The primary objective of science is to gain an understanding of the universe in which we live; that is, to acquire knowledge. Other branches of human endeavor share the same objective, but the special feature of science which sets it apart from the others is that it restricts its inquiry to those items which are inherently factual; that is, if they are anything other than observable facts, they are derived initially from a consideration of such facts and are capable of being tested by comparison with other facts. When so verified, these items become part of a permanent and ever-growing body of factual knowledge: scientific knowledge, we may say.
One of the ways in which this permanent store of scientific knowledge is built up is by ascertaining more physical facts through processes of observation and measurement. This is the activity in which the great majority of scientists, aside from the teachers, are engaged, and the facts that are thus discovered are the foundation stones of science. But if scientific knowledge consisted entirely of a vast accumulation of isolated facts, it would be impossible for anyone to achieve more than a tiny fraction of the understanding which is the primary objective of scientific activity. In order to gain a broad understanding, it is necessary to classify these facts and to discover some general relations between the classes, so that we can deal with a reasonable number of items rather than with the enormous mass of separate facts that emerge from the labors of the observers and experimenters.
The process by which these general relations are derived from the individual items is inductive reasoning. Unlike the inverse process, deductive reasoning, which proceeds in a straightforward way from the general to the particular, and arrives at incontrovertible conclusions, providing that both the premises and the reasoning are valid, inductive reasoning is essentially a recourse to probability. An independent verification of the conclusions thus reached is essential. The standard procedure recognized by science consists first of a study of the facts that appear to be relevant to the situation under consideration and an attempt to locate some systematic variation or other indication of a connection between two or more classes of items (Step 1). On the basis of whatever may be found in this study, a theory is devised to account for the findings (Step 2). If it is narrow in scope, or lacking in adequate support, the theory is usually called a hypothesis. The consequences of the theory are then developed in detail (Step 3). Finally the scientist goes back to the accumulated store of scientific knowledge, perhaps augmented by further observations or experiments suggested by the theory, and tests the theory by comparing its consequences with the observed facts (Step 4).
If there is a complete and exact agreement, the validity of the theory is confirmed—in the language of science, the theory is verified—providing that the facts available for comparison are reliable and adequate in scope and number. If verification is not possible, but there is a reasonable degree of agreement between theory and observation, the theory is usable in practical application until something better comes along, and it also constitutes a base from which a more accurate theory may possibly be derived by addition or modification. If there are major disagreements between the theory and the facts, the theory is neither correct nor useful. Some theories are called laws. This term is usually defined in a way which equates it with a verified theory, an item of established scientific knowledge, but in practice, it is applied rather indiscriminately to any of the theories in current use.
The procedure as described is subject to some degree of variation, although the variability is more apparent than real. Many scientists insist that certain theories which they have formulated were the result of “hunches” or accidents rather than being due to a systematic study of the relevant facts. But it is evident that the benefits of serendipity seldom accrue to those who are not qualified to receive them. “Chance favors only the prepared mind,” as Louis Pasteur expressed it. Here the study of the facts has taken place just as surely, even though less obviously, as in the normal situation. Similarly, many scientists omit all or part of the verification procedure. But sooner or later someone has to complete the job, and either supply the verification or demonstrate that the theory is incorrect.
In order to qualify for the status of verified scientific knowledge, an item must be capable of being stated explicitly so that it can be tested by observation or measurement, it must have been so tested in a very large number of individual cases distributed over the region to which the item is applicable, it must agree with observation in a substantial number of these tests, and it must not be inconsistent with observation in any instance. These are rigid rules, to be sure, but an immense number of individual items have already qualified under them, and more are continually being added.
Some philosophers contend that there can be no such verification; that we cannot be absolutely certain of anything in the physical realm, and hence there is nothing that we know with certainty. The best we can do, they say, is to establish a strong probability of being correct. From a strict mathematical point of view, this is quite true. It must be admitted that physical issues cannot be settled with mathematical certainty. But we are not mathematical abstractions existing in a vacuum; we are human beings existing in a physical universe, and our science is an activity aimed at gaining an understanding of that universe. So we are not striving for an unobtainable mathematical certainty, a state in which the probability of error is zero. The objective of science is physical certainty, a state in which the probability of error is negligible.
