In his unfinished work, Dialectics of Nature, Frederick Engels wrote that Hegel, in his laws of dialectics, formulated for the first time in its universally valid form a general law of development of nature, society, and thought. Marx and Engels further demonstrated the power of dialectics by applying it to their analysis of social development. To do so, they had to link Hegel's dialectics to a materialist basis. The resulting dialectical-materialist methodology was further strengthened by Lenin in his philosophical writings. Ignoring Marx's statement in a letter to Kugelmann (27 June 1870) that the dialectical method is the method for dealing with matter, Marxist-influenced philosophers not associated with the Communist movement often claim that a philosophical dichotomy exists between a humanist Marx on the one hand, and the coarse and unfeeling Engels and Lenin, on the other, who erroneously sought to impose dialectics on nature. Characteristically, these philosophers sink into one or another form of philosophical idealism even when claiming to be materialists. This denial of the applicability of dialectics to nature has increased since the collapse of the Soviet Union and other socialist countries.

Many reasons make this question important for Marxists. The most important reason is, as Marx wrote in 1844: "The weapon of criticism cannot, of course, replace criticism of the weapon, material force must be overthrown by material force; but theory also becomes a material force as soon as it has gripped the masses." Lenin, with his concept of a party of the new type, recognized that such a party, guided by a socialist consciousness, was necessary to instill a socialist consciousness in the masses and thus assemble the material force needed to effect a socialist transformation.

To understand this in depth requires an understanding of the relationship between the material conditions of our existence and the way our minds generate an understanding of them. The natural sciences provide a rich source for understanding the basis of this relationship because they make possible the repeated testing necessary to form and confirm our theoretical representation of material reality in the sphere of nature. It is therefore not surprising that as part of the division of labor between Marx and Engels, Engels specialized in part in the natural sciences. Lenin devoted much time to writing and publishing in 1908 his second most extensive major work, Materialism and Empirio-Criticism, because he felt it necessary to counter the idealist philosophy of the Austrian physicist Ernst Mach when Mach's positivist views began to make inroads in the Russian revolutionary movement.

If one accepts the validity of the dialectical-materialist worldview, it is not surprising that dialectical materialists can assert that elements of dialectical-materialist thought are reflected in all advances in human knowledge made by natural and social scientists and other great thinkers whether or not they were consciously aware of this dialectical-materialist content.

To illustrate this, I will start with Hegel himself. At the time he published his Vorlesungen über die Naturphilosophie [Lectures on the Philosophy of Nature] in 1817, Kant's view of the a priori character of space and time was the dominant view. Kant's a priori notion of space and time included their existence independently of their being matter associated with them. Yet Engels was able to cite Hegel's understanding of the dialectical unity of space and time with matter, citing (among others) Hegel's statement that it is "the concept of space itself that creates its existence in matter." (G. W. F. Hegel, Naturphilosophie. Quoted in F. Engels, Dialectics of Nature, ed. (New York: International Publishers, 1940), 343).

Contemporary physics is able to view the path followed by a ray of light in some situations as the criterion for what is considered to be a straight line. According to Einstein's general theory of relativity, first enunciated in 1915, the properties of space and time are shaped by the distribution of matter. This was first confirmed in 1919 when the light from the planet Mercury, bent by the gravitational field of the Sun, became visible from the Earth before the planet had emerged from passing behind the Sun. The contradictory notion of the curvature of straight-line motion was also thereby confirmed.

In 1961, I attended a lecture at the University of Warsaw by Jerzy Plebański, a protégé of the well-known Polish theoretical physicist specialist on relativity theory, Leopold Infeld. At that time, only one of the dozen professors of physics at the University of Warsaw was a member of the Polish United Workers Party. In his talk, Plebański stated that Einstein never relied on results of experimental physics in his formulation of general relativity theory, that Einstein arrived at the theory through aesthetic principles in mathematical physics, unrelated in any way to results of experimental physics. During the discussion period that followed the talk, I rose to point out that the Polish mathematicians, Karol Borsuk and Wanda Szmielew, in their book, Podstaw Geometry [Fundamentals of Geometry], published in 1955, stated that the question of whether Euclidean or the non-Euclidean Lobachesky/Bolyai geometry better describes physical space can be settled, if at all, only by way of experiment. I had been familiar with this point made by Borsuk and Szmielew, because I had discussed it with Professor Borsuk while doing the translation of the book for publication in English in 1960. Plebański's philosophical prejudices were clearly evident in his reply: "Professor Borsuk is a Party member." I then stated that Borsuk had told me that this was the view expressed by the famous German mathematician Bernhard Riemann in his habilitation lecture in 1854 and asked, "Was Riemann also a Party member?"

A striking example of dialectical thought in mathematics is given by the German mathematician Richard Dedekind in what has become known as the Dedekind cut. The concept of continuity in mathematics and mathematical physics is important for determining whether the range of values that can be assigned to a property constitutes a continuous set of values. I will give a simplified description of Dedekind's reasoning. Divide all numbers into two sets, set A being all numbers less than any given number, say the number two, and set B consisting of the number two and all numbers greater than two. Dedekind's criterion for the undivided set's being continuous is that in set A there is no highest number. It is clear that if you mention any number less than two with as many decimal places as you wish, there are numbers with more decimal places greater than that. Hence to establish continuity, Dedekind introduced its opposite, a discontinuity.

