, the resultant theorems of which are correlated with observable data. Thus, although the forms of space and time, or, to speak more accurately, the form of space-time, is a priori in the sense that it is not given empirically and must be brought to and combined with the local, diverse, contingent, inductive data located within it, nonetheless it is not a priori in the Kantian sense of being a universal and necessary form of any possible empirical experience whatever.

Nor is it a priori in the Kantian sense that it is brought to the Humean sensuous, contingent data of science by the epistemological knower. Thus Albert Einstein writes that it "cannot be justified … by the nature of the intellect…" Instead, it belongs to and is the public physical relatedness of the public physical field of nature—in fact, it is that particular relatedness which exhibits itself as the gravitational field. Thus, in the epistemology of Albert Einstein, the structure of space-time is the structure of the scientific object of knowledge; it is not something which merely seems to belong to the object when its real basis supposedly is solely in the character of the scientist as knower.

This ultimate basis of space-time in the public, contingent, physical object of knowledge, rather than in the necessary constitution of the epistemological knower, follows from the tensor equation of gravitation in Einstein's general theory of relativity. Its ten potentials defining the gravitational field at the same time prescribe the metrical structure of space-time. Thus space-time has all the contingent character that the field strengths, determined by the contingent distribution of matter throughout nature, possess. Not even Kant would have referred these contingently distributed field strengths to the necessary constitution of the scientist as knower. The verification of the general theory of relativity indicates that there is no more justification for finding the basis of space-time in the knower.

Furthermore, this structure remains invariant for all possible physical objects which are chosen as the reference points for the empirical measurements of the astronomer or experimental physicist. Thus space-time escapes all relativity, not merely to frames of reference, but also to all the millions upon millions of human observers upon a single frame of reference such as the earth.

This means that, notwithstanding Albert Einstein's use of the word "fictitious" to designate the non-empirically given, theoretic component in scientific knowledge, this component is nonetheless not a Kantian or neo-Kantian or semantic logical positivist's subjective construct. The space-time of Einsteinian physics is the relatedness of the gravitational field of nature. It is fictitious in the sense that it is not a positivistically immediate, purely denotatively, inductively given datum; it is fictitious in the sense that it is discovered only by a free play of the scientist's imagination and not by the inductive method of extensive abstraction from empirical immediacy; it is fictitious also in the sense that it is only known positively by a leap of the imagination, a leap even of the formal, purely intellectual imagination; but it is not fictitious in the sense that the sole source of its being is in the knower or subject of knowledge. Instead, it constitutes and is literally the physical relatedness of the physical object of knowledge. It belongs to nature. It has its roots in nature; it is not restricted solely to the mind of man.

The foregoing consideration reminds us of the extent to which the Kantian epistemology is still working surreptitiously in the minds of even the contemporary logical positivists who suppose that they have repudiated Kant. The logical positivists thesis that anything not given with Humean, inductive, purely empirical immediacy is a mere subjective logical construct is a hangover from the epistemology of Kant, a hangover, moreover, which the contemporary mathematical physics of Einstein has unequivocally repudiated.

This is why Albert Einstein is able to make another somewhat startling affirmation. It has been noted that he emphasizes the tentative character of the hypotheses embodied in the deductively formulated, indirectly verified theory of mathematical physics. So great, in fact, is the difference between nature as theoretically designated in its systematic relatedness by deductively formulated theory and nature as given with positivistic, empirical immediacy that Einstein affirms that neither the formal, logical relation of implication nor any probability or other formulation of induction can define the method by which the scientist goes from the empirical data to the basic postulates of scientific theory. The scientist has, by trial and error and the free play of his imagination, to hit upon the basic notions. Moreover, it has been noted that these basic notions receive their verification only through a long chain of deductive proofs of theorems which are correlated with the inductive data.

