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Philosophy of Physics in General Physics Courses

Erwin Marquit

School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455

(Received 25 April 1997; accepted 28 February 1979)

 

 

[ABSTRACT] General physics textbooks usually introduce fundamental concepts on the basis of controversial philosophical outlook—usually one or another form of philosophical empiricism—without indicating this either to the student or the instructor. The philosophical approaches in a number of currently used textbooks are examined critically from a dialectical materialist viewpoint.

 

 

One of my colleagues, when invited to speak to a philosophy class on his philosophy of physics, replied that he did not use any philosophy at all. His reply reflects a view probably shared by most American physicists that philosophy is irrelevant to physics, be it teaching or research. Nevertheless, textbooks in physics invariably have a philosophical content whether or not the authors are conscious of it, and the students are usually exposed to this philosophy without being so informed, even in cases where the authors may be well versed in the philosophy of physics. In this way students are taught possibly highly controversial philosophical viewpoints with no indication that there are alternative outlooks.

The most commonly encountered philosophical viewpoint in textbooks used in the United States is that of logical positivism, which appears primarily through the use and interpretation of operational definitions. There has recently developed a marked tendency among philosophers of science to move away from logical positivism to other forms of philosophical empiricism and this shift too is reflected in recent books, but often in an eclectic manner. In what follows, we will discuss the relevant aspects of the philosophies encountered and consider their implications for the exposition of physics as a science.

OPERATIONALISM, LOGICAL POSITIVISM, AND EMPIRICISM

In the second paragraph of the first page of the well-known textbook of Halliday and Resnick, Fundamentals of Physics, the definition of physical quantities is discussed in the following way:

One view is that the definition of a physical quantity has been given when the procedures for measuring that quantity are specified. This is called the operational point of view because the definition is, at root, a set of laboratory operations leading to a number with a unit.

These two sentences contain some of the most basic philosophical ideas of the logical positivist approach to physics. Although the attention of the students (or of the instructor) is not drawn to this at all, the authors were certainly aware of the full implications of the philosophical views thus expressed. In Sec. 13 of Halliday’s Intro­ductory Nuclear Physics² we find the following exposition of the connection between logical positivism and operationalism:

In nuclear physics, as in all branches of science, a unified point of view is desirable. One that is accepted by some, but by no means all, scientists today is logical positivism whose founding father was the Austrian physicist Ernst Mach. It was developed in its modern form largely by the members of the so-called Vienna Circle. It is no coincidence that this development took place during the period that saw the rise of relativity theory and the quantum. In our own country important contributions have been made by P. W. Bridgman of Harvard University. Here are its main features:

1. Quantities such as the charge, temperature, mass, and length of a body are not thought of as things whose nature is intuitively understood; they are defined as the objective results of certain prescribed operations that can be carried out in the laboratory. ‘Length of a rod’ has meaning in this view; ‘length’ as an abstract concept is of less interest. This operational viewpoint is the basis of this philosophy.

2. Physical laws are relationships between operationally defined quantities that always occur when certain experiments are performed. Laws may be expressed in symbols that are not defined directly in an operational way (the wave function for example). However, it must be possible to deduce operationally definable quantities from these symbols in a logical way.

3. It is the role of theory to give, on the basis of as few hypotheses as possible, a simple description of as many experiments as possible. The question of the ultimate truth of the hypotheses simply does not arise.

4. Theories and hypotheses may be replaced at any time by more useful ones, i.e., by ones that describe more experiments or that describe the same experiments in a simpler way . . . .

A positivist, committed as he is to operationalism, sees no way to decide whether a given theory or hypothesis represents ‘absolute truth’ or not. As a result he tends to discard such a concept. His goal is to describe as compactly as possible the sense perceptions that come (or that can be made to come) within his experience. . .

