Newton General Scholium Etc

Newton’s Theory of Universal Gravitation,

the Cause of Gravity, and the General Scholium

Sheldon Chow

September 2008

Newton’s famous General Scholium did not appear in the first edition of the Principia, but

was included in the second and third editions (appearing with revisions in the third edition). I.

Bernard Cohen reports that Newton was constantly changing his mind about how he would

conclude the Principia—Newton suppressed a draft conclusion intended for the first edition; he

abandoned his initial ideas for a final discussion for the second edition, composing the General

Scholium instead; and he had intended a number of revisions to the General Scholium for the

third edition, some of which were never included in the final publication (Cohen, 1999).1

As it appears in the second and third editions, the General Scholium can be divided into four

distinct, yet related, parts. In the first part, Newton reaffirms that the celestial phenomena are

not compatible with the Cartesian vortex theory. More particularly, Newton stresses that the

regular orbital motions of the heavenly bodies cannot be explained by mechanical causes. The

second part is devoted to a relatively lengthy discussion on God, and how God relates to space

and time. The penultimate paragraph of the General Scholium is its third section. This third part

has been given much attention by scholars—“the most discussed portion of all of Newton’s

writings”, according to Cohen (1999, p. 275). It is here where Newton explains that, while the

cause of gravity remains a mystery, he has sufficiently shown (in the Principia) that his theory of

universal gravitation explains the planetary motions. The final paragraph of the General1See in particular Cohen, 1999, p. 274; see also translator’s footnotes to the General Scholium in the Cohen &

Whitman translation of the Principia, pp. 939-944.

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Newton’s Theory of Universal Gravitation,the Cause of Gravity, and the General Scholium Sheldon Chow

Scholium has also received much scholarly attention, though Newton had intended to omit it

altogether from the third edition of the Principia (Cohen, 1999, p. 279).2 In this final paragraph,

which is the fourth part of the General Scholium, Newton introduces “a certain very subtle spirit”

which is supposed to be the agent which is responsible for certain forces and actions.

This paper concerns Newton’s theory of universal gravitation and his philosophical views on

the cause of gravity. My intent is to shed light on these matters by an examination of the General

Scholium. Each of its parts bears importantly and in interrelated ways on Newton’s theory of

universal gravitation and the cause of gravity. By examining each part, I will argue for four

things: (1) I reject the possibility that Newton believed that a “subtle spirit”—which is

introduced in the final paragraph of the General Scholium and discussed in the Queries to the

Opticks—is the cause of gravity; (2) I also reject the possibility that he believed that God is the

cause of gravity. (3) I argue instead that Newton, on his own methodology, was not required to

seek out the cause of gravity, and that he deliberately withheld from making claims about it. (4)

I conclude that gravity’s cause, for Newton, is an issue that does not bear on the truth of his

theory of universal gravitation.

1 The penultimate paragraph of the General Scholium:Situating the issue

The penultimate paragraph of the General Scholium is what I call its third part. This is the only

part of the General Scholium in which Newton mentions gravity. In that paragraph, Newton

affirms that gravity is that force which acts on heavenly bodies according to the laws he has set

forth in the Principia, and is responsible for celestial and terrestrial phenomena, in particular, the

planetary motions and the tides. Though he admits that he has not discovered a cause of gravity,

Newton declares that gravity “is enough” to explain these phenomena. As Newton writes:2See also the translator’s footnote to the final paragraph of the General Scholium (Cohen & Whitman translation,

pp. 943-944).

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Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity,but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause thatpenetrates as far as the centers of the sun and planets without any diminution of its power toact, and that acts not in proportion to the quantity of the surfaces of the particles on which itacts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter,and whose action is extended everywhere to immense distances, always decreasing as thesquares of the distances. . . . I have not as yet been able to deduce from phenomena the reasonfor [the] properties of gravity, and I do not feign hypotheses. For what ever is not deducedfrom the phenomena must be called a hypothesis; and hypotheses, whether metaphysical orphysical, or based on occult qualities, or mechanical, have no place in experimental philosophy.In this experimental philosophy, propositions are deduced from the phenomena and are madegeneral by induction. The impenetrability, mobility, and impetus of bodies, and the laws ofmotion and the law of gravity have been found by this method. And it is enough that gravityreally exists and acts according to the laws that we have set forth and is sufficient to explainall the motions of the heavenly bodies and of our sea. (Principia, p. 943, original emphases)3

Cohen reports that Ernst Mach hailed Newton as an early positivist given his “it is enough”

remark, and other scholars have followed Mach in this ascription to Newton. Cohen himself,

however, believes that “Newton’s position was altogether free of any taint of positivistic

philosophy” (Cohen, 1999, p. 277). As Cohen rightly points out, Newton did in fact attempt to

find some causal account for gravity as a force, and this task occupied Newton in varying degrees

from the time of composing the Principia in the 1680s, to 1717 when he published the second

revised English edition of the Opticks wherein he introduced his Queries (Query 21 in particular,

to be discussed below), and even unto his death. According to Cohen, this indicates that it was

never “enough” for Newton that the explanation for the observed celestial and terrestrial

phenomena rests on a force that (in Newton’s plain words) “really exists”.

What is certain is that Newton believed that gravity and its effects were real. In particular,

he believed that the force that keeps the planets and their satellites in their orbits is the same

force as that which causes bodies to fall towards the center of the earth; it is this force that

“really exists” for Newton. So, as Cohen claims, although Newton did not understand the cause

and mode of action of universal gravity, it nevertheless provided him a fruitful means by which to3All citations of Newton’s Principia will refer to The Principia, Mathematical principles of natural philosophy: A

new translation, translated by I.B. Cohen & A. Whitman, 1999.

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move ahead with the science of rational mechanics and celestial dynamics. However, this insight

still leaves us wanting an understanding of Newton’s continual search for gravity’s cause, and we

must inquire into why it was not “enough” for Newton “that gravity really exists”. I will return

to this issue in section 4, where I consider the first part of the General Scholium. Examining the

rest of the General Scholium will assist us in understanding Newton’s motivations. I will begin

this task by looking at its final paragraph.

