Dr. Clarke's Fifth Reply.

As Multitudes of Words are neither an Argument of clear Ideas in the Writer, nor a proper means of conveying clear Notions to the Reader; I shall endeavour to give a distinct Answer to this Fifth Paper, as briefly as I can.

1, ——20. THERE is no [1] similitude between a Balance being moved by Weights or Impulse, and a Mind moving itself, or acting upon the View of certain Motives. The Difference is, that the one is entirely passive; which is being subject to absolute Necessity: The other not only is acted upon, but acts also; which is the essence of Liberty. To [2] suppose that an equal apparent Goodness in different Ways of acting, takes away [3] from the Mind all Power of Acting at all, as an equality of Weights keeps a Balance necessarily at Rest; is denying the Mind to have in itself a Principle of Action; and is confounding the Power of Acting, with the Impression made upon the Mind by the Motive, wherein the Mind is purely passive. The Motive, or thing considered as in View, <283> is something extrinsick to the Mind: The impression made upon the Mind by that Motive, is the perceptive Quality, in which the Mind is passive: The Doing of any thing, upon and after, or in consequence of, that perception; this is the Power of Self-Motion, or Action: Which, in All animate Agents, is Spontaneity; and, in moral Agents, is what we properly call Liberty. The not carefully distinguishing these things, but confounding [4] the Motive with the Principle of Action, and denying the Mind to have any Principle of Action besides the Motive, (when indeed in receiving the impression of the Motive, the Mind is purely passive;) This, I say, is the Ground of the whole Error; and leads Men to think that the Mind is no more Active, than a Balance would be with the Addition of a Power of Perception: Which is wholly taking away the very Notion of Liberty. A Balance pushed on Both sides with equal force, or pressed on Both sides with equal Weights, cannot move at all: And supposing the Balance indued with a Power of Perception, so as to be sensible of its own incapacity to move; or so as to [5] deceive itself with an imagination that it moves itself, when indeed it is only moved; it would be exactly in the same state, wherein this learned Author supposes a free Agent to be in all cases of absolute Indifference. But the Fallacy plainly lies here: The Balance, for <285> want of having in itself a Principle or Power of Action, cannot move at all when the Weights are equal: But a Free Agent, when there appear two, or more, perfectly alike reasonable ways of acting; has still within itself, by virtue of its Self-Motive Principle, a Power of acting: And it may have very strong and good Reasons, not to forbear acting at all; when yet there may be no possible reason to determine one particular Way of doing the thing, to be better than another. To affirm therefore, [6] that, supposing two different ways of placing certain particles of Matter were equally good and reasonable, God could neither wisely nor possibly place them in either of those ways, for want of a sufficient Weight to determine him which way he should chuse; is making God not an Active, but a Passive Being: Which is, not to be a God, or Governor, at all. And for denying the Possibility of the Supposition, that there may be two equal Parts of Matter, which may with equal fitness be transposed in situation; no other reason can be alleged, but this [7] petitio Principii, that Then this Learned Writer's Notion of a sufficient Reason would not be well-grounded. For otherwise, how can any Man say, that 'tis [8] impossible for God to have wise and good reasons to create many particles of Matter exactly alike in different Parts of the Universe? In which case, the parts of Space being alike, 'tis <287> evident there can be no reason, but mere Will, for not having originally transposed their Situations. And yet even This cannot be reasonably said to be a [9] Will without Motive; forasmuch as the wise reasons God may possibly have to create many particles of Matter exactly alike, must consequently be a Motive to him to take (what a Balance could not do,) one out of two absolutely Indifferents; that is, to place them in one Situation, when the transposing of them could not but have been exactly alike good.

Necessity, in Philosophical Questions, always signifies absolute Necessity. [10] Hypothetical Necessity[11], and Moral Necessity, are <289> only Figurative Ways of Speaking, and in Philosophical strictness of Truth, are no Necessity at all. The Question is not, whether a Thing must be, when it is supposed that it is, or that it is to be; (which is Hypothetical Necessity:) Neither is it the Question whether it be True that a good Being, continuing to be Good, cannot do Evil; or a wise Being, continuing to be Wise, cannot act unwisely; or a veracious Person, continuing to be veracious, cannot tell a Lie; (which is moral Necessity:) But the true and only Question in Philosophy concerning Liberty, is, whether the immediate Physical Cause or Principle of Action be indeed in Him whom we call the Agent; or whether it be some other Reason sufficient, which is the real Cause of the Action, by operating upon the Agent, and making him to be, not indeed an Agent, but a mere Patient.

It may here be observed, by the way; that this learned Author contradicts his own Hypothesis, when he says, that [12] the Will does not always precisely follow the practical Understanding because it may sometimes find Reasons to suspend its Resolution. For are not those very Reasons, the last Judgment of the practical Understanding?


21——25. If it is possible for God to make or to have made two Pieces of Matter exactly alike, so that the transposing them in Situation would be perfectly indifferent; this learned Author's Notion of a sufficient Reason, falls to the Ground. To this he answers; not, (as his Argument requires,) that 'tis [13] Impossible for God to make two Pieces exactly alike; but, that 'tis not Wise for him to do so. But how does he know, it would not be Wise for God to do so? Can he prove that it is not possible God may have Wise Reasons for creating Many Parts of Matter exactly alike in different Parts of the Universe? The only Argument he alledges, is, that then there would not be a sufficient Reason to determine the Will of God, which Piece should be placed in which Situation. But if, for ought that any otherwise appears to the contrary, God may possibly have many wise Reasons for creating many Pieces exactly alike; will the Indifference alone of the Situation of such Pieces, make it impossible that he should create, or impossible that it should be Wise in him to create them? I humbly conceive, this is an [14] express Begging of the Question. To the like Argument drawn by me from the absolute Indifferency of the original particular Determination of Motion, no Answer has been returned.