I am not suggesting that Halliday and Resnick deliberately hid the philosophical content outlined above. There are advantages to introducing a discipline within what the authors believe to be a consistent logical framework. In this way one can move the students quickly into the subject matter and familiarize them with fundamental concepts and, at the same time, lay a basis for subsequent critical reexamination of the assumptions underlying the conceptual framework. I question, however, whether it is advisable to do this in a college-level general physics course, which, for many students, will be the only opportunity for discussion of the conceptual framework of physical theories. In most textbooks, Halliday and Resnick included, this critical reexamination never takes place. The qualifying phrase “one view” in Halliday and Resnick is quite likely to pass by the notice of a reader without evoking the clement of caution it implies, especially since the nature of the other views is not discussed. We thus find that the philosophical approach of the authors is never allowed to come under scrutiny and becomes inseparable from the students’ knowledge of physics. Authors of textbooks also have to bear in mind the fact that at present few physicist-instructors are equipped to discuss such topics without guidance from the texts.

It is not our purpose here to offer a thorough critique of the philosophical views of Ernst Mach and logical positivism.³ But it will be useful to consider some criticism of operational definitions, since it is in this form that the student of a general physics course first encounters logical positivism in the physics classroom.

In discussing operational definitions, Mario Bunge notes:

When applied to the case of the electric field strength E this dogma holds that E acquires a physical meaning only when a procedure for measuring the values of E is prescribed. But this is impossible; measurements allow us to determine only a finite number of values of a function, and moreover they yield only rational or fractionary values. Besides, the numerical value of a magnitude or physical quantity is only one constituent of it. For example, the concept of electric field is, mathematically speaking, a function and therefore it has three ingredients: two sets (the domain and the range of the function) and the precise correspondence between them. A set of measured values is only a sample of the range of the function. Unless one has a fairly well-rounded idea of the whole thing one would not even know how to go about taking such a sample. That is, far from assigning meanings, measurement presupposes them.

Moreover, the measurements of the value of E are always indirect: fields are accessible to experience only through their ponderomotive actions. What is more, there are many ways of measuring values of E. Hence if every one of them were to determine one concept of electric field strength, we would have a number of different concepts of electric field rather than the single concept entering Maxwell^’s theory.⁴

In a discussion along similar lines, Hempel⁵ points out that the use of two different microscopes for determining the length of bacteria would have to count as determining two different kinds of length, since ^.the operations would be different to some extent. “Thus,” says Hempel, “the operationalist maxim under discussion would oblige us to countenance a proliferation of concepts of length, of temperature, and of all other scientific concepts that would not only be practically unmanageable, but theoretically endless.”

Elsewhere,⁶ Hempel raises another important objection to operational definitions. He notes that operational definitions are conceived as requiring a characteristic observable response under specified test conditions. Hence an operational definition of a concept such as mass, temperature, or charge would have to be understood as ascribing the concept to all those cases that would exhibit the characteristic response if the test conditions should be realized, since physical bodies have masses, temperatures, charges and so on even at times when these magnitudes are not being measured. Hempel then argues that to attribute a disposition to exhibit a certain characteristic response to a case in which the specified test condition is not realized (e.g., to attribute solubility-in-water to a lump of sugar that is not actually put into water) is to make a generalization, and this involves an inductive risk. “Thus,” says Hempel, “the application of an operationally defined term to an instance of the kind here considered would have to be adjudged not ‘safe^’ in precisely the same sense in which Bridgman (who first introduced operational definitions—E.M.) insists it is ‘not safe’ to assume that two procedures of measurement that have yielded the same results in the past will continue to do so in the future . . . . [I]f we were to reject any procedure that involves an inductive risk, . . . the use of dispositional concepts would, in effect, be prohibited.”

Despite his effective criticism of operationalism, Hempel still shares much of the empiricism to which operationalism is rooted. Empiricism, roughly speaking, holds that the source of all knowledge is sensory experience—directly, or indirectly through, say, measurement. Empiricists often divide sciences into two major groups: empirical sciences (natural and social sciences such as physics, chemistry, biology, sociology, economics) and nonempirical sciences or sciences of abstraction (such as logic and pure mathematics). The emphasis which modern empiricists place on the logical structure of scientific knowledge has greatly reduced the dependence of modern sciences on unscientific speculative and intuitive methods. There are many schools of empiricism and it is impossible here to deal adequately with its various forms. In general, however, we can say that the empiricists are concerned with the manifestations of the “behavior” of matter (e.g., instrumental operations in the case of operationalists, “disposition to exhibit a certain characteristic response under specified test conditions” in the case of Hempel). Empiricists tend to focus attention on relationships and correlations among these manifestations rather than seek sources of internal development and change which give rise to the manifested behavior.