2 The final paragraph of the General Scholium: Does Newtonposit some entity to explain gravity?

Newton had for a short while entertained the possibility that the cause of gravitational forces

were the result differences in density of an “aetherial medium” which permeates all matter and

empty space. Some scholars speculate that this aetherial medium can be identified with, or is at

least somehow related to, the “subtle spirit” Newton mentioned in the final paragraph of the

General Scholium (which I call the fourth part). Interestingly enough, however, though Newton

mentions many phenomena concerning this spirit in his brief discussion in that final paragraph,

he does not include gravity among such phenomena:

A few things could now be added concerning a certain very subtle spirit pervading gross bodiesand lying hidden in them; by its force and actions, the particles of bodies attract one anotherat very small distances and cohere when they become contiguous; and electrical [i.e., electrified]bodies act at greater distances, repelling as well as attracting neighboring corpuscles; and lightis emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and thelimbs of animals move at command of the will, namely, by the vibrations of this spirit beingpropagated through the solid fibers of the nerves from the external organs of the senses to thebrain and from the brain into the muscles. But these things cannot be explained in a fewwords; furthermore, there is not a sufficient number of experiments to determine anddemonstrate accurately the laws governing the actions of this spirit. (Principia, pp. 943-944)

There is now no doubt that Newton was referring to an electrical spirit in this final

paragraph; as Cohen (1999, p. 282) reports, Newton, in his intended emendations to the second

edition of the Principia, qualified the “spirit” with the adjectives “electric and elastic”. Though

this emendation did not make it into the third Latin edition, it did make it into the English

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translation (by Andrew Motte). Nonetheless, Cohen remarks, that perhaps Newton was not ready

at the time “to do more than hint—by implication of my context—that this spirit might somehow

be related to gravity” (Cohen, 1999, p. 279). Cohen later expresses a similar comment when he

states that his impression after reading Newton’s unpublished conclusion to the Principia (which

will be discussed presently) is “that if more were known about the action of this spirit, then we

would understand the nature of attractive forces in general and so be in a better position to

understand the action of gravity” (Cohen, 1999, p. 286). However, I am not so sure about

Cohen’s speculation. For it seems as if Newton’s concern for the (electric) spirit is not meant to

suggest anything about gravity or its cause, but rather to indicate a different research

program—one of electric forces. Evidence for this is found in the aforementioned draft version of

a conclusion Newton intended for the second edition of the Principia, but which was replaced by

the General Scholium.4

Newton begins his unpublished conclusion by comparing and contrasting three forces of

attraction: gravity, electricity, and magnetism. This comparison is absent from the General

Scholium, though it helps us understand Newton’s mention there of the subtle spirit. Among the

similarities and differences Newton cites in his unpublished conclusion, he observes the following:

• The laws of the respective attractions of gravity, electricity, and magnetism are dissimilar.

• Electrical and magnetic attractions are intended and remitted; gravity cannot beintended or remitted.

• Gravity always attracts, whereas electricity and magnetism sometimes attracts andsometimes repel.

• Electricity and magnetism act at small distances; gravity at very great distances.

• All bodies gravitate in proportion to their quantity of matter; most bodies are electric,and only iron is magnetic; but neither the electric nor magnetic forces acts in proportionto their quantity of matter.

• Gravity is not at all impeded by the interposition of bodies; electric force is impeded anddiminished so; while iron is not impeded by the interposition of cold and nonferrousbodies, yet it is impeded by the interposition of “ignited” bodies and is propagatedthrough interposed iron bodies.

4The final portions of Newton’s unpublished conclusion is presented in Cohen (1999, pp. 287-292).

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• Gravity is not changed by friction; iron is strongly agitated by friction or percussion, andthereby readily receives the “virtue of magnetism”; electric force (“in sufficiently electricbodies”) is greatly excited by friction (sometimes the electric “spirit” is emitted frombodies (e.g., amber, diamond) by heat without friction; the same spirit may also attractbodies at small distances without friction or heat).

Simply put, gravity is a different sort of thing than electricity and magnetism.

Newton continues in the unpublished conclusion by describing and discussing various

experiments (primarily ones performed by Francis Hauksbee) in which Newton believes the

electric spirit is at work. It is important to note that once Newton begins his discussion of such

experiments, he no longer mentions the actions of gravitational or magnetic forces. Newton

explores the possibility that the electric spirit is responsible for other types of phenomena (e.g.,

the reflection and refraction of light), but again, in these speculative remarks Newton does not

mention gravitational or magnetic forces. Thus, as in the General Scholium, Newton does not

include gravity among the actions of this spirit. This seems to indicate that Newton believed that

gravitational forces (and its phenomena) were distinct from electric forces (and its phenomena).

At the very least, this suggests that Newton believed that gravity and electricity lacked a

common cause.

The draft conclusion is not the only other place where Newton discusses the electric spirit. As

Cohen reports, in all of the draft versions of the “Recensio Libri” (or “An Account of the Book

entitled Commercium Epistolicum”5), Newton was especially concerned with explaining what his

“spirit” is. Newton wrote that the subtle spirit or agent to which he refers in the final paragraph

of the General Scholium is “latent in bodies by which Electrical Attraction & many other

phaenomena may be performed” (quoted by Cohen, 1999, p. 280). In one draft, however, Newton

asserts that he “has nowhere denyed that the cause of gravity is Mechanical nor affirmed whether

that subtile spirit be material or immaterial nor declared any opinion about their causes” (quoted5This was a review written by Newton, and published anonymously, of the Royal Society’s report on priority of

the invention of the calculus. The relevant passages of the drafts of Newton’s “Account” are presented in Cohen(1999, pp. 280-282).

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by Cohen, 1999, p. 281). The same sentiment is found in the published version of the “Account”,

though Newton does not express it in these words. Here, too, we find that Newton is not

confounding the cause of gravity with the actions and nature of the “subtle spirit”—he is here

addressing these issues separately, and he is not implicating gravitational forces with his talk of

the “subtle spirit”.

Query 31 to Newton’s Opticks has much in common with the draft conclusion. In Query 31,

Newton likewise speaks of three forces of attraction: gravity, electricity, and magnetism. And he

also discusses Hauskbee’s experiments. Yet, he does not mention any kind of spirit. In fact,

Newton refrains from speculating about the causes of these forces altogether. He writes, “I

scruple not to propose the principles of motion, they being of very general extent, and leave their

causes to be found out” (Opticks, p. 542)6.

