SOURCE: "Discussion: Is Einstein a Positivist?" in Philosophy of Science, Vol. 30, No. 2, April, 1963, pp. 173-88.

[In the following essay, which originally appeared as part of a doctoral dissertation presented at Yale University in 1959, Neidorf considers whether or not Einstein's theories fit a positivistic epistemology.]

There are in fact two cases to be decided, one textual and one technical. The textual question: Does Einstein, in his thinking and writing about the philosophy of science, advocate a positivistic (or empiricist) position? Most of the literature on this subject, both by Einstein and by commentators, turns on the special theory of relativity; accordingly, the discussion which follows will be oriented mostly towards that theory. The technical question: Does Einstein's work, particularly his presentation of the special theory of relativity with its associated critique of classical physics, commit one to a positivistic philosophy of science? I begin with the latter problem.

1. THE TECHNICAL QUESTION: THE CASE FOR AN AFFIRMATIVE ANSWER.

The nerve of Einstein's special theory of relativity is contained in his redefinition of simultaneity for spatially separate events. To see the sense in which Einstein appears to be applying or recommending a positivistic epistemology, we need first to examine the reasons why a redefinition seems to be required at all. For this purpose, I shall introduce below some general (and familiar) considerations with respect to simultaneity and the measurement of time-intervals. The treatment is written initially from the Newtonian or classical standpoint, which (sadly) has almost come to be the standpoint of common sense. In so far as that standpoint is subjected to criticism, the treatment of course leans heavily on Einstein's theory, and on considerations implicitly or explicitly contained in it. The theory itself will be discussed at a later stage.

Suppose a man judges that two events, occurring at different locations, are simultaneous. He makes this judgment because (say) the sounds characteristic of each event arrive at his ear at certain given times. Taking into account the velocity of sound and the distances between himself and the event-loci, he then calculates that they went off at the same time. On the peculiarly convenient assumption that he stands midway between the event-loci, he will hear both sounds simultaneously if and only if they are in fact proceeding from simultaneous events. It is convenient to elevate this last observation into a general principle: Spatially separate events are known to be simultaneous if observers midway between them receive signals proceeding from them simultaneously. In the present case we are assuming that the signals in question are sound waves.

Now we know that this method of judging simultaneity or the lack of it (i.e. time-interval) is not in general dependable. We can list two obvious circumstances which will upset this technique. (i) If a wind is blowing, the sound waves coming from one event to the observer will be hastened, while those coming from the other will be retarded. This will delude him into thinking that the upwind event was earlier than the downwind one, even though they were "really" simultaneous. What this means is that another set of observations are relevant to the determination of simultaneity: namely, those observations by which we may determine that a wind is (or is not) blowing. (ii) Suppose the observer is midway between the event-loci at the moment the events go off, but moving from one toward the other. He will then advance to meet one wave front and retreat from the other. In the absence of any awareness of the fact that he is moving, he would then judge that one event was prior to the other, even though they were both "really" simultaneous. What this means, again, is that another set of observations are relevant to the determination of simultaneity: namely, those by which we determine that the observer is moving (or not moving) with respect to the event-loci. It is of course possible for the observer to establish his location relative to the event-loci with standard rods in advance of the simultaneity-determination. But in that case it will still have to be asked how he knows that the distance-relations have not been altered in the interim, and the means by which he knows this latter fact (or its negative) will constitute another set of data relevant to the determination of the time-interval between the events themselves.

In point of fact, the complications introduced by winds and motions are usually not a problem. We can correct for relative motions, for example, by "looking around" to be sure that no motions are in fact taking place. That is, we employ electromagnetic phenomena. Supposing, then, that we decide to make our simultaneity judgments more accurate at the outset by using light-signals (or other electromagnetic devices) instead of sound. Then, analogously to the situation with sound if I am midway between two event-loci at the time that two simultaneous flashes are fired off, I will see the corresponding flashes simultaneously. Pursuing the analogy, we see that two possible qualifications can upset the validity of this technique. Either (i) the "ether" through which the light travels may be blowing past, or (ii) I may be in relative motion with respect to the event-loci, so that additional data are required to establish the fact (if it is a fact) that I am still midway between them when I perceive the flashes. How can we determine whether there is an ether wind blowing, or (which comes to the same thing in the end) whether there is a motion of myself as observer with respect to the event-loci? And if either of these circumstances do obtain, how can we measure them so as to compensate for their effects?

1. To find out whether an "ether wind" is blowing we shall want to measure the apparent velocity of light as it goes past. For this purpose we can set up an auxiliary experiment such that a light-flash will set out from a point which is a known distance away, at a known time. We then note the time at which the signal arrives at our point of observation. Knowing the distance and the time-interval, it requires no sophistication to calculate the velocity of the light-signal. But the logical intolerability of this situation is evident—we wanted to employ the velocity of light to measure time-intervals between distant events, but now, in our auxiliary experiment, we are employing time-intervals between distant events to measure the velocity of light.
2. Again, suppose we want to measure the motion between us and the event-loci. For simplicity, consider only the observer and one event-locus, and assume that the motion (if any) is uniform. The general method is to arrange an auxiliary experiment in which, at known times, two light-flashes will leave the event-locus. We then note the times at which the flashes arrive at the observation-locus. This gives us a pair of time-intervals, and if there is a relative motion, one of the intervals will be larger than the other, and the velocity of relative motion will be calculable therefrom. But here again, we are guilty of a logical circle—we are using time-intervals to measure a motion in the auxiliary experiment, so that in the original circumstances we could use the measured motion to help in the estimation of time-intervals. If we are seeking a fundamentally valid method of estimating time-intervals between spatially-separated events, these techniques are useless.

