SOURCE: "The Philosophical Significance of Newton's Science," in The Texas Quarterly, Vol. X, No. 3, Autumn 1967, pp. 201-15.

[In the following essay, Shapere explores the relationship of philosophy and science in Newton's thought, suggesting that Newton approached scientific study in a philosophical manner.]

In a famous passage in the preface to the first edition of his Principia, Newton declared that:

I offer this work as the mathematical principles of philosophy, for the whole burden of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena.… I wish we could derive the rest of the phenomena of Nature [besides those dealt with in this work] by the same kind of reasoning from mechanical principles, for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards one another, and cohere in regular figures, or are repelled and recede from one another.'

Newton's statement is characteristically cautious: the "burden of philosophy" is not described categorically; it only "seems to be.…" Again, he only suspects, on the basis of "many reasons," that his view is correct—phenomena "may all depend upon certain forces," etc. And finally, at the end of the paragraph from which the quoted passage is taken, he notes the possibility that there may be "some truer method of philosophy." In spite of these qualifications, however, and in spite of some more specific uneasiness which, as we shall see later, Newton himself (to say nothing of his contemporaries) felt about the adequacy of this statement as a description of the whole, ultimate burden of philosophy—despite all this, the passage is important for understanding the logic behind the greater part of Newton's own scientific (or "philosophical") reasoning, as well as the problems and approaches of a whole tradition of succeeding thinkers. For in many ways, this passage defines those problems and approaches—that tradition. Besides prefacing a monumental example of "philosophy," reaching specific conclusions, in terms of the motions and forces of particles, about a vast body of "phenomena of Nature," and thus providing "many reasons" for suspecting that the approach may prove successful in other domains, this statement of "the whole burden of philosophy" lays down a program for further work. It establishes at once an ideal or goal of scientific investigation—a picture of what a completed science would look like—and a set of categories in terms of which the attempt to reach that goal should be made. It provides, that is, a statement of the terms in which proper possible ultimate explanations are to be formulated. The phenomena of nature—all of them—are to be approached and explained in terms of "forces" directed radially toward or away from "particles" which (to add a gloss to the passage) are at rest or in motion in an infinite space. And a completed science would be one which explained all the phenomena of nature in terms of the interactions, through such forces, of such particles moving in space. And, finally, the principles of explanation of nature are to be expressed in the language of mathematics, the symbols of which are to be interpreted as standing for the forces, particles, and motions which exist in nature.

More detailed examination of the body of Newton's writings brings out further features of this picture of the aims, language, and subject-matter of science. At the end of the Opticks, Newton suggests, after having presented a number of reasons, that

All these things being consider'd, it seems probable to me, that God in the Beginning form'd Matter in solid, massy, hard, impenetrable, moveable Particles, of such Sizes and Figures, and with such other Properties, and in such Proportion to Space, as most conduced to the End for which he form'd them; and that these primitive Particles being Solids, are incomparably harder than any porous Bodies compounded of them; even so very hard, as never to wear or break in pieces; no ordinary Power being able to divide what God himself made one in the first Creation. While the Particles continue entire, they may compose Bodies of one and the same Nature and Texture in all Ages: But should they wear away, or break in pieces, the Nature of Things depending on them, would be changed.… And therefore, that Nature may be lasting, the Changes of corporeal Things are to be placed only in the various Separations and new Associations and Motions of these permanent Particles.²

Stripped of their theological trappings, these remarks stand out both as a sketch of the "particles" of Nature and as a sketch of units to be appealed to in proper ultimate explanations. For to say that "God in the Beginning form'd Matter" in such a manner is, in part, one way of saying that no further explanation need be sought for the particles and their properties: they are explanatory, not in need of explanation. The assertion of their indestructibility has the same logical force. And, finally, the location of all "Changes of corporeal Things … only in the various Separations and new Associations and Motions of these permanent Particles" tells us what it is that needs to be explained: changes, under which heading must be included qualitative changes, e.g., of color, sound, etc., which are to be explained in terms of the motions (and forces) of particles. (It should also be added that differences of such qualities, e.g., of colors, as well as changes thereof, are to be explained thusly.) Further, as we shall see, the "changes" which are to be explained also include, for Newton, certain types of motions of the particles themselves, while other such types do not (at least in the same sense) require such explanation.³

The "other Properties" with which the particles are endowed are forces; one, a vis inertiae, which Newton equates (Definition III, Principia) with the vis insita:

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 of rest, or of moving uniformly forwards in a right line … this vis insita may, by a most significant name, be called inertia (vis inertiae) or force of inactivity.

This "innate force of matter," as has often been noted,⁴ is akin to the "impetus" of the fourteenth-century Parisian school of Buridan, Oresme, and others; but the differences between the two concepts must not be passed over lightly. In the first place, Newton's vis insita opposes change of state of rest as well as of motion; impetus was definitely only a moving force, fully in the Aristotelian tradition of omne quod movetur ab alio movetur (everything that moves must be moved by something). A body at rest had no impetus. Secondly, Newton's force is "innate" and invariable; for most of the impetus theorists, on the other hand, impetus was something which could be added to or taken away from a body.⁵ Thirdly, the vis insita or vis inertiae acts to keep a moving body moving in a specific way: rectilinearly, and at a uniform velocity; but there was rarely, among the fourteenth-century impetus theorists, a clear statement of precisely how impetus would affect the velocity of the body, and much confusion existed as to the kind of curve in which the body would move under the influence of impetus.⁶ And finally, impetus was a force which kept the body (particle) going in motion, which drove it as a mover, in the old Aristotelian sense, the only difference being that impetus was an internal mover. Newton's vis inertiae, on the other hand, does not act to keep the body moving, but manifests itself only when its response is called up to resist some external agency which is trying to alter the state of motion or rest of the body.⁷

In addition to the vis inertiae, there are other sorts of forces also:

It seems to me farther, that these Particles have not only a Vis inertiae, accompanied with such passive Laws of Motion as naturally result from that Force, but also that they are moved by certain active Principles, such as is that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies.'