Newton does, however, refer to an “aetherial medium” in some of the other Queries. This is

the aetherial medium I mentioned above, which Newton had entertained as the possible cause of

gravitational forces. This occurs particularly in Query 21 where Newton famously speculates that

a universal aetherial medium, growing denser at greater distances from the heavenly bodies,

might explain the gravitational interactions between celestial bodies. He writes, “if the elastic

force of this medium be exceedingly great, it may suffice to impel bodies from the denser parts of

the medium towards the rarer [less dense], with all that power which we call gravity” (Opticks, p.

521). It should be noted that, unlike the vortex theory favoured by the mechanical philosophers

of Newton’s day (i.e., the Cartesians), this aether does not act by impact, but is rather governed

by short-range repulsive forces (between the particles of the aether) which are responsible for the

pressure exerted on bodies and its density, ultimately emulating gravitational forces. This

speculation about a possible cause for gravity is consistent with Newton’s remarks in the third6All citations of Newton’s Opticks will refer to Opticks: or A treatise of the reflexions, refractions, inflexions and

colours of light, based on the fourth edition London, 1730, Robert Maynard Hutchings (Ed.), Great books of theWestern world. Encyclopedia Britannica, Inc., 1952.

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part of the General Scholium where he distinguishes the cause of gravity from mechanical causes:

this force arises from some cause that penetrates as far as the centers of the sun and theplanets without any diminution of its power to act, and that acts not in proportion to thequantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do)but in proportion to the quantity of solid matter, and whose action is extended everywhere toimmense distances, always decreasing as the squares of the distances. (quoted above)

It seems unlikely, however, that Newton had transformed his thoughts on the spirit into the

action of the aetherial medium.7 Again, Newton does not mention this aetherial medium in

Query 31 where he discusses the phenomena he believed to be caused by the electric spirit, as he

also did not do so in his unpublished conclusion.

I will later return to Newton’s speculations on an aetherial medium, though it is dubious that

Newton’s aetherial medium should be identified with his electric spirit. At the very least, it is

dubious that Newton intended his electric spirit to serve as the cause of gravitational forces.

Howard Stein, in a footnote in his “Newtonian Space-Time” (1967) paper, suggests that

arguments that Newton was confronted with concerning the absence of any effect of a material

aether in planetary gravitational interactions—specifically, Newton’s Third Law applies only to

the two gravitating bodies, whereas if a material aether was responsible for propagating

gravitational forces, his Third Law would have to be applied to the interactions of the two bodies

and the intervening medium—contributed to Newton’s doubt whether a material aether causes

gravity. Stein indicates, however, that Newton was not wholly decided against an aether theory of

gravitation. However, he continues to say that Newton’s leaning away from an aether theory of

gravitation does not entail Newton’s rejection of aethers altogether in physics. He writes, “One

should distinguish skepticism about the ether as a cause of gravitation from skepticism about the

existence of hidden elastic fluid media affecting some physical interactions. I am not convinced

that Newton ever showed serious doubt on the latter point” (Stein, 1967, p. 283, footnote 6,

original emphasis). This may help us understand why Newton was interested in discussing an7Cohen, on the other hand, expresses the opposite opinion (see Cohen, 1999, p. 286, footnote 24).

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aetherial medium without committing himself to the view that it is the cause of gravity.

Cohen suggests that Newton’s consideration of the “subtle spirit” is an attempt at

introducing “new areas of research that may illuminate fundamental problems of cause and mode

of operation” (Cohen, 1999, p. 279). As Cohen indicates, this reading of Newton’s talk of his

spirit explains Newton’s final remarks in (the fourth part of) the General Scholium. I believe that

such a reading can just as well be taken to explain Newton’s unpublished conclusion, and his

draft versions of the “Account”. Indeed, in one draft of his “Account”, Newton writes (of

himself), “But what is this Agent or spirit & what are the laws by which it acts he leaves to be

decided by experiments” (quoted by Cohen, 1999, p. 281). And in yet another draft version,

Newton declares that he “did not propose [the hypothesis of a very subtile spirit at the end of the

Principia] by way of an Hypothesis but in order to [lead to] an inquiry” (quoted by Cohen, 1999,

pp. 281-282). We might likewise understand Newton’s talk of the aetherial medium as suggesting

new areas of research. In this vein, we need not take Newton to be intending his “spirit” or

aetherial medium to serve as an explanation of the cause of gravity.

3 The second part of the General Scholium: Does Newton positGod as the cause of gravity?

The second part of the General Scholium is devoted to a relatively lengthy discussion on God,

and how God relates to space and time. For instance, he writes,

[God] rules all things, not as the world soul but as the lord of all. . . . For “god” is a relativeword and has reference to servants, and godhood is the lordship of God, not over his own bodyas is supposed by those for whom God is the world soul, but over servants. . . . [God] is notduration [i.e., time] and space, but he endures and is present. He endures always and is presenteverywhere, and by existing always and everywhere he constitutes duration and space. . . .

. . . God is one and the same God always and everywhere. He is omnipresent not onlyvirtually but also substantially ; for action requires substance. In him all things are containedand move, but he does not act on them nor they on him. God experiences nothing from themotions of bodies; the bodies feel no resistance from God’s omnipresence. (Principia, pp.941-942, original emphases)

The importance of this part of the General Scholium pertains not only to Newton’s theology, but

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also to his metaphysics. In turn, from Newton’s metaphysics we could glean his thoughts on the

ultimate cause of gravity.

A more detailed account of Newton’s metaphysics, and in particular his conceptions of God

and how God relates to space, time, and matter, can be found in Newton’s “De Gravitatione et

Aequipondio Fluidorum”, an essay Newton wrote prior to the first edition of the Principia, but

which was never published in his lifetime. “De Gravitatione” provides explicit arguments against

the Cartesian doctrines of matter and motion, dismissing them as “fictions”. Newton then

proceeds to expound his absolutist doctrine of space, and discuss how this doctrine relates to his

conception of matter (or body).

