Isaac Newton founded classical mechanics on the view thatspace is distinct from body and thattimepasses uniformly without regard to whether anything happensin the world. For this reason he spoke ofabsolute space andabsolute time, so as to distinguish these entities from thevarious ways by which we measure them (which he calledrelativespaces andrelative times). From antiquity into theeighteenth century, contrary views which denied that space and timeare real entities maintained that the world is necessarily a materialplenum. Concerning space, they held that the idea of empty space is aconceptual impossibility. Space is nothing but an abstraction we useto compare different arrangements of the bodies constituting theplenum. Concerning time, they insisted, there can be no lapse of timewithout change occurring somewhere. Time is merely a measure of cycles of change within the world.

Associated with these issues about the ontological status of spaceand time was the question of the nature of true motion. Newton definedthe true motion of a body to be its motion through absolutespace. Those who, before or shortly after Newton, rejected the realityof space, did not necessarily deny that there is a fact of the matteras to the state of true motion of any given body. They thought ratherthat the concept of true motion could be analyzed in terms of thespecifics of the relative motions or the causes thereof. Thedifficulty (or, as Newton alleged, the impossibility) of so doingconstituted for Newton a strong argument for the existence of absolutespace.

In recent literature, Newton's theses regarding the ontology of spaceand time have come to be calledsubstantivalism in contrasttorelationism. It should be emphasized, though, that Newtondid not regard space and time as genuine substances (as are,paradigmatically, bodies and minds), but rather as real entities withtheir own manner of existence as necessitated by God's existence (morespecifically, his omnipresence and eternality).

• 1. Overview of the Scholium
• 2. The Legacy from Antiquity
  • 2.1 The Void
  • 2.2 Aristotle's Doctrines
  • 2.3 Sixteenth-Century Innovations
  • 2.4 Charleton and the Seventeenth-Century Revival of Atomism
• 3. Descartes' Innovation
• 4. Newton's Manuscript:De Gravitatione…
• 5. The Structure of Newton's Scholium on Time, Space, Place and Motion
  • 5.1 Arguments for Absolute Time
  • 5.2 Direct Arguments for Absolute Space
  • 5.3 The Arguments from Properties, Causes, and Effects
  • 5.4 Discriminating in Practice between Absolute and Apparent Motion
• 6. Common Impediments to Understanding the Scholium
  • 6.1 What the Major Impediments Are
  • 6.2 Why They Are Indeed Impediments
• 7. Newton's Legacy
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Overview of the Scholium

Today, Newton is best known as a physicist whose greatest singlecontribution was the formulation of classical mechanics andgravitational theory as set out in hisPhilosophae NaturalisPrincipia Mathematica (Mathematical Principles of NaturalPhilosophy), first published in 1687, and now usually referred tosimply as “Newton'sPrincipia”. Newton's views onspace, time, and motion not only provided the kinematical basis forthis monumental work and thus for the whole of classical physics upuntil the early twentieth century, but also played an integral role inNewton's general system of philosophy and theology (largely developedprior to thePrincipia). Because Newton never drafted atreatise on, or even a digest of, this general system, his stature asone of the great philosophers of the seventeenth century, indeed, ofall time, is no longer widely appreciated.

A “Scholium” at the beginning of thePrincipia,inserted between the “Definitions” and the “Laws ofMotion”, lays out Newton's views on time, space, place, andmotion. He begins by saying that, since in common life thesequantities are conceived of in terms of their relations to sensible bodies, it isincumbent to distinguish between, on the one hand, the relative,apparent, common conception of them, and, on the other, the absolute,true, mathematical quantities themselves. To paraphrase:

• Absolute, true, and mathematicaltime, from itsown nature, passes equably without relation to anything external, andthus without reference to any change or way of measuring of time(e.g., the hour, day, month, or year).
• Absolute, true, and mathematicalspace remainssimilar and immovable without relation to anything external. (Thespecific meaning of this will become clearer below from the way itcontrasts with Descartes' concept of space.) Relative spaces aremeasures of absolute space defined with reference to some system ofbodies or another, and thus a relative space may, and likely will, bein motion.
• Theplace of a body is the space which itoccupies, and may be absolute or relative according to whether thespace is absolute or relative.
• Absolutemotion is the translation of a body fromone absolute place to another; relative motion the translation fromone relative place to another.

Newton devotes the bulk of the Scholium to arguing that thedistinction between the true quantities and their relative measures isnecessary and justified.

It is evident from these characterizations that, according to Newton:

1. space is something distinct from body and exists independently ofthe existence of bodies,
2. there is a fact of the matter whether a given body moves and whatits true quantity of motion is, and
3. the true motion of a body does not consist of, or cannot bedefined in terms of, its motion relative to other bodies.

The first of these theses was a point of major contention in17th-century natural philosophy and one assailed by Newton's criticssuch as Leibniz, Huygens, and Berkeley. The second wasnot ingeneral dispute. Descartes, Leibniz, and Berkeley all believed that,to put it in somewhat scholastic terms, the predicate ‘x isin true motion’ is a complete predicate in the sense that it holds orfails to hold for any given body. (Huygens, at least in hispost-Principia views, constitutes a special case.) Thus, forthose who denied the first thesis, it was necessary to secure adefinition, or an analysis, of what it means for a body be in truemotion (and what determines the quantity of that motion), so as to beas adequate to the facts as Newton's characterization of truemotion. The figures mentioned above all deemed that motion relative toother bodies is anecessary condition for true motion,although not, by itself, asufficient condition.