With time and new empirical information the traditional basic postulates have to be rejected and replaced by new ones. Thus no theory in mathematical physics can be established as true for all time. Nor can the probability of the truth of any given theory be scientifically formulated. For there is neither an empirical frequency nor a theoretical a priori definition of all the possibles with respect to which any particular theory can function as a certain ratio in which the number of all the possibles is the denominator term. This was implicit in Albert Einstein's statement that there is no formulated method taking the scientist from the empirical data to the postulates of his deductively formulated theory.

Nonetheless, Einstein writes as follows: "If, then, it is true that this axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? Nay more, has this right way any existence outside our illusions?" There could hardly be a more unequivocal formulation of the query concerning whether the systematic spatio-temporal relatedness of nature, as specified in the postulates of the theory of mathematical physics, is a mere subjective construct.

Einstein's answer is unequivocal; he answers

without hesitation that there is, in my opinion, a right way, and that we are capable of finding it. Our experience hitherto justifies us in believing that nature is the realisation of the simplest conceivable mathematical ideas. I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other, which furnish the key to the understanding of natural phenomena. Experience may suggest the appropriate mathematical concepts, but they most certainly cannot be deduced from it. Experience remains, of course, the sole criterion of the physical utility of a mathematical construction. But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.

Nor is this mere faith or conjecture on Albert Einstein's part. For we have noted previously that it is an essential point in his general theory of relativity that the form of space-time is not something having its basis in a necessary form of the intellect of the scientist as knower; instead, it is the relatedness of the gravitational potentials of the gravitational field. Thus it belongs to the object of scientific knowledge, as designated by the postulates of Einstein's general theory of relativity. When these postulates become verified through their deductive consequences, then nature as thus conceived—a gravitational field, with such and such potential distribution and such and such a space-time metric—is thereby confirmed as existing.

Albert Einstein supports this conclusion. For in the paragraph immediately succeeding the sentence last quoted he writes,

In order to justify this confidence ["that pure thought can grasp reality, as the ancients dreamed"], I am compelled to make use of a mathematical conception. The physical world is represented as a four-dimensional continuum. If I assume a Riemannian metric in it and ask what are the simplest laws which such a metric system can satisfy, I arrive at the relativist theory of gravitation in empty space. If in that space I assume a vector-field or an anti-symmetrical tensor-field which can be inferred from it, and ask what are the simplest laws which such a field can satisfy, I arrive at Clerk Maxwell's equations for empty space.

These considerations indicate that if we are going to make scientific theory and scientific method our criterion of the epistemology of science, then the form of space-time belongs to physical nature, not to the knower. Thus Albert Einstein's contention that "pure thought can grasp reality, as the ancients dreamed" is justified.

Moreover, the scientific method by means of which this grasp is possible is evident. It is the method of postulation, with indirect verification by way of deduced consequences. There is nothing whatever in scientific method or in the relation of the scientist as knower to the subject matter he is trying to know which prevents the scientist from formulating postulationally the properties and systematic relatedness of the thing in itself, which is the subject matter. In fact, one of the outstanding accomplishments of the general theory of relativity is its scientific demonstration that, notwithstanding all the relativity of reference frames and standpoints, inevitable in making specific measurements, science nonetheless arrives at a systematic conception of this subject matter which remains constant through all the relative standpoints.

Considerations such as these make it evident that science is much more than a weapon for utilitarian technology and prediction. It is also an instrument by means of which men are able to obtain systematic, deductively formulated, empirically verified conceptions of reality. Upon this point also Albert Einstein is explicit. He writes:

It is, of course, universally agreed that science has to establish connections between the facts of experience, of such a kind that we can predict further occurrences from those already experienced. Indeed, according to the opinion of many positivists the completest possible accomplishment of this task is the only end of science. I do not believe, however, that so elementary an ideal could do much to kindle the investigator's passion from which really great achievements have arisen. Behind the tireless efforts of the investigator there lurks a stronger, more mysterious drive: it is existence and reality that one wishes to comprehend.… When we strip [this] statement of its mystical elements we mean that we are seeking for the simplest possible system of thought which will bind together the observed facts.… The special aim which I have constantly kept before me is logical unification in the field of physics.