In Article 4 of “De Gravitatione”, Newton declares, “Space is an affection of a being just as a

being. No being exists or can exist which is not related to space in some way. God is everywhere,

created minds are somewhere, and body is in the space that it occupies . . . . And hence it follows

that space is an emanative effect of [God] . . . ” (from Janiak, 2004, p. 25). Later in “De

Gravitatione”, Newton explains the nature of matter (or body). He asserts that “we may suppose

that there are empty spaces scattered throughout the world, one of which [is] defined by certain

limits” (from Janiak, 2004, p. 28). The limits to which Newton is referring define matter (or

body)

as determined quantities of extension with omnipresent God endows with certain conditions.These conditions are: (1) that they be mobile, . . . ; (2) that two of this kind cannot coincideanywhere, that is, that they may be impenetrable, and hence that oppositions obstruct theirmutual motions and they are reflected in accord with certain laws; (3) that they can excitevarious perceptions of the senses and the imagination in created minds, and conversely movedby them . . . (From Janiak, 2004, p. 28, original emphasis)

Hence, according to Newton, God endows certain regions of space with matter (or body)

primarily by instituting the laws of motion, distinguishing it from empty space. These regions are

thus matter (or body).

Michael Friedman (unpublished paper) believes that this formulation of space and matter

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leads Newton to his theory of universal gravitation of Book 3 of the Principia. This seems,

however, to be a bit of an overstatement. Strictly speaking, Newton derived his theory of

universal gravitation from astronomical phenomena—data on the motion of the planets and their

satellites—and the laws he expounded in Books 1 and 2. However, to be charitable, we might

understand Friedman’s point as claiming that Newton’s theory of universal gravitation is

metaphysically based on his conception of space and matter—that gravity and its effects result

from matter’s mobility, impenetrability, and obedience to the laws of motion. This, at least, is a

good starting place for us to follow Friedman in an investigation of the metaphysical assumptions

underlying Newton’s theory of gravity, and how God figures into it.

Friedman believes that Newton is suggesting that the true cause of gravity may be an

immaterial agent, perhaps even God himself.8 He asks us to consider Newton’s remark in “De

Gravitatione” that “God is everywhere” (quoted above). This assertion can also be found in

Query 31 to the Opticks where Newton describes God as “a powerful ever-living agent, who [is] in

all places” (Opticks, p. 542). Newton continues in this passage by saying, “[God] is [therefore]

more able by his will to move the bodies within his boundless uniform sensorium, and thereby to

form and reform the parts of the universe, than we are by our will to move the parts of our own

bodies” (Opticks, p. 542). A similar remark to this latter one is found in “De Gravitatione”:

Since each man is conscious that he can move his body at will, and believes further that othermen enjoy the same power of similarly moving their bodies by thought alone, the free power ofmoving bodies at will can by no means be denied to God, whose faculty of thought is infinitelygreater and more swift. (From Janiak, 2004, p. 27).

Friedman then gestures toward Newton’s words in the General Scholium, where he writes, “God

is one and the same God always and everywhere. He is omnipresent not only virtually but also8Friedman gestured toward this position in an earlier paper of his in which he commented, “Newton does not of

course explicitly assert that the ‘Agent’ responsible for gravity is either immaterial or divine. Nevertheless, althoughwe are clearly on shaky ground here, it is perhaps permissible to speculate that this is in fact his true conviction”(Friedman, 1990, p. 199). Friedman then briefly provides evidence that this position is not inconsistent with Newton’swritings. However, he does not there produce any substantial argument for his position as he does in his unpublishedpaper.

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substantially ; for action requires substance” (quoted above). This, then, is the evidence he

provides for his assertion that it is likely that Newton believed that God was the cause of gravity.

However, Friedman leaves the remainder of the latter passage for a short comment in a

footnote; recall that Newton continues this passage by saying, “In [God] all things are contained

and move, but he does not act on them nor they on him. God experiences nothing from the

motions of bodies; the bodies feel no resistance from God’s omnipresence” (quoted above, my

emphasis). In his footnote, Friedman suggests that we might suppose that Newton’s “subtle

spirit”, which is mentioned at the end of the General Scholium, is the cause of gravitational

attraction. However, as I had argued in the previous section, it is doubtful that Newton believed

his spirit is responsible for gravity and its effects. Nevertheless, Friedman insists that Newton

definitely excludes mechanical impact from the possible causes of gravity. This seems to be the

case given Newton’s remarks in the third part of the General Scholium: “this force [of gravity]

. . . acts not in proportion to the quantity of the surfaces of the particles on which it acts (as

mechanical causes are wont to do) but in proportion to the quantity of solid matter” (quoted

above). But precluding mechanical causes does not necessarily lead Newton to the conclusion

that some immaterial agent (perhaps God) is responsible for gravitational forces.

On Friedman’s argument, since God creates matter and its fundamental laws by an immediate

act of the divine will, “it is natural to suppose that the ubiquitous immaterial agent ultimately

responsible for gravitational attraction is either God himself or an ubiquitous immaterial spirit

directly resulting from God’s own ubiquity” (Friedman, unpublished paper). Friedman refers to

Query 31 to the Opticks where Newton suggests that God’s act of creating matter in space is

responsible not only for impenetrability and matter (in accordance with the three “passive” Laws

of Motion), but also for specific forces or “active principles”, including gravity:

[I]t seems probable to me, that God in the beginning formed matter in solid, massy, hard,impenetrable, moveable particles, of such sizes and figures, and with such other properties, andin such proportion to space, as most conduced to the end for which he formed them; . . .

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It seems to me farther, that these particles have not only a vis inertiae, accompanied withsuch passive laws of motion as naturally result from that force, but also that they are movedby certain active principles, such as is that of gravity. (Opticks, pp. 541-542)

Friedman thus maintains that it is Newton’s metaphysics of space and matter that provide the

grounds for universal gravitation acting at a distance—an immediate exchange of momentum

across empty space. Friedman may be right about this. However, he takes the further step of

asserting that Newton’s metaphysics introduces an immaterial agent to explain how this action at

a distance can occur. Yet, Friedman recognizes, referring to Robert DiSalle, that the requirement

that “all causal interaction in the material world be limited to the communication of motion by

impact” seems to be “an entirely arbitrary restriction on the basic principles governing the

exchange of momentum” (Friedman, unpublished paper). Consequently, Friedman claims that

there does not seem to be any reason that “a direct (equal and opposite) exchange of momentum

at a distance via universal gravitation may not be viewed as a perfectly legitimate example of

causal interaction” (Friedman, unpublished paper). Nevertheless, he dismisses this view as

post-Newtonian, claiming this was not Newton’s opinion, since in Newton’s time it was taken for

granted that one substance can act on another by efficient causality only if they are locally

present to each other.