This circularity of measurement can be broken only if there is some further meaning for time-interval or simultaneity (as applied to distant events), over and above the meaning which can be determined through the use of light-signals. That is, we seek a method of assigning time-coordinates to events which will be independent of light-velocity, just as the use of light gave us a method of assigning time-coordinates to events independent of sound-velocity. But there is no such method. We are able to use light as a corrective for sound because, for terrestrial purposes, light travels at an infinite velocity and sound at a very finite one. But for astronomical purposes, and in general for theoretical purposes, light too has a genuinely finite velocity. Lacking any phenomena of genuinely infinite velocity, we lack any physical means for the assignment of time-coordinates as called for in the Newtonian conception of space and time.

These results can be summarized in more abstract terms. Everything turns on the answer to this question: "What time is it over there when it is a certain time over here?" Pre-relativity physics assumes that the answer is always, "The same time." Attention then turns to the problem of assigning time-coordinates to happenings over there. It is observed that a time-lag always exists between the happening (over there) and the reception (over here) of a report of it. It is further observed that this time-lag is a function of certain physical processes (velocities) which are themselves measured in terms of the time-lag. For this reason, we have no method for measuring the time-lag independent of physical processes, and hence no independent method for assigning time-coordinates to happenings perceived over there.

The conclusion to be drawn at this stage of analysis is that there is no meaning for "simultaneity," and hence no meaning for "time-interval" and "time," independent of physical processes; the reason is that we require a physically significant procedure for the assignment of time-coordinates to spatially separate events.

2. THE TEXTUAL QUESTION: THE CASE FOR AN AFFIRMATIVE ANSWER.

It certainly seems as if the above considerations, which are central in the special theory of relativity, entail an empirical or positivistic turn, especially if the demand for "physically significant" methods be interpreted as a demand for empirical significance in terms of sensory experience. This impression can be reinforced by selections from Einstein's non-technical writings. The following, for example, is famous in this regard:

We encounter [a] difficulty with all physical statements in which the conception "simultaneity" plays a part. The concept does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case. We thus require a definition of simultaneity such that this definition supplies us with the method by means of which … he can decide by experiment whether or not both the [events in question] occurred simultaneously. As long as this requirement is not satisfied, I allow myself to be deceived as a physicist (and of course the same applies if I am not a physicist) when I imagine that I am able to attach a meaning to the statement of simultaneity.

[Einstein, The Principle of Relativity]

Many of positivist persuasions have seized upon this aspect of relativity. Their interpretations of it, phrased differently, amount to the assertion that Einstein's work demonstrates the correctness of their own epistemological views, and that indeed their views are the only correct interpretation of Einstein's work. For example, Reichenbach:

The physicist who wanted to understand the Michelson experiment had to commit himself to a philosophy for which the meaning of a statement is reducible to its verifiability, that is, he had to adopt the verifiability theory of meaning if he wanted to escape a maze of ambiguous questions and gratuitous assumptions. It is this positivist, or let me rather say, empiricist commitment which determines the philosophical position of Einstein.

["The Philosophical Significance of the Theory of Relativity"]

Again, Bridgman:

Let us examine what Einstein did in his special theory. In the first place, he recognized that the meaning of a term is to be sought in the operations employed in making application of the term.

["Einstein's Theories and the Operational Point of View"]

The kernel common to both of these quotations is the idea of reducing, in principle, the theoretical entities and concepts of mathematical physics to some aspect of the sense-experiences with which they are generally associated. Reichenbach's statement suggests that the entities and laws of physics are reducible to certain complex predictions concerning the frequency with which we shall have immediate experiences of a certain sort; and the laws are valid, and the entities real, if the predictions are borne out. Similarly Bridgman's statement suggests that the entire meaning of a concept is contained in the immediately sensed laboratory manipulations and operations involved whenever the concept is relevant to the physical processes under study. This general reductionist tendency can also be ascribed to Einstein by careful choice of writings. As late as 1945 he wrote:

We are accustomed to regard as real those sense perceptions which are common to different individuals, and which therefore are, in a measure, impersonal. The natural sciences, and in particular, the most fundamental of them, physics, deal with such sense perceptions.… The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy.

[The Meaning of Relativity]

We can carry the proposed identification of Einstein with positivism two steps further. First, empiricist and positivist strains of thought arose in modern times partly as protest movements, directed against the abstractive excesses of "metaphysicians and theologians." In the same context with the last citation, Einstein voices the conviction that

… the philosophers have had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori.

