PAPERS

IV - OCKAM'S RAZOR AND THE UNIFICATION OF PHYSICAL SCIENCE*

by     Reginald O. Kapp

Offprint from THE BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE
Vol. VIII No 32 1958
Thomas Nelson & Sons Ltd Edinburgh 9


1 The Unification of Physical Science

As understood here the unification of physical science constitutes the replacement of many specific laws, principles, and hypotheses by a smaller number of more general ones. An example of the process, which is frequently quoted and which stands out as pre-eminent, is the unification achieved by Newton.

Before his day there were no general laws of mechanics ; there were only a variety of specific laws, each applicable to a specific mechanical system. It was believed that a specific law, applicable only to planets, required these to move in elliptical orbits; that a quite distinct specific law, applicable only to pendulums, required their period of swing to bear a specific relation to the length of the pendulum; that yet another specific law, applicable only to vacuous spaces, required these to be filled. If there were such a thing as a Cosmic Statute Book, this would have had to contain, according to the pre-Newtonian view, separate entries under the respective headings Planets, Pendulums, Vacuum. The book would have been a bulky one.

But Newton showed that many such specific laws were implicit in other more general ones. A large number of observed facts could be inferred from his laws of motion and gravitation. If the Cosmic Statute Book contained these all-embracing laws, there would be no need for further entries to say that planets shall move in elliptical orbits, that the period of swing of a simple pendulum shall be proportional to the square root of its length, that a projectile shall have a parabohc path, that a vacuous space shall be filled: Newton, it might be said, did much to whittle down the Cosmic Statute Book.

Another way of describing the same achievement is to say that Newton 'explained' a large number of facts. For in physics a fact is explained by showing how it can be inferred from something more general. All explanations there are steps in the direction of greater unification.

Since Newton's day the unifying process has extended into more and more branches of physical science. The first and second laws of thermo-dynamics have had great unifying power. From them much can now be inferred that would otherwise have to be attributed to specific, ad hoc, laws. The relation between the once quite distinct subjects of electricity and magnetism is found to be so close that they are now considered as one subject. A study of the relation between chemical reactions and thermo-dynamics, as also of that between chemical reactions and atomic structure, has led to the new branch of science called physical chemistry. This has taught us that chemical processes and properties are implicit in atomic structure. At one time it must have appeared that an entry in the Cosmic Statute Book would be necessary to say that hydrogen shall combine with oxygen and form a substance with the properties of water. But we now know that such a clause would be redundant. Physical chemists can tell us that, provided there be atomic nuclei with, respectively, one and eight positive unit charges, the rest is assured. One can infer, with the help of certain general laws, that atoms having such nuclei must combine and that the resultant compound must have the properties of water. This unification is making it possible to explain more and more chemical facts in terms of atomic structure.

A most valuable feature of unification is that it enables one to replace observation and experiment by inference and calculation. Galileo could only discover the law of the pendulum by observing pendulums; but after Newton anyone who had never seen a pendulum could have discovered the law. He would have done so by the reasoning that is now taught in schools, where the formula is deduced from first principles. Similarly, the elliptical orbits of planets could only have been discovered before Newton's day by making careful observations of successive positions of planets. But now a person who had lived all his life under a blanket of impenetrable cloud and learnt for the first time that there was a massive sun surrounded by less massive bodies could predict that, when the cloud lifted, one would observe the less massive bodies to move in elliptical orbits. There was a time, again, when the chemical properties of substances seemed only to be discoverable by observing those substances. But this is not necessary today. Long before the element Hafnium had been found chemists did not only say that there was such an element; they also predicted its properties. The properties are implicit in the general laws that chemists have discovered and can be inferred from these laws.

It is this kind of unification that has made the rapid progress of technology possible. If every chemical substance had to have a clause in the Cosmic Statute Book defining its properties, chemists would have to make the substance and submit it to a laborious series of tests before they knew what the properties were. But the properties are implicit in general laws. If these are known, the properties follow automatically. Hence it is a commonplace of chemical research to predict the properties of a new compound before making it.