But I do not think that Friedman’s account provides sufficient grounds for assuming that

Newton posited an immaterial medium through which gravity works its effects. Rather, it seems

that what is (minimally) required by Newton’s metaphysics is that gravity is a law among those

which God bestowed upon matter. Positing some immaterial medium therefore seems superfluous

to his metaphysics. A similar position was held by Robert DiSalle (1990, p. 206), and it seems to

be representative of Newton’s thoughts given Newton’s later remarks in Query 31: “These

principles [the active principles including gravity] I consider, not as occult qualities, supposed to

result from the specific forms of things, but as general laws of nature, by which the things

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themselves are formed; their truth appearing to us by phenomena, though their causes be not yet

discovered” (Opticks, p. 542). Such a sentiment may also be gleaned from Newton’s remark in the

third part of the General Scholium: “it is enough that gravity really exists and acts according to

the laws we have set forth”. That gravity is a God-given law does not imply, however, that God,

as an immaterial medium, is directly involved in all gravitational interactions.

This objection to Friedman’s argument mirrors the way in which Newton responded to a

criticism given by Leibniz. Leibniz wrote a letter to Nicholas Hartsoeker in which he claimed that

the Principia renders gravitation a “perpetual miracle” because it fails to specify its physical

causal mechanism underlying it.9 This sentiment was repeated in Leibniz’ letter to Samuel Clarke:

If God wanted to cause a body to move free in the aether round about a certain fixed center,without any other creature acting upon it, I say it could not be done without a miracle, sinceit cannot be explained by the nature of bodies. For a free body naturally recedes from a curvein the tangent. (Quoted in DiSalle, 2002, p. 47)

In his (unpublished) rebuttal to Leibniz, Newton wrote,

But he [Leibniz] goes on and tells us that God could not create planets that should moveround of themselves without any cause that should prevent their removing through thetangent. For a miracle at least must keep the planet in. But certainly God could createplanets that should move round of themselves without any other cause than gravity thatshould prevent their moving through the tangent. For gravity without a miracle may keep theplanets in. (From Janiak, 2004, p. 117)

Given Newton’s remarks here, as well as what he has written in his Query 31 and in the third

part of the General Scholium cited above, it seems as if Newton turned away from invoking God

or some immaterial entity to explain gravitational effects.

However, if we are to endorse the view that Newton believed that gravity is a law among

those of which God had bestowed upon matter, we must reconcile it with Newton’s assertion that

gravity is not an essential property of matter (or body). In a remark he made in the

Advertisement to the second edition of the Opticks, Newton wrote, “to show that I do not take9See Janiak, 2004, pp. xxix-xxx.

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gravity for an essential property of bodies, I have added one question concerning its cause”

(Opticks, p. 378); and in a letter to Richard Bentley in 1693, Newton wrote,

It is inconceivable that inanimate brute matter should, without the mediation of somethingelse, which is not material, operate upon and affect other matter without mutual contact, as itmust be, if gravitation in the sense of Epicurus, be essential and inherent in it. And this is onereason why I desired you would not ascribe innate gravity to me. That gravity should beinnate, inherent, and essential to matter, so that one body may act upon another at a distancethrough a vacuum without the mediation of anything else, by and through which their actionand force may be conveyed from one to another, is to me so great an absurdity, that I believethat no man who has in philosophical matters a competent faculty of thinking can ever fallinto it. (From Janiak, 2004, p. 102-103)

Some insight into this matter can be gained by returning to Newton’s “De Gravitatione”.

After expounding his doctrine of space, Newton writes,

it remains to give an explanation of the nature of body. Of this, however, the explanationmust be more uncertain, for it does not exist necessarily but by divine will, because it ishardly given to us to know the limits of the divine power, that is to say, whether matter couldbe created in one way only, or whether there are several ways by which different beings similarto bodies could be produced. And although it scarcely seems credible that God could createbeings similar to bodes which display all their actions and exhibit all their phenomena, andyet would not be bodies in essential and metaphysical constitution, as I have no clear anddistinct perception of this matter I should not dare to affirm the contrary, and hence I amreluctant to say positively what the nature of bodies is, but would rather describe a certainkind of being similar in every way to bodies, and whose creation we cannot deny to be withinthe power of God, so that we can hardly say that it is not body. (From Janiak, 2004, p. 27)

According to Stein (2002), Newton is here admitting that his doctrine of matter is fundamentally

conjectural, since bodies (unlike space) are effects of God’s will, and we do not know the ways in

which God may accomplish such effects. There remains, then, the possibility that observable

phenomena, or matter in particular, are effected in some different way than what Newton had

conceived. We might thus observe further that, although Newton asserts earlier in “De

Gravitatione” that in constituting or creating matter God must impose (among other properties)

gravity and its laws, he refrains from asserting that gravity (and the other properties) is essential

to matter, since he is ignorant of the workings of God, and God could have brought about

gravitational forces in some other way than which he conceives. Stein asserts that “the demand

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for a further ‘explanation’ [for the fundamental constitution of corporeal nature] . . . stems from

the Cartesian illusion that we must in principle have a ‘clear and distinct’ apprehension of the

necessity of the basic constitution of nature” (Stein, 2002, p. 279).

Stein continues by claiming that Newton’s discovery of the law of universal gravitation led

him “to a new conception of how it may be fruitful—not, as for Descartes, how it is necessary—to

conceive of the ‘actions’ that characterize nature, with a view to the deeper understanding of

natural phenomena” (Stein, 2002, p. 282, original emphases). The deeper understanding of

natural phenomena, as Stein asserts, comes from Newton’s program for natural philosophy. As

Stein understands it, Newton’s program for natural philosophy is spelled out in the Preface to the