The individual who applies the principles of science to practical problems, the engineer, is perfectly safe in basing his calculations on Newton’s Laws of Motion, or on Ohm’s Law, or on the conservation laws. Even though the validity of these laws, within the range in which he uses them, may not be mathematically certain from the viewpoint of philosophers, it is physically certain, and there is no need to give the philosophers’ hair-splitting a second thought. Our permanent store of scientific knowledge consists of an accumulation of items of this kind, the validity of which is physically certain.
Even those philosophers and philosophically oriented scientists who stress the lack of mathematical certainty in science are compelled by the weight of circumstances to admit that mathematical certainty is not an essential factor in human knowledge. Bertrand Russell, for example, tells us very explicitly that there is no certainty outside mathematics:
The inferences upon which we implicitly rely in this [scientific] investigation… differ from those of deductive logic and mathematics in being not demonstrative… . Except in mathematics, almost all of the inferences upon which we actually rely are of this sort.22
But having made this point, he immediately draws the teeth out of it by admitting that “In some cases the inference is so strong as to amount to practical certainty.” This practical certainty is, of course, the same thing that we have called physical certainty. The terms “physical certainty” and “mathematical certainty” have been used in this work in preference to any of the alternatives that are available primarily as a means of emphasizing the fact that these are the kinds of certainty that apply in the physical and mathematical fields respectively. It should be recognized, however, that, as here used, these terms specify only the nature of the certainty, not the nature of the knowledge. The validity of a logical proposition, for instance, may be a matter of mathematical certainty, whereas it is possible, as will be shown in the pages that follow, to establish the validity of certain metaphysical propositions with physical certainty, as herein defined.
Physical certainty should not be regarded as an inferior kind of certainty. It is not only all that we need for physical purposes; it is all that we can use. The task of science is to identify and accumulate physically certain items of knowledge and to assemble them into a systematic and orderly structure. Of course, the subject matter with which science is concerned cannot all be classified as scientific knowledge. Many of the items with which scientists are currently dealing have not yet been verified, and these are merely “work in progress” for the present. In the course of further processing of these items, many of them will be found defective and must be discarded, just as is true in the fabrication of physical goods. But inclusion of such items within the scientific field is justified on the ground that the processing which they are undergoing is directed toward qualifying them as scientific knowledge. Any item which is inherently incapable of being factually tested in some manner is not scientific, irrespective of whether or not it may be regarded as knowledge on the basis of some other criterion, but those items which can be so tested, at least in principle, and are now in the process of clarification and development, are scientific even though they are not yet knowledge. When and if they are verified, they become scientific knowledge and are added to the growing accumulation.
Many scientists and philosophers deny the existence of permanent and certain scientific knowledge, even when certainty is defined in a manner similar to that in which the term is used in this work. For instance, Marshall Walker, a physicist, tells us that “The notion that scientific knowledge is certain is an illusion,” and in support of this assertion he says that “new models are often quite radically different from their predecessors and often require the abandonment of ideas that have long been considered obvious and axiomatic.”23 Max Black, a philosopher, has this to say: “We want to stress particularly the fact that all scientific generalizations, laws, and principles are approximations.”24
Walker’s comment is an illustration of one of the common errors in thinking that underlies this denial of scientific certainty. He bases his conclusion on the fact that many “models” and presumably “obvious and axiomatic” ideas ultimately had to be abandoned. But the truth is that few models ever qualify as scientific knowledge, since they rarely attempt to cover all aspects of the phenomenon with which they deal, and consequently they are inherently erroneous in part or in their entirety. As Walker himself points out, “Scientists have learned by humiliating experience that their model is not reality.”25 The failure of models to stand the test of time has no relevance to the status of firmly established knowledge. Likewise, if an assertedly “obvious and axiomatic” idea can be definitely verified, then it constitutes scientific knowledge and it is both certain and permanent. If it cannot be so verified, then it is not, in fact, “obvious and axiomatic,” nor is it scientific knowledge, and the necessity of discarding it has no significance in the present context.