I have never seen a university textbook in general physics in the United States that states qualitatively what is meant by energy. The textbooks invariably show only how to calculate the various forms of energy and demonstrate quantitatively the Law of Conservation of Energy. Some years ago, in examining a doctoral candidate during his qualifying examination, I asked him to discuss the concept of energy without reference to any mathematical formulas or specific forms of energy. My two colleagues on the examining committee immediately objected. We had to ask the student to leave the examining room while I established the legitimacy of the question, pointing out that my students in first-year physics could provide the answer.

I had asked the question because Engels, in his Dialectics of Nature, criticized Helmholtz for failing to recognize the deeper import of his 1849 Law of Conservation of Energy, namely "that any form of motion, under conditions fixed for each case, is both able and compelled to undergo transformation directly into any other form of motion." In 1966, Engels's view of the law of conservation of energy as a law of transformation reappeared in a book Six Lectures on Modern Natural Philosophy, by Clifford A. Truesdale, in which the author, clearly not an adherent of dialectical materialism, himself grasped the dialectical character of the concept of energy by stating, "Energy is the measure of the capacity of a system to undergo change." All that is needed to impart a materialist content to this formulation is to add a phrase at the end of it so that it would read: "Energy is the measure of a system to undergo change from one form and motion of matter to another."

Despite his reputation as a mechanist, Isaac Newton was very dialectical in arriving at the laws of motion as he presented them in Latin in his major work, Mathematical Principles of Natural Philosophy, often referred to by the Latin word in its title, Principia.

One U.S. physics textbook, Physics by Paul A Tipler (1976), using the logical positivist concept of operational definitions in its discussion of Newton's First Law of Motion, states that "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." In an article entitled "Philosophy of Physics in General Physics Courses" published in the American Journal of Physics in 1978, I pointed out that there is 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. More importantly, I pointed out that there was a problem with the way Newton's law of inertia was usually translated.

Until recently, what was usually cited by U.S. and British scholars as the standard translation into English of Newton's first law of motion-the law of inertia-was the inaccurate so-called Mott-Cajori translation of the Principia published in 1934 by the University of California Press:

"Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

With the term unless in the English translation and solange in the German, the law states that the body either goes in a straight line or, because of an impressed force, its motion deviates from a straight line. But if one looks at Newton's earlier attempts to formulate the law of inertia throughout the twenty-year period prior to its publication, one finds that he usually used the word cause instead of the word force. At that time, force was considered an intensity; it had not yet been quantified. In his first law, Newton was attempting to express a causality principle that, in its final form, expressed his conclusion that there is a determinable quantitative relationship between the cause and the change, thereby projecting the existence of a law-governed relationship of changes of motion of material bodies. Newton's second and third laws of motion elaborate this law-governedness quantitatively and qualitatively. Law-governedness in the material worlds of society and nature is what Marx revealed in his economic studies and what Engels stressed in his writings on nature. The fact that Newton, twenty years earlier had already written down in English what seemed to be equivalent to the first law, including the word unless, and waited twenty years before publishing it, prompted me to look at Newton's Latin text of the first law, saying to myself, "if only he had said "except insofar as," then he would have had a law-governed causality statement. I found that instead of only the word unless (or nisi in Latin), he had indeed used the phrase nisi quatenus, the term quatenus being a quantitative modifier. Therefore, the law should have been translated

"Every body continues in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed upon it.

I made this point in passing in my 1978 article, but repeated it in a separate article on the subject, "A Plea for a Correct Translation of Newton's Law of Inertia," published in the American Journal of Physics in 1990. A new translation of the Principia by I. B. Cohen and A. Whitman published by the University of California Press, Berkeley, in 1999 that has now become the current authoritative translation now contains the phrase "except insofar as." Many recent U.S. physics textbooks are using this correct translation of the law.

The manner in which Newton arrived at his law of inertia is profoundly dialectical. In his Definition III, in the section entitled "Definitions," he describes how a body's inertia manifests itself when an attempt is made to change its state of motion:

The vis insita or innate force of matter is a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be at rest or of moving uniformly forwards in a right line.

The phrase "as much as it lies" for the first time established the quantitative and qualitative interconnection for the physical property force as a distinctive fundamental category of physics by relating the magnitude of the inertial force to the mass of the body. In the explanation of the law he states: "This force is always proportional to the body whose force it is."

His Definition IV states

An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line.

His commentary on this definition includes the following:

This force consists in the action only, and remains no longer in the body when the action is over.

In this brilliant example of the dialectical relationship of phenomena and essence, Newton asserts that the innate force, that is, the force of inertia, is the phenomenal manifestation of the mass of the body in response to an impressed force. The impressed force, which vanishes when its action is over, exists only in relation to the resistance of the body to a change in motion-that is, its existence is conditioned by the existence of the innate force. Innate and impressed forces are therefore two distinct (i.e., mutually excluding) mutually conditioned forces.

Newton could not complete the quantification of the force until he embraced all of these concepts in the three laws of motion.

I hope these few examples of the dialectical-materialist content of some of the conceptual foundations of physics will encourage others to look at the dialectical-materialist content of the conceptual foundations of other areas of scholarly investigation, in the natural, biological, and social sciences. The Marx-Engels Center being opened here tonight can play a vital role for stimulating such a project, which would underline the continuing relevance of the contributions of Marx and Engels to our understanding of nature, society, and thought.

Erwin Marquit is Professor Emeritus at the University of Minnesota. This article was presented at the opening ceremony of the Marx-Engels Center in Berlin on October 5, 2012. The author was an invited speaker.

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