Principia (first edition). Newton there wrote,

rational mechanics will be the science, expressed in exact propositions and demonstrations, ofthe motions that result from any forces whatever and of the forces that are required for anymotions whatever. . . . [S]ince we are concerned with natural philosophy . . . , we concentrate onaspects of gravity, levity, elastic forces, resistance in fluids, and forces of this sort, whetherattractive or repulsive. And therefore our present work sets forth mathematical principles ofnatural philosophy. For the basic problem of philosophy seems to be to discover the forces ofnature from the phenomena of motions and then to demonstrate the other phenomena fromtheses forces. It is to these ends that the general propositions on books 1 and 2 are directed,while in book 3 our explanation of the system of the world illustrates these propositions. Forin book 3, by means of propositions demonstrated mathematically in books 1 and 2, we derivefrom celestial phenomena the gravitational forces by which bodies tend toward the sun andtoward individual planets. Then the motions of the planets, the comets, the moon, and the seaare deduced from these forces by propositions that are also mathematical. If only we couldderive the other phenomena of nature from mechanical principles by the same kind ofreasoning! For many things lead me to have a suspicion that all phenomena may depend oncertain forces by which the particles of bodies, by causes not yet known, either are impelledtoward one another and cohere in regular figures, or are repelled from one another and recede.Since these forces are unknown, philosophers have hitherto made trial of nature in vain. But Ihope that the principles set down here will shed some light on either this mode ofphilosophizing or some truer one. (Principia, pp. 382-383)

Newton’s program for natural philosophy, then, as Stein describes, is one of “deriving the

phenomena of nature from ‘mechanical principles,’ not in the sense previously understood by

mechanical philosophy, but in the sense of principles governing forces of attraction and

repulsion—themselves to be discovered by reasoning from the phenomena” (Stein, 2002, p. 283,

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original emphasis).

Stein further claims that the last few words of the sentence, “But I hope that the principles

set down here will shed some light on either this mode of philosophizing or some truer one”

(quoted above), indicates that Newton’s program is put forward as tentative and open to revision.

This position is certainly consistent with Newton’s exclamation, “I do not feign hypotheses”.

Stein later writes, “we are not to suppose, dogmatically, that whatever principles we have

managed to discover are necessarily ‘the’ fundamental ones: it will be a question for the future

whether (yet deeper) causes of these principles may remain to be found out. In particular, this

explains why Newton never claimed—and strongly denied holding—that gravity is ‘essential’ to

bodies” (Stein, 2002, p. 291, original emphasis).

Stein later comments that Newton intended “to bring emphatically forward a new notion of

the unity of interaction as the form of a force of nature. . . . [T]his means that exactly those bodies

that are susceptible to the action of a given interaction-field [i.e., a central field constituting forces

of nature] are also the sources of the field” (Stein, 2002, p. 288). Bringing this to bear on

Newton’s metaphysics in “De Gravitatione”, “it implies that in creating a body, God (or in the

‘constitution’ of a body, nature) must impose, not only the field of impenetrability and the laws

of motion appropriate thereto, but other fields as well, with their laws, characterizing forces of

interaction” (Stein, 2002, p. 288-289). Newton expresses this sentiment in Query 31 to the

Opticks: “These principles [the active principles such as gravity] I consider, not as occult

qualities, supposed to result from the specific forms of things, but as general laws of nature, by

which the things themselves are formed ; their truth appearing to us by phenomena, though their

causes be not yet discovered. For these are manifest qualities, and their causes only are occult”

(Opticks, p. 542, my emphases). The task of natural philosophy, as seen in Newton’s Preface to

the Principia (first edition), is to discover these fields constituting the forces of nature—“the basic

problem of [natural] philosophy seems to be to discover the forces of nature from the phenomena

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of motions and then to demonstrate the other phenomena from these forces” (quoted above).

It is, therefore, not necessary for Newton to conceive of gravity as essential to matter. Yet,

according to Newton’s program, we may “discover” that certain forces are essential to matter,

and gravity may be among such essential forces. Nevertheless, such a discovery will not be

something that acts as a constraint on Newton’s natural philosophy or his metaphysics. Rather, it

will be the result of us learning something about matter (DiSalle, 1990).

4 The first part of the General Scholium: An indication thatNewton’s methodology did not need a cause of gravity

In the Scholium to Section 11 of Book 1 of the Principia, Newton describes a two-tiered analysis

of force:

Mathematics requires an investigation of those quantities of forces and their proportions thatfollow from any conditions that may be supposed. Then, coming down to physics, theseproportions must be compared with the phenomena, so that it may be found out whichconditions [or laws] of forces apply to each kind of attracting bodies. And then, finally, it willbe possible to argue more securely concerning the physical species, physical causes, andphysical proportions of those forces. (Principia, p. 589)

Thus, the two tiers, for Newton, are a physical treatment of force and a mathematical treatment

of force. Whereas a physical treatment of force describes, among other things, the causes and

qualities of forces, a mathematical treatments eschews such a description, providing instead a

characterization of its quantities (Janiak, 2004). In Definition 8, Newton declares that he is

treating the concept of force as “purely mathematical, for I am not now considering the physical

causes and sites of forces” (Principia, p. 407). The physical treatment of force is given in Book 3,

which, as mentioned, is the culmination of his argument for universal gravitation. George Smith

observes that Newton can characterize forces by its mathematical components (e.g., direction,

magnitude) “without regard to the particular physical components that happen to be giving rise

to it” (Smith, 2002, p. 149). As he explains further,

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the mathematical theories of motion of Galileo and Huygens are primarily aimed at predictingand explaining phenomena. The mathematical theories of motion developed [by Newton] inBooks 1 and 2 of the Principia do not have this aim. Rather, their aim is to provide a basisfor specifying experiments and observations by means of which the empirical world can provideanswers to questions—this in contrast to conjecturing answers and then testing theimplications of these conjectures. Newton is using mathematical theory in an effort to turnotherwise recalcitrant questions into empirically tractable questions. (Smith, 2002, p. 147)

Hence, all that Newton really needs for his theory of universal gravitation is the fit of the

evidence with the mathematical theory; the physical cause of gravity does not figure into the

mathematical description of the force of gravity. In a similar vein, Cohen remarks that “There is

no way of telling whether the Newtonian style of initially dealing with the subject on a

mathematical rather than a physical plane was only a subterfuge to avoid criticism or a sincere

expression of methodological principle. But, from Newton’s point of view, this style enabled him

to develop the laws of the action of a gravity-like force in a mathematical analogue of the world of

nature without having to be concerned with whether or not gravity exists” (Cohen, 1999, p. 278).

It is no wonder, then, why the lack of a physical cause of gravity did not hinder Newton in

the advancement of his theory of universal gravitation. As Newton remarks in Query 31 to the

Opticks, “we must learn from the phenomena of Nature what bodies attract one another, and

what are the laws and properties of attraction, before we enquire the cause by which the

attraction is performed” (Opticks, p. 531). Newton’s main concern, in the Principia and in his

natural philosophy in general, was to “discover” or establish the manifest principles of motion.