Secondly, there are even hints that Einstein may belong to that school of extreme positivists (early Hume and Mach) who hold always in the forefront the "fact" that all scientific discourse is concerned with the immediate data of experience; on this view scientific and philosophic soundness is to be obtained by de-emphasizing and cutting away, whenever possible, the fictitious structure of concepts and principles with which we have unwittingly overlaid bare experience. Discussing his discovery of the special theory of relativity, Einstein wrote in later years that he was indebted to Hume and Mach for showing him the type of "critical reasoning" which he required [Autobiographical Notes]. And in his original presentation of the general theory of relativity we find the following enunciation of principle:

No answer [to a physical question] can be admitted as epistemologically satisfactory unless the reason given is an observable fact of experience. The law of causality has not the significance of a statement as to the world of experience, except when observable facts ultimately appear as causes and effects.

["The Foundation of the General Theory of Relativity"]

3. THE TEXTUAL QUESTION: THE CASE FOR A NEGATIVE ANSWER.

We have now seen the evidence and the fundamental argument in favor of the view that Einstein is a positivist, or that Einstein's special theory of relativity somehow entails positivism. Preliminary doubts can be cast upon this thesis by a wider survey of Einstein's writings. There are available, first, some comments directed specifically against the empiricist trend in philosophy of science. In 1922, he had this to say of Mach:

Mach's system studies the existing relations between data of experience; for Mach, science is the totality of these relations. That point of view is wrong, and, in fact, what Mach has done is to make a catalogue, not a system … His view of science, that it deals with immediate data, led him to reject the existence of atoms.

[Nature, 18 August 1923]

Mach's scepticism in regard to atoms apparently made a great impression on Einstein, for over twenty-five years later we find him writing as follows:

The antipathy of [Oswald and Mach] towards atomic theory can indubitably be traced back to their positivistic philosophical position. This is an interesting example of the fact that even scholars of audacious spirit and fine instinct can be obstructed in the interpretation of facts by philosophical prejudices. The prejudice—which has by no means died out in the meantime—consists in the faith that facts by themselves can and should yield scientific knowledge without free conceptual construction.

[Autobiographical Notes]

This is an astounding statement. We have become accustomed to hearing this kind of accusation from members of the Vienna Circle and their followers. Those whose philosophical tastes lie in other directions may take comfort from the fact that Einstein turns their own shaft against them.

Against Hume, we find the following remarks:

As soon as one is at home in Hume's critique one is easily led to believe that all those concepts and propositions which cannot be deduced from the sensory raw-material are, on account of their "metaphysical" character, to be removed from thinking. For all thought acquires material content only through its relationship with that sensory material. This latter proposition I take to be entirely true; but I hold the prescription for thinking which is grounded on this to be false. For this claim—if only carried through consistently—absolutely excludes thinking of any kind as "metaphysical."

["Remarks on Bertrand Russell's Theory of Knowledge"]

These citations record Einstein's objections to any movement which tends to define away conceptual structures. The evident alternative to such views is to maintain that "thinking", as distinct from picturing and perceiving generally, is not only irreducibly relevant to the scientific enterprise, but autonomous in the sense that concepts entering constitutively into physics are neither derivable from nor exclusively determined by sensory experience. And this is just what we find Einstein claiming, in the same context with the previous citation:

In thinking we use, with a certain "right," concepts to which there is no access from the materials of sensory experience, if the situation is viewed from the logical point of view.… The concepts which arise in our thought and in our linguistic expressions are all—when viewed logically—the free creations of thought which can not be inductively gained from sense-experiences. This is not so easily noticed only because we have the habit of combining certain concepts and conceptual relations (propositions so definitely with certain sense-experiences that we do not become conscious of the gulf—logically unbridgeable—which separates the world of sensory experience from the world of concepts and propositions.)

Three times Einstein uses the qualification, "from a logical point of view." This is to warn against mistaking constant association (of "certain concepts" with "certain sense-experiences") for logical identity. Einstein is not trying to cut concepts loose from experience, nor does he wish to deny that experience may—often does—seem so closely interwoven with some concept or conceptual relation as to suggest a continuity or identity between them. All that lie wishes to assert—and this is a great deal—is that such intimacy is always psychological or pragmatic, never logical. Concepts, or at least the key concepts of mathematical physics, are always distinct from the sense-data with which they are customarily associated.

At this stage we have the kernel of a theory of the epistemology of science; fortunately, it has been spelled out in somewhat greater detail by Einstein himself in the 1936 article, "Physics and Reality." To anticipate, it will be seen that Einstein firmly recommends a dualistic epistemology, as over and against the monisms implicit in positivistic attempts to reduce theoretical structures to functions of sensory experience.

The exposition in "Physics and Reality" is designed to account, step by step, for the concept of the "real external world" which we develop first in common sense and later in mathematical physics. The first step is as follows:

I believe that the first step in the setting of a "real external world" is the formation of the concept of bodily objects and of bodily objects of various kinds. Out of the multitude of our sense experiences we take, mentally and arbitrarily, certain repeatedly occurring complexes of sense impression (partly in conjunction with sense impressions which are interpreted as signs for sense experiences of others), and we attribute to them a meaning—the meaning of the bodily object. Considered logically this concept is not identical with the totality of sense impressions referred to; but it is an arbitrary creation of the human (or animal) mind. On the other hand, the concept owes its meaning and its justification exclusively to the totality of the sense impressions which we associate with it.