DIALECTICAL MATERIALISM

In building a wall between the sciences of the physical (or material) world and those of the abstract mental world, empiricists, to a greater or lesser extent, ignore or downplay the social and historical roots of the latter. This leads them to undervalue the contribution of conscious mental or theoretical activity to the process of acquiring an understanding of the physical world. Such mental or theoretical activity, in combination with practical activity or experiments producing changes in the physical world, are inseparable elements of the process by which we acquire knowledge.

This interconnection between human theoretical and practical activity (practice in the broad meaning includes experiment) is an intrinsic part of the general philosophical system developed by Karl Marx and elaborated together with his co-worker Frederick Engels. This system is most commonly referred to by the name Marxism, all the more so since Engels attributed to Marx the greater part of its leading principles.^? Since the term Marxism is also used to refer to Marx’s social, political, and economic thought, the term dialectical materialism is often used to describe the general philosophical system of Marxism.

In contrast to empiricists, Marxists regard matter and not experiment or experience as the ultimate source of knowledge—hence the term materialism. The term dialectical is used to describe the way Marxists view processes of change. The main features of the dialectical view are as follows. All things are universally interconnected in a continuous process of change and development. The changes are a consequence of interaction or interpenetration of opposing or contrary tendencies of quantitative and qualitative character—changes in quantity leading to changes in quality and vice versa; in this, some aspects of the old are retained in the new, while others are destroyed or vanish, so that changes are not viewed as cyclical, but rather as processes of development. These dialectical characteristics are considered to apply equally to the physical (or natural) world, to the social world (the latter being a special form of the former), and to the mental world (the mind being regarded as thinking matter). As in the case of the dialectical system of Hegel, Marx viewed the development of thought as subject to the same general dialectical principles as developments in nature and society. But Marx noted:

My dialectic method is not only different from the Hegelian, but is its direct opposite. To Hegel, the life-process of the human brain, i.e., the process of thinking, which under the name of ‘the Idea,’ he then transforms into an independent subject, is the demiurgos of the real world, and the real world is only the external, phenomenal form of the ‘the Idea.’ With me, on the contrary, the ideal is nothing else than the material world reflected by the human mind, and translated into forms of thought.⁸

For Marx, however, the starting point of theory is not the material world, but idealized abstractions and general relations among these abstract concepts, although the concrete material world is the source of these concepts or abstractions. The properties of matter are then abstracted in idealized form to become building blocks for the theoretical description of the concrete world outside us. For example, there is no real object that can be called a perfect or ideal square in the sense of Euclidean geometry, but we make use of the ideal square in theory. Theoretical elaboration then consists of adding and combining increasing numbers of abstractions and general relations. “[T]he method of rising from the abstract to the concrete,” wrote Marx, “is the only way in which thought appropriates the concrete, reproduces it as the concrete in the mind.”⁹ Elaboration of a theory requires, of course, a logical apparatus. The basic dialectical materialist view of the source of logic is “the practical activity of man had to lead his consciousness to the repetition of the various logical figures thousands of millions of times in order that these figures could obtain the significance of axioms.”¹⁰

To a dialectical materialist the study of physics is the study of matter in its various forms and its interactions giving rise to change or development. Since matter itself is the ultimate source of all knowledge, it cannot be defined in a closed way. But the properties of matter can be elaborated through a never-ending series of abstractions, which at any given time only approximately and conditionally grasp its true nature. Given any particular form of matter, say, a particle such as the electron, our knowledge of its properties is always incomplete; any sample of matter has its history, its origin in other forms of matter which can never be investigated to completion: “The electron is as inexhaustible as the atom, nature is infinite.”¹¹

CRITIQUE OF PHYSICS TEXTBOOKS

The empiricist influence often finds its expression in the opening lines of physics textbooks. “Physics has been called the science of measurement,^” begin Sears, Zemansky, and Young.¹² Weidner and Sells¹³ begin similarly: “Physics is the fundamental experimental science.” On the other hand, Classical and Modern Physics by Kenneth W. Ford begins with an approach quite consistent with a dialectical materialist position: “Physics, once called natural philosophy, is the discipline of science most directly concerned with the fundamental laws of nature.”¹⁴ Ford then refers to physics also as “the study of matter and motion” and as “the study of matter and its interactions.”