It is the same in all other branches of technology. Without a unified physics one would have to make a gun and fire it before one could know what path the projectile would take. One would have to make and test a bridge in order to discover its strength. One would have to make and test every new kind of engine before one could determine its thermal efficiency or the critical speed of its shaft. But the technologist's aim is to substitute inference for observation wherever possible. Doing this, he can predict the performance of guns, the strength of bridges, the efficiency of steam engines while they are still in the blue-print stage. In technology tests, observations, experiments, do not serve the purpose of facilitating predictions but of verifying them and of correcting errors and oversights. This can be done because what is predicted is implicit in general and known laws and principles.

By the process of unification the whole of physical science is gradually being fashioned into one complete and consistent structure of thought in which the various parts bear a logical relation to each other. Mechanics, electricity, magnetism, thermo-dynamics, chemistry, heat, light, sound, to mention only some branches, have been brought under one common roof.

During the present century we have seen two conservation principles, those respectively of energy and mass, united. Einstein has established in the general theory of relativity a connection between gravitation and space and has thereby brought space under the common roof with the rest of physics. There has, further, been the formulation of the very basic and comprehensive law according to which physical changes cannot be by indefinitely small amounts. This law forms the foundation of the quantum theory and has brought under the common roof a large number of observations that previously seemed to be isolated and each to require its own clause in the Cosmic Statute Book. Predictions of all sorts are being based every day on the principle that all physical changes are quantised.

The search for greater and ever greater unification continues, but with varying success. One of the failures is worth mentioning because it illustrates the nature of the problem. Three different types of field of force have been observed: magnetic, electrostatic, and gravitational. Something is known about how the first two are related to each other, and one commonly speaks of them jointly as the electromagnetic field. But yet they remain distinct from each other and quite distinct from the gravitational field, which has been shown by Einstein to be a region where the geometry of space-time differs in a specific way from Euclidean geometry. The difference can be expressed in a mathematical formula.

The hypothesis is near at hand that the magnetic field is also a region where the geometry of space-time differs from Euclidean geometry, though in a different way, and that the electrostatic field represents a third departure. If so, one might expect to be able to generalise Einstein's relativity equations in such a way that they would represent any kind of field. If that could be done, one specific value of a term in the equation would define the gravitational field only, another the magnetic field only and a third the electrostatic field only. Each field would then appear as a special case of something common to them all; its properties could be predicted from the great sweeping law that was applicable to all fields; magnetic, electrostatic, and gravitational fields would be brought under a common roof. The attempt to achieve this has been called the search for a unified field theory.

Assiduously though it has been conducted by a number of scientists, of whom Einstein was one, the search has so far only led to disappointment. It is impossible to say yet whether the failure is due to the inherent difficulty of the subject or because the search has taken a false hypothesis as its starting point, i.e. that all fields of force have enough in common for them to be represented in terms of the geometry of space-time. Yet, in spite of the apparent reasonableness of this assumption, it may not be true. Electrostatic and magnetic fields may be so different from gravitational ones in their nature, their effect, their cause, that they cannot be represented in any comparable terms at all. Some other hypothesis, one that has not yet been formulated or even thought of, might prove a better starting point for bringing electromagnetism and gravitation under a common roof.

Be that as it may, no attempt will be made here to succeed where Einstein and others have failed. The present study is in no way concerned with the search for a unified field theory, desirable though it is that the search should continue. But the example will help to define the scheme according to which unification in physics occurs.

How is unification achieved? A general principle is first found. Examples are Newton's laws of motion, the great conservation laws, the principle of least action, the principle according to which all observable physical changes are quantised, the principle of the equivalence of mass and energy, the principle by which the chemical properties of substances are related to the number of electrons that surround the neutral atoms of the constituent elements.

At the next step towards unification various phenomena are shown to be implicit in one or other of these principles. They can therefore be inferred from them and so could be struck off the Cosmic Statute Book as redundant.

Sometimes the phenomena are observed first and the principles are found later. The principles are then said to explain the phenomena. Thus the observed behaviour of planets was explained by the laws of motion and gravitation. Similarly, attempts to make a perpetual motion machine failed for unexplained reasons until the principle of conservation of energy provided the explanation.