The statement by Black is equally erroneous. In many areas, observation and experiment yield results that are physically certain. “Science does possess a consolidated corpus, much of which does not change,”26 says Alvin M. Weinberg. L. L. Whyte is similarly explicit, and goes into more detail:
Physical results which do not depend on measurement can be precise; some numerical conclusions are final, being free from possible sources of ambiguity or error; many aspects of the universe are of finite complexity; various forms of equilibrium ordering, once identified, are wholly objective; in many realms the scope for discovery may be finite.27
Generalizations based on these physically certain facts are themselves physically certain if properly derived and verified. Furthermore, the results of other less accurate observations or measurements are equally certain if properly expressed. The point that often leads to a misunderstanding of the true situation is that generalizations based on such results can usually be verified only to a certain degree of accuracy and within certain limits. Thus we cannot ordinarily verify a statement in the form of y = 3x, where x and y are physical variables. In order to be verifiable, the statement will usually have to be put in the form: Within the limits x - a and x = b, y = 3x to an accuracy of one part in 10Z. When thus expressed and verified, this statement constitutes exact and permanent knowledge, regardless of whether some future findings may show that the relationship is invalid somewhere outside the limits specified, or that there is a deviation of less than one part in 10Z under some circumstances. As du Nouy points out, “Science has never had to retract an affirmation based on facts that are well established within accurately defined limits.”28
The essential difference between science and the non-scientific branches of human thought is that, instead of deriving all of his conclusions from factual foundations and verifying them by checking them against the facts in the manner described in the preceding paragraphs, the non-scientist bases many of his most significant conclusions on assumed premises of some kind: principles, forces, or existences postulated for specific purposes and not capable of any independent factual verification. In earlier days, these ad hoc assumptions were made in terms of “demons”—supernatural beings of one kind or another who took care of whatever could not be explained on the basis of available factual information. Today the language is different, but otherwise there is no change. The demons are still with us under other names.
A corollary of the foregoing which is of particular significance in connection with the objective of this present work is that there is no inherently scientific field or inherently non-scientific field. The essence of science is not in the subject matter but in the factual treatment. Science has left certain fields to the philosopher or to the theologian, not because the subject matter is necessarily non-scientific but because it has not heretofore been possible to assemble enough facts in these areas to make scientific treatment possible. What this present work has done is to take advantage of an opportunity to obtain some new factual knowledge about these matters, and thus to surmount the obstacle that has hitherto stood in the way of the application of scientific techniques. Metaphysical subjects have previously been non-scientific, not because they are metaphysical, but because no one has been able to see any way in which they could be connected with facts susceptible to observation. Such subjects became scientific work-in-progress just as soon as a possible means of connecting them with observed facts was discovered, and all of the relations derived through exploitation of this connection became scientific knowledge just as soon as they were firmly established.
The concept of science and the scientific method that has been described in the foregoing paragraphs, and will be used in the exploration of the metaphysical field in this work, is what may be called the traditional concept: the viewpoint of Galileo, Newton, and the other great pioneers of science, and the concept to which most rank-and-file scientists, in both the pure and applied branches of science, still subscribe (usually without realizing that there is any option). But in order to understand why a major overhauling of scientific theory was necessary before the physical situation could be clarified to the extent required to make an advance into the metaphysical region possible, it must be realized that science is no longer following the traditional practices and procedures. Theoretical physics, generally regarded as the science par excellence, so much so that the term “modern science” more often than not refers to physics alone, is now dominated by a group of individuals who have repudiated almost all of the items included in the traditional concept of scientific practice.