It is characteristic of many books to begin the study of physics not with matter, but with units of length and time. Examples of this are Halliday and Resnick; also Sears, Zemansky, and Young. The students are not informed that concepts of length and time are meaningless in the abstract, that they are closely related to, and dependent on, the existence of matter in some form (as material bodies or fields).

Space and time can be introduced as modes of existence of matter. Thus, before considering standards of length, one can discuss, for example, the concept of space qualitatively as an expression of the coexistence and separateness of things, their extent and order of their disposition in relation to one another. The concept of time should also be introduced qualitatively. Actually, it is not unusual to find elements of qualitative discussion of time in the textbooks. Halliday and Resnick indicate that any phenomenon that repeats itself can be used as a measure of time (p. 4). Ford too writes “The idea of time is essentially an idea of periodic repetition” (p. 24). But a dialectical materialist sees the essential feature of time as its relationship to processes of development and change, which are, in general, nonrepetitive. The concept of time characterizes the sequence of the occurrence of material processes, the separateness of the various stages of these processes, their duration and their development. It thus becomes necessary to distinguish between the philosophical categories¹⁵ of quantity, quality, and measure, the last serving to unite the first two. It is not time, but the measure of time that is derived from the cyclical processes. Thus space and time are found to have a much richer content than one obtains by merely specifying the operations by which units of space and time are determined.

As we probe various physical concepts we find that, as in the case of space and time, we encounter both qualitative and quantitative features. The qualitative and quantitative characteristics never exist in isolation from one another, but the current practice of physics textbooks usually is to put the full stress on the quantitative side. (Unfortunately, we seem to be locked into the term physical quantity.)

Differences around the question of fundamental physical quantities serve as another illustration of philosophical difficulties. In Halliday and Resnick we read: “Physical quantities are often divided into fundamental quantities and derived quantities. Such a division is arbitrary in that a given quantity can be regarded as fundamental in one set of operations and as derived in another” (p. 1). If, like the logical positivists, one is not interested in physical properties, but only in correlating numerical data, nothing can ever be more fundamental than anything else. One is reminded of Mach’s praise of Fourier’s equation of thermal conduction: “Fourier’s theory of thermal conduction may be termed a model physical theory. It is not based on a hypothesis but on an observable fact, namely, that the rate of equalization of small temperature differences is proportional to the differences themselves” (cited by Bunge,¹⁶ who added that the equation was praised because it does not tell what heat is or why it flows, but is instead limited to telling how it flows”). This stress on viewing physics as the search for phenomenological correlations, rather than the essential properties of matter which manifest themselves in the phenomena, is clearly seen in the book by Melissinos and Lobkowicz, Physics for Scientists and Engineers: “In the most abstract sense, physics is the science that correlates a set of experimental observations with the results of other observations, either made or yet to be made.”¹⁷ Melissinos and Lobkowicz even follow the practice Dirac introduced in his treatment of quantum mechanics and use the term physical observable in place of physical quantity. Like Halliday and Resnick, they adopt the position that the choice of fundamental “observables” is arbitrary (p. 8).

Sears, Zemansky, and Young also have their initial focus on defining a physical quantity by means of a “set of rules for calculating it in terms of other quantities that can be measured” (p. 1). They do, however, try to move away from the logical positivist position of the book of Halliday and Resnick by not asserting the arbitrariness of the division between fundamental and derived quantities: “The defi­nition of velocity is given in terms of length and time, but there are no simpler or more fundamental quantities in terms of which length and time may be expressed. Length and time are two of the indefinables of mechanics.” But continuing, Sears, Zemansky, and Young also reduce physics to the results of measurements when they state: “The rule of measuring an indefinable takes the place of a definition.” A similarly eclectic position is taken by Zafiratos in his textbook Physics. On the one hand he recognizes the need for fundamental quantities: “A certain bare min­imum of the above quantities must be fundamental quantities, which are not derived from others.”¹⁸ However, unlike Halliday and Resnick, he avoids reference to the arbitrariness or nonarbitrariness of the physical quantities to be so designated and simply states: “The commonly used fundamental quantities in mechanics are length, mass, and time.” He then goes into operationalism by adding: “The quantities are defined by operational definitions” and then back to pure logical positivism when, after giving an ex-ample of a definition of the second by means of a simple pendulum, he writes: “In this manner the romantic, philosophical question, ‘What is time?’ is ignored in favor of a definition so that we can get on with the study of motion.”