At other times the principle is found first and some phenomenon that is implicit in it is described before it has ever been observed. In such instances it may, or may not, be observed later. One then says that the phenomenon is predicted by the principle. Engineers, as mentioned already, follow this course as a matter of routine. They invent and design new kinds of machines on the basis of the great sweeping principles of physics and they predict their performance. Observation and experiment come later and not to test the principles but to test the soundness of the designer's reasoning. In physics, too, it sometimes happens that a phenomenon is predicted as an inference from a general principle before it has been observed. The properties of Hafnium have already been quoted as an example. But physicists work most often with things that they are observing at the time. Their concern, unlike that of the machine designer and the industrial chemist, is more often to explain observed effects than to predict those that will only later become observable.

The striving to bring ever more phenomena under the common roof, to unify the whole of physics is, of course, not the whole of the physicist's work. Indeed most research workers are concerned only with the discovery of the detailed facts, qualitative and quantitative, of the physical world; and necessarily so, for we still have much to learn about the laws of mechanics, heat, light, sound, electricity and magnetism, about the physical and chemical properties of solids, liquids, and gases, about the macrostructure and the microstructure of the material universe, about the positions and movements of the heavenly bodies. But, nevertheless, it is worth stressing that much of the thinking done by most physicists is directed towards the discovery of generalisations and that it is on these as much as on collections of observed facts that physical science is based.

The distinction between the search for isolated facts and the search for unifying generalisations is well illustrated by the elliptical orbits of planets. We can now understand why these orbits could not be explained before Newton's day. It was because of a wrong outlook. During and for some time after the Middle Ages the notion was prevalent that every phenomenon was the result of what might be called a distinct act of legislation, that it was ensured by what I have metaphorically called a separate clause in a Cosmic Statute Book. Those who held this view were bound to think that one could only find out anything important about planets by studying planets; and that it was idle to ask why they moved in ellipses. The acceptable answer was that such orbits were a legislative requirement, about which no further questions could or should be asked.

But we can now realise that, if the elliptical orbits could not be explained before Newton, it was not that they were inexplicable. Nor was it that not enough was known about planets. It was that not enough was known about mechanics. No further astronomical research, no careful observation of the orbits, no precise measurement could have provided the explanation. But Newton's laws of motion and gravitation did so. In other words, scientists only found the answers to some specific questions about planets when they had found statements that were general enough to apply to all ponderable objects. In medical metaphor, ignorance about planets proved to be, not the disease itself, but a symptom of the disease. Newton followed the course of a doctor who seeks to treat the disease rather than the symptom.

Similarly our inability until a short while past to explain why given chemical substances react in the observed ways proved to be due, not to our ignorance of the substances, but to our ignorance of the more general subject of atomic structure. The great generalisations on which modern chemistry is based could not have been discovered by work conducted only in the field of chemistry.

These considerations are relevant to the present study because I propose to demonstrate here the great explanatory power of the generalisation that is reached when one pursues the search for a unifying principle in physics with uncompromising consistency. It will be shovm below that one then reaches a very comprehensive principle, one that is apphed by physicists on occasion but which has not been given the status it deserves.

2 The Principle of Minimum Assumption

Any search for greater unification of physics must have a reasoned beginning; it must be conducted methodically; the unifying principle sought must conform to the requirements of scientific method. So let the starting point of this enquiry be one of the commonplaces of scientific method the rule of economy of hypotheses, sometimes called Ockam's razor. This says that when more than one explanation of an observation is available one must provisionally choose the one that involves the least number of assumptions. The rule is so well known and so generally accepted that there is no need to illustrate it by examples. Most of us never doubt that it is a good rule, although we may differ as to how rigidly it should be applied. To assess its value we must first consider its nature and then the place that it occupies in scientific research. We shall find that in the history of physics the importance of this rule is very great indeed.

The rule of economy of hypotheses is one of the tenets of scientific method. It tells the scientist what to do when more than one explanatory hypothesis is available, but it does not guarantee that the recommended choice will be justified by events. This is evident from the use of the word 'provisionally'. By advising that the minimum assumption be made provisionally the rule allows for the possibility that another hypothesis, one that does not meet the criterion of minimum assumption, may have to replace it some day.

The great principles of physics are in a different category. They are not mere rules of procedure but statements about the very nature of the physical world. They are so well established that the word 'provisional' is omitted from their formulation. The principle of conservation of energy is an example. It is concerned with the energy in a given system, which may be energy of motion, of position, of chemical structure, of mass. The principle asserts that, provided the system be self-contained, the total quantity of energy in it is constant. Many conclusions can be inferred from this great principle. One of them is that a perpetual motion machine is impossible. So the principle of conservation of energy suffices to refute a person who claims to have invented such a machine. It would be highly exaggerated caution to tell him that his idea has to be rejected provisionally; one rejects it outright. One does not say that it is unlikely that the machine will work; one says that the principle of conservation of energy proves the inventor's idea to be wrong.