Over the course of years, the consensus in the 17th and early 18thCenturies on thesis (2) was lost sight of, and it became common tocharacterize Newton's opponents as denying that there is afact of the matter as to whether a body is in true motion andmaintaining instead thatall motion is merely relativemotion. Thus, modern readers expect that Newton's Scholium onspace, time, and motion should be read as arguing not only thesis (1)above, but also thesis (2), that all motion is not merely relativemotion, but that some motions are true and absolute. Newton'sarguments concerning motion, however, are designed to show, not thattrue motion is distinct from merely relative motion (which is grantedby all), but rather that the only feasible analysis of true motionrequires reference to absolute places, and thus the existence ofabsolute space.

In particular it has been assumed that Newton's so-called “rotatingbucket experiment”, together with the later example of a pair ofglobes connected by a chord and revolving about their center ofgravity, is supposed to argue, or provide evidence for, the existenceof true, or absolute, motion. Not only is this false, but the twocases have distinct purposes in the framework of the Scholium. Therotating bucket experiment is the last of five arguments from the“properties, causes, and effects of motion” designed to showcumulatively that an adequate analysis of true motion must involvereference to absolute space. In contrast, the example of the revolvingglobes is intended to illustrate how it is that, despite the fact thatabsolute space is invisible to the senses, it is nonetheless possibleto infer the quantity of absolute motion of individual bodies invarious cases.

2. The Legacy from Antiquity

2.1 The Void

The most important question shaping 17th-century views on the natureof space, time and motion is whether or not a true void or vacuum ispossible, i.e., a place devoid of body of any sort (including rarifiedsubstances such as air). Ancient atomism, dating back at least to thepre-Socratic philosopher Democritus (5th century, B. C.), held thatnot only is such possible, but in fact actually exists among theinterstices of the smallest, indivisible parts of matter and extendswithout bound infinitely. Following Plato, Aristotle rejected thepossibility of a void, claiming that, by definition, a void isnothing, and what is nothing cannot exist.

2.2 Aristotle's Doctrines

According to Aristotle, the universe is a material plenum, finite inextent, bounded by the outermost sphere of the fixed stars. Beyondthat there is no void, i.e., empty places, since, as Aristotle defines‘place’, the place of something is the outermost of “theinnermost motionless boundary of what contains it.” Hence, since thereare no boundaries outside the outermost celestial sphere, there are noplaces or space outside of it.

Time, according to Aristotle, is just the measure of motion, where by‘motion’ he means change of any sort, includingqualitative change. In order to define the uniformity of time, thatis, the notion of equal intervals of time, Aristotle was guided byastronomical practice, which in antiquity provided the most practical and accurate measures of time. He identified uniform motion with the rate of motion ofthe fixed stars, a choice for which he found a dynamical justificationin his celestial physics.

“Local” motion is but one species of motion, viz., change ofplace. Motion, in general, he defined as the actualization ofpotentiality, a notion commonly held in the 17th century to be soobscure as to be either useless or meaningless. However, as far aslocal motion is concerned, there is no difficulty as to whatconstitutes the true or absolute motion of a body in a finitegeocentric universe. Indeed, elementary substances in the sub-lunarrealm (earth, air, fire, and water) move of their own accord either upor down, i.e., toward the center or away from the center by their verynature. The celestial realm, beginning with the orbit of the moon,consists of an interlocking network of celestial spheres composed of afifth element (aether), which by its nature is disposed to circularmotion about the center of the of universe (i.e., the center of theearth). If the motion of this substance is taken to be the measure oftime, the celestial spheres necessarily rotate uniformly. Since thenet motion of an embedded sphere is the sum of its natural motionsuperimposed on the natural motions of the spheres in which it isembedded, and since the axes of rotation are in general set atslightly different angles in order to account for why the sun does notmove on the celestial equator and the planets and the moon do not movestrictly on the ecliptic (i.e., the path of the sun against the fixedstars), the motions of the moon, planets, and even the sun are notnecessarily uniform. However, since the sphere of the fixed stars isembedded in no other celestial sphere in motion, the motion of thefixed stars isde facto the measure of all motion.

The motions spoken of so far are allnatural motions of thesubstances in questions, motions induced by the body being the verysubstance that it is. In contrast, other motions, in which the causeof the motion is external rather that internal to the body, Aristotlesubsumed under the concept ofviolent motion. Violent motionrequired for its continuation the constant application of an externalcause.

2.3 Sixteenth-Century Innovations

Although Aristotle's views dominated medieval scholasticism, thereoccurred a renewed interest in atomism in the early 17thCentury. Apart from general factors such as the Renaissance, Humanism,and the Reformation, specific innovations of the 16th Century made itattractive. Although Copernicus' introduction of a helio-static systemwas motivated by a strict adherence to Aristotle's dynamics ofcelestial spheres, it brought into question his terrestialphysics. Galileo's telescopic observations of the surface of the moon andhis discovery of moons orbiting about Jupiter brought into questionthe very distinction between the terrestial and thecelestial. Moreover, the visibility of an abundance of new stars,apparently without end, suggested that the universe may in fact bewithout bound.