These "active forces" also originate in particles, but it is they that act to change the state of motion or rest of other particles. They are thus, in the language of Principia, "impressed forces" (or, perhaps better, the causes of impressed forces).

Definition IV. 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.

This force consists in the action only, and remains no longer in the body when the action is over. For a body maintains every new state it acquires, by its inertia only. But impressed forces are of different origins, as from percussion, from pressure, from centripetal force.

Indeed, Newton maintained an open mind as to the kinds of such "active forces" there might be:

… it's well known, that Bodies act one upon the other by the Attractions of Gravity, Magnetism, and Electricity; and these Instances shew the Tenor and Course of Nature, and make it not improbable but that there may be more attractive Powers than these. For Nature is very consonant and conformable to her self.⁹

There are some crucial differences between the concepts of vis inertiae and vis impressa. The vis inertiae of a body, as was remarked above, does not (as the concept of impetus did) explain the continuance of a body in its state of rest or uniform rectilinear motion, in the sense of being an internal pushing agent causing that body to be or continue in that state. Let us examine this point further; for one might suppose that, even though Newton's own definition is (or should be) perfectly clear on this point, it would at least have been consistent for the concept of inertia to be interpreted as referring to an internal force causing a body to continue at rest or with uniform velocity. That this is not even a possible interpretation—that to treat vis inertiae as a cause in the same sense as impressed force (the only difference being that the former is internal, the latter external) would lead to contradiction—is shown by the following considerations. First, if it were such a force, then, as Jammer points out,¹⁰ the third law of motion would be violated: for what would be the equal and opposite reaction? And if there were, in this exceptional sort of case, no equal and opposite reaction, then the unresisted force constantly acting on the body (from within) should, on other sound Newtonian principles, produce a constant acceleration instead of a constant velocity. Furthermore, inertia is a constant, unvarying property of a body, while the uniform rectilinear velocity which the body possesses can take on any of an infinite number of values. But it is a logical property of the notion of "cause" (or "causal explanation"), or at least of the most usual usage of that expression, that a variation in an effect requires a corresponding variation in the cause.¹¹ Thus it is no accident that inertia—the inertial mass—enters into calculations in Newtonian physics not as a "force" causing or explaining the rest or uniform rectilinear motion of a body; rather, it enters into other sorts of calculations entirely: fundamentally,¹² into calculations of the impressed forces acting on the body (or, when the forces are known, into calculations of the body's response thereto); or, when inertia acts as "impulse," when "the body, by not easily giving way to the impressed forces of another, endeavors to change the state of that other" (Definition III), it enters into calculation of the impressed forces which the body exerts on other bodies. Inertia, like other characteristics of bodies (particles), manifests itself in interactions with other bodies—in its effects on and responses to other bodies—not as an internal driving vis maintaining the body in its "inertial" state.

The differences between vis inertiae and vis impressa may be characterized in either of two alternative ways. On the one hand, we may rest content with Newton's use of the term "vis" in connection with inertia, and, concomitantly, we may describe the role of the vis inertiae as being that of a cause (or as providing a causal explanation) of a body's maintaining an inertial state. But if we do so speak, we must remember that the terms "vis" and "cause" are being used in a sense very different from that in which they are used in connection with impressed forces. It is clearly the latter that, in Newton's physics, play the role of "causes" in the sense that they are (or, more precisely, originate in) independent agencies in terms of which variable effects are to be explained. And in this sense, the vis inertiae is not an internal pushing-agent counterpart of the vis impressa—a distinct agent causing a certain kind and degree of effect; it is essential to particles, definitory (or at least forming part of the definition) of them.

There are undoubtedly historical precedents for Newton's use of the word "vis" in connection with inertia, and for our describing the role of inertia as that of a "cause" of a body's maintaining its state of rest or uniform rectilinear motion: Aristotle himself, after all, spoke of "nature" as "a source or cause (aitia) of being moved and of being at rest …" etc.¹³ But on the other hand, it must also be recalled that it was against just such sorts of "explanations," among others, that sixteenth- and seventeenth-century philosophical revolutionaries were objecting when they protested all appeals to internal, invisible, "occult" causes as not being truly explanatory.