26,——32. In these Articles, there seem to be contained many Contradictions. It is allowed [15] that Two Things exactly alike, would really be Two; and yet it is still alledged, that they would want the Principle of Individuation; And in Paper 4th, § 6. it was expresly affirmed, that they would be only the same Thing under two Names. A [16] Supposition is allowed to be possible, and yet I must not be allowed to make the Supposition. The [17] Parts of Time and Space are allowed to be exactly alike in Themselves, but not so when Bodies exist in them. Different co-existent Parts of Space, and different successive Parts of Time, are [18] compared to a strait Line cutting another strait Line in two coincident Points, which are but one Point only. 'Tis affirmed, that [19] Space is nothing but the Order of Things co-existing; and yet it is [20] confessed that the material Universe may possibly be Finite; in which Case there must necessarily be an empty extra-mundane Space. 'Tis [21] allowed, that God could make the material Universe Finite: And yet the supposing it to be possibly Finite, is stiled not only a Supposition unreasonable and void of Design, but also an [22] impracticable <295> Fiction; and 'tis affirmed, [23] there can be no possible Reason which can limit the Quantity of Matter. 'Tis affirmed, that the Motion of the material Universe would produce [24] no Change at all; and yet no Answer is given to the Argument I alledged, that a sudden Increase or Stoppage of the Motion of the Whole, would give a sensible Shock to all the Parts: And 'tis as evident, that [25] a circular Motion of the Whole, would produce a vis centrifuga in all the Parts. My Argument, that the material World must be moveable, if the Whole be Finite; is [26] denied, because the Parts of Space are immoveable, of which the Whole is Infinite and necessarily existing. It is affirmed, that Motion necessarily implies a [27] Relative Change of Situation in one Body, with regard to other Bodies: And yet no way is shown to avoid this absurd Consequence, that then the Mobility of one Body depends on the Existence of other Bodies; and that any single Body existing Alone, would be incapable of Motion; or that the Parts of a circulating Body, (suppose the Sun,) would lose the vis centrifuga arising from their circular Motion, if all the extrinsick Matter around them were annihilated. Lastly, 'tis affirmed that the [28] Infinity of Matter is an Effect of the Will of God; And yet Cartesius's Notion is [29] approved as irrefragable; the only Foundation of which, all Men know to have been this Supposition, <297> that Matter was infinite necessarily in the Nature of Things, it being a Contradiction to suppose it Finite: His Words are, [30] Puto implicare contradictionem, ut Mundus sit finitus. Which if it be true, it never was in the Power of God to determine the Quantity of Matter; and consequently he neither was the Creator of it, nor can destroy it.

And indeed there seems to run a continual Inconsistency through the Whole of what this Learned Author writes concerning Matter and Space. For sometimes he argues against a Vacuum (or Space void of Matter,) as if it was [31] absolutely impossible in the Nature of Things; space and Matter being [32] inseparable: And yet frequently he allows the Quantity of Matter in the Universe, to depend upon the [33] Will of God.

33,——35. To the Argument drawn against a Plenum of Matter, from the Want of Resistance in certain Spaces; this Learned Author answers, that those Spaces are filled with a Matter which has no [34] Gravity. But the Argument was not drawn from Gravity, but from Resistance; which must be proportionable to the [35] Quantity of <299> Matter, whether the Matter had any Gravity, or no.

To obviate this Reply, he alleges that [36] Resistance does not arise so much from the Quantity of Matter, as from its Difficulty of giving Place. But this Allegation is wholly wide of the Purpose; because the Question related only to such Fluid Bodies which have little or no Tenacity, as Water and Quicksilver, whose Parts have no other Difficulty of giving Place, but what arises from the Quantity of the Matter they contain. The Instance of a [37] floating Piece of Wood, containing less of heavy Matter than an equal Bulk of Water, and yet making greater Resistance; is wonderfully unphilosophical: For an equal Bulk of Water shut up in a Vessel, or frozen into Ice, and floating, makes a greater Resistance than the floating Wood; the Resistance Then arising from the whole Bulk of the Water: But when the Water is loose and at Liberty in its State of Fluidity, the Resistance Then is made not by the whole, but by part only, of the equal Bulk of Water; and then it is no wonder that it seems to make less Resistance than the Wood.

36,——48. These Paragraphs do not seem to contain serious Arguments, but only represent in an ill Light the Notion of <301> the Immensity or Omnipresence of God; who is not a mere Intelligentia supramundana, [Semota à nostris rebus sejunctaque longè;] is not far from every one of us; for in him we (and all Things) live and move and have our Being.

The Space occupied by a Body, is not the [38] Extension of the Body; but the extended Body exists in that Space.

There is no such Thing in reality, as [39] bounded Space; but only we in our Imagination fix our Attention upon what Part or Quantity we please, of that which it self is always and necessarily unbounded.

Space is not an [40] Affection of one Body, or of another Body, or of any finite Being; nor passes from Subject to Subject; but is always invariably the Immensity of one only and always the same Immensum.

Finite Spaces are not at all the [41] Affections of Finite Substances; but they are only those Parts of Infinite Space, in which Finite Substances exist.

If Matter was infinite, yet infinite Space would no more be an [42] Affection of that infinite Body, than finite Spaces are the Affections of finite Bodies; but, in that Case, the infinite Matter would be, as finite Bodies now are, in the infinite Space.


Immensity, as well as Eternity, is [43] essential to God. The [44] Parts of Immensity, (being totally of a different kind from corporeal, partable, separable , divisible, moveable Parts, which are the ground of Corruptibility;) do no more hinder Immensity from being essentially One, than the Parts of Duration hinder Eternity from being essentially One.

