Concepts of Force

Concepts of Force

by Max Jammer

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"Professor Jammer's book traces the rise of force from the primordial 'nht' in Egyptian antiquity through its zenith as the central element of physical reality in classical mechanics to its near demise under modern criticism … a veritable tour de force … To read Concepts of Force is to gain a new and profound understanding of force and dynamics."

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"Professor Jammer's book traces the rise of force from the primordial 'nht' in Egyptian antiquity through its zenith as the central element of physical reality in classical mechanics to its near demise under modern criticism … a veritable tour de force … To read Concepts of Force is to gain a new and profound understanding of force and dynamics." — R. T. Weidner, Physics Today
Both a historical treatment and a critical analysis, this work by a noted physicist takes a fascinating look at one of the fundamental and primordial notions in physical theory, the concept of force.
Tracing its development from ancient times to the twentieth century, the author demonstrates how Kepler initiated the scientific conceptualization of the idea of force, how Newton attempted a clear and profound definition, and how post-Newtonian physicists reinterpreted the notion — contrasting the concepts of Leibniz, Boscovich, and Kant with those of Mach, Kirchhoff, and Hertz. In conclusion, the modern trend toward eliminating the concept of force from the conceptual scheme of physical science receives an in-depth analysis.
Philosophically minded readers interested in the basic problems of science will welcome this volume, as will historians of science and physicists who wish to better understand the historical and epistemological foundations of their discipline. Saluted by Science as "an excellent presentation," and by The British Journal for the Philosophy of Science as "a highly stimulating and informative study," Concepts of Force offers an unsurpassed treatment of a vital subject. 1962 edition.

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<:st> Reprint of the classic Harvard University Press edition of 1957 (which is cited in ) Annotation c. Book News, Inc., Portland, OR (

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Dover Publications
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Dover Books on Physics Series
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A Study in the Foundations of Dynamics


Dover Publications, Inc.

Copyright © 1999 Max Jammer
All rights reserved.
ISBN: 978-0-486-15056-7



The purpose of the present study is a presentation of the historical development of the concept of force in physical science. Though recognized as one of the fundamental and primordial notions in physical theory, the concept of force, it seems, has never heretofore been the object of a comprehensive historical analysis and critical investigation. In general, the concept is taken for granted and considered as sanctioned by its successful applications. In fact, standard textbooks, and even elaborate treatises, present little information, if any, on the nature of this concept; its problematic character is completely ignored in the maze of practical utilizations.

The argument, often heard, that the scientist is little concerned with the history of the concepts which he applies in his work, has lost much of its strength in view of the importance that modern physics attaches to concept-formation. Once held as a monopoly of antiquarian historians of science and of pedantic epistemologists, the problem of concept-formation in scientific theory gained vital importance and notable prominence in modern research.

The study of the historical aspects of concept-formation in physical science is admittedly no easy task. In addition to a thorough historical and philological training, necessary for a skillful command of the source material, it requires comprehension of physical theory, instrumental for the critical comparison and interpretation of the sources under discussion and indispensable for the evaluation of their significance for science as a whole.

A serious difficulty in the study of the development of a scientific concept lies in the necessarily inherent vagueness of its definition. This complication arises from the fact that the concept in question finds its strict specification only through its exact definition in science. This definition, however, historically viewed, is a rather late and advanced stage in its development. To limit the discussion to the concept thus defined means to ignore a major part of its life history. The history of a concept has not yet run its course, it is true, even once it has achieved such a "defined" position, since it attains its complete meaning only through the ever-increasing and changing context of the conceptual structure in which it is placed. However, from the standpoint of the history of ideas, the most interesting and important part of its biography is passed, namely the period of its vigor and creative contribution to the advancement of scientific thought. When studying the development of a scientific concept one has, therefore, to cope with an essential vagueness of definition of the subject under discussion and one faces equally the danger of either drawing the limits too narrow or too wide.

As a result of modern research in physics, the ambition and hope, still cherished by most authorities of the last century, that physical science could offer a photographic picture and true image of reality had to be abandoned. Science, as understood today, has a more restricted objective: its two major assignments are the description of certain phenomena in the world of experience and the establishment of general principles for their prediction and what might be called their "explanation." "Explanation" here means essentially their subsumption under these principles. For the efficient achievement of these two objectives science employs a conceptual apparatus, that is, a system of concepts and theories that represent or symbolize the data of sense experience, as pressures, colors, tones, odors, and their possible interrelations. This conceptual apparatus consists of two parts: (1) a system of concepts, definitions, axioms, and theorems, forming a hypothetico-deductive system, as exemplified in mathematics by Euclidean geometry; (2) a set of relations linking certain concepts of the hypothetico-deductive system with certain data of sensory experience. With the aid of these relations, which may be called "rules of interpretation" or "epistemic correlations," an association is set up, for instance, between a black patch on a photographic plate (a sensory impression) and a spectral line of a certain wavelength (a conceptual element or construct of the hypothetico-deductive system), or between the click of an amplifier coupled to a Geiger counter and the passage of an electron. The necessity for physical science of possessing both parts as constituents results from its status as a theoretical system of propositions about empirical phenomena. A hypothetico-deductive system without rules of interpretation degenerates into a speculative calculus incapable of being tested or verified; a system of epistemic correlations without a theoretical superstructure of a deductive system remains a sterile record of observational facts, devoid of any predictive or explanatory power.