The individuals, the inventive scientists we may call them, reject the traditional view that the results of scientific activity take the form of a permanent and ever growing store of scientific knowledge. “Scientific truth is necessarily tentative, subject to correction,”29 asserts Margenau, while Bronowski tells us that “Scientists know what the layman seldom grasps, that a scientific law is not permanent.”30 Max Black, looking at the situation from a position farther over on the philosophical side, puts it in this fashion:
Scientists can never hope to be in a position to know the truth, nor would they have any means of recognizing it if it came into their possession.31
The great gulf between this pattern of thinking and the traditional viewpoint of science is well illustrated by comparing the foregoing statements with the following quotations from two of the foremost scientists of modern times:
It is the characteristic mark of every true science that the general and objective knowledge which it arrives at has a universal validity. Therefore the definite results which it obtains demand an unqualified acknowledgment and must always hold good.32 (Max Planck)
It must be remembered that in the sphere of exact natural science conclusive solutions have repeatedly been found for certain limited fields of experience. The questions, for instance, which can be formulated with the concepts of Newton’s mechanics also found their eternally conclusive answers in Newton’s laws and their mathematical inferences.33 (Werner Heisenberg)
Some of the inventive scientists go a step farther and not only contend that we cannot know the truth, but that the rational external world which the traditional scientists have attempted, and are attempting, to explore in search of that truth does not actually exist, and that scientific concepts and theories are merely inventions of the human mind, useful for dealing with relationships between physical phenomena, but having no deeper significance. R. B. Lindsay points out that the essence of the difference between the two viewpoints is contained in the question as to whether the task of physical science is discovery or invention:
Application of the term “discovery” implies that there is an external world “out there,” wholly independent of the observer and with built-in regularities and laws waiting to be uncovered and revealed. They have always been there and presumably always will be; our task is by diligent search to find out what they are.34
This is the traditional viewpoint on which the present work is predicated. For his part, Lindsay rejects this concept and sets forth his creed in these words:
We are essentially viewing the purpose of physics as a scientific discipline as invention rather than discovery… . The term “invention” implies that the physicist uses not only his observations but his imaginative powers to construct points of view that identify with experience.
The most significant result of this substitution of “invention” for “discovery” by a large and influential segment of the scientific community has been the introduction of demons into physical theory on a wholesale scale. “Arbitrary abstract constructs and postulates are freely used in the building of physical theories,” Lindsay admits, and many of these “abstract” inventions—probably most of them—are simply demons, ad hoc assumptions no different, except in their semantic dress, from the demons of the non-scientific disciplines. Inventive science, the science of these modern theorists, therefore differs from traditional science in exactly the same way in which non-science differs from traditional science. Most of the fundamental concepts of so-called “modern science” (that is, present-day theoretical physics) are demons, not essentially different in their logical status from the demons of primitive human thought.
There is no significant difference, for instance, between the “rain god” that brings a much-needed shower for the benefit of the crops of the primitive tiller of the soil and the “nuclear force” that holds the hypothetical nucleus of the atom together for the benefit of the modern theoretical physicist. In each case, some kind of an explanation of a phenomenon is wanted, and in the absence of anything concrete, the expedient adopted is to invent a demon, a hypothetical entity designed specifically for the purpose, which has no other function and whose existence cannot be substantiated by any independent evidence. Strictly speaking, the “nuclear force” is even less scientific than the “rain god,” since it is what we might call a double demon; that is, the nucleus itself is a demon, an ad hoc invention totally lacking in any independent confirmation, and the “nuclear force” is thus hypothesis piled upon hypothesis.
Each cultural or professional group has its own jargon, and this makes the explanations sound different, but their essential character would remain unchanged if the primitive man propitiated the “rain force” and the physicist invoked the aid of the “god of the nucleus.” A demon is a demon, whatever linguistic clothes he may wear. The occupational status of the individual who invents him and the field of thought in which he is located are both irrelevant. A purely factual conclusion reached by a philosopher or a theologian, or in the field of philosophy or the field of religion, is just as scientific as a factual conclusion reached by a scientist in the physical field. On the other hand, non-factual conclusions derived on the basis of a demon are just as non-scientific if they are reached by a scientist in the field of physics as they are if they are reached by a theologian in the field of religion.