God himself suffers no [45] Change at all, by the Variety and Changeableness of Things which live and move and have their Being in him.

This [46] strange Doctrine, is the express Assertion of [47] St. Paul, as well as the plain Voice of Nature and Reason.

God does not exist [48] In Space, and In Time; but His Existence [49] causes Space and Time. And when, according to the Analogy of vulgar Speech, we say that he exists in All Space and in All Time; the Words mean only that he is Omnipresent and Eternal, that is, that Boundless Space and Time are necessary Consequences of his Existence; and not, that Space and Time are Beings distinct from him, and IN which he exists.

[50] How [51] Finite Space is not the exten <305> sion of Bodies, I have shown just above, on § 40. And the two following Paragraphs also, (§ 47 & 48.) need only to be compared with what hath been already [52] said.

49,——51. These seem to me, to be only a quibbling upon Words. Concerning <307> the Question about Space having Parts, see above; Reply 3, § 3; and Reply 4, § 11.

52, and 53. My Argument here, for the Notion of Space being really independent upon Body, is founded on the Possibility of the material Universe being finite and moveable: 'Tis not enough therefore for this Learned Writer to reply, that he thinks it would not have been wise and reasonable for God to have made the material Universe finite and moveable. He must either affirm, that 'twas impossible for God to make the material World finite and moveable; or else he must of necessity allow the Strength of my Argument, drawn from the Possibility of the World's being finite and moveable. Neither is it sufficient barely to repeat his Assertion, that the Motion of a finite material Universe would be nothing, <309> and (for want of other Bodies to compare it with) would [53] produce no discoverable Change: Unless he could disprove the Instance which I gave of a very great Change that would happen; viz. that the Parts would be sensibly shocked by a sudden Acceleration or stopping of the Motion of the Whole: To which Instance, he has not attempted to give any Answer.

53. Whether this learned Author's being forced here to acknowledge the difference between absolute real Motion and relative Motion, does not necessarily infer that Space is really a quite different Thing from the Situation or Order of Bodies; I leave to the Judgment of those who shall be pleased to compare what this learned Writer here alleges, with what Sir Isaac Newton has said in his Principia, Lib. I, Defin. 8.

54. I had alleged that Time and Space were QUANTITIES, which Situation and Order were not. To this, it is replied; that Order has its Quantity; there is that which goes before, and that which follows; there is Distance or Interval. I answer: Going before, and following, constitutes Situation or Order: But the Distance, Interval, or Quantity of Time or <311> Space, wherein one Thing follows another, is entirely a distinct Thing from the Situation or Order and does not constitute any Quantity of Situation or Order: The Situation or Order may be the same, when the Quantity of Time or Space intervening is very different. This learned Author further replies, that Ratio's or Proportions [54] have their Quantity; and therefore so may Time and Space, though they be nothing but Relations. I answer 1st; If it had been true, that some particular Sorts of Relations, such as Ratio's or Proportions, were Quantities; yet it would not have followed, that Situation and Order, which are Relations of a quite different Kind, would have been Quantities too. But 2dly; Proportions are not Quantities, but the Proportions of Quantities. If they were Quantities, they would be the Quantities of Quantities; which is absurd. Also, if they were Quantities, they would (like all other Quantities) increase always by Addition: But the Addition of the Proportion of 1 to 1, to the Proportion of 1 to 1, makes still no more than the Proportion of 1 to 1; and the Addition of the Proportion of half to 1, to the Proportion of 1 to 1, does not make the Proportion of 1 and a half to 1, but the Proportion only of half to 1. That which Mathematicians sometimes inaccurately call the Quantity of Proportion, is (accurately and strictly speaking,) only <313> the Quantity of the Relative or Comparative Magnitude of one Thing with regard to another: And Proportion is not the comparative Magnitude it self, but the Comparison or Relation of the Magnitude to Another. The Proportion of 6 to 1, with regard to that of 3 to 1, is not a double Quantity of Proportion, but the Proportion of a double Quantity. And in general, what they call Bearing a greater or less Proportion, is not bearing a greater or less Quantity of Proportion or Relation, but, bearing the Proportion or Relation of a greater or less Quantity to Another: 'Tis not a greater or less Quantity of Comparison, but the Comparison of a greater or less Quantity. The [55] Logarithmick Expression of a Proportion, is not (as this learned Author stiles it) a Measure, but only an artificial Index or Sign of Proportion: 'Tis not the expressing a Quantity of Proportion, but barely a denoting the Number of Times that any Proportion is repeated or complicated. The Logarithm of the Proportion of Equality, is 0; and yet 'tis as real and as much a Proportion, as any other: And when the Logarithm is negative, as ī; yet the Proportion, of which it is the Sign or Index, is it self affirmative. Duplicate or Triplicate Proportion, does not denote a double or triple Quantity of Proportion, but the Number of Times that the Proportion is repeated. The tripling of any Magnitude or Quantity once, pro <315> duces a Magnitude or Quantity, which to the former bears the Proportion of 3 to 1. The tripling it a second time, produces (not a double Quantity of Proportion, but) a Magnitude or Quantity, which to the former bears the Proportion (called duplicate) of 9 to 1. The tripling it a third time, produces (not a triple Quantity of Proportion, but) a Magnitude or Quantity, which to the former bears the Proportion (called triplicate) of 27 to 1: And so on. 3dly, Time and Space are not of the Nature of Proportions at all, but of the Nature of absolute Quantities to which Proportions belong. As for Example: The Proportion of 12 to 1, is a much greater Proportion, (that is, as I now observed, not a greater Quantity of Proportion, but the Proportion of a greater comparative Quantity,) than that of 2 to 1; and yet one and the same unvaried Quantity, may to one Thing bear the Proportion of 12 to 1, and to another Thing at the same time the Proportion of 2 to 1. Thus the Space of a Day, bears a much greater Proportion to an Hour, than it does to half a Day; and yet it remains, notwithstanding Both the Proportions, the same unvaried Quantity of Time. Time therefore, [and Space likewise by the same Argument,] is not of the Nature of a Proportion, but of an absolute and unvaried Quantity, to which different Proportions belong. Unless this Reasoning can be shown <317> to be false, our Learned Author's Opinion still remains, by his [56] own Confession, a Contradiction.