The main idea is quite clear: concepts are built up out of sense experience but in an arbitrary or free way. The last sentence, to the effect that the concept "owes its meaning and justification exclusively [ausschliesslich] to the totality of the sense impressions …" looks perhaps like a reductionist statement, yet runs directly counter to the assertion that the concept is "not identical" with its associated sensory materials. Apparently, Einstein is aware that the early part of the paragraph, with its emphasis on (logical) arbitrariness and freedom, might suggest that science is engaged in telling fairy stories; the point is that verification in the field of sensory experience is always required, and is to be accomplished in ways to emerge shortly. We are, after all, only in the first step.

The second step is to be found in the fact that, in our thinking (which determines our expectation), we attribute to this concept of the bodily object a significance, which is to a high degree independent of the sense impression which originally gives rise to it. This is what we mean when we attribute to the bodily object "a real existence." The justification of such a setting rests exclusively on the fact that, by means of such concepts and mental relations between them, we are able to orient ourselves in the labyrinth of sense impressions. These concepts and relations, although free statements of our thoughts, appear to us as stronger and more unalterable than the individual sense experience itself, the character of which as anything other than the result of an illusion or hallucination is never completely guaranteed. On the other hand, these concepts and relations, and indeed the setting of real objects and, generally speaking, the existence of the "real world," have justification only in so far as they are connected with sense impressions between which they form a mental connection.

In this paragraph, the emphasis on mental aspects is strengthened, although we are warned again that a "connection" with experience is still required. The passage from the "first step" to the "second step" is roughly this: In the first stage a collection of sensory materials is selected out and made to carry a significance. The significance lies, presumably, in the very fact that this collection of sense qualities enjoys a regularity of association such that a unity over and above their bare togetherness in sensation is suggested. This unity comes from us, however, not from the manifold of sensation. In the second stage, a real existence is attributed to this unified collection, such that they become the characters (in some sense) of an object supposed to have an independent and continuing existence. It is in this respect that the concept of the object begins to be "to a high degree independent of the sense impression which originally gives rise to it." The similarity of this analysis to Kantian developments is evident, and I hardly think it would be denied that the basic insight is Kant's. The advantage of Einstein's formulation here is that it suggests a mechanism of prediction and verification. "It is our thinking," he avers, "which determines our expectation." When our expectations are disappointed, we have a case where our thinking has gone wrong; and the more our expectations are fulfilled, the more confident we become that our thinking is on the right lines.

Einstein next turns briefly to the fact that the sensory manifold is open to the manipulations of mind so as to produce an "order" in it. This, he thinks, is an ultimate mystery: the comprehensibility of experience is itself incomprehensible. He then continues with the main theme:

In my opinion, nothing can be said concerning the manner in which the concepts are to be made and connected, and how we are to coordinate them to the experiences. In guiding us in the creation of such an order of sense experiences, success in the result is alone the determining factor. All that is necessary is the statement of a set of rules, without which knowledge in the desired sense would be impossible.

This passage offers two significant aspects. In the first place, it reaffirms, unmistakably, the freedom of mind to construct at will, provided that the resulting constructions are adequate to the ultimate task of explicating sense experience, i.e., provided they furnish a genuinely public world of genuine predictive power. Second, a distinction is opened out between the concepts themselves and their relations to the sensory manifold. This distinction must be kept separate from the primary distinction between concepts and sensations, as will be seen in the sequel.

What is meant by the necessity of "the statement of a set of rules?" Presumably, such rules are required primarily for the relations of the concepts as among themselves. What then shall we say of the connections between the concepts and sensation?

The connection of the elementary concepts of everyday thinking with complexes of sense experiences can only be comprehended intuitively and it is unadaptable to scientifically logical fixation. The totality of these connections—none of which is expressible in conceptual terms—is the only thing which differentiates the great building which is science from a logical but empty scheme of concepts. By means of these connections, the purely conceptual theorems of science become statements about complexes of sense experiences.

Here the distinction between concepts on the one hand and their connection to experience on the other is deepened. The former are the very stuff of science, and the latter (the connections) can only be grasped intuitively; yet it is only through the latter that science is rooted in experience, i.e., it is through them that empirical verification is possible at all.

Here, Einstein's vocabulary and the evident drift of his thought are reminiscent of later epistemological developments due to Northrop and Margenau. In their view, there are two dimensions in any deductive science. One dimension consists of entities postulated for existence, with postulated properties expressible in mathematically precise ways; it may also be true that the properties are expressible only in mathematical ways. Further properties of, and relations among, these entities are then deducible. The other dimension consists of relations between some entities, or states of those entities, and the realm of immediate sensory experience. These relations are called "rules of correspondence" (Margenau) or "epistemic correlations" (Northrop). On this view, the postulated theory gives science its objectivity, while the epistemic correlations provide its predictive power. It seems to be no small advantage of this approach that the same view, or something very much like it, is recommended by Einstein. The principal point is the sharp distinction, already noted, between theoretical structures themselves and the rules which relate them to associated complexes of sensory experience. I do not wish, here, to aver that this theory is necessarily correct, or that it solves all problems; but it does seem to me to offer a logical minimum which any non-positivist view of the nature of scientific knowing must embody. Accordingly, I shall avail myself in what follows of the terminology of the (Einstein-) Northrop-Margenau epistemology. In particular, the phrase "epistemic correlation," as referring to relations between the two epistemological realms, will be useful. It should be noted that this view is avowedly a "bifurcation" theory, in the sense that it holds that there are two "natures" available for analysis and discrimination: the "sensed nature" of immediate experience, and the "postulated nature" of (verified) theoretical construction.