The adoption of rules of interpretation introduces, to some extent, an arbitrariness in the construction of the system as a whole by allowing for certain predilections in the choice of the concepts to be employed. In other words, arbitrary modifications in the formation of the conceptual counterparts to given sensory impressions can be compensated by appropriate changes in the epistemic correlations without necessarily destroying the correspondence with physical reality. In consequence of this arbitrariness, scientific concepts "are free creations of the human mind and are not, however it may seem, uniquely determined by the external world."

When science attempts to construct a logically consistent system of thought corresponding to the chaotic diversity of sense experience, the selection of concepts as fundamental is not unambiguously determined by their suitability to form a basis for the derivation of observable facts. In the first place, some element of contingency is introduced by the somehow fortuitous sequence of experimentation and observation, an idea recently emphasized by James Bryant Conant: "It seems clear that the development of our modern scientific ideas might have taken a somewhat different course, if the chronological sequence of certain experimental findings had been different. And to some degree, at least, this chronology can be regarded as purely accidental." In the second place, a certain climate of opinion, conditioned by subconscious motives, is responsible to some extent for the specific character of the basic conceptions or primitive concepts. It is a major task of the historian of science to study this climate of opinion prevailing at a certain period and to expose the extra-scientific elements responsible for the finally accepted choice of those concepts that were to play a fundamental role in the construction of the contemporaneous conceptual apparatus. The history of science can often show in retrospect how alternative concepts have, or could have, been employed at the various stages in the development of the physical sciences in a provisionally satisfactory manner.

Let us illustrate this point by an example that has some importance for our subject: the Jaina physics of ancient Indian philosophy. The Jainas, followers of Jina (Vardhamna), an elder contemporary of Buddha, developed a realistic and relativistic atomistic pluralism (anekntarda), without the slightest allusion to a concept of force, in contrast to Western science in which the idea of force plays, as we shall see later in detail, a fundamental role. In the Jaina physics, the category of ajva is subdivided into matter (pudgala), space (ksha), motion (dharma), rest (adharma), and time (kla). Dharma and adharma designate the conditions of movement and of rest respectively. Being formless and passive, they do not generate motion or arrest it, but merely help and favor motion or rest, like water, which is instrumental for the motion of a fish, or like the earth, which supports objects that rest on it. Essentially it is "time" that originates "activity" (kriya) and "change" (parinma), and it does so without becoming thereby some kind of a dynamic agent, something equivalent to the concept of force in Western thought. A more familiar, but less striking, example of a conceptual scheme that does not employ the notion of force is, of course, the physics of Descartes, which, at least in the view of its propounder, was based only on purely geometrico-kinematic conceptions in addition to the notion of impenetrable extension.

Numerous factors compel the scientist to revise constantly his conceptual construction. Apart from general cultural predispositions, conditioned by specific philosophical, theological, or political considerations, the three most important methodological factors calling for such revisions seem to be: (1) the outcome of further experimentation and observation, introducing new effects hitherto unaccounted for; (2) possible inconsistencies in the logical network of derived concepts and their interrelations; (3) the search for maximum simplicity and elegance of the conceptual construction. In most cases it is a combination of two of these factors, and often even the simultaneous consideration of all of them, that leads to a readjustment or basic change of the conceptual structure. A well-known example is the Michelson-Morley experiment which revealed the independence of the velocity of light with respect to the motion of the earth, a phenomenon unaccounted for and inconsistent with the existing ether theory at the turn of the last century; this effect could have been fitted into the conceptual scheme of that time by certain ad hoc assumptions (the Lorentz contraction) which would, however, lead to serious complications and violate the principle of simplicity. Einstein's ingenious reinterpretations of space and time, expounded in his special theory of relativity, are essentially a revision of the conceptual apparatus of classical mechanics.

A modification of the prevailing conceptual apparatus has not always, of course, to be so drastic and revolutionary as Einstein's theory of relativity. A common feature of great importance for the historian of scientific concept-formation is the process of "redefining" a concept and changing thereby its status and position in the logical texture of the system. A classical example of this process of redefinition is the concept of temperature. Originally taken as a qualitative expression of heat sensation, it became a quantitative notion when defined as a state of matter measured by the scale reading on a mercury thermometer.