2.4 Charleton and the Seventeenth-Century Revival of Atomism

An important representative of the revival of atomism and itsconcomitant views concerning the void is Walter Charleton'sPhysiologia Epicuro-Gassendo-Charltoniana: Or a Fabrick of ScienceNatural, upon the Hypothesis of Atoms, “Founded by Epicurus, Repairedby Petrus Gassendus, Augmented by Walter Charleton”, whichappeared in English in 1654, twelve years after Newton's birth. It isa text with which Newton became familiar as an undergraduate, and someof the core theses concerning time and space later put forth in thePrincipia and various unpublished manuscripts in Newton's hand can befound in Charleton. These include:

• that time and space are real entities even though they fit neitherof the traditional categories of substance or accident (i.e., propertyof a substance),
• that time “flow[s] on eternally in the same calm and equal tenor,”while the motion of all bodies is subject to “acceleration,retardation, or suspension”,
• that time is distinct from any measure of it, e.g., celestialmotion or the solar day,
• that space is “absolutely immoveable” and incorporeal,
• that bodies, or “Corporeal Dimensions” are everywhere “Coexistentand Compatient” with the “Dimensions” of the parts of space theyoccupy,
• that space distinct from body existed before God created the worldand that God's omnipresence is his literal presence everywhere, and
• that motion is the translation or migration of body from oneplace, as an immovable part of space, to another.

Charleton's arguments for his views concerning time have much thesame tenor as those given by Newton in thePrincipia. Inmarked contrast, though, those for empty, immense, and immutable spaceare quite different. Charleton appeals to the explanation of suchphenomena as rarefaction and condensation, the differences in “degreesof Gravity” of bodies, and the numerous ways in which bodies caninterpenetrate at the micro-level in terms of solubility, absorption,calefaction, and diverse chemical reactions. However, Charleton doesnot introduce the terminology of “relative” time, “relative” spaces,or “relative” places, and nowhere raises concerns regarding true(absolute) motion versus merely relative motion. Oddly enough,although Charleton occasionlly mentions and criticizes Descartes withregard to other matters, no note of the fact is made that Descartes, adecade earlier, had proposed explanations, in detail or in outline,for just these sorts phenomena according to a system of nature inwhich the world is completely filled with matter and in which spacedistinct from body cannot exist. Descartes, it can be justly said, isthe founder of the other main school of the “mechancal philosophy” ofthe 17th Century, which stood in direct opposition to atomism on theissue of the possibility of a vacuum and which adapted theAristotelian doctrines on the nature of time, space, and motion to thenew world view.

3. Descartes' Innovation

Although avowedly anti-Aristotelian in many regards, particularly onthe view, shared with atomists, that all qualitative change on themacroscopic scale is reducible to the rearrangement and/or motion ofmatter on the microscopic scale, it was Descartes' ambition to carryout this program by retaining what is essentially Aristotle's notion ofPrime Matter. The pure elements (earth, air, fire, and water) ofAristotle's physics could mutate into one another by alteration of thefundamental qualities definitive of them. These were the four hapticqualities of hot, cold, wet, and dry. Because of this, there had to besomething distinguishable, at least in thought, from qualities thatpersist during elemental alteration. This quality-less substratum iswhat Aristotle referred to simply as matter, or as it is often called,Prime Matter, in order to avoid confusion with the macroscopicallyidentifiable, quality-laden, homogenous portions of everydayobjects. Unlike atomists, who attributed at least the quality ofhardness (impenetrability) to the ultimate particles of matter,Descartes argued that matter, or synonymously, body [corpus] has noqualities whatsoever, but only quantity, i.e., extension. In otherwords, body and extension are literally one and the same [resextensa]. An immediate corollary is that there can be no vacuum, forthat would require an extended region devoid of body --- a manifestcontradiction. The task, then, was to show how all apparent qualitiescan be explained in terms of the infinite divisibility andrearrangement of extension with respect to itself. The task was grandindeed, for its goal was to develop a unified celestial andterrestrial physics that could account equally for the ductility ofmetals, magnetic attraction, the tides, the mechanism of gravity, themotion of the planets, the appearance and disappearance of comets, andthe birth and death of stars (supernovae).

Descartes published his system of the world in 1644 as thePrinciples of Philosophy (PrincipiaPhilosophae). Part II of thePrinciples lays out thethesis of the identity of space (extension) and matter, develops adefinition of motion in the “true, or philosophical sense”, and setsout the fundamental dynamical laws of his system. Motion, according to“the truth of the matter”, is defined to be “the translation of onepart of matter, or one body, from the vicinity of those bodies, whichare immediately contiguous to it and are viewed as if at rest, to thevicinity of others.” In consequence, Descartes points out, each bodyhas a single motion proper to it (in contrast to the numerous relativemotions that can be ascribed to it depending on which other bodies areselected in order to determine its place). It is this single propermotion that figures in his laws of motion. Of particular importancefor Descartes' entire system, is that a body in circular motion has anendeavor [conatus] to recede from the center of rotation.

4. Newton's ManuscriptDe Gravitatione …

This fact, together with Descartes' contention that a body alsoparticipates in the motion of a body of which it is a part, makes itdifficult to reconcile Descartes' system of the world with hisdefinition of proper motion. Newton concluded that the doctrine is infact self-refuting and that, where Descartes needed to, he hadsurreptitiously helped himself to a notion of space independent ofbody, particularly in order to assign the desired degree ofcentrifugal conatus to the planets and their satellites asthey are swept about by celestial vortices of “subtle” matter.

The untitled and unfinished manuscript which begins “De Gravitationeet aequipondio fluidorum et solidorum …”, written perhaps a decadeor more before thePrincipia, consists for the most part ofan extensive and scathing critique of Descartes' doctrine ofmotion. The document, published for the first time in (Hall and Hall,1962), is well worth the study for a glimpse at the development ofNewton's thinking at a relatively young age. It manifestly embracesthe doctrines of space and time later codified in thePrincipia. Notable, as well, is that each of the fivearguments from the properties, causes and effects of motion advancedin the Scholium has a clearly identifiable antecedent in DeGravitatione. (See Rynasiewicz 1995 for details.) This makes itclear the extent to which the Scholium is concerned to arguespecifically against the Cartesian system (as pointed out by Stein1967), which Newton perceived to be the only other viable contender atthe time.