In this connection it must be kept in mind, as has been previously noted, that this theoretically designated, logical unification is not a mere abstraction from purely empirical, positivistic immediacy, nor can it be logically deduced from this empirical immediacy. The postulated, deductively formulated, theoretically known component in scientific knowledge contributes something of its own. As Albert Einstein writes in his paper on "Clerk Maxwell's Influence on the Evolution of the Idea of Physical Reality," "the axiomatic sub-structure of physics" gives "our conception of the structure of reality.…"

It may seem that Albert Einstein's conception of scientific procedure as "tentative deduction," which, because of the fallacy of affirming the consequent involved in its indirect method of verification, prevents the achievement of scientific theories which are timelessly true, enforces the conception of such theory as a mere subjective construct and invalidates his conclusion that such theory designates the character and "the structure of reality." He is fully aware of the indirect method of verification, as a subsequent quotation from him will demonstrate. He knows that the scientifically verified conceptions of this structure change with the discovery of new empirical evidence and the investigations into the theoretical problems of physics by the theoretical physicists. But this means merely that our verified scientific theories give us more and more adequate conceptions of what the character and structure of reality are. It by no means follows from the tentative character of scientific theories that they are mere subjective constructs.

Furthermore, Albert Einstein points out that it is easy to exaggerate this tentativeness. Thus, in a paper entitled "Principles of Research" delivered before the Physical Society in Berlin, he writes:

The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all with an equal amount to be said for them; and this opinion is no doubt correct, theoretically. But evolution has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself absolutely superior to all the rest. Nobody who has really gone deeply into the matter will deny that in practice the world of phenomena uniquely determines the theoretical system, in spite of the fact that there is no logical bridge between phenomena and their theoretical principles; … Physicists often accuse epistemologists of not paying sufficient attention to this fact.

The point here is that while Poincaré is undoubtedly right theoretically in his contention that no one knows all the possible theories of reality, and hence the uniqueness of any present theory can never be established, nevertheless, for all the possible theories which scientists are able to formulate in the light of mathematical and logical investigations into the possibles, it is actually the case that mathematical physicists, using the deductive method with its indirect mode of empirical verification, are able to show that, among the present possible theories, one is unique in its capacity to bring the widest possible range of empirical data under a single minimum set of assumptions. Moreover, it is not any subjective constructive power of the scientist which is the criterion of this uniqueness, but the correlation of the theory with the empirical data of nature. In short, the criterion of uniqueness is grounded in nature rather than in the subjective, constructive capacity of the knower of nature.

The manner in which the postulationally or axiomatically designated structure of nature is connected with the "wild buzzing confusion" of empirically given data, so that nature is found in itself to be a systematic unity, must now concern us. This connection becomes evident when one examines the method of mathematical physics as a whole. No one has stated the epistemological situation within which this method operates and to which it conforms more concisely than has Albert Einstein. In the first paragraph of his previously mentioned paper "On Clerk Maxwell's Influence" he writes:

The belief in an external world independent of the perceiving subject is the basis of all natural science. Since, however, sense perception only gives information of this external world or of 'physical reality' indirectly, we can only grasp the latter by speculative means. It follows from this that our notions of physical reality can never be final. We must always be ready to change these notions—that is to say, the axiomatic substructure of physics—in order to do justice to perceived facts in the most logically perfect way. Actually a glance at the development of physics shows that it has undergone far-reaching changes in the course of time.

It will be worth our while to take up the sentences in the foregoing quotation one by one, bringing out the full content of their significance. The first sentence reads: "The belief in an external world independent of the perceiving subject is the basis of all natural science." The justification for this belief exhibits itself in Einstein's special theory of relativity.

Albert Einstein has emphasized that the key idea in this theory is the thesis that the simultaneity of spatially separated events is not given empirically. It is the case, however, as Alfred North Whitehead has emphasized, that we do immediately apprehend the simultaneity of spatially separated events. An explosion can be sensed beside one at the same time that one sees a distant flash in the sky. Clearly, these two events are separated spatially and they are sensed as occurring simultaneously. Why, then, does Einstein insist that the simultaneity of spatially separated events is not directly observed? The answer to this is that physicists want and require a simultaneity which is the same for all human beings at rest relative to each other on the same frame of reference.