55, ——63. All this seems to me to be a plain Contradiction; and I am willing to leave it to the Judgment of the Learned. In [57] one Paragraph, there is a plain and distinct Supposition, that the Universe might be created as much sooner or later as God pleased. In the [58] rest, the very Terms [sooner or later] are treated as unintelligible Terms and [59] impossible Suppositions. And the like, concerning the Space in which Matter subsists; See above, on § 26— —32.

64, and 65. See above upon § 54.

66,——70. See above, on § 1,——20; and on § 21— —25. I shall here only add, that [60] comparing the Will of God when it <319> chooses one out of many equally good ways of acting, to Epicurus's Chance, who allowed No Will, No Intelligence, No Active Principle at all in the formation of the Universe; is comparing together Two things, than which No Two things can possibly be more different.

71. See above, on § 21,——25.

72. See above, on § 1,———20.

73,——75. In the consideration whether Space be independent upon Matter, and whether the material Universe Can be Finite and Moveable, (See above, on § 1——20, and on 26,——32;) the question is not concerning the Wisdom or [61] Will of God, but concerning the absolute and necessary Nature of Things. If the Material Universe CAN possibly, by the Will of God, be Finite and Moveable; (which this learned Author here finds himself necessitated to grant, though he perpetually treats it as an impossible supposition;) then Space, (in which that Motion is performed,) is manifestly independent upon Matter. But if, on the contrary, the material Universe [62] Cannot be finite and moveable, and Space cannot be independent upon Matter; then (I say) it follows evidently, that God neither Can nor ever Could set Bounds to Matter; and consequently the material Universe must be not only boundless, but [63] eternal also, both a parte ante and a parte <321> post, necessarily and independently on the Will of God. For, the Opinion of those who contend, that the World [64] might possibly be Eternal, by the Will of God exercising his Eternal Power; this has no Relation at all, to the Matter at present in Question.

76 and 77. See above, on § 73——75; and on § 1——20. And below, on § 103.

78. This Paragraph contains no new Objection. The Aptness and Intelligibleness of the Similitude made use of by Sir Isaac Newton, and here excepted against, has been abundantly explained in the foregoing Papers.

79,——82. All that is objected in the [65] two former of these Paragraphs, is a mere quibbling upon Words. The Existence of God, (as has often been already observed,) causes Space; and In that Space, All other Things exist. It is therefore [66] the Place of Ideas likewise; because it is the Place of the Substances themselves, in whose Understandings Ideas exist.

The Soul of Man being [67] the Soul of the Images of the Things which it perceives, was alledged by me, in way of comparison, as an Instance of a ridiculous Notion: And this learned Writer pleasantly argues against it, as if I had affirmed it to be my own Opinion.


God perceives every Thing, not [68] by means of any Organ, but by being himself actually present every where. This every where therefore, or universal Space, is the Place of his Perception. The Notion of Sensorium, and of the Soul of the World, has been abundantly explained before. 'Tis too much to desire to have the Conclusion given up, without bringing any further Objection against the Premises.

83,——88; and 89——91. That [69] the Soul is a Representative Principle; That [70] every simple Substance [71] is by its Nature a Concentration and living Mirror of the whole Universe; That [72] it is a representation of the Universe, [73] according to its Point of View; and that all simple Substances will always have a Harmony between themselves, because they always represent the same Universe: All This, I acknowledge, I understand not at all.

Concerning the [74] Harmonia præstabilita, by which the Affections of the Soul, and the Mechanic Motions of the Body, are affirmed to agree, without [75] at all influencing each other; See below, on § 110——116.

That the Images of Things are conveyed by the Organs of Sense into the Sensory, where the Soul perceives them; is affirmed, <325> but not proved, to be an [76] unintelligible Notion.

Concerning [77] immaterial Substance affecting, or being affected by, material Substances; See below, on § 110——116.

That God [78] perceives and knows all Things, not by being Present to them, but by continually producing them anew; is a mere Fiction of the Schoolmen, without any Proof.

The Objection concerning God's being [79] the Soul of the World, has been abundantly answered above; Reply II, § 12; and Reply IV, § 32.

92. To suppose, that all the Motions of our Bodies are necessary, and caused entirely [80] by mere [81] mechanical Impulses of Matter, altogether independent on the Soul; is what (I cannot but think) tends to introduce Necessity and Fate. It tends to make Men be thought as mere Machines, as Des Cartes imagined Beasts to be; by taking away [82] all Arguments drawn from Phænomena, that is, from the Actions of Men, to prove that there is any Soul, or any thing more than mere Matter in Men at all. See below, on § 110——116.

93——95. I alledged, that every Action is the giving of a New Force to the Thing <327> acted upon. To this it is objected, that two equal hard Bodies striking each other, return with the same Force; and that therefore their Action upon each other, gives no New Force. It might be sufficient to reply, that the Bodies do Neither of them return with their own Force, but each of them [83] loses its own Force, and each returns with a new Force impressed by the others Elasticity: For if they are not elastical, they return not at all. But indeed, all mere mechanical Communications of Motion, are not properly Action, but mere Passiveness, both in the Bodies that impell, and that are impelled. Action, is the beginning of a Motion where there was none before, from a Principle of Life or Activity: And if God or Man, or Any Living or Active Power, ever influences any thing in the material World; and every thing be not mere absolute Mechanism; there must be a continual Increase and Decrease of the whole Quantity of Motion in the Universe. Which this learned Gentleman [84] frequently denies.