5. Newton's Scholium on Time, Space, Place and Motion

The Scholium has a clearly discernible structure. Four paragraphsmarked by Roman numerals I–IV follow the opening paragraph, givingNewton's characterizations of time, space, place and motion,respectively, as summarized in the third paragraph of Section 1above. If we were to extend Newton's enumeration to the remainingparagraphs, then paragraphs V–XII constitute a sustained defense ofthe distinctions as characterized in I–IV. Paragraph XIII thenstates the general conclusion that the relative quantities aregenuinely distinct from the respective absolute quantities and makescomments on the semantic issue of the meanings of these terms in theBible. There follows one remaining, and quite extensive paragraph[XIV], which takes up the question how in practice one can ascertainthe true motions of bodies and concludes: “But how we are to obtainthe true motions from their causes, effects and apparent differences,and vice-versa, will be explained at length in the treatise thatfollows. For that is the end to which I composed it.”

In what follows, links have been inserted to the text of the Scholiumaccording to the extended enumeration suggested above. Clicking on alink will open a new window in such a way that the reader can navigateback and forth between a given paragraph of the text and thecommentary elucidating that paragraph.

5.1 Arguments for Absolute Time

ParagraphVappeals to the fact that astronomy distinguishes between absolute andrelative time in its use of the so-called equation of time. Thisserves to correct for inequalities in the commonly adopted standard oftime, the solar day, which most people mistakenly believeto be uniform. The solar day, defined as the period of time it takesthe sun to return to zenith, varies by as much as 20 minutes over thecourse of a year. The standard of correction in the equation of timeused in Ptolemaic astronomy was based upon the assumption that thesidereal day—the period of time it takes a fixed star to returnto zenith—is constant, because the celestial sphere on whichthe fixed stars are located should not be assumed to speed up and slowdown. With the demise of the Ptolemaic system and Aristoteliancosmology, this rationale was no longer compelling, and at least someastronomers, most notably Kepler, called into doubt whether the rate ofrotation of the earth remained constant over the course of theyear. (Kepler considered that its rotation would be faster when closerto the sun due to an excitatory effect of the sun.) Thus, the issue ofthe correct measure of time occupied considerable attention in 17thCentury astronomy, especially because the ability to measure the rateof rotation of the earth is equivalent to the problem of determininglongitude, which, for sea-faring nations, was critical for navigation(and hence military and economic dominance). Huygens' pendulum clockprovided the first terrestrial candidate for a decently accuratemeasure of uniform time. Newton mentions this, as well as the eclipsesof the moons of Jupiter, an alternative method based on Kepler'speriod law.

The invocation of the need for an equation of time in astronomy isnot just an appeal to a well entrenched scientific practice. In thecourse of his discussion, Newton explains why he thinks the need isjustified. Although he will argue in BookIII of thePrincipia that the diurnal rotation of the earthis uniform, this is a contingent fact. It could have been otherwise.Indeed, it could have been that there areno uniform motions to serve as accurate measures oftime. The reason is that all motion is subject to being accelerated orretarded (by the application of external forces). In contrast,absolute time (which is nothing other than duration or theperseverance of the existence of things) remains the same, whether themotions be be swift, slow, or null.

5.2 Direct Arguments for Absolute Space

ParagraphVI defendsthe thesis of the immobility of (absolute) space, which against thebackdrop of Descartes, clearly means that the parts of space, just asthe parts of time, do not change their relation with respect to oneanother. Newton argues that the parts of space are their own places,and for a place to be moved out of itself is absurd. A more expansiveantecedent of this argument occurs inDe Gravitatione,applied specifically to time: if yesterday and tomorrow were tointerchange their temporal relations with respect to the remainder oftime, then yesterday would become today, and today yesterday. Thus,Newton held an interestingly holistic identity criterion for the partsof space and time.

5.3 The Arguments from Properties, Causes, and Effects

Newton devotes five full paragraphs to justifying hischaracterization of the distinction between absolute and relativemotion. The first three present arguments from properties of absolutemotion and rest, the next presents an argument from their causes, andthe final an argument from their effects. The force of these hasconfused modern commentators for a combination of reasons which,historically, are difficult to untangle. Since only those not alreadyprejudiced by those commentaries, directly or indirectly, will findwhat follows unusual, it is best to defer an autopsy of those reasonsuntil Section 6, after an exposition of the arguments.

Suffice it to say for the moment that it is a common misunderstandingthat in these arguments Newton intends to develop empiricalcriteria for distinguishing cases of absolute motion from merelyapparent motion and thereby to disprove the thesis that all motion is merely relative motion. To the contrary,the arguments take as their point of departure the assumption, commonto Cartesian and Aristotelian philosophy, that each body has a uniquestate of true motion (or rest). Throughout the arguments, the terms‘true motion’ and ‘absolute motion’ aretreated synonymously. At issue is whether true motion (and rest) canbe reduced to some special instance of relative motion (or rest) withrespect to other bodies. In announcing at the outset of thesearguments that “absolute and relative rest and motion aredistinguished by by their properties, causes, and effects”, Newtonindicates his intent to show that they cannot, at least if true motionand rest are to have those features we generally associate, or oughtto associate, with them.