There are some books which avoid the usual operationalist language in their introductory material, but introduce precursors of these concepts and then fill in the operation­alism later on. An example of this is Tipler’s Physics, where physical quantities are introduced in discussions of their measurement by comparison with standards.¹⁹ For example, Tipler introduces the concept of space (distance) by discussing the measurement of length: “The most elementary measurement is probably that of distance. In order to measure the distance between two points we need a standard unit, e.g., a meter stick or a ruler.” And so on (p. 5). He waits until the discussion of Newton’s laws before developing the concept of operational definitions. “To understand Newton’s laws fully and be able to apply them we must define these words carefully. This we do by outlining methods for their measurement, in what is called an operational definition” (p. 81). He then proceeds to do this by describing the motion of a block of wood or metal on a horizontal surface (a table) and then extrapolates to the case of an ideal smooth surface.

We thus define the situation in which there are no (horizontal) forces acting on the body. If there are no forces acting on the body, the velocity of the body remains constant. This is Newton’s first law, the law of inertia. . . . The significance of the first law, or law of inertia, is that it defines, by an operational means, what we mean by saying there is no net or resultant force acting upon an object. (pp. 81–82)

There is, however, no place accessible to us where there is a complete absence of forces acting on a body, so that the condition of uniform velocity predicted by Newton’s first law cannot, in fact, be tested operationally. P. W. Bridgman introduced the concept of operational definitions precisely so that testing criteria could be applied in actual practice. We have already seen Bunge’s and Hempel’s objections to Bridgman’s conceptions. Tipler’s concept of operationalism is far more vulnerable to the same criticisms.

The operationalist approach to physical laws results, in fact, in the loss of much of the significance of Newton’s first law. For example; Newton’s first law qualitatively establishes the concept of force as that something external to the body which is necessary to change the velocity of the body; in other words it asserts that the change in motion has a cause and that this cause is external to the body. The first law has other significance which cannot be seen from the versions of the law cited in any of the textbooks to which reference has been made. For example, Halliday and Resnick give the following translation of Newton’s first law:

Every body persists in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed on it (p. 62).

All the textbooks mentioned, except Weidner and Sells, have similar versions with the word unless used to translate the phrase nisi quatenus in Newton’s original Latin formulation.²⁰ This phrase does not mean unless, but except in so far as. (Weidner and Sells give an entirely different form of the law, but with the meaning of unless.)

At first glance, it may seem that to make a distinction between the two ways of translating nisi quatenus is simply hair-splitting. Indeed, the difference is subtle. The first law tells us that in the presence of a force, the motion of a body changes out of its previous state of uniform straight-line motion. But the term unless gives us no indication of the existence of a law-governed relationship between the new state of motion and the old, although it does not preclude the existence of such a relationship. Without an explicit statement of the existence of such a relationship, the first law would not be a statement of causality in mechanics, as it is generally considered to be. The phrase except in so far as does imply the existence of quantitative (and also qualitative) connection between the new state and the old state of motion. This quantitative element is not present in the expression unless. The assertion of a quantitative connection then implies a determinable relationship between the force and the change in velocity, a relationship which is elaborated in the second law. The first law itself thus constitutes an almost complete causality principle,²¹ the second law being required to complete this. It thus turns out that the operationalist preoccupation with measurements and quantitative correlations not only results in the neglect of qualitative properties, but also results in the loss of some quantitative aspects of the first law as well, this loss being connected with the insensitivity to the loss of meaning resulting from the use of the word unless for the Latin nisi quatenus.