96 and 97. Here this learned Author refers only to what he has said elsewhere: And I also am willing to do the same.


98. If the Soul be a Substance which fills the Sensorium, or Place wherein it perceives the Images of Things conveyed to it; <333> yet it does not thence follow, that it must consist of corporeal Parts, (for the Parts of Body are distinct Substances independent on each other;) but the Whole Soul sees, <335> and the Whole hears, and the Whole thinks, as being essentially one Individual.


99. In order to show that the [86] Active Forces in the World (meaning the [87] Quantity of Motion or Impulsive Force given to <339> Bodies,) do not naturally diminish; this Learned Writer urges, that two soft un-elastick Bodies meeting together with equal <341> and contrary Forces, do for this only Reason lose each of them the Motion of their Whole, because it is communicated and dispersed into a Motion of their small Parts. But the Question is; when two perfectly HARD un-elastick Bodies lose their whole Motion by meeting together, what then becomes of the Motion or active impulsive Force? It cannot be dispersed among the Parts, because the parts are capable of no tremulous Motion for want of elasticity. And if it be denied, that the Bodies would lose the Motion of their Wholes; I answer: Then it would follow, that Elastick Hard Bodies would reflect with a double Force; viz. the force arising from the elasticity, and moreover all (or at least part of) the original direct force: Which is contrary to Experience.

At length, (upon the Demonstration I cited from Sir Isaac Newton,) he is obliged to [88] allow, that the Quantity of Motion in the World, is not always the same; And goes to another refuge, that Motion and Force are not always the same in Quantity. But this also is contrary to Experience. For the Force here spoken of, is not the <343> [89] Vis inertiæ of Matter, (which continues indeed always the same, so long as the Quantity of Matter continues the same:) but the Force here meant, is relative Active impulsive Force; which is always [90] proportional to the Quantity of Relative Motion: <345> As is constantly evident in Experience; except where some Error has been committed, in not rightly computing and subducting the contrary or impeding Force, which arises from the Resistance of Fluids to Bodies moved any way, and from the continual contrary Action of Gravitation upon Bodies thrown upwards.

100——102. That [91] Active Force, in the Sense above-defined, does naturally diminish continually in the material Universe; hath been shown in the last Paragraph. That this is no Defect, is evident; because 'tis only a Consequence of Matter being lifeless, void of Motivity, unactive and inert. For the Inertia of Matter, causeth, not only (as this learned Author observes,) that Velocity decreases in proportion as Quantity of Matter increases, (which is indeed no decrease of the Quantity of Motion;) but also that solid and perfectly hard Bodies, void of Elasticity, meeting together with equal and contrary Forces, lose their whole Motion and Active Force, (as has been above shown,) and must depend upon some other Cause for new Motion.


103. That none of the things here referred to, are Defects; I have largely shown in my former Papers. For why was not God at Liberty to make a World, that should continue in its present Form as long or as short a time as he thought fit, and should then be altered (by such Changes as may be very wise and Fit, and yet Impossible perhaps to be performed by Mechanism,) into whatever other Form he himself pleased? Whether my Inference from this Learned Author's affirming [92] that the Universe cannot diminish in Perfection, that there is no possible Reason which can [93] limit the Quantity of Matter, that [94] God's Perfections oblige him to produce always as much Matter as he can, and that a Finite Material Universe is an [95] Impracticable Fiction; whether (I say) my Inferring, that (according to these Notions) the World must needs have been both Infinite and Eternal, be a just Inference or no, I am willing to leave to the Learned, who shall compare the Papers, to judge.

104——106. We are Now told, that [96] Space is not an Order or Situation, but an Order of Situations. But still the Objection remains; that an Order of Situations is not Quantity, as Space is. He re <349> fers therefore to § 54, where he thinks he has proved that Order is a Quantity: And I refer to what I have said above in this Paper, upon that Section; where I think I have proved, that it is not a Quantity. What he alledges concerning [97] Time likewise, amounts plainly to the following Absurdity: that Time is only the Order of Things successive, and yet is truly a Quantity; because it is, not only the Order of Things successive, but also the Quantity of Duration intervening between each of the Particulars succeeding in That Order. Which is an express Contradiction.

To say that [98] Immensity does not signify Boundless Space, and that Eternity does not signify Duration or Time without Beginning and End, is (I think) affirming that Words have no meaning. Instead of reasoning upon this Point, we are referred to what certain Divines and Philosophers (that is, such as were of this Learned Author's Opinion,) have acknowledged: Which is not the Matter in Question.

107——109. I affirmed, that, with regard to God, no one Possible thing is more miraculous than another; and that therefore a Miracle does not consist in any Difficulty in the Nature of the Thing to be done, but merely in the Unusualness of <351> God's doing it. The Terms, Nature, and Powers of Nature, and Course of Nature, and the like, are nothing but empty Words; and signify merely, that a thing usually or frequently comes to pass. The Raising a Human Body out of the Dust of the Earth, we call a Miracle; the Generation of a Human Body in the ordinary way, we call Natural; for no other Reason, but because the Power of God effects one usually, the other unusually. The sudden stopping of the Sun (or Earth,) we call a Miracle; the continual Motion of the Sun (or Earth,) we call Natural; for the very same Reason only, of the one's being usual, the other unusual. Did Men usually arise out of the Grave, as Corn grows out of Seed sown, we should certainly call That also natural: And did the Sun (or Earth) constantly stand still, we should then think That to be natural, and its Motion at any time would be miraculous. Against these evident Reasons, [ces [99] grandes Raisons,] this learned Writer offers nothing at all; but continues barely to refer us to the Vulgar Forms of Speaking of certain Philosophers and Divines: Which (as I before observed) is not the Matter in Question.