For this reason, as well as because of the potential confusion resulting from the use of the same term for two very different ideas, it is therefore tempting to make the distinction between vis inertiae and vis impressa explicit by saying that the fact that a body is at rest, or is in uniform rectilinear motion, is not to be explained (causally) in terms of the vis inertiae—or, for that matter, for Newton, in terms of any other sort of "force." (That is, in this sense of the word "cause," and in the sense in which a "force" is a "cause" of the behavior of particles, vis inertiae is not a force.) Being in an inertial state is, indeed, on this use of the term "cause," not to be explained causally in terms of anything: bodies (particles) simply do continue in a state of rest or uniform rectilinear motion unless compelled to change that state by external (impressed) forces. Inertial motion (or rest) is thus uncaused; and it is further tempting to put this point positively by saying that the inertial state is "natural" to bodies, what requires causal explanation being any deviation from such a state.

Characterization of the inertial state as "natural" is not uncommon. One of the most recent descriptions in this vein is that given by Margula Perl, who also quotes a very early similar description:

The first [law of motion, the] "Law of Inertia," is probably the least problematic, and Maclaurin's comment that "From this law it appears why we inquire not in philosophy concerning the cause of the continuation of the rest of bodies, or of their uniform motion in a right line" is still probably the best comment on the law.¹⁴

In spite of the frequency of this way of characterizing the inertial state, and of contrasting it with accelerated motion, however, calling the inertial state of a body "natural" has its dangers too. As with all such technical terms, one must be wary here of being misled. For example, the notion of "natural" applied as above to inertial motion (or rest) is not in every way the same as the notion of "natural" in Aristotle. For bodies in Newton's science to respond to impressed forces by accelerating in specific ways can in one sense be characterized as being just as "natural" as for them to continue in uniform rectilinear motion in the absence of such forces. Thus the word "natural" applied to the inertial state must not be taken as the opposite of "unnatural"—a contrast that is easy to make in connection with Aristotle's usage. But if we understand the term "natural" as meaning simply "not in need of explanation in terms of external agencies," we shall see shortly that Newton's science may be viewed in an illuminating way in terms of this distinction: in a way which, in taking account of the differences between vis inertiae and vis impressa in Newton's science, does not do violence to the actual intent of those concepts, and in a way which, further, brings out important features of his science as compared and contrasted with other scientific traditions.¹⁵

The preceding discussion enables us to see, behind the Newtonian views outlined above, a deep background framework of ideas concerning the nature of explanation and related notions. For there is, lying behind Newton's approach, a family of concepts or terms which, in at least some important uses, are strongly interlocked with one another—so much so that the applicability of one such concept or term may (in those uses or senses) be said to "imply" something about the applicability of the others. Whether such relationships should be referred to as "logical," or, with Wittgenstein, as "grammatical" (suggesting that they are relationships between linguistic terms or usages), or simply as "conceptual," and whether (and in precisely what way) anything would be gained by referring to them as "non-empirical," are real and important issues. But I will not consider these issues at present, but will simply use the terms "logical," "conceptual," "grammatical," and "non-empirical" indiscriminately.¹⁶ In any case, the family of thus interrelated terms (concepts) relevant to the present discussion includes "explanation," "change," and "cause."¹⁷ And the relevant relationship between these concepts is expressed adequately enough for present purposes in the philosophical dictum, "Every change (or every event) must have a cause (or, requires a causal explanation).¹⁷

In many uses—the uses which are of primary relevance to the discussion of Newton's science—these terms are also linked "logically" to another class of terms which includes the terms "entity" and "behavior (of entities)," in such a way that implications hold between the concepts of "change," "cause," and "explanation" on the one hand, and "entity" and "behavior (of entities)" on the other. Thus it is a logical truth—not an "empirical" one, in any clear sense of that difficult term—that, in the senses relevant here, "The cause of any change must lie in the behavior of an entity." Further, a very important point, for our purposes, is that the "entity" whose "behavior" causes a "change" must—and this "must" is, again, a sign that the point is a logical (conceptual, grammatical) one, not an "empirical" one—lie "outside of," or be "extemal to" or "independent of the change (changing event, changing entity) itself¹⁸

But all this network of interconnected concepts is not sufficient for the purpose of application: for that, it must be made specific. For, though the interrelationships outlined do hold for those uses of these terms which are relevant here, they leave open a number of questions. What, precisely, is to count as an "entity"—something capable of behaving, of causing (and, it may be added, of being affected)? What is to count as the behavior of an entity? As a change? As something happening "outside of or "independent of an event or change? And how, specifically, is the behavior of an entity linked to the causing (the causal explanation) of some change or event?

The principle of inertia as contrasted with the Aristotelian view of motion provides a well-known example of how such specification can, and needs to be, made, and of how it can be made differently by different thinkers (and, indeed, of how the specifications can be characteristic of the theories and their differences from one another). For the Aristotelian tradition, rest—at least of an element in its natural place—was "natural" (in our sense, even if in others also) to a body: it did not constitute a change requiring a causal explanation in the sense outlined above (the "nature" of the body was the "cause" of that behavior¹⁹). Motion, on the other hand—or at least violent motion²⁰—did count as such a change, and required an external cause constantly applied in contact with the moving body. Upon removal of the cause, the body would (if in its natural place) come to rest immediately or (if not in its natural place) immediately assume its natural motion toward its natural place of rest.