It is not so with a statement that violates the rule of economy of hypotheses. Almost every week letters appear in the daily press and articles in scientific journals, papers are presented to learned societies, in which hypotheses are put forward that involve more, sometimes much more, than a minimum assumption. One may deplore such hypotheses, but it is not customary to use Ockam's razor to prove them wrong.

Here is a significant difference between a principle and a rule of procedure. One can refute a statement that violates the principle of conservation of energy, but one can do no more than deprecate a statement that violates the rule of economy of hypotheses.

In making this distinction do we give a sufficient status to the rule of economy of hypotheses? It depends, I am venturing to suggest, on the discipline with which one is concerned. In history, in biology, in the social sciences, the rule can be no more than a useful guide to procedure; statements that conform to it can only be accepted provisionally; they may eventually have to be replaced by statements that violate the rule. But I wish to make the bold claim here that, in physics, the rule of economy of hypotheses can be so expressed and defined that it acquires a status far higher than the one usually accorded to it; I wish to raise it from a mere rule of procedure to one of the great universal principles to which the whole of the physical world conforms. At this level it would be worded as follows: In physics the minimum assumption always constitutes the true generalisation. It needs a name so I propose to call it the Principle of Minimum Assumption.

This claim is, itself, a hypothesis and has to be justified. I claim that one is able to do this by showing that a unified cosmology is achieved by the consistent, uncompromising, and methodical application of the principle of minimum assumption to theories about the past and future duration of matter. But before I do this I shall have to discuss the nature and meaning of the principle and show that it is applied by scientists already and more often than is always appreciated.

What is a minimum assumption? One sometimes hears the remark 'that is a big assumption', just as one hears 'that is a big lie'. The implication of such colloquial habits of speech is that qualitative distinctions can be made between different assumptions and between different lies; that one could arrange a collection of assumptions or lies in a row, with the biggest at one end and the smallest at the other; that the magnitude of assumptions and lies could be expressed in units, like that of temperature, hardness and other measurable quantities.

It may be so for all I know. But I am not concerned here with the grading of assumptions according to size. I am concerned instead with the search for a criterion by which an assumption that is defined as a minimum one can be clearly distinguished from assumptions that cannot be so defined. I do not think that the criterion is hard to find. I think it is whether the assumption is specific or not; so I shall define a minimum assumption as one that is completely unspecific. What this means can best be explained with the help of some examples. The first of them will be deliberately chosen to be extreme to the point of absurdity.

A young man who has had a predominantly humanistic education has been fascinated by a popular book on astronomy and has become enthusiastic about what he calls the beauties of science. He has read in his book that most stars do not have planets but that a very small proportion of them do and that these form solar systems like our own. The total number of stars is great, he learns, and so even the tiny fraction that have solar systems amounts to millions of stars.

He has also read in earlier books that planets are sublime bodies, constrained by their noble natures to move in orbits of geometrical perfection. In doing so, he has gathered, they produce a lovely harmony, known as the music of the spheres. He reaches the not unnatural conclusion that, where perfection is displayed in terms of geometry and music, it must also be displayed in terms of number, so he arrives at the hypothesis that every one of those millions of distant solar systems must have a pleasing number of planets. He can well believe that this may be the mystical number seven, or the virile number nine, or occasionally perhaps the round number ten. But he feels sure that no solar system can be cursed with the unlucky number thirteen.

An astronomer friend reproves him for his unscientific outlook. To believe that the number thirteen is precluded is, he says, a big assumption and an unjustified one. He tells the young man that some solar systems do have thirteen planets. The young man remains puzzled. Why, he asks, is it a big and forbidden assumption to believe that no solar system has thirteen planets and a small and permitted assumption to believe that some solar systems do have thirteen planets?

The question is not a silly one. It must not be dismissed with a shrug and a smile. It is basic to scientific method and it behoves us to find a clear and direct answer to it.