110——116. It is here very surprizing, that, in a Point of Reason and not of Authority, we are still again [100] remitted to the Opinions of certain Philosophers and Divines. But, to omit This: What does this Learned Writer mean by a [101] real internal Difference between what is miraculous, and not miraculous; or between [102] Operations natural, and not natural; absolutely, and with regard to God? Does he think there are in God two different and really distinct Principles or Powers of Acting, and that one thing is more difficult to God than another? If not: then either a natural and a supernatural Action of God, are Terms whose Signification is only relative to Us; we calling an usual Effect of God's Power, natural; and an unusual one, supernatural; the [103] force of Nature being, in truth, nothing but an empty word: Or else, by the One must be meant That which God does immediately Himself; and by the Other, that which he does mediately by the instrumentality of second Causes. The former of these Distinctions, is what this Learned Author is here professedly opposing: The latter is what he expresly disclaims, § 117, where he allows that Angels may work True Miracles. And yet, <355> besides these Two, I think no other Distinction can possibly be imagined.

It is very unreasonable to call [104] Attraction a Miracle, and an unphilosophical Term; after it has been so often distinctly [105] declared, that by That Term we do not <357> mean to express the Cause of Bodies tending towards each other, but barely the Effect, <359> or the Phænomenon it self, and the Laws or Proportions of that Tendency discovered by Experience; whatever be or be not the Cause of it. And it seems still more unreasonable, not to admit Gravitation or Attraction in This sense, in which it is manifestly an actual Phænomenon of nature; and yet at the same time to expect that there should be admitted so strange an Hypothesis, as the [106] harmonia præstabilita; which is, [107] that the Soul and Body of a Man have no more Influence upon each others Motions and Affections, than two Clocks, which, at the greatest distance from each other, go alike, without at all affecting each other. It is alleged indeed, that God, [108] foreseeing the Inclinations of every Man's Soul, so contrived at first the great Machine of the material Universe, as that, by the mere necessary Laws of Mechanism, suitable Motions should be excited in Human Bodies, as Parts of that great Machine. But is it possible, that such [109] Kinds of Motion, and of such variety, as those in Human Bodies are; should be performed by mere Mechanism, without any Influence of Will and Mind upon them? Or is it credible, that when a Man has it in his Power to resolve and know a Month before-hand, what he will do upon such a particular Day or Hour to come; is it credible, I say, that his Body shall by the mere Power of Mechanism, impressed originally upon the ma <361> terial Universe at its Creation, punctually conform it self to the Resolutions of the Man's Mind at the Time appointed? According to This Hypothesis, All Arguments in Philosophy, taken from Phænomena and Experiments, are at an end. For, if the Harmonia præstabilita be true, a Man does not indeed see, nor hear, nor feel any thing, nor moves his Body; but [110] only dreams that he sees, and hears, and feels, and moves his Body. And if the World can once be perswaded, that a Man's Body is a mere Machine; and that all his seemingly voluntary Motions are performed by the mere necessary Laws of corporeal Mechanism, without any Influence, or Operation, or Action at all of the Soul upon the Body; they will soon conclude, that this Machine is the whole Man; and that the harmonical Soul, in the Hypothesis of an harmonia præstabilita, is merely a Fiction and a Dream. Besides: What Difficulty is there avoided, by so strange an Hypothesis? This only; that it cannot be conceived (it seems,) how immaterial Substance should act upon Matter. But is not God an immaterial Substance? And does not He act upon Matter? And what greater Difficulty is there in conceiving how an immaterial Substance should act upon Matter, than in conceiving how Matter acts upon Matter? Is it not as easy to conceive, how certain <363> Parts of Matter may be obliged to follow the Motions and Affections of the Soul, without corporeal Contact; as that certain Portions of Matter should be obliged to follow each others Motions by the Adhæsion of Parts, which no Mechanism can account for? or that Rays of Light should reflect regularly from a Surface which they [111] never touch? Of which, Sir Isaac Newton in his Opticks has given us several evident and ocular Experiments.

Nor is it less surprizing, to find this Assertion again repeated in express Words, that, after the first Creation of Things, [112] the continuation of the Motions of the heavenly Bodies, and the Formation of Plants and Animals, and every Motion of the Bodies both of Men and all other Animals, is as mechanical as the Motions of a Clock. Whoever entertains this Opinion, is (I think) obliged in reason to be able to explain particularly, by what Laws of Mechanism the Planets and Comets can continue to move in the Orbs they do, thro' unresisting Spaces; and by what mechanical Laws, both Plants and Animals are formed; and how the infinitely various spontaneous [113] Motions of Animals and Men, are performed. Which, I am fully persuaded, is as impossi <365> ble to make out, as it would be to show how a House or City could be built, or the World it self have been at first formed by mere Mechanism, without any Intelligent and Active Cause. That Things could not be at first produced by Mechanism, is expresly allowed: And, when this is once granted; why, after That, so great Concern should be shown, to exclude God's actual Government of the World, and to allow his Providence to act no further than barely in concurring (as the Phrase is) to let all Things do only what they would do of themselves by mere Mechanism; and why it should be thought that God is under any Obligation or Confinement either in Nature or Wisdom, never to bring about any thing in the Universe, but what is possible for a corporeal Machine to accomplish by mere mechanick Laws, after it is once set a going; I can no way conceive.