The physical cause of the resulting forces, on the other hand, can be left to “hypotheses” or

speculation, though no further than this unless there is sufficient empirical evidence to support

them. As Newton remarks in the third part of the General Scholium, “whatever is not deduced

from the phenomena must be called a hypothesis” (quoted above). Later on in Query 31, Newton

writes,

These principles [the active principles such as gravity] I consider, not as occult qualities,supposed to result from the specific forms of things, but as general laws of nature, by which

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the things themselves are formed; their truth appearing to us by phenomena, though theircauses be not yet discovered. For these are manifest qualities, and their causes only are occult. . . Such occult qualities put a stop to the improvement of natural philosophy, and therefore oflate years have been rejected. To tell us that every species of things is endowed with an occultspecific quality by which it acts and produces manifest effects, is to tell us nothing; but toderive two or three general principles of motion from phenomena, and afterwards to tell ushow the properties and actions of all corporeal things follow from those manifest principles,would be a very great step in philosophy, though the causes of those principles were not yetdiscovered: and therefore I scruple not to propose the principles of motion above mentioned,they being of very general extent, and leave their causes to be found out. (Opticks, p. 542)

We might therefore understand Newton’s exclamation in the third part of the General

Scholium, “I do not feign hypotheses”, as an assertion that he does not propose or adopt any

hypothesis regarding the physical treatment of gravitational forces (as opposed to the

mathematical treatment, on which the cause and nature of gravity simply does not bear). Newton

thus eschews the physical hypotheses which are supposed to account for the celestial phenomena,

such as the Cartesian vortex theory,10 not only because they cannot recover the celestial

phenomena, but because they make reference to entities that lack independent empirical support.

This is exactly what Newton is conveying in the first part of the General Scholium, in which he

reaffirms that the celestial phenomena are not compatible with the Cartesian vortex theory. In

particular, Newton stresses there that the regular orbital motions of the heavenly bodies cannot

be explained by mechanical causes. As Cohen astutely observes, Newton “does not contrive

fictions (or ‘hypotheses’) to be offered in place of sound explanations based on phenomena”

(Cohen, 1999, p. 275).

It must be acknowledged, however, that Newton’s concern was for whether empirical

phenomena fits physical theory. Newton’s use of empirical evidence to argue for theory can be

found in the first part of Book 3 of the Principia, where Newton presents his central argument for

the law of universal gravitation. This is the argument Newton is recapitulating in the first part of10Leibniz’ fluid theory is another example of a theory that employs the kinds of hypotheses Newton eschews.

In his Essay on the Causes of Celestial Motions (or Tentamen) of 1689, Leibniz introduced some kind of fluid thatsurrounds, and is contiguous to, the planetary bodies, and he argued that this fluid is in motion causing the planetarymotion. Of course, there is no empirical evidence to support the existence of such a fluid.

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the General Scholium. The premises of the argument, as mentioned, are celestial

phenomena—data on the motions of the planets and their satellites essentially in the form of

Kepler’s laws. Stein asserts, however, that Newton’s “conclusions (so far from being logical

consequences) stand in formal contradiction to its premises. For according to the theory of

universal gravitation, which is of course the product of this argument, Kepler’s laws (which were

its premises) cannot give an exact representation of the motion of the planets” (Stein, 1967, p.

261, original emphasis). According to Stein, Newton had not found “a simple general postulate

which accounts for the phenomena in close approximation—and that he then chose to regard the

general postulate as exact, in preference to the empirical laws of the phenomena” (Stein, 1967, p.

261). Rather, Stein claims that Newton’s analysis entails that the celestial phenomena with which

he begins can be represented by supposing that the celestial bodies are surrounded by “central

acceleration-fields whose intensities vary inversely with the square of the distance from the

center” (Stein, 1967, p. 262); and this supposition yields Kepler’s laws exactly. This was a great

strength for Newton’s theory. Stein reports that this result led Leibniz and Huygens to accept the

inverse square law in astronomy, although they rejected the theory of universal gravitation “as

theoretically objectionable and empirically unproved” (Stein, 1967, p. 262). Stein suggests,

however, that “there is a prima facie reason to consider that there may be something both sound

and deep in the method that led Newton along this path where his great contemporaries could

not follow” (Stein, 1967, p. 262).

It is interesting to note, as Stein has, “that when Newton responds to criticism of the

Principia, he appears to rest his case for universal gravitation, not upon the argument leading to

the theory, but upon the extremely detailed agreement of its consequences with observed

phenomena” (Stein, 1967, p. 264, original emphases). The “detailed agreements” Stein is

referring to are things such as the a satisfactory representation of the motion of the moon, an

explanation of the precession of the equinoxes, the theory of the tides, and the mutual

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perturbation of the orbits of Saturn and Jupiter when the planets were near each other.11 A great

importance of the first part of the General Scholium, then, is that it is a demonstration of

Newton’s reliance on empirical evidence to argue for his theory, where he recapitulates his

arguments presented in the Principia against the Cartesian vortex theory; his arguments concern

whether the vortex theory is compatible with observed celestial phenomena:

The hypothesis of vortices is beset with many difficulties. If, by a radius drawn to the sun,each and every planet is to describe areas proportional to the time, the periodic times of theparts of the vortex must be as the squares of the distances from the sun. . . . If the smallervortices revolving about Saturn, Jupiter, and the other planets are to be preserved and are tofloat without agitation in the vortex of the sun, the periodic times of the parts of the solarvortex must be the same. The axial revolutions [i.e., rotations] of the sun and planets, whichwould have to agree with the motion of the vortices, differ from all these proportions. Themotions of comets are extremely regular, observe the same laws as the motions of planets, andcannot be explained by vortices. Comets go with very eccentric motions into all parts of theheavens, with cannot happen unless vortices are eliminated.