Argument 1 from Properties [Paragraph VIII]

Property: Bodies that are truly at rest are at rest with respect to one another.

Conclusion: True rest cannot be defined simply in terms of position relative to other bodies in the local vicinity.

Reasoning: Suppose there were a body somewhere inthe universe absolutely at rest, say far away, in the region of thefixed stars, or even farther. (Whether or not that body might ever beobserved doesn't enter into what follows.) Clearly it is impossible toknow just from considering the positions of bodies in our regionrelative to one another whether any of these latter bodies maintains afixed position with respect to that hypothetical distant body. Toamplify, let B be one of the local bodies, C the relativeconfiguration over time of the set of local bodies, and A the fardistant body at absolute rest. The specification of C alone fails toestablish the position of B relative to A over time. In particular, Cfails to establish whether B is relatively at rest with respect A,which, by the property stated above, is a necessary condition for B tobe absolutely at rest. Hence, specification of the local configurationC underdetermines whether or not B is at absolute rest. Thus theconclusion: it is impossible to define what it is for a body such as Bto be at absolute rest [i.e., to give necessary and sufficientconditions for when it is that B is at rest] simply in terms of how Bfits into the local configuration C.

Argument 2 from Properties [Paragraph IX]

Property: If a part of a body maintains a fixedposition with respect to the body as a whole, then it participates inthe motion of the whole body.

Conclusion: True and absolute motion cannot bedefined as a translation from the vicinity of (the immediatelysurrounding) bodies, viewing the latter as if they were at rest.

Reasoning: Newton first introduces twoconsiderations that can be taken either to support, or to illustrate,or to amplify upon the import of the stated property. The first isthat if a part of a rotating body is at rest relative to the body as awhole, it endeavors to recede from the axis of rotation. The second isthat the impetus of a body to move forward arises from the combinationof the impetus of its parts.

From the property it follows that if those bodies surrounding a givenbody move (either rotationally or progressively forward as a fixedconfiguration) while the surrounded body is at rest relative to thesurrounding ones, then the surrounded body partakes in the (true)motion of the group of surrounding bodies. Hence, if the surroundingbodies move truly, then so does the surrounded body. But according tothe (Cartesian) definition of motion—which identifies the truemotion of a body with its transference from the vicinity ofimmediately surrounding bodies, regarding the surrounding bodies to beas though they are at rest—it would have to be said (wrongly)that the surrounded body is truly at rest. Hence that definition isuntenable.

Argument 3 from Properties [Paragraph X]

Property: Anything put in a moving place moves alongwith that place, and hence a body participates in the motion of itsplace when it moves [relatively] away from that place.

Conclusion: The complete and absolute motion of abody cannot be defined except by means of stationary places.

Reasoning: From the property, the [relative] motionof a body out of a given place is only part of the motion of the bodyif the place in question is itself in motion. The complete and truemotion of the body consists of its motion relative to the moving placeadded vectorially to whatever motion the place may have. Should theplace be moving relative to a place which is in turn moving, then themotion of that place must be added, and so on. Barring infiniteregress, the sum must terminate with a motion relative to a stationaryplace.

Addended Argument: After deriving this conclusion,Newton amplifies upon the consequences. The only places that arestationary are all of those that that stay in fixed positions withrespect to one another from infinity to infinity, and since thesealways remain stationary, they make up what Newton calls immobileabsolute space.

The Argument from Causes [Paragraph XI]

Causes: the forces impressed upon bodies. The majorpremise is that application of a [non-zero net] force on a body isboth a necessary and sufficient condition for either generating oraltering its true motion. More specifically:

(A) Impressed force is a necessary condition for generating oraltering true motion (but not, as remains to be shown, merely relativemotion).

(B) Application of a [non-zero net] force is a sufficient conditionfor the generation or alteration of true motion (but not, as will beshown subsequently, merely relative motion).

Conclusion: The true motion of an individual bodycannot be defined as any particular sub-instance of its motionrelative to other bodies.

Reasoning: Newton seeks to establish thatapplication of a positive net force to a body is neither a necessarynot a sufficient condition for the generation of motion relative toother bodies. The two lines of reasoning are given separately, callthem ‘Prong A’ and ‘Prong B’, respectively.

Prong A: To be established is that, although an impressedforce is necessary for the generation or alteration of true motion ina body, it is not necessary for the generation of motion relative toother bodies. The reasoning is quite simple: pick a given body andmerely apply the same [accelerative] force to all other bodies inquestion. These other bodies will then remain in the same relativeconfiguration with respect to one another, but a relative motion withrespect to the original body [to which no force has been applied] willeither be generated or altered.

Prong B: To be established is that, although an impressedforce is sufficient for the generation or alteration of true motion ina body, it is not sufficient for the generation of motion relative toother bodies. Again, the line of reasoning is quitestraightforward. Consider an arbitrarily given body amongst a systemof bodies and simply apply the same [accelerative] force to all bodiesin question. Then, despite the fact that a force has been impressedupon the originally given body, there is neither generation noralteration of relative motion with respect to the remaining bodies.

The Argument from Effects [Paragraph XII]

Effects: the forces of receding from the axis ofrotational motion [centrifugal endeavor]. The major premise is thatthe centrifugal endeavor of bodies [or parts of bodies] to recede fromthe axis of rotation is directly proportional to the quantity of thetrue circular motion.

Conclusion: True rotational motion cannot be definedas relative rotation with respect to the surrounding bodies.