The answer is not that solar systems with thirteen planets have been observed. The astronomer admits that his belief in the existence of such solar systems is a hypothesis. The resolving power of our best telescopes is not sufficient to reveal any solar system but our own. So far as observation goes we have no proof that there is any other solar system at all.

Nor is the answer that there is a law of physics by which some solar systems are required to have thirteen planets. The reason for the astronomer's belief is, on the contrary, the very absence of any known law to require that solar systems shall have a specific number of planets. Here the minimum assumption is the unspecific one, i.e. that any number of planets can occur. This is therefore the assumption that, in conformity with the demands of scientific method, is made by our astronomer. He would not feel justified in making any other.

From the above little story one may learn the operative word by which to recognise a minimum assumption. It is 'any'. It need not apply only to numbers, but can also apply to quantities, properties, relationships, configurations, to any feature that one likes to mention. When there are only two alternative possibilities the grammatical substitute for 'any' is 'either' as, for instance, when there is a choice between the positive and the negative sign. So a minimum assumption can be recognised by the use in its formulation of the words 'any' or 'either'.

In practice it is not difficult to distinguish between a minimum assumption, as just defined, and one that is not a minimum one. But the question remains whether, when one has recognised a minimum assumption, one is always justified in making it. In the example of the number of planets in a solar system one cannot be sure whether the minimum assumption is the true generalisation or not. For it is impossible to prove by observation that solar systems may have any number of planets. But there are many occasions in the history of physics when the minimum assumption has proved to be the true generalisation. Let this be demonstrated with the help of some real examples.

3 Use of the Principle of Minimum Assumption in Physics

Minimum assumptions have not received as much attention as one might have expected in the philosophy of science. The distinction between specific and unspecific assumptions is not a textbook subject; and so but little has hitherto been done to clarify thought about it. But the history of science shows that specific assumptions have been made in the past time and time again; that they have been treated as generalisations about the nature of the physical world, and have eventually had to be replaced by unspecific ones. Whenever this has happened new light has been shed on a wide range of subjects; the unifying and explanatory power of the unspecific assumption has been demonstrated.

Thus it was assumed at one time that a specific law, applicable only to planets, constrained these to move in elliptical orbits. But Newton replaced the hypothesis that the planetary orbits were the consequence of a specific law by the hypothesis that they were the consequence of the circumstances in which the planets found them- selves. The assumption that certain bodies are required by their natures to move in specific ways was replaced by the assumption that any body may move in any way, its actual path being determined by the forces exerted on it. This proved to be the true generalisation.

Similarly, it was assumed at one time that Nature has specific likes and dislikes; for instance, that she abhors a vacuum. This could be translated into contemporary language as the specific assumption that a law of physics prevents the density of matter from falling below a specific value. But it is now known that the true generalisation about the density of matter is unspecific. The laws of physics permit any density, ranging from the high concentration that occurs in the white dwarf stars to the extreme tenuousness of extragalactic space.

A further illustration may be taken from more recent history the geometry of space. Until some fifty years ago it was assumed that this was required by the laws of physics to be of the kind known as Euclidean. If the assumption was not recognised as a specific one, it was only because it was not recognised as an assumption at all; it was thought of as a self-evident truth. Nevertheless, mathematicians had already shown that other geometries were logically possible. But very few persons believed that they were also physically possible.

Einstein, however, was prepared to take the same view about the geometry of space that the astronomer in our little story took about the number of planets in solar systems. Knowing of no law to preclude non-Euclidean geometries, he made the minimum assumption, namely that they can occur. The unifying and explanatory power of this assumption has proved to be enormous.

Yet another, rather simple, example is provided by the periodic table of the elements. The basic feature by which the chemical properties of an element are determined is the number of unit charges on the nuclei of its atoms. For the elements to be found in nature the maximum number of such charges is ninety-two, a stability limit. This limit provided a logical reason why no nucleus could be observed in nature with more than ninety-two unit charges, for a greater number would be inconsistent with the definition of a stable particle. But there was no logical reason why a smaller number should not occur. The minimum assumption is that a stable nucleus may carry any number of unit charges up to ninety-two.

There was a time, not so very long ago, when observation had nearly, but not quite, justified this assumption. Nearly all the numbers had been observed, but there were a few gaps. One of these was seventy-two. Another was zero.