When it became apparent, in the further development of this concept, that "temperature" thus defined depended on certain properties of the thermometric substance, it was redefined by the introduction of the so-called "absolute" scale in thermodynamics. Thus it became finally incorporated into a larger and more comprehensive set of relations, forming an integral part of the kinetic theory of matter. It is obvious that by this process the historically and psychologically posterior concept (in the case of "temperature" the kinetic energy of a gas molecule) is treated as the systematically and logically prior, more basic and more fundamental notion.

Not only can concepts which have once been considered as primitive, that is, as basic for nominal definitions of derived concepts, undergo the process of redefinition and thus become derived concepts; although rarely encountered in the history of scientific concept formation, a concept originally classified as derived may, at a later stage, be chosen as primitive for the redefinition of other concepts. Velocity is generally regarded in classical mechanics as a derived concept, namely, as the ratio of the distance s to the time t, or in the limit, as ds/dt, while distance and time are considered primitive concepts. It would, however, be quite conceivable to formulate a consistent theory of motion by taking the concepts of time t and velocity v as primitive, velocity being measured directly by some kind of speedometer, and to regard distance as a derived quantity according to the defining formula s = tv, or more generally s = ?vdt. In fact, modern astronomy, at least to some extent, does this consistently. The assignment of physical dimensions to these concepts is, of course, no obstacle, since their choice, as is shown conspicuously in electromagnetic theory, is wholly arbitrary and can be chosen in complete conformance with the selection of primitive concepts.

As to the concept of force, taken originally in analogy to human will power, spiritual influence, or muscular effort, the concept became projected into inanimate objects as a power dwelling in physical things. Omitting at present some intermediate stages, the concept of force became instrumental for the definition of "mass," which in its turn gave rise to the definition of "momentum." Subsequently classical mechanics redefined the concept of force as the time rate of change of momentum, excluding thereby, at least prima facie, all animistic vestiges of earlier definitions. Finally, "force" became a purely relational notion, almost ready to be eliminated from the conceptual construction altogether.

Now, a serious question may be asked: does not the recurrent process of redefinition imbue our concept for the most part with a succession of essentially new meanings, so that we should no longer be justified in regarding the various phases as belonging to the same concept? The operationalist who claims that the meaning of a concept is identical with the procedure for measuring it would certainly object to having these various phases treated as different modifications of the same notion ; the realist, on the other hand, as well as the advocate of the theory of convergency, for whom scientific statements are more than a complex of mere conventions, would most probably raise no objection. For the historian of science, however, this problem is only a question of words. Not being primarily interested in the problem of reality, that is, in the question how far the internal structure of the hypothetico-deductive system of science reflects or transcribes a possible real substratum underlying the undifferentiated continuum of sensory impressions, the student of the history of ideas stands here on the same footing as the active scientist in his laboratory. Whether his research is a study of the development of one single concept or of a chain of related notions is a completely irrelevant question for him. In other words, whether the various definitions aim at one and the same definiendum as part of the reality which transcends consciousness, or whether each modification of the concept has to be regarded as an independent element of the logical system, is a problem to be left for the metaphysician.

Even in the case of a so-called "formalistic" and contextual method of definition, a concept-formation process that is still more problematic in this respect, the attitude of the scientist is the same. In this process the formation of a concept arises from the constancy of certain experimental relations, whereby the constant value obtained is given a special name. Mach's well-known definition of "mass" is an important example: when two bodies, denoted by the subscripts 1 and 2, are acting on each other under the same external conditions, the constant (negative) inverse ratio of their mutually induced accelerations, (–a2/a1) is given a new name, the "relative mass" of the two bodies or, more precisely, the mass of the first body relative to the second. If, in particular, the second body is a certain standard body ("standard mass"), then the "relative mass" becomes the "mass" of the first body (with subscriptI). It is this highly sophisticated notion of mass that plays the important role in modern physics, both in quantum mechanics (in the determination of the masses of elementary particles) and in the theory of relativity (the dependence of mass on velocity). The earlier, unsophisticated, primitive notion of "moles," "quantity of matter," the mass concept of Kepler and Galileo and to some extent even that of Newton, although exhibiting a much closer linkage to elements of sense impressions, would hardly be compatible with the context in which the more refined, essentially relational, Machian concept is integrated. It is important to note that a formalistic definition need not necessarily be a redefinition; the concept of entropy is an example.


Excerpted from CONCEPTS OF FORCE by MAX JAMMER. Copyright © 1999 Max Jammer. Excerpted by permission of Dover Publications, Inc..
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