The concept of inertia constituted a shift as to what it is about motion that needs to be explained in terms of an external cause, and what does not. Certain sorts of motions—uniform rectilinear ones—are now put into the same category as rest had been in for the Aristotelian tradition. For whereas uniform rectilinear motion (at least when "violent") required, in Aristotelian physics, a constantly applied external cause, it no longer does so in Newtonian physics. To put the point in terms of the preceding discussion, inertial motion no longer counts as the kind of "change" that requires a causal explanation: accelerations are such "changes." Care must be exercised here: for though it is true that, in one sense, even inertial motion can be called a "change"—it is change of position—nevertheless the mere fact that a body changes position is not, for Newton, sufficient ground for asking for a causal explanation—an explanation in terms of an external agency responsible for the behavior. What counts as the kind of "change" requiring a "cause" has, in Newtonian science, shifted from its Aristotelian meaning; in the sense of the term "change" in which "every change requires a cause," not all kinds of motion are "changes."²¹

The whole of Newton's conception of the subject-matter of science can, in fact, be profitably viewed as a set of such specifications of the general network of concepts involving "change," "explanation," "cause," "extemality," "entity," and "behavior." The kind of "change" that requires explanation in terms of a "cause" is, as we have seen, acceleration—and, it must be added, all "qualities," such as colors and sounds and their differences and changes. What does not require such explanation is the state of uniform rectilinear motion, of which rest is a special case. This is in opposition to the Aristotelian specification, according to which rest and motion (at least when violent) are not on a par, uniform rectilinear motion (at least when violent) being included in the class of changes requiring explanation in terms of a cause.

Further, the notion of "mass" is a specification, in Newton's physics, of what counts as an entity (or at least as an ultimately real or fundamnental entity, all other so-called entities being associations of mass-particles, and all their properties and behavior being ultimately explainable in terms of the motions of masses and the forces centered therein). The notion of mass-centered, centrally-directed forces is a determinate expression of what counts as a cause, along with the motions of bodies which alter the strength of those forces with respect to other bodies within their range. The motions of particles, and their impression of forces on other bodies (including the variation of those impressed forces with the changes of relative position of the particles concerned) specifies what counts as the "behavior" of entities. And, finally, the notion that a cause must be "external" to its effect is reflected, and specified, in the fundamental explanatory role played in Newtonian physics by impressed forces.

These specifications are summarized in part, though implicitly, in the laws of motion, particularly in the first two. For we can look on those laws as making, in effect, the distinction made above between "natural" and "deviant" behavior—between behavior that does not require explanation in terms of a cause (an "external" cause) and behavior that does. The laws distinguish, that is, between "behavior" that is "uniform," and which therefore (logically) does not require a causal explanation, and "behavior" that is not "uniform"—behavior that counts as "change" in the sense in which it is a "logical" truth that "every change requires a cause (causal explanation)." The first law of motion ("Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon") has, among other jobs, the function of telling us that it is only deviations from uniform straight-line motion (or rest) that need to be accounted for in terms of a cause (in the form of an external agency)—ordinarily, at least²²—and that such deviations are to be accounted for (causally) in terms of "impressed forces." The second law ("The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed") spells out in more detail the precise characteristics (the direction and amount) of the forces required to produce a given amount of deviation. And elsewhere in Newton's writings we learn that such forces acting on any particle must ultimately originate in other centers of mass.²³

In this paper, we have distinguished between two levels in Newton's view of the subject-matter which science is to investigate: first, a general conceptual framework consisting of "logically" related concepts like "change," "cause," and "entity"; and second, a set of specifications of that background framework in terms of such notions as "accelerated motion," "force," and "mass." What seems peculiarly Newtonian is the way the general framework has been specified; for Aristotelian science specified some of the same (or, more precisely, a closely related) background framework differently.²⁴ A number of questions arise concerning these different specifications. What warrant is there, ultimately, for selecting one set of specifications of a general background framework rather than another? Are there really "many reasons" which support the Newtonian specification of what counts, e.g., as a "change" requiring a "cause," and which cannot be taken account of in terms of the Aristotelian specification? Or is the difference merely a matter of "handling the same bundle of data as before, but placing them in a new system of relations with one another by giving them a different framework, all of which virtually means putting on a different kind of thinking-cap"²⁵? Is it a matter of adopting a different "paradigm"²⁶ with which to approach nature, in the sense that a radically new set of problems to meet, definitions of facts, and standards of acceptability, replaces an old one with which it is not only incompatible but even "incommensurable," and such that no good reasons can really be given for its acceptability?

These are important questions, to be sure; but there are also questions that need to be asked about the background framework itself. Is there—can there be—only one such framework, which lies (or even which must lie) behind all science, past, present, and future? Need there always be one, or is the reliance on such backgrounds something that science outgrows with maturity? (Or, alternatively, does the development of science make it more and more impossible for philosophers to abstract from concrete scientific theories any such "background framework"?) And if there is more than one background, are there any good reasons for employing, in science, one rather than another, or for abandoning one in favor of another? Is the background framework (whatever may be said about its set of specifications) described adequately as a set of "a priori assumptions," as "metaphysical presuppositions," or at least as containing a strong element thereof? Again, we may ask whether the background framework is described adequately as a set of "metascientific concepts," the special concern of philosophers, who are supposed to deal (according to some views) not with the actual content of science, but rather with the analysis of those terms which are used in talking about science ("metascientific" ones, including such terms as "explanation," "cause," "entity").