To return to Einstein, there are several points from the essay "Physics and Reality" which need further discussion, and which perhaps need to be taken with some caution.

1. Although the nominal subject of his discussion is a technical science, Einstein is nevertheless seen to be speaking primarily (so far) about the "elementary concepts of everyday thinking." Apparently, he is here thinking of common-sense or "perceptual" objects: chairs, stones, people, etc. In maintaining that these are designated by concepts, he is in effect maintaining that these objects as conceived are distinct from what is given to sense-experience. This notion harks back at least to Berkeley, although he drew a very different moral from the fact. That it is a fact is, I should think, beyond doubt. One is reminded in this connection of Russell's "neutral monism"; desiring to draw a connection between immediate sense-experience and theoretical physics, Russell nevertheless found himself entangled in Herculean struggles, attempting to cope with the far simpler fact that we think of a penny as a three-dimensional disc, and perceive it as a flat ellipse. The point is that Einstein, by distinguishing sharply between the perceived world and the conceived world, is not placing science in some mysterious realm whose inner workings are open only to a trained priesthood; he is thinking of science as a systematic refinement of certain methods which pervade common sense as well.
2. The character of science as a refinement of common sense methods emerges in subsequent passages of the essay in question. Einstein speaks of a hierarchy of concepts and relations, such that the lower levels can be logically derived from the higher levels, while the higher levels are increasingly spare, increasingly abstract, and increasingly powerful in their deductive scope. On this view, the function of science is the elaboration of increasingly abstract postulate-sets from which the rest of the structure can be deduced. The whole structure is then anchored to experience (if it is; and it has to be if it is to be science and not pure mathematics) through the fact that the concepts of the lower layer are epistemic correlates of certain sense experiences.

   This is a sweeping vision. It shows, for example, how it is that gross perceptual objects sitting on a laboratory bench can mediate between abstractly-defined entities and certain sensory occurrences; they can do so simply because they are designated by concepts of the lower layer. But this vision needs to be qualified, since it is perhaps a little too sweeping, and too simple. It suggests, first, that the concepts of the lower layer are frozen, and this ignores the sweeping changes in theoretical understanding which can—and sometimes do—modify the "elementary concepts of everyday thinking." It is extremely doubtful that a meteorologist thinks of, say, a cloud in the same way as a resident of fifth-century Athens, although there is a good chance that the latter had a better education and a more open mind. Secondly, Einstein's spare statement encourages one to think that only concepts of a certain layer (the lowest) can be epistemic correlates. This may be usually true, but it is evidently not necessarily the case. Consider, for example, the correlation of a certain shade of blue with a certain electromagnetic frequency; the postulated phenomenon which is the epistemic correlate of the sensed blue is not designated by an "elementary concept" in Einstein's sense. Other examples are easily found, and there is no logical reason why epistemic correlations cannot be chosen arbitrarily, in violence to the instincts of common sense, where the demands of theory seem to require it.

3. Lastly, Einstein has said (see above) that the connection between concepts and sensory experience is "unadaptable to scientifically logical fixation." At first glance this is a puzzler: he appears to be saying that epistemic correlations are themselves somehow outside the range of science, whereas in one sense it is precisely the job of science to explicate that which lies "behind" or within our experience, and to specify the relations between them. There are three possible interpretations of this somewhat cryptic remark, and all are illuminating.

First, he could be using the phrase "scientifically logical fixation" to refer to the deductive relations which are exhibited in a developed science like physics. Deductions, however, are possible only with concepts, not with sensations. In order to define, as it does, a public world, the deductive conceptual structures of a science cannot contain private episodes of sensory experiences as ingredients. This is so merely because the episodes are private. You cannot have my sensations. To be sure, you can have sensations very much like mine, and you can know that the sensations you are having which are very much like mine are very much like mine, but you cannot have mine. What science requires is something shareable—and it is the concept which fulfills this need (although there may be deeper phenomenological mysteries surrounding this fact). Consequently, no concrete episode of sensory experience can legitimately appear inside the deductive structure of a science like physics. For Einstein, not only is physics not about sensations, but in its theoretical part it is logically indifferent to the existence of sensory experience at all. It follows that epistemic correlations between the theoretical part of science and immediate experience are likewise not candidates for direct inclusion in the main deductive structure, and can only be "comprehended intuitively."

As a second possibility, attention can be fixed on the term "unadaptable." The meaning may be that the detailed structure of concepts and epistemic correlations which obtains at some given time is theoretically open to complete logical anatomization, but presents in practice a task so prolix as to suggest that the correlations at least are "unadaptable" to such "logical fixation." If this is not Einstein's meaning, the point still seems good. A complete specification of the correlations and concepts involved in a deductive science would amount to a complete axiomatization of that science: an axiomatization, moreover, which would require both a specification of fundamental entities and relations and a specification of the epistemic correlations which (hopefully) link selected parts of the theoretical structure with immediate experience in precise ways.