Those who subscribed to the doctrine that a scientist must never, never believe what he cannot observe would have been precluded from believing that nuclei with seventy-two unit charges could occur. But few, if any, scientists carried their faith in empiricism thus far. Their faith in the principle of minimum assumption was the stronger, at least about the number seventy-two. So an element corresponding to this number was predicted purely on the basis of this principle. Its properties were also inferred and predicted. The event justified faith in the principle, for the time came when an element with seventy-two unit charges was observed and found to have the predicted properties. It received the name Hafnium.

Had faith in the principle of minimum assumption been a little stronger and the word 'any' taken a little more literally, scientists would also have predicted nuclei, or at least particles, with zero charge. For they would have noticed that there was neither a law nor a logical reason why such particles should not occur. Having satisfied themselves about their logical possibility, they would next have worked out what properties would follow logically from the definition of a particle with zero charge. They would have decided that it could not attract any satellite electrons; that it would pass through any atom without being deflected by the charges on the nucleus of the atom; that therefore no vessel could contain it; that it would not enter into any chemical reaction. They would, in short, have pre- dicted the neutron together with its properties. Subsequent observation of neutrons would then have served to justify the choice of a minimum assumption.

Actually the sequence of events was reversed. The neutron was observed first and its occurrence and properties were explained afterwards. But no other hypothesis was needed for the explanation than that any particle may carry any number of unit charges, including zero. The neutron provides one of many illustrations of the great explanatory power of the principle of minimum assumption.

Let me quote one further illustration of the power of this principle. It is the discovery of the positron by Dirac. The scientific work that led him to predict it is recondite and need not be described in detail. A few salient facts, deliberately presented in an over-simplified form, will suffice to point a moral.

One of Dirac's equations had two solutions, as happens when one solves a quadratic equation. One of the terms in both these solutions represented energy; but it occurred with the positive sign in one of them and with the negative sign in the other. The positive sign caused no difficulty. It represents energy as we know it. But the negative sign could only mean that the solution applied to a system that contained negative energy. It was difficult to give meaning to negative energy; but this was not the only objection to the second solution. Just as, at one time, no-one had observed particles that had seventy-two or zero charges, so no-one had observed a state of negative energy.

Had Dirac been a slave to the doctrine that what is not observable has no place in reality he would have had to assume that a specific law of physics prohibits a state of negative energy. But instead of assuming this he allowed himself to be guided by the principle of minimum assumption. He saw that it would involve a specific assumption to deny the possibility of negative energy and a minimum assumption to accept that possibility. His reasoning was strictly analogous to that of the astronomer who finds it more consistent with scientific method to postulate than to deny that some solar systems have thirteen planets.

Dirac's next step was to seek possible reasons why negative energy had never been observed. He rejected the facile answer that there was no such thing. Having satisfied himself that negative energy was logically possible he was convinced that it was also physically possible. The answer that Dirac did find need not concern us, but what is relevant is that in seeking it he reached the conclusion that evidence for negative energy would be provided by a particle with the mass of an electron and positive unit charge. This conclusion did not involve any additional hypothesis or assumption; it was a logical inference from work based on no other hypothesis than that the minimum assumption is always the true generalisation.

That the predicted particle had no more been observed than a state of negative energy did not shake Dirac's faith in the principle, a faith that was justified when, some years later, the particle was actually observed. It is called the positron.

Until this happened there were doubts about Dirac's prediction; and it is important to appreciate their nature. It was thought that the reasoning might have been faulty; that some essential fact might have been overlooked; that the mathematics might have contained an undetected error. The eventual discovery of the positron served to allay doubts of this kind. But they were all doubts as to whether a state of negative energy was really logically possible. Few doubted that, if it was, it was also physically possible and would occur occasionally.

Examples where, in physics, the principle of minimum assumption has led to new and valuable discoveries, when it has served to predict, to explain, to unify could be multiplied indefinitely. When a minimum assumption has been used as a basis of the subsequent reasoning, a number of valuable conclusions have followed from it by a process of logical inference and without the need for any additional hypotheses. But I cannot recall a single instance in physics where a specific assumption has, after scrutiny, been maintained as a true generalisation. For such examples one has to turn to history, to biology, to the social sciences, to the study, in other words, of systems that come under the influence of life.