Another familiar demon of modern science is Einstein’s “curved space.” Here, again, there is no independent evidence of the postulated phenomenon: no evidence that space is, or can be, curved or distorted in any way. The postulated curvature is purely an ad hoc construction, designed for this particular purpose and not applicable to anything else: a typical demon. A comparison of this theory of Einstein’s with Newton’s views of the gravitational phenomenon illustrates the difference between a purely scientific approach and one fortified with demonology. Newton utilized only observable physical entities and relationships derived from them. Mass, acceleration, and distance are all capable of observation and measurement. Force is defined as the product of mass and acceleration. Thus Newton’s gravitational force, unlike the “nuclear force” previously discussed, was not an unknown force—a purely hypothetical creation—it was a known force of unknown origin, a genuinely scientific concept.
If Newton had attempted to explain the origin of the gravitational force, he would have had no option but to resort to a demon, as he was unable to find any scientific explanation. But he resisted the temptation to indulge in speculation on this point, and confined his theories to factual matters. Einstein, however, belonged to the inventive school of science, and to him the proper procedure was to devise a demon, “a free invention of the human mind,” as he called it, to account for the gravitational phenomenon. He specifically condemned Newton’s factual approach. Newton, he points out, “believed that the basic concepts and laws of his system could be derived from experience.” But, says Einstein, the foundations of theory derived in this manner are “fictitious,”35 and he lays down the dictum that “the axiomatic basis of theoretical physics cannot be an inference from experience, but must be free invention.”36 In other words, theoretical physics, according to Einstein’s viewpoint, must be based on demons. In the theories developed by Einstein, Bohr, and others of the inventive school of scientists, this is just the course that has been followed. Quantum mechanics, the second of the two principal developments of modern physical theory, relies even more heavily on demons than Einstein’s relativity.
The retreat of the inventive scientists from the purely factual concepts and relations of traditional science back to the demons of the non-scientific disciplines has been due to identically the same factors that cause the non-scientists to adopt these tactics; that is, a strong desire to produce answers to important problems, coupled with an inability to find any logical and factual approach to these problems. At one time it was thought that conventional science would provide such an approach. The so-called “classical” laws of physics had scored some very impressive successes, and it seemed altogether possible that with a few additions and refinements these laws would ultimately encompass the whole of existence. Then, almost overnight, a series of new discoveries demolished this expectation, bringing to light new facts and new phenomena with which the classical laws were unable to cope. The most strenuous efforts to fit these discoveries into the classical system or to construct a new system of theory along traditional lines that would be applicable in the areas outside the scope of the classical laws have been completely unsuccessful.
As a result, those scientists closest to the problem, the theoretical physicists, have swung all the way from their original overoptimistic viewpoint, attributing almost unlimited capabilities to the theories then current, to the other extreme: an overpessimistic viewpoint which doubts the rationality of nature and denies the possibility of formulating clear and unequivocal theories to account for the new phenomena. In the bitterness of their disillusionment, these theorists have turned their backs on the traditional goals and methods of science, and like those of their predecessors who were confronted with similar difficult situations—primitive men, the philosophers, the theologians, and others—they have resorted to “free inventions,” calling upon demons to supply the theoretical foundations that they were unable to construct from facts.
For the last fifty years, our leading physicists have been engaged in ruthlessly discarding previously sacrosanct “laws of Nature” (or “rules of logic”), and replacing them with obscure mental constructs whose quasi-mystical implications are hidden in technical jargon and mathematical formalism.37 (Arthur Koestler)
The almost incredible extent to which the practitioners of “modern science” have jettisoned not only the traditional methods and goals of science, but established processes of reasoning and logic as well, is largely hidden from the general public because the current literature of the theoretical physicists employs a jargon that is incomprehensible not only to the layman but to the rank-and-file scientist as well. But a good idea of the true state of affairs can be gained from an examination of the statements of those scientific writers who are bold enough, or incautious enough, to comment on these matters in plain language.