Reasoning: The line of reasoning is in fact parallelto the preceding argument from causes, although this may not becompletely perspicuous due to the fact that the correlates of the twoprongs above are here stages of a single on-going experimentalsituation, the so-called “rotating bucket” experiment, which, Newtonintimates, he actually performed. In order to set up this experiment,one suspends a bucket using a long cord and by turning the bucketrepeatedly, winds up the cord until it is strongly twisted, then fillsthe bucket with water. During the course of the experiment, the degreeto which the water tries to climb up the sides of the bucket is usedas a measure of its centrifugal endeavor to recede from thecenter. Newton uses the experiment to establish that centrifugalendeavor is neither a necessary condition nor a sufficient conditionfor the existence of relative circular motion [of the water] withrespect to its surroundings [the bucket].

Stage 1: When the bucket is first released, it rotatesrapidly with respect to the rest frame of the experimenter while thewater remains at rest with respect to the experimenter. In otherwords, there is rapid relative motion of the water with respect to thebucket. However, the surface of the water remains flat, indicatingthat it has no tendency to recede from the axis of relativerotation. Thus, the existence of centrifugal endeavor in the parts ofa body is not a necessary condition for the body to be rotatingrelative to its surroundings. That is, such relative rotation withrespect to immediately adjacent bodies need not produce anycentrifugal endeavor in the parts of the body to recede from the axisof relative rotation.

In the further course of the experiment, as the bucket continues torotate, the water gradually begins to rotate with it, and as it doesso, begins to climb up the sides of the bucket. Eventually, accordingto Newton, the water acquires the same rotation of the bucket relativeto the lab frame, at which point we have the following situation.

Stage 2: The water and the bucket are at relative rest, yetthe water has achieved its highest ascent up the sides of the bucket,indicating a maximum centrifugal endeavor to recede from the axis ofcommon rotation. Hence, the existence of centrifugal endeavor is not asufficient condition for the presence of relative circular motionbetween a body and its surroundings, i.e., if a body, or rather itsparts, have a centrifugal endeavor to recede from a central axis, itdoes not follow that there is a relative circular motion of the bodywith respect to its immediate surroundings.

Astrophysical Application. After deriving theconclusion, Newton uses the premises of the first two arguments fromproperties, together with the premise of the argument from effects, tocritique the vortex theory of planetary motion. According to thattheory, each of the planets (and most notably the earth) is relativelyat rest with respect to the “subtle” matter of the celestial vortex ofour own sun. Hence, according to Descartes' own definition of truemotion (as well as his explicit insistence), they have no truemotion. However, it is manifest that they do not maintain fixedpositions with respect to one another. So, according to the propertyinvoked in the first argument, they cannot [all] be truly atrest. Moreover, from the property invoked in the second argument, theypartake in the circular motion of the solar vortex [assuming thatmotion to be true motion, as Descartes implicitly assumed]. Finally,because they would accordingly participate in the true circular motionof this hypothetical vortex, they should have an endeavor to recedefrom the axis of its rotation.

This completes the sequence of arguments from the properties, causes,and effects of motion. The next paragraph [XIII] states the cumulative conclusions of the arguments marshalledbeginning with the arguments for absolute time in paragraph V: “Hencerelative quantities are not the quantities themselves, whose namesthey bear, but are only sensible measures of them (either accurate orinaccurate), which are commonly used in place of the quantities theymeasure.” Having made his case, Newton comments on the ordinarylanguage meaning of the terms for these quantitiesin order to address contemporary issues of dogmaand heresy.

Galileo's condemnation by the Catholic Church for asserting that theearth is in motion was still recent history at the time Newtoncomposed thePrincipia. Descartes, who lived in reach ofPapal authority and feared similar fate, had found a clever way ofespousing Copernicanism without falling prey to accusation ofheresy. According to his definition of motion “properly speaking”, hecontends, the earth is truly at rest.

In Newton's system of the world as set out in Book III of thePrincipia, the earth patently moves absolutely. Inanticipation, Newton indicates how to reconcile this with scripture byobserving that, if usage determines the meanings of words, then inordinary discourse (including the Bible) the terms ‘time’,‘space’, ‘place’, and ‘motion‘ areproperly understood to signify the relative quantities; only inspecialized and mathematical contexts do they denote the absolutequantities. (Keep in mind Newton's title,TheMathematical Principles of Natural Philosophy.)He proceeds to chastise Descartes on two counts, first for doingviolence to the scriptures by taking them to refer to the absolutequantities, and second, for confusing the true quantities with theirrelative measures.

5.4 Discriminating in Practice between Absolute and Apparent Motion

Having argued his case that true motion consists in motion withrespect to absolute space, and thus having dealt to his satisfactionwith themetaphysics of motion, Newton turns in the finalparagraph of the Scholium toepistemological strategiesavailable on his account. On an Aristotelian or Cartesian account, onecan directly observe the allegedly absolute motion of a body if bothit and its immediate surroundings are visible. In contrast, becausethe parts of absolute space are not directly accessible to the senses,it is very difficult, Newton confesses, to ascertain the true motion ofindividual bodies and to discriminate them in practice from theapparent motions. “Nevertheless,” he remarks in a rare moment of wit,“the situation is not entirely desperate.” Evidence is available inpart from apparent motions, which are the differences of true motions,and in part from the forces, which are the causes and effects of truemotions.

Newton illustrates with an example. Imagine a pair of globes,connected by a cord, revolving about their common center ofgravity. The endeavor of the globes to recede from the axis of motionis revealed by the tension in the cord, from which the quantity ofcircular motion can be estimated. Furthermore, whether the direction oftheir revolution is clockwise or counterclockwise can be detected byapplying forces to opposite faces of the globes to see whether thetension in the cord increases or decreases. All this can be done inempty space where no other bodies are present to serve as points ofreference.