4 The Concept of a Cosmic Statute Book

I have introduced the expression Cosmic Statute Book above and have discussed this concept in detail elsewherel It must suffice to mention here only one or two points connected with it.

Laws are always concerned with generalisations. The laws that govern the formation of companies, finance acts, the rule of the road, apply to all companies, to all tax payers, to all road users within the country for which they are enacted. This holds equally for what are called the laws of physics. But there the resemblance ends.

Laws imposed by authority can be, and often are, recorded in statute books, so I shall say that they are of the statute book kind. What characterises them is that they demand a specific choice between alternatives all of which are logically possible. They require, for instance, that traffic shall keep to its own side of the road and prohibit passage on the opposite side.

In the formulation of such laws the words 'any' and 'either' may not occur. If they did the law would be meaningless. Further, such laws do not include what is the logical consequence of other accepted principles. If they did they would be redundant. Thus no country would enact a law to say that people may drive either on the right or on the left. Such a law would enforce nothing and prohibit nothing. Nor would any country enact a law to require that two twos shall be four. It would be so whether the law were enacted or not.

The question now arises whether there are laws of physics that demand a specific choice between alternatives that are logically possible. We believe that it is logically possible for a solar system to have thirteen planets, and we know that it is logically possible for a particle to have seventy-two and zero unit charges, for space to have a variety of different geometries, for energy to occur in the negative state. If, nevertheless, a law of physics prevented any of these possibilities, it would be of the statute book kind. Such a law would have no place in a unified physics. It could not be inferred from any known principle. It could not be explained. It could only be discovered by observation.

According to the principle of minimum assumption there are no such laws in physics and I have shown above with the help of a few examples that physicists often act on the belief that it is so. Their belief can be expressed by rewording the principle of minimum assumption as follows: In physics a generalisation that is logically possible is also physically possible. It can therefore be represented by an actual example and is so represented with a frequency that is determined by statistical considerations only.

Yet another formulation of the same principle is as follows: For the physicist there is no such thing as a Cosmic Statute Book.

This negative formulation brings the principle into the category of what Sir Edmund Whittaker called 'postulates of impotence'. It tells us what one cannot do. It says that one cannot base a true generalisation in physics on a specific assumption. Therewith it has a faint resemblance to a formulation of the principle of conservation of energy that says: One cannot make a perpetual motion machine. This negative wording has its advantages sometimes. In mechanics one tests conclusions for their conformity to the principle of conservation of energy and one may reject them by saying, 'That is equivalent to inventing perpetual motion'. If we got into the habit of testing our conclusions for their conformity to the principle of minimum, assumption we should similarly find ourselves saying sometimes,' That is equivalent to an entry in a Cosmic Statute Book'.

However, the principle of minimum assumption is far from having reached universal acceptance. People have not become very articulate about it. It is by no means applied with the uncompromising consistency that it needs. Those who do apply it do so more instinctively than with deliberation and many of them would oppose my plea for elevating the rule of economy of hypotheses to the status of a great principle of physics.

Nevertheless, this is exactly what, I claim, should be done. On the more superficial view many discoveries in physics might be regarded as ingenious explanations of certain observed phenomena. But what I want to emphasise is that they need not have been found as a result of a search for ad hoc explanations. They have a different status, that of inferences. For they could equally well have been found as a result of exploring some implications of the principle of minimum assumption.**

c/o Kennedy & Donkin
12 Caxton St.
London, S.W.I

* This paper is an elaboration of the preamble to Professor Kapp's Chairman's address to the Philosophy of Science Group on I4th October, 1957 (Ed)

** During my address I developed in detail the theme of the predictive and explanatory power of the principle of minimum assumption. I showed that one can infer from this principle, and without the need for any further hypotheses, a number of cosmic phenomena that have hitherto eluded explanation. The selected examples were the expansion of space, the occurrence and detailed structure of the spiral nebulae, and the familiar observation that every large accumulation of inertial mass is the source of a gravitational field.

References
1   R. 0. Kapp, Science versus Materialism, London, 1940, Chapters XXII and XXV; Facts and Faith, London, 1955

 

Acknowledgement
This paper and any subsequent discussions and rejoinders are reproduced from the British Journal for the Philosophy of Science with the kind permission of the Oxford University Press.
Website home page:
http://bjps.oxfordjournals.org/

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