Immediately sensed simultaneity does not have this characteristic. If the observer is equidistant from two events he may sense them as simultaneous. Then any observer not equidistant from the two events will not sense them as simultaneous.

It is the required public simultaneity which is one of the elements going into the notion of the external world. In fact, the concept of the external world is the scientist's terminology for the distinction between publicly valid elements in scientific knowledge and purely private factors varying from one observer to another even on the same frame of reference. Thus Einstein's contention that belief in an external world is at the basis of science is not a dogmatic selection of one epistemological theory of physical science from many possible theories, but is something grounded in distinctions required by scientific evidence itself.

In this connection it may be noted also that Alfred North Whitehead's philosophy of physics, which affirms an immediately sensed meaning for the simultaneity of spatially separated events, is far nearer to positivism than is Albert Einstein's theory. Furthermore, Alfred North Whitehead's theory that all scientific concepts are derived from "the terminus of sense awareness" by abstraction is much nearer to positivism than is the physics of Einstein, in which the theoretical concepts cannot be abstracted from or deduced from the empirical data.

Consider now Einstein's second sentence in the foregoing quotation: "Since, however, sense perception only gives information of this external world or of 'physical reality' indirectly, we can only grasp the latter by speculative means." The basis for this statement scientifically is in the method of hypothesis which deductively formulated scientific theory uses. But Albert Einstein realizes also that it follows epistemologically from Bishop Berkeley's analysis of the empirically given. Bishop Berkeley noted that all that is empirically given are sense qualities, that these are relative, private things, varying from person to person and hence relative to the mind that is apprehending them. Thus the physicist's concept of a physical object as something three-dimensional, possessing a back side which we do not sense, with right-angle corners constant through the varying sensed angles which we sense empirically is not guaranteed by positivistic, empirical observation. Even the notion of a common-sense object involves an imaginative leap by the method of hypothesis beyond pure fact. Not merely scientific objects such as electrons and electromagnetic fields, but also common-sense objects entail indirectly verified postulation.

Once this is noted, the shift of the logical positivists from the Berkeleyan sensationalism of Carnap's Logischer Aufbau to "physicalism" is seen to be a departure from positivism. The reason for this shift confirms the present analysis. The logical positivists wanted a scientific verification which gave objective, publicly valid meanings, not Berkeleyan solipsistic, private subjective meanings merely. But such objectivity is not given empirically; it is only given theoretically by postulation indirectly verified. This is what Einstein means when he says that "since sense perception only gives information of the external world or of 'physical reality' indirectly, we can only grasp the latter by speculative means."

His next sentence reads: "It follows from this that our notions of physical reality can never be final." The basis for this conclusion is that formal logic in scientific method runs not from the empirical data to the postulates of the deductively formulated theory but in the converse direction, from the postulates back through the theorems to the data. This means that, in scientific verification, the logic of verification is always committing the fallacy of affirming the consequent of the hypothetical syllogism. This does not entail that a theory thus verified is false. It means merely that it cannot be shown to be necessarily true. The fact that the theory is thus indirectly confirmed justifies its retention. The fact, however, that it is not related to empirical data necessarily forces one to hold it tentatively. But this is an asset rather than a liability; for otherwise we would be at a loss to explain how scientific, or even humanistic religious, theories can be empirically verified and yet shown later, with the advent of further empirical information and further theoretical investigation, to be inadequate and to require replacement by a different theory grounded in different postulates. Hence Albert Einstein's final two statements: "We must always be ready to change these notions—that is to say, the axiomatic sub-structure of physics—in order to do justice to perceived facts in the most logically perfect way. Actually a glance at the development of physics shows that it has undergone far-reaching changes in the course of time."