The discussion so far has been conducted from the vantage point of the philosophical system of dialectical materialism. A philosophical system cannot be a substitute for the science of physics, but it can serve as a methodological guide for scientific investigation and exposition. Dialectical materialism is not a dogma, and dialectical materialists do not claim any monopoly on access to scientific knowledge. When other methodological approaches are successful in expanding our scientific horizons, it may turn out that modifications are needed in the way one comprehends dialectical materialist methodology. Instances of this kind have occurred in the area of quantum mechanics. More often, however, such other methodologies are not part of a well-elaborated philosophical system and contain elements in common with dialectical materialism. The textbook of Ford, which we have already discussed, was not written from the viewpoint embraced by a comprehensive philosophical system. Ford’s book does reflect a basically materialist viewpoint and although Ford relies on operational definitions, he utilizes an essentially dialectical approach to them in that he does not introduce operationally defined physical quantities independently of the laws that embrace them. “It is not possible,” writes Ford, “to set down precise definitions of all or even most of the important concepts of physics at one time and then build the theories of physics upon these, a technique that might seem appealing from a logical point of view. This is so because the concepts cannot be divorced from its laws” (p. 23). Ford’s position is incompatible with the already ‘cited logical positivist position outlined by Halliday: “Physical laws are relationships between operationally defined quantities that always occur when certain experiments are performed.” In fact, Ford’s position reflects the dialectical concept of inseparable unity of theory and experiment. Thus Ford writes, “How can we be sure that the time intervals between successive cycles of a clock’s repeating motion are the same? We cannot . . . . Time, like every other concept, cannot escape to a status independent of the laws in which it is employed” (p. 26). It is in this context that Ford considers as an operational definition the comparison of time intervals with a cesium clock as a standard. But is a far cry from the logical positivism expressed, say, in Zafiratos’s rejection of what he called the “romantic philosophical question ‘What is time?’”

It thus becomes clear that any discussion of fundamentals of physics cannot avoid dealing with the most crucial question facing the schools of philosophy. As Cornforth put it, “Either we regard scientific theory as knowledge of the objective material world, or else we regard it merely as a set of useful rules summing up the orders in which data of various sorts are presented to us in experience” (p. 227).

SUGGESTIONS FOR DEEPENING CONCEPTUAL CONTENT

To conclude this discussion it would seem worthwhile to outline some suggestions that could enhance the conceptual content of a general physics course.

It would not be practical to attempt a philosophical discussion of the kind presented here as part of a lower-level general physics course. But the students should be exposed to a discussion which provides a clue to the contrasting viewpoints we have been considering. The introductory material should deal with the following questions: What is the subject matter of physics? How do we come to know it? What is the relation of physics to the other sciences and to technology? How do we abstract the concepts of physics from the material world without rupturing the ties that permit theoretical conclusions to find their realization in the physical world? As regards this last question, it would be useful to discuss the relationship between geometrical figures as abstract concepts and as properties of material bodies.

I think it is essential to introduce the notion of physical space as a variable property of matter and the concept of time as a characterization of the sequence of occurrence of processes. To do this very early in the course will deepen the students’ appreciation of the qualitative aspects of physical properties. The classical concepts of space and time can then be presented immediately as a first level of approximation, thus introducing no impediments to the later introduction of relativistic and quantum-mechanical concepts.

Particle kinematics immediately provides another opportunity for demonstrating the technique of idealization and abstraction by consideration of cases in which the extent of a body plays a negligible role in its motion, that is, where its size is much smaller than the scale of motion. In this way we can demonstrate the usefulness of the concept of a material point whose sole property of significance is its motion in a coordinate system fixed to a reference body. While physics textbooks usually introduce the concept of a material point as an abstraction (although not necessarily using the same words), it is usually done so within the framework of absolute space and time. With the introduction of particle kinematics on the background of matter-dependent concepts of space and time, we find ourselves dealing with a simple description involving at least seven general philosophical categories: matter, motion, quantity, quality, space, time, and measure (not to mention the specialized categories of physics and mathematics), whereby no category exists autonomously, but all are joined together in a single conceptual framework reflecting what dialectical materialists refer to as the unity of the world.

Finally, it is important to note that if matter is to be taken as the ultimate source of our ideas about it, then it cannot be defined, but only its properties elaborated. This is the task not only of physics, but of all science.

NOTES

¹David Halliday and Robert Resnick, Fundamentals of Physics, revised printing (New York: Wiley, 1974), p. 1. Henceforth, page references to this textbook will appear in parentheses in the text. The same practice will be followed for other books cited.

²David Halliday, Introductory Nuclear Physics, 2nd ed. (New York: Wiley, 1955), pp. 4, 5.