As a third possibility, and again a point worth noting, Einstein may be thinking here of the "haziness" which seems to infect much if not all of our perceptual experience in varying degrees. A relation, one of whose relata is not a precisely delimitable and distinct entity, will be itself infected with the contagion of vagueness to some degree, and consequently resistive to "scientifically logical fixation." In any case, these three considerations taken together should suffice to warn us against an easy identification of all the epistemic correlations vital to the empirical grounding of any particular science at any particular time. In part, this is due to the fact that the worker in the field always tends to ignore or take for granted the epistemological and logical foundations of his science, sometimes to his peril but often to his advantage. It may then require considerable interpretation and reinterpretation before an analytically clear structure begins to emerge. Even worse, there may be contending interpretations. What remains outside contention (on this view) is the picture of an ideally logically pure science exhibiting the two dimensions of theoretical construct plus epistemic correlation, this picture functioning as a guide for criticism and analysis, and as a source of possibilities for new researches.

4. THE TECHNICAL QUESTION: THE CASE FOR A NEGATIVE ANSWER.

In a well-known remark, Einstein has warned that "if you want to find out anything from the theoretical physicists about the methods they use,… stick closely to one principle: don't listen to their words, fix your attention on their deeds" ["On the Method of Theoretical Physics"]. Accordingly, we shall now take a brief glance at the special theory of relativity in Einstein's own presentations of it. Two treatments will be examined, one technical and one "popular." It will be found that the first best exhibits the necessity for speculative freedom, and the other exhibits the necessity for holding to the distinction between concepts and epistemic correlations.

In his first relativity paper published at the beginning of the century, Einstein begins his considerations with a review of the difficulties in classical physical theory which he intended to overcome. These difficulties were of two sorts. In the first place, there were "asymmetries" of a disturbing character in Maxwell's theory of electromagnetism. If a conductor is in motion relatively to a magnet in its neighborhood, a potential difference will in general appear between the ends of the conductor. The amount of potential difference depends only on the relative motion between conductor and magnet. In the event that the conductor is stationary (in the Newtonian sense of absolute rest) while the magnet moves, Maxwell's equations specify the existence of an electrical field of force in the vicinity of the magnet; in the converse case, with magnet stationary and conductor moving, no such field occurs. This creates a muddle, for Maxwell's equations call for the existence of an entity (electrical field of force) in some circumstances and not in others, while no experimentally specifiable means of distinguishing the two sets of circumstances is at hand. (The voltage which appears depends only on the relative motion.) ["On the Electrodynamics of Moving Bodies"]

Closely related to this difficulty is another, now well-known. Electromagnetic signals (including light) are propagated with a finite and measurable velocity. When they cross an "empty space," they "move" with a fixed velocity relative to that space (or to the "ether" as its material embodiment). The earth and all things on it also so move. By measuring the relative velocity of the earth and an electromagnetic signal, the possibility is opened to a detection of the earth's motion in absolute space. The Michelson-Morley experiments were a definitive failure in this direction.

It should be noted, however, that there are troubles with the classical structure quite aside from the ether-drift experiments. The difficulty over the asymmetry of Maxwell's equations is peculiarly illuminating because of its almost purely speculative character: it expresses an intellectual unhappiness over something which has been detected in the theoretical structure of physics itself. The Michelson-Morley experiments occasioned the discovery—by Einstein—of other difficulties in explicating the physical significance of such fundamental conceptions as space and time. In no sense is it to be thought that relativity theory is invented to explain the ether-drift experiments, nor would it be possible to return to pre-relativity physics if those experiments were repeated with a positive result.

To return to Einstein's presentation. The conclusion to be drawn from both difficulties is that "the phenomena of electrodynamics … possess no properties corresponding to the idea of absolute rest." Of course, the same is true for the Galilean-Newtonian laws of mechanics, the equations for which are equally valid for all unaccelerated frames of reference, a fact sometimes referred to as the "classical principle of relativity." Alternatively, it is said that the equations of classical mechanics are invariant in form with respect to transformations leading from one unaccelerated frame of reference to another. In contrast with mechanics, classical electrodynamics (and optics) does not enjoy such invariance; to put the same point differently, the equations are not the same when referred to a system of reference at absolute rest as when referred to a system in uniform motion (as we have just seen). Einstein suggested that the laws of electrodynamics and optics should be equally "valid for all frames of reference for which the equations of mechanics hold good." And of course this desideratum can only be effected by a considerable modification of the fundamental conceptions of space and time. Again, attention is called to the highly theoretical level in which these considerations occur. It is clear that Einstein is not merely engaged in the positivistic task of reconstructing a conventional scheme of concepts (or functions) in order to bring it into harmony with a hitherto unknown and jarring datum.

The first constructive step is the elevation of the above desideratum into a postulate, known later as the "restricted principle of relativity":

1. All frames of reference, whether "at rest" or "in motion" in the classical sense, are equally valid for the description of physical processes, provided only that the "motion" (if any) is uniform.