One additional element, often overlooked in scientific method, which Albert Einstein clearly recognizes, remains to be indicated in order to complete his conception of science. It has been noted that the basic concepts of deductively formulated scientific theory as conceived by him are neither abstracted from nor deduced from empirically given data. Consequently, they do not "reduce" to sentences about sense data, nor can they be derived from such sentences. In short, they are concepts of a kind fundamentally different from the nominalistic particulars which denote data given empirically.

This presents a problem so far as scientific verification is concerned. For, if the primitive concepts, in terms of which the deductively formulated scientific theory is constructed, gain their meanings by postulation, in terms of the formal properties of relations and other such logical constants, then the theorems deduced from the postulates of such theory must be concepts of the same character. An examination of scientific theory such as Maxwell's electromagnetic theory shows also that the concepts in the theorems refer no more to sense data than do the concepts in the postulates. They refer, instead, to numbers for wave lengths, etc. These are not sensuously qualitative things. But if this is the case, how, then, can concepts with such meanings, designating such empirically unobservable scientific structures and entities, be verified? For verification requires the relating of the theoretically designated to the positivistically and empirically immediate. This relation which must exist in scientific method remains, therefore, to be specified.

The foregoing considerations of this paper indicate that this relation, joining the theoretically designated factor in nature to the empirically given component, cannot be that of identity. What then, is the relation? In his paper "Considerations Concerning the Fundaments of Theoretical Physics" (Science, May 24, 1940), Albert Einstein answers this question as follows: "Science is the attempt to make the chaotic diversity of our sense experience correspond to a logically uniform system of thought. In this system single experiences must be correlated with the theoretic structure in such a way that the resulting coordination is unique and convincing." In other words, the relation between the theoretic component and the empirical component in scientific knowledge is the relation of correlation. Analysis of scientific method shows that this relation is a two-termed relation.

The recognition of the presence of this relation in scientific method is the key to the understanding of Albert Einstein's conception of scientific method and scientific epistemology. Because the empirical component is joined to the theoretic component by correlation, one cannot get the latter from the former by either extensive abstraction or logical implication. For, in the two-termed relation of epistemic correlation, one term does not logically imply the other, nor is the theoretic term a mere abstraction from the empirical term. And because the theoretic term cannot be derived from the empirical term, theoretic physics contributes something of its own to the scientific conception of nature and reality.

This means that the positivistic theory that all theoretical meanings derive from empirical meanings is invalid. Furthermore, the thesis that the theoretically designated knowledge gives us knowledge of the subject matter of science and of reality, rather than merely knowledge of a subjective construct projected by a neo-Kantian kind of knower, confirms the thesis that the thing in itself can be scientifically known and handled by scientific method. Thus ontology is again restored, as well as epistemology, to a genuine scientific and philosophical status.

Hence, although the positivists are wrong in their purely empirical theory of meaning in empirical science, they are right in their contention that philosophically valid propositions are scientifically verifiable propositions. The important thing is not where the meanings of scientific concepts come from, but that they be verified through their deductive consequences and attendant epistemic correlations with empirically given data, before anyone claims that they have philosophical validity as a correct designation of the nature of things.

The foregoing analysis of Einstein's conceptions of science shows that scientific concepts have two sources for their meanings: The one source is empirical. It gives concepts which are particulars, nominalistic in character. The other source is formal, mathematical and theoretical. It gives concepts which are universals, since they derive their meaning by postulation from postulates which are universal propositions.

It should be noted also that for Albert Einstein scientific method entails the validity of the principle of causality, not as conceived by Hume in terms of the hope that present sensed associations of sense data will repeat themselves, but in the sense of the mathematical physicist—the sense, namely, that with the empirical determination of the present state of a system, as defined by theoretical physics, the future state is logically implied. Albert Einstein tells us that he refused to accept certain ideas of his general theory of relativity for over a period of two years, because he thought they were incompatible with this theory of causality. When this compatibility did become evident to him, he went on with the investigation and publication of the general theory of relativity. Its type of causality is a theoretically given, indirectly verified causality, not a Humean empirical one. But this point is a special, more technical case of the general thesis that scientific knowledge involves a correlation of an empirically given component with a postulationally prescribed, systematic, theoretically designated component.