Not all of these questions can be answered here, of course; but some light can be thrown on the issues concerned by contrasting the view presented here with certain traditional philosophical doctrines. For, after all, such concepts as "cause," "change," and "entity," which form part of the background of Newton's science as interpreted here, have traditionally been discussed or employed in writings referred to as "metaphysical." The latter word covers so many different ideas as to be almost useless; but there are a few reasonably clear allegations which have been made as to the role of such concepts with regard to science. And none of these roles is played by the background framework as conceived here. Thus, if that framework is characterized as "metaphysical," it is not metaphysical in the most usual or clear senses of classical philosophy. It does not consist of a set of propositions from which the substantive propositions of science can (allegedly) be deduced; nor does it consist of a set of propositions which (allegedly) must be added as premises to some or any scientific propositions in order to deduce further consequences; nor does it consist of a set of "presuppositions" guaranteeing that scientific method will work as a tool of discovery or of induction. On the contrary, the background framework as conceived here consists of a set of concepts (and propositions relating those concepts) which are made specific and applicable by a particular scientific theory."

Nor, again, is there any implication, in the view presented in this paper, that the background framework of Newtonian science consists of a set of concepts which cannot be avoided—which must be employed in any attempt, past, present, or future, to characterize the scientific endeavor. Indeed, I have suggested elsewhere, "There is in the range of scientific theories a spectrum of departures from such everyday-life concepts as 'entity' and 'behavior' that makes those terms inadequate to a lesser or greater degree for talking about those theories."²⁸ Unless we stretch the meanings of the words beyond utility, the concepts of (for example) "entity" and "behavior of entities," which are so naturally applied in discussion of Newtonian physics, become harder to apply to theories which talk, e.g., about electromagnetic fields and variations in field intensities. Thus the framework in terms of which Newtonian science has been discussed here does not consist of a set of necessary, a priori propositions (and concepts) in terms of which any scientific system must be specified. Nor, correlatively, does it consist of a set of "metascientific" concepts, at least in the sense of a set of category-terms for characterizing any scientific theory.

The interpretations given in this paper must not be considered as being concerned with all aspects of Newton's work, but only with that facet, illustrated by the passages referred to earlier, which was most influential on the subsequent history of thought: which provided a conception of the aims, methods, and subject-matter of science, and the clarification and extension of which set the problems for a whole tradition of succeeding philosophers and scientists. There are, however, other sides of Newton. Two of these stand out most prominently, though not as facets completely independent of that outlined here, but rather as attempts to answer criticisms, levelled chiefly by continental thinkers, against views connected with those discussed here. On the one side, we find him attempting to answer such objections by giving an account of gravitation in terms of an "Aethereal Medium."²⁹ And on the other side, we see him answering the same objections by maintaining that, in speaking of attraction, he is not attempting to give an explanation at all, but only a description. The present interpretation is not meant to apply to those views, but rather to provide an account of a central body of Newtonian doctrine in terms of which his adoption of those other views can be understood.

Notes

¹ 1. Newton, Philosophiae Naturalis Principia Mathematica, Berkeley, University of California Press, 1946, pp. xvii-xviiI.

² Newton, Opticks, New York, Dover, 1952, p. 400. Another list of properties of particles, somewhat, though not fundamentally, different from the account in the Opticks, occurs in Principia: "The extension, hardness, impenetrability, mobility, and inertia of the whole, result from the extension, hardness, impenetrability, mobility, and inertia of the parts; and hence we conclude the least particles of all bodies to be also all extended, and hard and impenetrable, and movable, and endowed with their proper inertia. And this is the foundation of all philosophy." (Principia, p. 399) The basis of this inference from "macroscopic" to "microscopic" characteristics is Rule III of the Rules of Reasoning in Philosophy: "The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever." (p. 398) In the light of contemporary quantum theory, such a principle of inference appears naïve and erroneous.

Note the absence of gravity from Newton's lists of the properties of particles. For though gravity, like inertia, is universally found in the bodies we experience, and admits of "neither intensification nor remission of degrees," Newton refuses to draw the conclusion that it is essential to matter, a primary property of particles, like inertia: "we must … universally allow that all bodies whatsoever are endowed with a principle of mutual gravitation.… Not that I affirm gravity to be essential to bodies: by their vis insita I mean nothing but their inertia." (Principia, pp. 399-400) Action at a distance proved embarrassing enough to Newton to lead him here to make an exception in the application of Rule III, and to distinguish, in this case, between what is essential and what is merely universal in matter.

³ The concept of explanation has traditionally exerted more or less definite types of intuitive appeals, directing analyses of that concept, and, correlatively, of nature and of science, along certain general paths. Such tendencies of analysis have, however, usually been left tacit, and, furthermore, are not necessarily consistent with one another. Among the historically and philosophically more important of these tendencies (together with some sketch of the kind of tacit line of argument accompanying them) are the following. "What require explanation are changes; and therefore what does not require explanation, i.e., the fundamental explanatory factors themselves, must be absolutely unchanging. For if they changed (or even, perhaps, if they could change), then those changes (or the possibility thereof) would have to be subject to explanation, and so those factors would not be fundamental explanatory factors at all. And thus if explanation—or at least ultimate explanation—is to be possible at all, there must be explanatory factors which are not subject to change." What require explanation are differences; therefore what does not require explanation, the fundamental explanatory factors themselves, must be factors which are 'alike.'" (The remainder of the accompanying argument in this and the succeeding cases is similar to that in the first example.) "What requires explanation is diversity; hence what is used to explain must be a 'unity'." "What requires explanation is complexity; therefore what is appealed to for the sake of explaining must be 'simple.'" The rationale behind various interpretations of the aims and subject-matter of scientific investigation—e.g., those interpretations associated with atomistic "theories"—have thus not always been purely empirical, but have often rested on such a priori considerations as these. There have been a multitude of other such "tendencies," some associated with conflicts between continuum and discrete theories of matter, others connected with controversies as to the respective roles of the concepts of space ("geometry") and matter in scientific explanation, and still others with the tension between traditional "metaphysical" and "empiricist" approaches to explanation. These forces in the development of science have received little or no attention from philosophers of science: yet a thorough analysis of them, and of their precise logical role in the scientific endeavor, seems very much needed.