117. This learned Author's allowing in this Place, that there is greater and less in true Miracles, and that Angels are capable of working some true Miracles; is perfectly [114] contradictory to that Notion of the Nature of a Miracle, which he has all along pleaded for in these Papers.

118——123. That the Sun attracts the Earth, through the intermediate void Space; that is, that the Earth and Sun gravitate towards each other, or tend (whatever be the Cause of that Tendency) towards each other, with a Force which is in a direct proportion of their Masses, or Magnitudes and Densities together, and in an inverse duplicate proportion of their Distances; and that the Space betwixt them is void, that is, hath nothing in it which sensibly resists the Motion of Bodies passing transversly through: All This, is nothing but a Phænomenon, or actual Matter of Fact, found by Experience. That this Phænomenon is not produced [115] sans moyen, that is, without some Cause capable of producing such an Effect; is undoubtedly true. Philosophers therefore may search after and discover That Cause, if they can; be it mechanical, or not mechanical. But if they cannot discover the Cause, is therefore the Effect it self, the Phænomenon, or the Matter of Fact discovered by Experience, (which is [116] all that is meant by the Words Attraction and Gravitation,) ever <369> the less True? Or is a manifest Quality to be called [117] occult, because the immediate efficient Cause of it (perhaps) is occult, or not yet discovered? When a Body [118] moves in a Circle, without flying off in the Tangent; 'tis certain there is something that hinders it: But if in some Cases it be not mechanically [119] explicable, or be not yet discovered, what that something is; does it therefore follow, that the Phænomenon it self is false? This is very singular Arguing indeed.

124——130. The Phænomenon it self, the Attraction, Gravitation, or Tendency of Bodies towards each other, (or whatever other Name you please to call it by;) and the Laws, or Proportions, of that Tendency, are now sufficiently known by Observations and Experiments. If This or any other learned Author can by [120] the Laws of Mechanism explain these Phænomena, he will not only not be contradicted, but will moreover have the abundant Thanks of the Learned World. But, in the mean time, to [121] compare Gravitation, (which is a Phænomenon or actual Matter of Fact,) with Epicurus's Declination of Atoms, (which, according to his corrupt and Atheistical Perversion of some more antient and perhaps better Philosophy, was an Hypothesis or Fiction only, and an impossible one <371> too, in a World where no Intelligence was supposed to be present;) seems to be a very extraordinary Method of reasoning.

As to the grand Principle of a [122] sufficient Reason; all that this Learned Writer here adds concerning it, is only by way of Affirming, not proving, his Conclusion; and therefore needs no Answer. I shall only observe, that the Phrase is of an equivocal Signification; and may either be so understood, as to mean Necessity only, or so as to include likewise Will and Choice. That in general there [123] is a sufficient Reason why every Thing is, which Is, is undoubtedly true, and agreed on all Hands. But the Question is, whether, in some Cases, when it may be highly reasonable to act, yet different possible Ways of acting may not possibly be equally reasonable; and whether, in such Cases, the [124] bare Will of God be not it self a sufficient Reason for acting in this or the other particular manner; and whether in Cases where there are the strongest possible Reasons altogether on One Side, yet in all Intelligent and Free Agents, the Principle of Action (in which I think the Essence of Liberty consists,) be not a distinct Thing from the Motive or Reason which the Agent has in his View. All these are constantly denied by this Learned Writer. And his [125] laying down his grand Principle of a sufficient Reason <373> in such a Sense as to exclude all these; and expecting it should be granted him in that Sense, without Proof; This is what I call his Petitio Principii, or Begging of the Question: Than which, nothing can be more unphilosophical.

N. B. Mr. Leibnitz was prevented by Death, from returning any Answer to this last Paper.

[1] § 3.

[2] § 14.

[3] See Appendix, No 4.

[4] § 15.

[5] See Appendix, No 12.

[6] § 16, 17, 18, 19, and 69.

[7] § 20.

[8] § 16, 17, 69, and 66.

[9] § 16 and 69.

[10] § 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

[11] See my Sermons at Mr. Boyle's Lecture, Part I. Pag. 106. Edit. 4.

[12] § 11.

[13] See Mr. Leibnitz's Fourth Paper, § 2, 3, 6, 13, & 15.

[14] § 20.

[15] § 26.

[16] § 26.

[17] § 27.

[18] § 28.

[19] § 29.

[20] § 30.

[21] § 30, & 8, & 73.

[22] § 29.

[23] Fourth Paper, § 21.

[24] § 29.

[25] See Appendix, No 10.

[26] § 31.

[27] § 31.

[28] § 32.

[29] Ibid.

[30] Epist. 69, Partis primæ.

[31] § 29, 33, 34, 35, 62, 63.

[32] § 62.

[33] § 30, 32, & 73.

[34] § 35.

[35] Otherwise, What makes the Body of the Earth more difficult to be moved, (even the same way that its Gravity tends,) than the smallest Ball?

[36] § 34.

[37] Ibid.

[38] § 36, 37.

[39] § 38.

[40] § 39.

[41] § 40.

[42] § 41.

[43] § 42.

[44] See above, in my Third Reply. § 3; and Fourth Reply, § 11.

[45] § 43.

[46] § 44.

[47] Acts xvii. 27, 28.

[48] § 45.

[49] See above, the Note on my Fourth Reply, § 10.

[50] § 40.


* Note: The principal Occasion or Reason of the Confusion and Inconsistencies, which appear in what most Writers have <305> advanced concerning the Nature of Space, seems to be This: that (unless they attend carefully,) men are very apt to neglect That Necessary Distiction, (without which there can be no clear Reasoning,) which ought always to be made between Abstracts and Concretes, such as are Immensitas & Immensum; & also between Ideas and Things, such as are The Notion (which is Within our own Mind) of Immensity, and the real Immensity actually existing Without us.