   To this is joined another postulate suggested by the results of the Michelson-Morley experiment:

2. The velocity of light in vacuo is constant, regardless of the state of motion of the emitting body.

Here we meet the fundamental difficulty, since these two principles appear to be contradictory, a fact which is easily seen intuitively. The apparent contradiction is removed in ways too familiar to warrant repeating. The point is that the first of these postulates (and possibly the other as well) is quite independent of direct experience; it tells us that our concepts must have a certain invariant structure, regardless of the experiences which confirm or disconfirm them.

The removal of the apparent contradiction between the two postulates above is of course accomplished through a redefinition of the meaning of simultaneity, and hence of space and time. Einstein begins with some considerations similar to those of section 1 of this paper, emphasizing the importance of a clear experimental or operational significance for physical ideas. He turns specifically to the problem of assigning time-coordinates to distant events. With each point in the space of some unaccelerated frame of reference a clock is associated, and events at or near the clock receive their time-coordinates through the empirical observation of spatially contiguous simultaneities. Using two clocks "similar in all respects," we can establish local timescales associated with, say, two points A and B. "But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B." We must now inquire as to the "further assumption."

From this point on, Einstein begins to build anew. As he proceeds in the construction of theory, appeal to sensation will fall further and further into the background. The leading idea in what follows is that the needed principles can and will be "established by definition."

Suppose A is a stationary point in some unaccelerated frame of reference. We wish to assign time-coordinates to events at B in such a way that these coordinates can in general be calculated from A. It is not enough that there should be a clock at B which we can inspect by telescope or get reports about, for then we should still lack any means of comparing the time-scale at B with our timescale at A; in particular, we should not know whether the two clocks were synchronous, and we should not know how much time (measured in A's scale) elapsed while the report of the reading of B's clock was moving from B to A. Indeed, we so far have no meaning for synchronousness (simultaneity) aside from the case where the clocks are practically in the same place.

The bridge between A and B is then built with the aid of light-signals: "We establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A." Then we imagine a lightray departing from A, traveling to B, and being immediately reflected back to A. At A we note the time of departure and the time of return. In accordance with our "definition" we now assign to the event at B a time-coordinate mid-way between those noted at A. If, by observation or report, we find that the clock at B generally agrees with these assignments, the clocks are said to synchronize. It is assumed that the relation of synchronization as holding among clocks is symmetrical and transitive. From the logical point of view, the essential work in the establishment of the special theory of relativity has now been done.

It is important to be clear on the status of the "definition" just established. Everything turns on the notion that a light-signal goes from here to there and from there to here in equal times. There is no legitimate sense in which this stipulation can be directly verified. It would of course be an easy matter to reproduce the conditions of the imaginary experiment, and directly "measure" the time required for the light-rays to traverse the gap in either direction. But such "measurements" will always entail either the very principle in question, or some equally arbitrary (in the logical sense) assumption as to the comparability of separated clocks.

The theorems which emerge in the special theory, and their dramatic empirical confirmations, are a fascinating and familiar story. It is however fruitful to notice that the special theory does not seem to be complete in itself. Its success in deriving physical laws invariant with respect to all unaccelerated reference frames inevitably raises a question as to the distinction between accelerated and unaccelerated frames. Why should the former be invalid as standpoints from which to observe the physical scene? A few years later Einstein asserts, in fact, that "the laws of physics must be of such a nature that they apply to all systems of reference in any kind of motion" ["The Foundation of the General Theory of Relativity"]. This, the so-called general principle of relativity, is embodied in Einstein's general theory of relativity. Even there one cannot, I suppose, rest content, for this reason: there is a kind of unity between electrodynamics and mechanics at the level of the special theory (the laws of both are invariant with respect to the Lorentz transformations) which is lost in the general theory. Reestablishment of that unity at a higher level provides part of the motive for attempts to develop a "unified field theory."

The whole movement is an extension, more or less natural, of the methods of special relativity. It seeks to establish a public world of ever wider range of application, and in so doing it involves an ever greater retreat from any philosophical tradition which tends to make direct experience the archetype of knowledge. Einstein's words:

The characteristics which especially distinguish the general theory of relativity and even more the new third stage of the theory, the unitary field theory, from other physical theories are the degree of formal speculation, the slender empirical basis, the boldness in theoretical construction and, finally, the fundamental reliance on the uniformity of the secrets of natural law and their accessibility to the speculative intellect.

[New York Times, 3 February 1929]

I should like now to turn to Einstein's own popular presentation of the foundations of his theory in The Principle of Relativity. In part, this will provide a further documentation of the argument of this section. It will also provide an opportunity to exhibit the power of the distinction between constructs and epistemic correlations (neither of which are to be confused with immediate experience) implicitly laid down in "Physics and Reality." And lastly, the discussion of Relativity will provide a model of Einstein-the-supposed-positivist at work; if it is possible to understand the relevant portions of Relativity without supposing that Einstein is committed to some form of reductionistic empiricism, I will conclude that all the citations of section 2 of this paper have, in principle, been answered.