⁴ For example, by Dijksterhuis: "Newton still shares Aristotle's view that every motion requires a motor, in the modified form of it given by the Paris Terminists, who assumed that this motor resides in the body. The Vis Inertiae apparently is identical with the Impetus of this school and the Vis Impressa of Galileo." (E. J. Dijksterhuis, The Mechanization of the World Picture, Oxford, Clarendon, 1961, p. 466.) Dijksterhuis does not discuss any differences between Newton's conception and these earlier ones, but apparently simply equates them.

⁵ With regard to this point (as in many other respects), the closest parallel to Newton's view among the impetus theorists, at least until the sixteenth century, was the view of John Buridan. Buridan did look upon impetus as something which was not self-expending (as his chief predecessor, Franciscus of Marchia, and his chief immediate successor, Nicole Oresme, maintained); in the absence of counterforces, the impetus will be conserved, according to Buridan, and in this sense is "permanent." It will, however, be destroyed by contrary agencies, if any are present—as Newton's inertia cannot be. For Newton, the measure of inertia is the (inertial) mass of the body, and this is invariant: a body at rest still has it. For Buridan, however, presumably when the impetus is used up in combating extemal resisting or otherwise corruptive influences, the body comes to rest and is left with no further impetus. Buridan's view that the impetus of the celestial spheres, at least, is incorruptible is, of course, no argument against this interpretation; for those impetuses are incorruptible as a matter of fact rather than of logic. ("… these impetuses which [God] impressed in the celestial bodies were not decreased or corrupted afterwards because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus." (M. Clagett, The Science of Mechanics in the Middle Ages, Madison, University of Wisconsin Press, 1959, p. 525)) For such impetuses would be corrupted if as a matter of fact there were any contrary agencies present. In other words, Buridan's celestial impetus is something imposed by God, inessential to the heavenly bodies. Newton's inertia cannot be corrupted; it is constitutive, indeed definitive (at least partially) of particles. A body may be brought to rest (for example) by contrary forces; but it still has the same amount of inertia.

⁶ As Clagett (op. cit., p. 520) notes, the successors of Buridan (at least until the sixteenth century) were generally confused as to whether impetus tends to produce uniform motion or accelerated motion; further, "One serious defect of this medieval theory is that there was no sure distinction between rectilinear and circular impetus. It was equally possible to impose rectilinear or circular impetus. We must await the sixteenth century for a clarification of the directional aspects of impetus." (Clagett, op. cit., p. 525) Buridan did, in a "quasi-quantitative" way, according to Clagett, hold that impetus is proportional to the velocity of the projectile (as well as to the quantity of matter—but note that this makes the concept analogous not to inertia, but rather to momentum). (Clagett, pp. 522-23) The impetus theory, in its various manifestations (especially with Buridan) was certainly an important step on the way to the Newtonian conception of inertia, and shows many vital similarities to the Newtonian idea, as I have tried to point out elsewhere (D. Shapere, "Meaning and Scientific Change," in R. Colodny (ed.), Mind and Cosmos, Pittsburgh, University of Pittsburgh Press, 1966, pp. 41-85; see especially pp. 71-81). But the differences noted here must not be ignored. It is also true that, with the sixteenth century, particularly with Benedetti, the impetus theory tended more and more clearly toward the Newtonian conception. Even there, however, many of the differences noted here remained.

⁷ We must not be deceived here by Newton's remark that inertia "is resistance so far as the body, for maintaining its present state, opposes the force impressed; it is impulse so far as the body, by not easily giving way to the impressed force of another, endeavors to change the state of that other." (Def. III) For this passage does not imply that inertia, like impetus, is the cause of the motion of the body itself.

⁸ Newton, Opticks, p. 401.

⁹Ibid., p. 376. In this connection, the Halls have noted that Newton "was not even sure whether there was one basic force, or a pair of repulsive and attractive forces, or as many forces as there were classes of phenomena—gravitational, magnetic, electrical, optical, chemical, and. physiological—involving such forces." (A. R. Hall and M. B. Hall (eds.), Unpublished Scientific Papers of Isaac Newton, Cambridge, Cambridge University Press, 1962, p. 203.)

Newton also considered forces to be effects of (accelerated) motions as well as causes thereof; this aspect of his work will not, however, be considered in this paper.

¹⁰ M. Jammer, Concepts of Mass, Cambridge, Harvard University Press, 1961, p. 71.

¹¹ Mill's "Method of Concomitant Variation," when filtered of its many errors and misleading features, reduces essentially to this logical point.