. . . All bodies must move freely in [the celestial spaces above the earth], and thereforeplanets and comets must revolve continually in orbits given in kind and in position, accordingto the laws set forth above [in the Principia]. They will indeed preserve in their orbits by thelaws of gravity . . . (Principia, p. 940)

To be sure, the General Scholium itself was added to the second addition of the Principia to

answer the Cartesian critics and other adherents of the mechanical philosophy of the day (Cohen,

1999). But even before the second edition of the Principia, we find Newton defending his theory

of universal gravitation by means of the agreement with its consequences with observed

phenomena. In a letter Newton wrote to Leibniz in 1693 (between the first and second editions of

the Principia) in response to certain criticisms regarding the physical cause of gravity, he says,

For since celestial motions are more regular than if they arose from vortices and observe otherlaws, so much so that vortices contribute not to the regulation but to the disturbance of themotions of planets and comets; and since all phenomena of the heavens and of the sea followprecisely, so far as I am aware, from nothing but gravity acting in accordance with the lawsdescribed by me; and since nature is very simple, I have myself concluded that all other causesare to be rejected and that the heavens are to be stripped as far as may be of all matter, lestthe motions of planets and comets be hindered or rendered irregular. (From Janiak, 2004, p.108).

11This last point, according to Stein, would have converted Huygens to believing at least of the mutuality ofastronomical forces, if not universal gravitation, had it been established when Huygens read the Principia.

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Stein continues by commenting that “it is a fundamental principle of method [for Newton] to

press empirical generalizations as far and as exactly as possible, subject to empirical correction;

and to do so without regard for theoretical considerations of a speculative kind” (Stein, 1967, p.

263). The fundamental principle of method Stein is referring to is spelled out in Newton’s Rule 4

of his “Rules for the Study of Natural Philosophy” given in the Principia:

In experimental philosophy, propositions gathered from phenomena by induction should beconsidered either exactly or very nearly true notwithstanding any contrary hypotheses, until yetother phenomena make such propositions either more exact or liable to exceptions. (Principia,p. 796)

Newton follows this rule with the remark, “This rule should be followed so that arguments based

on induction may not be nullified by hypotheses” (Principia, p. 796)—hence, the “theoretical

considerations of a speculative kind”, in Stein’s words, are Newton’s dreaded “hypotheses”.

5 Conclusion

In conclusion, I echo Newton’s remarks in the third part of the General Scholium:

Notwithstanding that he had not established a cause of the gravity, his theory of gravitation “is

enough” to show “that gravity really exists and acts according to the laws that [he has] set forth

and is sufficient to explain all the motions of the heavenly bodies and of our sea”. Although

Newton did not “discover” a mechanical explanation for gravity, he maintained that he

nonetheless had established that gravity itself was causal—gravity had been successfully identified

as the cause of the celestial phenomena of planetary orbits. Thus, Newton argued that one should

not infer that gravity itself is not a cause—or, more precisely, a force which causes action—given

that there is no intelligible cause of gravity. Indeed, in the Principia Newton defines gravity as a

type of cause (i.e., as one sort of force that alters the states of motion of material bodies). And it

is this force that alters the states of motion of material bodies within his theory of universal

gravitation, and is responsible for the celestial phenomena of planetary orbits. Newton believed

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that the the celestial phenomena is evidence enough to establish his theory of universal

gravitation, and the cause of gravity is an issue that does not bear on the truth of the theory. In

Newton’s own words (in his letter to Bentley, referred to above), “Gravity must be caused by an

agent acting constantly according to certain laws; but whether this agent be material or

immaterial, I have left to the consideration of my readers” (from Janiak, 2004, p. 103). In short,

all that needs to be established and affirmed is that the celestial motions accord with his laws of

motion and his theory of universal gravitation; the nature of the cause of the celestial motions

(i.e., the cause of the apparent force of gravity) is an issue that need not be resolved to accept

that gravity is indeed the force responsible for the phenomena.

References

Cohen, I. B. (1999). Guide to Newton’s Principia. In The Principia, Mathematical principles ofnatural philosophy: A new translation (p. 1-370). University of California Press: Berkeley.

Cohen, I. B. (2002). Newton’s concepts of force and mass, with notes on the Laws of Motion. InI. B. Cohen & G. E. Smith (Eds.), The Cambridge companion to Newton (p. 57-84).Cambridge University Press: Cambridge, U.K.

DiSalle, R. (1990). The “essential properties” of matter, space, and time: Comments on MichaelFriedman. In P. Bricker & R. Hughes (Eds.), Philosophical perspectives on Newtonianscience (p. 203-209). The MIT Press: Cambridge, Mass.

DiSalle, R. (2002). Newton’s philosophical analysis of space and time. In I. B. Cohen & G. E.Smith (Eds.), The Cambridge companion to Newton (p. 33-56). Cambridge UniversityPress: Cambridge, U.K.

Friedman, M. (1990). Kant and Newton: Why gravity is essential to matter. In Philosophicalperspectives on Newtonian science (p. 185-202). The MIT Press: Cambridge, Mass.

Friedman, M. (unpublished paper). Newton and Kant on absolute space: From theology totranscendental philosophy.

Gabbey, A. (2002). Newton, active powers, and the mechanical philosophy. In I. B. Cohen &G. E. Smith (Eds.), The Cambridge companion to Newton (p. 329-357). CambridgeUniversity Press: Cambridge, U.K.

Janiak, A. (Ed.). (2004). Cambridge texts in the history of philosophy. Newton: Philosophicalwritings. Cambridge University Press: Cambridge, U.K.

Opticks: or A treatise of the reflexions, refractions, inflexions and colours of light. Based on thefourth edition London, 1730. (1952). Robert Maynard Hutchings (Ed.) Great books of theWestern world. Encyclopedia Britannica, Inc.

The Principia, Mathematical principles of natural philosophy: A new translation (I. B. Cohen &

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A. Whitman, Trans.). (1999). University of California Press: Berkeley. Containing a “Guideto Newton’s Principia” by I. B. Cohen.

Smith, G. E. (2002). The methodology of the Principia. In I. B. Cohen & G. E. Smith (Eds.),The Cambridge companion to Newton (p. 138-173). Cambridge University Press:Cambridge, U.K.

Stein, H. (1967). Newtonian space-time. In R. Palter (Ed.), The Annus Mirabilis of Sir IsaacNweton 1666-1966 (p. 258-284). The MIT Press: Cambridge Mass.

Stein, H. (2002). Newton’s metaphysics. In I. B. Cohen & G. E. Smith (Eds.), The Cambridgecompanion to Newton (p. 256-307). Cambridge University Press: Cambridge, U.K.

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