Warren Weaver, for example, tells us that the close observer “finds that logic, so generally supposed to be infallible and unassailable, is, in fact, shaky and incomplete. He finds that the whole concept of objective truth is a will-o’-the-wisp.”38 Now where does this remarkable conclusion come from? A few pages later in the same work, Weaver answers this question. “A major consequence of the developments in relativity and quantum theory over the past half century,” he says, has been the destruction of “both ultimate precision and ultimate objectivity,” and he goes on to assert that “presuppositions which have neither a factual nor a logical-analytical basis… enter into the structure of all theories and into the selection of the group of ‘facts’ to be dealt with.”39 These words, which express the attitude of the present-day scientific Establishment, define the issue specifically. The most cherished products of modern science, including relativity and the quantum theories, are in conflict with logic, with the concept of “objective truth,” with the concept of causality, and with other basic concepts of traditional science. Something must therefore be discarded. To the modern theorist, sacrifice of relativity and the quantum theories is unthinkable; hence, he throws objective reality, logic, and causality to the wolves.
One might naturally assume, on the strength of this otherwise inexplicable procedure, that these two products of modern scientific ingenuity are so firmly established and incontrovertible that their scientific validity is beyond question. But this is not at all true. On the contrary, the leaders in the scientific profession freely admit that these theories are open to serious question. Many put the case in much harsher terms. Norwood R. Hanson, for instance, describes quantum theory as “riddled with formal inelegancies and inconsistencies.”40 Bryce DeWitt, a prominent investigator in the gravitational field, has this to say about general relativity, which purports to explain gravitation:
As a fundamental physical theory general relativity is a failure. It is a failure because it predicts that, under very general conditions, singularities must occur in space-time, beyond which the theory is incapable of saying anything. That is, the theory predicts that it cannot predict. It is not fundamental enough. It must eventually be superseded by something more universal.41
Furthermore, these scientific leaders are almost unanimously agreed that some totally new physical theory is essential for continuation of scientific progress, a conclusion that is equivalent to an admission that there are incurable weaknesses in current theories. Even Weaver, who gives these currently accepted theories precedence over logic and objectivity in arriving at his judgments, asks this significant question:
Will we ever have the courage and imagination to … construct a theory which starts at the right place and with the right conception? … If and when such a theory is available, certain presently unsatisfactory aspects of the explanation of physical events will have disappeared.42
The principal objective of the discussion in the preceding pages is to bring out the fact that the “right place to start” in developing a sound and truly scientific physical theory is the place where the trouble started: the point at which the theorists abandoned the traditional scientific methods and resorted to the demons of “free invention.” The “right conception” of how to go about such a development is not to discard the classical physical theories, but to examine the foundations of these theories carefully and painstakingly to locate the conceptual error that is responsible for the difficulties which have been encountered. The mere existence of difficulties of this nature is prima facie evidence of such an error. As Fred Hoyle comments:
It is almost a matter of principle that in any difficult unsolved problem the right method of attack has not been found; failure to solve important problems is rarely due to inadequacy in the handling of technical details.43
The necessary first step is to locate and correct the basic error. Extension of the existing theories into the newly discovered areas can then be carried out by standard scientific methods. This is the policy that has been followed in the development of the Reciprocal System of theory. That theory employs no demons. No ad hoc assumptions are utilized anywhere in the theoretical development; in fact, no assumptions of any kind are introduced other than those included in the fundamental postulates of the system. Every step that is taken, and every conclusion that is reached, results from the application of logical and mathematical processes to the basic postulates alone. This is a theory that meets the most exacting requirements, and it clearly qualifies as scientific knowledge.