The aspect of the notion of "cause" which will be central in the following discussion is that of "cause of a change"; such notions as "cause of existence" and "cause of difference" will not be discussed, despite the fact that the latter notion, in particular, is important in Newton's science. For in his theory of light, differences of color in a spectrum are explained (causally) by differences in the component rays of white light and their different degrees of refrangibility.

¹² I.e., except when the notion of (inertial) mass (which turns out in calculational practice to be the heart of the notion of "quantity of matter") enters into the definition of a quantity, as it does in the definition of "quantity of motion" (Def. II).

Jammer (Concepts of Mass, p. 72) argues that "for Newton, in contrast to 'Newtonian mechanics,' 'inertial mass' is a reducible property of physical bodies, depending on their 'quantity of matter.'" It is not easy to see what Jammer means by "reducible" in this connection; as he himself points out, "It is, of course, always rather difficult to state exactly whether two concepts are involved or only one, once a general proportionality between the concepts has been established." (This remark is not entirely correct, for inertial and gravitational mass are, despite their necessary proportionality, clearly distinct in Newtonian physics due to their independent mode of introduction.) Apparently the reasoning behind Jammer's view is that quantitas materiae has other properties than inertial mass; he cites gravitational mass. ("… it is fairly obvious that 'quantity of matter' is still a notion for itself. A careful examination of the text of Book III of the Principia, for instance, shows clearly that it is quantitas materiae in the original sense of the word which determines the magnitude of gravitational attraction.") Jammer's appeal to gravitation, however, is unfortunate; for, as was pointed out above, gravitational mass is not an essential characteristic of matter, while inertia is. ("Not that I affirm gravity to be essential to bodies: by their vis insita I mean nothing but their inertia.") On the other hand, it is true that, for Newton, there are characteristics besides inertia which are essential to matter—e.g., solidity, hardness, impenetrability. And in this sense, inertia (inertial mass) constitutes only part of the notion (definition, essence) of matter; and—still in this sense—inertia can be said, somewhat confusingly, to be "reducible" to quantitas materiae. Jammer's view, when properly interpreted, is thus defensible, although it is rather more innocuous than it might at first seem: for inertial mass is certainly not to be understood in terms of quantitas materiae; nor is it caused by the latter, and so is not "reducible" to the latter in either of these interesting senses.

¹³ Aristotle, Physics, Bk. II, 192b 22.

¹⁴ M. Perl, "Newton's Justification of the Laws of Motion," Journal of the History of Ideas, Vol. XXVII (1966), p. 585.

¹⁵ I do not, of course, wish to suggest that this distinction between "natural" and "deviant," as employed here in connection with Newton, is an essential feature of explanation, or of scientific explanation in particular. Specifically, I do not mean to imply that there must be, within any scientific theory, a distinction between two classes of events, one of which includes events always requiring causal explanation, and the other of which includes events not doing so.

¹⁶ Indeed, one must suspect that the distinction between "empirical" and "non-empirical," at least, is highly misleading when applied to the sorts of relationships being discussed here: for many of the same sorts of considerations that count for or against what are usually referred to as "empirical" propositions in science have also counted for or against ideas and interconnections in this "nonempirical" framework of ideas.

¹⁷ Not all types or facets of the uses of these terms exhibit the connections here noted, however; thus the term "explanation" has wider uses than those in which it is linked to the notions of "cause" and "change." For example, in such statements as, "Explain how to play chess," "Explain the theory of relativity to me," and "Einstein's theory explains the advance of the perihelion of Mercury," the sense of "explanation" is not that of what has been referred to here as "causal explanation." Again, it is not true that all "explanations" which are appropriately called "causal" are explanations of what may appropriately be called "changes": some causal explanations (e.g., explanations of difference of color in optics) are explanations of differences rather than of changes. (See Footnote 3, above.) And not all "changes" require "causes" either—as the present argument attempts to show, changes of position do not, for Newton, always require causes. There are similar exceptions in the cases of the other terms discussed here. Nevertheless, there do exist uses (senses) of these expressions in which the "logical" connections asserted do hold.

¹⁸ One sort of objection (there were others also) made in the seventeenth century against "occult causes" rested essentially on this point: that the supposed "causes" were really not explanatory at all, but rather were identical with the object or event to be explained. The requirement that the cause be "distinct from," "external to," or "independent of the effect thus involves not merely an objection against appealing to causes which cannot be discovered or observed; it involves a "logical" point as to what can count as an explanation—as to what can properly be called "an explanation."

¹⁹ See Aristotle's definition of "nature," quoted above.

²⁰ The Aristotelian and Newtonian conceptions of the relation between force and motion are often distinguished by saying that, for the former, force is the cause of motion, whereas for the latter, force is the cause of change of motion. This way of stating the difference, however, is misleading. For example, apart from reading the notion of force into Aristotelian physics, where it does not unambiguously belong, the view that, for that tradition, all motion requires a "force" applies primarily to violent motion. For while natural motion requires a mover, that mover is, for most of the tradition, the "nature" of the thing moved, and not an external (or, if internal, at least independent) agency.