The discussion in Relativity begins with the supposition that lightning has struck a railway embankment simultaneously "at two places A and B far distant from each other." An imaginary reader is then asked if "there is sense in this statement" and it is supposed that he replies in the affirmative. Upon being pressed to supply the sense, the "reader" avers that "the significance of the statement is clear in itself," although some additional consideration is necessary if one is to "determine by observation whether in the actual case the two events took place simultaneously." There follows Einstein's assertion, previously quoted, that simultaneity has no meaning for the physicist or anyone else unless the method for determining its fulfillment by observation is given.

In reply to this, the "reader" offers a new definition. He imagines an observer placed at a point midway between A and B, equipped with a V-shaped mirror by means of which he can observe both A and B at the same time. The lightning flashes are then said to be simultaneous if and only if they are seen in the mirror simultaneously. Einstein then raises the "objection" that a new presupposition has been brought in, namely, that light travels from A to M in the same time that it travels from B to M. "An examination of this suggestion," he continues, "would only be possible if we already had at our disposal the means of measuring time. It would thus appear that we are moving here in a logical circle." To this, the very wise reader is presumed to reply in the following way:

There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled.… That light requires the same time to traverse the path A—to—M as for the path B—to—M is in reality neither a supposition nor a hypothesis about the nature of light, but a stipulation which I can make of my own free will in order to arrive at a definition of simultaneity.

This all sounds very much as if the meaning of simultaneity is to be conventionally reduced to some immediately sensed character (sensed simultaneity at the mirror). But this would be an erroneous inference.

In part, the difficulty derives from Einstein's language, particularly the statement that there is "only one demand" to be made of the definition in question. But the impression that we are here dealing with a reduction-definition derives mainly from the context. Einstein is displaying as clearly as possible the logically arbitrary character of the assumption that light travels at the same speed in every direction. This is clear from the last citation, and it is this purpose which is admirably served by the definition in terms of the V-shaped mirror. But we recall from the original 1905 paper that the fundamental aim in all this is to assign time-coordinates to events at a distance. Even in the present context, Einstein is engaged in discussing the simultaneity of the events at A and B, and these latter are unequivocally thought of as real outer events, not sense-data or functions of sense-data. This being the case, it is exceedingly hard to understand how the meaning of simultaneity of events at A and B can be reduced to a sensed simultaneity at the mirror, while the events themselves at A and B are not so reduced.

In fact, this is where we can profit from "Physics and Reality." Confusion reigns here because of a failure to distinguish between the two non-sensory dimensions of the science in question. So far as the postulational structure of physics is concerned, the meaning of simultaneity is simply identity of time-coordinate, and this holds true both before and after Einstein. This conception has to be connected (not reduced) to experience, and this connection is effected through—if you wish—the definition in terms of the V-shaped mirror. But then the latter definition is not the sole meaning of simultaneity.

Again, Einstein sounds most like a positivist when he is emphasizing the necessity for having epistemic correlations; hence his constant demand that theoretically-conceived simultaneity for distant events be connected to some perceptual experience. The perceptual experience in question is a sensed simultaneity. In the context of Relativity, it is the sensed simultaneity of the two flashes seen side-by-side at the mirror. In the context of the 1905 paper, the required sensed simultaneity holds between the arrival of a signal and an observed position on the hands of a clock right along side. On the other hand, the existence of an epistemic correlation does not constitute a reduction of the concept to the perceptual experience; for the whole point is that it is through the concepts that the perceptual experiences fall into some kind of intelligible order.

Once more, the whole argument can be phrased in terms of the simultaneous events at the mirror themselves. Are these sensed events only, or is there some respect in which they are also physical events, i.e. occurrences postulated for existence whose whole nature is not exhausted by sensory components? Evidently they must also be physical events. For they bear a relevance to the distant events at A and B only because they are participants in a postulated physical process in which both pairs of events have a share. Consequently, the events at the mirror are themselves "bifurcated," i.e. they are both physical and sensed. We sense a pair of colored flashes against a shiny background, but we think of atomic or sub-atomic collisions involving light; otherwise it would be silly to suppose that events referred to the mirror are significant of a physical relation (simultaneity) between events elsewhere in space.

5. CONCLUSION: NEGATIVE.

I hope it is now clear that Einstein belonged, and rightly so, to the "metaphysical" school of the philosophy of science. Of course "metaphysical" has a pejorative meaning as well as a neutral one; in the former sense it means something like "unduly independent of experience." In that sense of the term, we owe to Einstein the discovery that some of our thinking about space and time had been "metaphysical," and we owe to him the discovery of a road leading away from the "metaphysical" to the more firmly "empirical." The hope of exhibiting these facts as clearly as possible formed part of the motive for sections I and IV of this paper.

But there is no rule restricting us to pejorative meanings unless we want to prejudice philosophical issues in advance. "Metaphysical" can also mean, vaguely speaking, "not wholly dependent upon experience." It is in this sense that Frank apparently intends the term, and it is in this sense that Einstein clearly belongs to the metaphysical school. For Einstein it is a patent fact that some kind of connection to the perceptual experience is always required for legitimate theory, but "connection to experience" does not imply derivation from experience, nor reduction to experience, nor exhibition as a conventional function of experience. The uncritical assumption that some such implication does hold good is responsible, I think, for much misunderstanding of Einstein.