³For a critique of logical positivism in physics. see, for example. Mario Bunge, Philosophy of Physics (Dordrecht, Holland: Reidel, 1973), chap. 1. For a Marxist analysis of logical positivism, see Maurice Cornforth, Science and Idealism (New York: International, 1947), chaps. 10–12. The philosophical view of Mach and his followers is the subject of Lenin’s Materialism and Empirio-Criticism, in Collected Works, vol. 14 (Moscow: Progress Publishers, 1972).

⁴Mario Bunge, note 3, p. 10.

⁵Carl G. Hempel, Philosophy of Nature (Englewood Cliffs, NJ: Prentice-Hall, 1966), p. 94.

⁶Carl G. Hempel, Aspects of Scientific Explanation (New York: Free Press, 1965), p. 126. From an article by Hempel first appearing in Scientific Monthly 79, 215–20 (1954).

⁷Frederick Engels, “Ludwig Feuerbach and the End of Classical German Philosophy,” in Karl Marx and Frederick Engels, Selected Works in Three Volumes (Moscow: Progress Publishers, 1970), vol. 3, footnote by Engels on p. 361.

⁸Karl Marx, Capital. Afterword to the 2nd German edition (New York: International, 1967), vol. 1, p. 19.

⁹Karl Marx, Grundrisse (New York: Vintage, 1973), p. 101. For a discussion of Marx’s method and serious misinterpretations of it in the translator’s Foreword to this edition. see my “Nicolaus and Marx’s Method of Scientific Theory in the Grundrisse,” Science and Society 41, 465–76 (1977–78), and erratum (to be published [42 (1978): 381)—erratum details added by author in 2008].

¹⁰V. I. Lenin, Philosophical Notebooks. Collected Works. Vol. 38 (Moscow: Progress Publishers, 1972). pp. 2–190.

¹¹V. I. Lenin, Materialism and Empirio-Criticism, Collected Works, Vol. 14 (Moscow: Progress Publishers, 1972), p. 262.

¹²Francis W. Scars, Mark W. Zemansky, and Hugh D. Young, University Physics. 5th ed. (Reading, MA: Addison-Wesley, 1976), p. 1.

¹³Richard T. Weidner and Robert L. Sells, Elementary Classical Physics (Boston: Allyn and Bacon, 1973), vol. 1, p. 1.

¹⁴Kenneth W. Ford. Classical and Modern Physics (Lexington, MA: Xerox College, 1972), Vol. 1 and Z. p. 3.

¹⁵The most general, fundamental concepts of philosophy are called categories. In his treatise On Categories, Aristotle listed ten categories (Plato had five): substance, quantity, quality, relation, place, time, position, state, action, and passion. Since then, many alternate systems of categories have been proposed. Dialectical materialism places no limit on the number of categories, but does distinguish between general categories of philosophy relevant to the entire sphere of thought (e.g., matter. motion, quantity, quality, space. time, etc.) and categories of the specialized sciences (e.g.. in physics: mass, temperature. charge). For fuller discussion, see Konstantinov et al., Fundamentals of Marxist-Leninist Philosophy (Moscow: Progress Publishers, 1974), chap. 6.

¹⁶Mario Bunge, Causality (Cleveland: Meridian, 1963), p. 77.

¹⁷Adrian C. Melissinos and Frederick Lobkowicz, Physics for Scientists and Engineers (Philadelphia: Saunders, 1975), vol. 1, p. 3.

¹⁸Chris Zafiratos, Physics ((New York: Wiley, 1976), pp. 3, 4.

¹⁹Paul A. Tipler, Physics ((New York: Worth, 1976).

^2Olsaac Newton. “The Mathematical Principles of Natural Philosophy,” in Sir Isaac Newton’s Mathematical Principles edited by F. Cajori (Berkeley: University of California, 1946), p. 644.

²¹The sense of a causal principle is given by Bunge as follows: If C happens, then (and only then) E is always produced by it. See Bunge, Causality, p. 47. Newton’s first law can also be viewed as establishing a measure for time. For discussions of this see A. d’Abro, The Evolution of Scientific Thought from Newton to Einstein (New York: Dover, 1927) and my paper, “Mechanism and the Unity of Matter, Space, and Time in Classical Mechanics,” Revolutionary World: An International Journal of Philosophy (to be published [in vol. 33, 1979, pp. 71–84—publication details added by author in 2008]).