²¹ This is presumably the point behind referring to uniform rectilinear motions (and rest) as states: "Status of motion: by using this expression Newton implies or asserts that motion is not, as had been believed for about two thousand years—since Aristotle—a process of change, in contradistinction to rest, which is truly a status, but is also a state, that is, something that no more implies change than does rest.… Nothing changes without a cause … as Newton expressly states. Thus, so long as motion was a process, it could not continue without a mover. It is only motion as state that does not need a cause or mover. Now, not all motion is such a state, but only that which proceeds uniformly and in a right line …" (A. Koyré, Newtonian Studies, Cambridge, Harvard University Press, 1965, pp. 66-67).

Later on page 67, Koyré makes an erroneous claim, which he and others have also made elsewhere, that "the law of inertia implies an infinite world." There is no logical reason, based on the law of inertia, why a body should not have its uniform rectilinear motion interfered with by impact against the "walls" of a finite universe.

²² It is, of course, possible to ask, within Newtonian physics, why a certain particular body continues to move in a straight line with uniform velocity. But though the answer to such a question is to be given in terms of the balance of forces originating in other masses, nevertheless a body would continue in its state of uniform rectilinear motion even if there were no other masses in the universe. Uniform rectilinear motion does not require explanatory appeal to the existence of other masses—as accelerated motion always does.

Reformulations of classical mechanics have been constructed which would make illegitimate (or even "meaningless") any talk of the motion of a body in a universe devoid of other bodies. Such a reformulation has the effect of restoring a complete symmetry between the kinds of questions that can be raised concerning uniform rectilinear and accelerated motion. This symmetry is purchased, however, only at the expense of creating another asymmetry—namely, between universes in which there is only one object (particle) and universes in which there is more than one object (particle). (Often the illegitimacy is not limited to universes of only one object, but is extended to those of as many as four or five, on the ground that a "reference-frame" is necessary in order to be able to speak meaningfully of the motion of a particle.)

²³ In this connection, a particularly revealing remark occurs in the context of an argument, in The System of the World, to the effect that the stars cannot really go around the earth. If that view were correct, he says, then those stars which do not lie on the celestial equator would describe, in their daily rotations around the earth, circles whose centers would be, not the center of mass of the earth, but rather points on the earth's axis or on extensions of that axis into empty space. But, he declares in refutation of such a possibility, "That forces should be directed to no body on which they physically depend, but to innumerable imaginary points in the axis of the earth, is an hypothesis too incongruous." (Newton, The System of the World, included in the California edition of Principia, p. 553.) "An hypothesis too incongruous": there must be a center of mass at the focus of the curve (or, if not, then the force centered there must be the resultant of forces which are centered in masses). Only an entity can cause an effect in another entity; and this, too, is a "logical" point.

²⁴ In what sense can the general background framework be said to be (or to have been) "presupposed"? In the case of Newton, it is certainly not suggested that he explicitly formulated such a "background framework," whether in advance of "specifying" it, or at any other period of his career. Nor, however—at the opposite extreme—would it be reasonable to contend that the set of background concepts outlined above constitutes merely a "reconstruction" of his scientific work, and one which, moreover, would have been fundamentally foreign to him and irrelevant to his own thought. There is abundant evidence throughout his writings that he thought of masses as entities acting on one another, causing them to behave in the ways they do (except for that "inertial" behavior which was "natural," requiring no such causal explanation). It is thus plausible to consider the present interpretation as lying between radical description and extreme reconstruction: although the background framework outlined here is not purely descriptive of Newton's most conscious, articulated thought, nevertheless it is an interpretation which has a solid grounding in his writings.

²⁵ H. Butterfield, The Origins of Modern Science, New York, Macmillan, 1958, p. I. The word "framework" in this passage, of course, does not correspond closely to the meaning of "background framework" in our usage.

²⁶ T. S. Kuhn, The Structure of Scientific Revolutions, Chicago, University of Chicago Press, 1962. For a discussion of Kuhn's views, see my "The Structure of Scientific Revolutions," Philosophical Review, LXXIII (1964), 383-394. The present essay may be looked upon, partly, as showing (with reference to a particular historical case) what elements of Kuhn's view (and that of Paul Feyerabend) are correct, while at the same time avoiding crucial objections against their views. In this connection, the present paper should be read as a continuation of the review of Kuhn and of my article, "Meaning and Scientific Change," referred to above in Note 6. The latter paper ends with a discussion of similarities and continuities between late medieval and Newtonian mechanics, as the present paper begins with a discussion of differences between those theories.

²⁷ The "specification" that has been spoken of in this paper cannot be looked upon as consisting simply of the statement of a premise (e.g., "Deviations from uniform rectilinear motion or rest are changes") which, when conjoined with a "background premise" (e.g., "Every change requires a cause") implies the scientific law (e.g., "Deviations from uniform rectilinear motion require a cause"—though here further specification is necessary to convert "cause" into "force"). For such a way of interpreting the relationship evades the crucial connections between the terms involved.

It is almost ironic that the "background concepts" might be looked upon as a set of purely "theoretical concepts," defined "implicitly" by their relations to one another, and given an "empirical interpretation" in terms of a set of "correspondence rules" (their specifications). Surely the positivistic tradition would have blanched at the possibility of thus letting "metaphysics" in through the "back door" of science! (This possible "positivistic" way of looking at our "background framework" was suggested to me by Peter Achinstein.)

²⁸ D. Shapere, "The Causal Efficacy of Space," Philosophy of Science, XXXI (1964), p. 115.

²⁹ E.g., in Book Three of the Opticks.