Suppose now that, in addition to the globes, there is second systemof bodies maintaining fixed positions with respect to one another (forexample, the fixed stars). If the two systems are in a state ofrelative rotation, one cannot gauge from just the relative rotation,which, if either, is at rest. However, from the tension in the cordconnecting globes, one can establish whether the relative rotation isdue entirely to the absolute rotation of the system ofglobes. Supposing so, the second system of bodies can then beexploited to provide an alternative technique for determining whetherthe globes revolve in a clockwise or counterclockwise direction—one simply consults the direction of rotation relative to the stationary system.

At this point Newton cuts off the Scholium, explaining that the wholepoint of having written the treatise to follow is to show how to inferthe true motions from their causes, effects, and apparent differences,and conversely the causes and effects from either the true or theapparent motions.

6. Common Impediments to Understanding the Scholium

As remarked in Section 5.3 above, the purpose of the arguments fromproperties, causes, and effects has been widely misunderstood in boththe historical and philosophical literature, and as a consequence, sotoo the relation of these to the example of the revolving globes inthe final paragraph. Some diagnosis as to why may help those readersalready steeped in tradition to overcome certain prejudices they bringto the Scholium and may also serve to further illuminate the frameworkin which Newton and his contemporaries struggle with the problem ofmotion.

6.1 What the Major Impediments Are

(1) Newton's stated intention in the Scholium is to maintain thatabsolute space, time, and motion are genuinely distinct from theirrelative counterparts. For the case of space, this clearly amounts toarguing the existence of an entity distinct from body in which bodiesare located—something denied by relationists. Similarly, forthe case of time, this involves arguing the existence of an entitydistinct from the succession of particular events in which the eventsare located—again, something denied by relationists. It mayseem then as a matter of course that, for the case of motion, Newtonshould argue for existence of something denied by relationists,presumably, absolute motion.

(2) It would amount to a virtualpetitio principii wereNewton to rest a case for absolute motion on the existence of absolutespace. Hence, one would expect him to appeal to various physicalphenomena that might provide independent warrant. Now it is well knownthat Newton's laws satisfy the principle of Galilean relativity,according to which there can be no experimental test to determinewhether a system is at rest or in a state of uniform rectilinearmotion. However, Newton's lawsdo support a distinctionbetween inertial and non-inertial motion in that they predict, innon-inertial frames, the appearance of so-called “fictitious forces,”for instance, centrifugal forces in rotating frames, resulting in atendency for bodies to recede from the axis of rotation. Since this isexactly the effect involved in the rotating bucket experiment, it istempting to interpret Newton as marshaling it as a case in which thisphenomenon suggests independent warrant for the existence of absolutemotion.

(3) Moreover, since the same effect is operative in the example ofthe revolving globes, it is hard to see why that example does notserve the very same purpose. In fact, in his famous critique of Newtonin theScience of Mechanics, Ernst Mach, in quoting from thePrincipia, cut out all of the intervening text to make itappear as though the two are but variant examples in the developmentof a single argument.

(4) Finally, the choice of language in Motte's 1729 translation,which is the basis for the most widely available twentieth centuryEnglish translation by Cajori, tends to reinforce the presumption thatthe arguments from properties, causes, and effects seek to identifyphenomena thatempirically distinguish absolute from (merely)apparent motion. In the Cajori version, the conclusions of the firstthree arguments, the arguments from the properties of motion and rest,read:

• … it follows that absolute rest cannot be determined fromthe position of bodies in our regions. [Paragraph VIII]
• …the true and absolute motion of a body cannot bedetermined by the translation of it from those which only seem torest; [Paragraph IX]
• Wherefore, entire and absolute motions can be no otherwisedetermined than by immovable places; [Paragraph X]

Thus, it is tempting to assume that both the argument from causes andthe argument from effects are likewise concerned to identify anempirical signature of absolute motion by which it can bedistinguished from (merely) apparent motion. (Reading the arguments inthis fashion, only the argument from effects, which deals with thecentrifugal effects of circular motion, appears to help Newton's cause—a commonly registered complaint.)

6.2 Why They Are Indeed Impediments

It will be more illuminating to respond to these in reverse order.

(Ad 4) It is an artifact of Motte's translation that the Latin verbdefiniri (passive infinitive) is rendered occasionally as‘be determined’ rather than as ‘bedefined’. According to seventeenth-century English usage, eitherchoice is acceptable. In appropriate contexts, the two function assynonyms, as in the Euclidean axiom, “Two points determine a line.”Motte's practice conforms with this. The conclusion of the argumentfrom effects, ‘definiri’ is translated as ‘bedefined’:

And therefore this endeavor does notdepend upon any translation of the water in respect of the ambientbodies, nor can true circular motionbe defined by suchtranslation. [Paragraph XII]

If one now goes back and substitutes ‘be defined’ for‘be determined’ into the conclusions from the argumentsfrom properties quoted above, they take on, to the modern ear, adifferent meaning. They make claims as to what constitutes an adequatedefinition of the concepts of true, or absolute, motion and rest.

(Ad 3) We have already seen howparagraph XIII signals the conclusion,not just of the arguments from properties, causes, and effects, butthe direct arguments for absolute time and absolute space as well,which, altogether, Newton takes establish the ontological distinctionbetween the absolute and the relative quantities. That the nextparagraph, in which the globes are introduced, concerns a different,epistemological issue would be apparent were it not for anotherartifact of the Motte translation, this time involving the Latin verb‘distinguere’. Newton uses the word again and again,almost thematically, in characterizing and arguing for the ontologicaldistinction between the absolute and the relative quantities; andMotte renders it in English as ‘todistinguish’. Unfortunately, the English verb appears in theMotte translation one more time at the start of the final paragraph:

It is indeed a matter of great difficulty to discover,and effectually to distinguish, the true motions of particular bodiesfrom the apparent;

But in the Latin, the word ‘distinguere’ is nowhere to befound. Rather, the sentence reads:

Motus quidem veros corporum singulorum cognoscere, &ab apparentibusactu discriminare, difficillimum est;

Thus, to the Latin reader, it is clear that Newton is moving on to adifferent consideration.

(Ad 2) What has been said in connection with (4) suffices against thefalse expectations developed in (2). However, there may remain somesense that, even on a proper reading, Newton tried to bluff his waypast the principle of Galilean relativity. Newton indeed acknowledgesthe principle, though not by name, in Corollary V to the laws ofmotion:

The motions of bodies in a given [relative] spaceare the same among themselves whether that space is at rest or movesuniformly in a straight line without uniform motion.

And there is no reason to think that he did not appreciate thelimitation it poses for experimentally differentiating betweenabsolute rest and uniform motion in a straight line. A particularinstance of Corollary V is the solar system as a whole. Assuming theabsence of external forces, it follows (from Corollary IV to the laws)that the center of gravity of the solar system is either at rest ormoves uniformly in a straight line. But which? Because of Corollary V,when Newton wishes to attribute a definite state of motion to thecenter of mass of the solar system in Book III, he must introduce the hypothesis that “The center of the system of the world is atrest.” Should this not be some source of embarrassment?

Apparently not. Immediately following the hypothesis, he writes:

This is conceded by everyone, although some contend it isthe earth, others the sun, that is at rest in the center. Let us seewhat follows from this.

According to Newton, the attribution of a state of absolute rest toone or the other of these bodies is universally taken forgranted. What does confound all conventional wisdom in what follows isthat neither the earthnor the sun is at rest, but rather thecenter of gravity of the solar system.

(Ad 1) Although arguing that absolute space and absolute time aredistinct from any relative spaces and relative times involves, in eachcase, arguing for the existence of an additional entity, it does notfollow that, in arguing that absolute motion is distinct from relativemotion, Newton is obliged to argue yet another existenceclaim. Unfortunately, the term ‘absolute motion’ is proneto be read in two distinct ways. On one reading, it means, as a matterof stipulative definition, ‘change of absolute place’. Inthis sense of ‘absolute motion’, the existence of absolutemotion (or more precisely, the possibility of the existence ofabsolute motion) follows immediately from the existence of absolutespace and absolute time. As indicated before, nothing further needsto be said. On the other reading, ‘absolute motion’ issynonymous with ‘true motion’. And as we have just seen,Newton finds no reason to doubt that his audience does not grant thata body is either truly at rest or truly in motion. The venerabletradition that takes motion and rest to be contraries has yet to bequestioned. So it is not incumbent on Newton make a case for thereality of absolute motion in the sense of true motion. What isincumbent is for him to argue that true motion just is change ofabsolute place. And that is the purpose of the arguments fromproperties, causes, and effects.

7. Newton's Legacy

Newton's views on space, time, and motion dominated physics from the17th Century until the advent of the theory of relativity in the 20thCentury. Nonetheless, these views have been subjected to frequentcriticism, beginning with contemporaries, such as Leibniz andBerkeley, and continuing on to the close of the 19th Century, mostnotably with Ernst Mach, whose writings influenced Einstein. In theearly twentieth century, Newton tended to be cast as a metaphysicaldogmatist by the early philosophical interpreters of relativity, inparticular Hans Reichenbach. Unfortunately, that stigma has tended tolinger.

More recent scholarship reveals a more sober picture of why Newtonfelt fully justified in positing absolute space, absolute time, andabsolute motion. Moreover, the novel feature of special relativity,the rejection of absolute simultaneity—something that neveroccurred to any of Newton's earlier critics—necessitated onlythat absolute space and absolute time be replaced with an absolutespace-time (Minkowski spacetime). And although Einstein's developmentof general relativity was in large part motivated by a desire toimplement a general principle of relativity, to wit that all motion isrelative motion, that it succeeds in doing so was questioned shortlyafter the theory was introduced. As for the question of theabsoluteness of space-time in general relativity, it no longer has thecharacter of something which acts without being acted upon, asEinstein himself pointed out. The space-time metric tensornot only encodes for spatiotemporal structure, but also represents thegravitational potentials, and thus gravitational energy. By Einstein'sfamous equation for the equivalence of energy and mass,it follows that the gravitational field possesses mass. Only, since gravitational energy can not be localized in terms ofan energy density tensor, but is possessed by the field holistically,neither can this mass be localized. Thus, philosophicalcontroversy as to whether space-time can exist without matter becomestendentious according whether one counts the gravitation field assomething material or not.

Thus, the question whether the revolution in our views about spaceand time in the last century vindicates Newton's critics as morephilosophically astute becomes a misplaced one. The distinctionbetween what counts as matter in contrast to empty space presupposedin the earlier debates has been eclipsed by possibilities undreamt ofbefore the introduction of modern field theory and relativity.^[1]

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• Andrew Motte's 1729 translation of thePrincipia
• Voltaire on Descartes and Newton

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Acknowledgments

I'd like to thank John Norton for observations which led to many improvements.