All the Conceptions (I think) that ever have been or can be framed concerning Space, are these which follow. That it is either absolutely Nothing, or a mere Idea, or only a Relation of one thing to another, or that it is Body, or some other Substance, or else a Property of a Substance.

That it is not absolutely Nothing, is most evident. For of Nothing there is No Quantity, No Dimensions, No Properties. This Principle is the First Foundation of All Science whatsoever; expressing the Only Difference between what does, and what does not, exist.

That it is not a mere Idea, is likewise most manifest. For no Idea of Space, can possibly be framed larger than Finite; and yet Reason demonstrates that 'tis a Contradiction for Space itself not to be actually Infinite.

That it is not a bare Relation of one thing to another, arising from their Situation or Order among themselves, is no less apparent: Because Space is a Quantity, which Relations (such as Situation and Order) are not; As I have largely shown below, on § 54. Also because, if the material Universe is, or can possibly be, Finite; there cannot but be, actual or possible, Extramundane Space: See on § 31, 52, and 73.

That Space is not Body, is also most clear. For then Body would be necessarily infinite; and No Space could be <307> void of Resistance to Motion. Which is contrary to Experience.

That Space is not Any kind of Substance, is no less plain. Because infinite Space is Immensitas, not Immensum; whereas infinite Substance is Immensum, not Immensitas. Just as Duration is not a Substance: because infinite Duration is æternitas, not æternum; but infinite Substance is æternum, not æternitas.

It remains therefore, by Necessary Consequence, that Space is a Property, in like manner as Duration is. Immensitas, is του Immensi; just as Æternitas is is του Æterni.

[52] See also below, on § 53, & on § 54.

[53] § 52.

[54] § 54.

[55] § 54.

[56] Fourth Paper, § 16.

[57] § 56.

[58] § 55, 57, 58,—63.

[59] Fourth Paper, § 15.

[60] § 70.

[61] § 73.

[62] Fourth Paper, § 21. and Fifth Paper, § 29.

[63] § 74.

[64] § 75.

[65] § 79, 80.

[66] § 80.

[67] § 81.

[68] § 82.

[69] § 83.

[70] § 87.

[71] See Appendix, No 2.

[72] § 91.

[73] See Appendix, No 11.

[74] § 83, 87, 89, 90.

[75] See Appendix, No 5.

[76] § 84.

[77] § 84.

[78] § 85.

[79] § 86, 87, 88, 82.

[80] § 92, 95, and 116.

[81] See Appendix, No 13.

[82] See Appendix, No 12.

[83] See more, on § 99.


There appears a great Confusion and Inconsistency in Mr Leibnitz's whole Notion of this Matter. For the Word, <329> Force, and Active Force, signifies in the present Question, the Impetus or relative Impulsive Force of Bodies in Motion: See my Third Reply, § 13. Mr. Leibnitz constantly uses the Word in this Sense: As when he speaks [§ 93, 94, 99, and 107, of this last Answer,] of Bodies not changing their Force after Reflexion, because they return with the same Swiftness: Of a Body's receiving a new Force from another Body, which loses as much of its own : Of the Impossibility, that one Body should acquire any new Force, without the Loss of as much in others: Of the new Force which the whole material Universe would receive, if the Soul of Man communicated any Force to the Body: And of Active Forces continuing always the same in the Universe, because the Force which un-elastick Bodies lose in their Whole, is communicated to and dispersed among their small Parts. Now this Impetus, or relative Impulsive Active Force of Bodies in Motion, is evidently both in Reason and Experience, always proportional to the Quantity of Motion. Therefore, according to Mr. Leibnitz's Principles, this impulsive active Force being always the same in Quantity, the Quantity of Motion also must of necessity be always the same in the Universe. Yet elsewhere, he inconsistently acknowledges, [§ 99,] that the Quantity of Motion is Not always the same: And in the Acta Eruditorum, ad Ann. 1686, pag. 161, he endeavours to Prove that the Quantity of Motion in the Universe is Not always the same, from that very Argument, and from that single Argument only, (of the Quantity of Impulsive Force being always the same,) which, if it was true, would necessarily infer on the contrary, that the Quantity of Motion could not but be always the same. The Reason of his Inconsistency in this Matter was his computing, by a wonderfully unphilosophical Error, the Quantity of Impulsive Force in an Ascending Body, from the Quantity of its Matter and of the Space described by it in Ascending, without considering the Time of its ascending. [85] "Suppono, says he, tantâ vi opus esse ad elevandum corpus A unius libræ usque ad altitudinem quatuor ulnarum, quantâ opus est ad <331> elevandum corpus B quatuor librarum usque ad altitudinem Unius Ulnæ. Omnia hæc à Cartesianis pariter ac cæteris Philosophis & Mathematicis nostri temporis conceduntur. Hinc sequitur, corpus A delapsum ex altitudine quatuor ulnarum, præcisè tantum acquisivisse virium, quantum B lapsum ex altitudine Unius Ulnæ". That is: "[I suppose the same Force is requisite to raise a Body A of one Pound Weight, to the Height of four Yards; which will raise the Body B of four Pounds Weight, to the Height of One Yard. This is Granted both by the Cartesians, and other Philosophers and Mathematicians of our Times. And from hence it follows, that the Body A, by falling from the Height of four Yards, acquires exactly the same Force, as the Body B by falling from the Height of One Yard".] But in this Supposition, Mr. Leibnitz is greatly mistaken. Neither the Cartesians, nor any other Philosophers or Mathematicians ever grant this, but in such Cases only, where the Times of Ascent or Descent are equal. If a Pendulum oscillates in a Cycloid; the Arch of the Cycloid described in ascending, will be as the Force with which the pendulous Body begins to ascend from the lowest Point; because the Times of ascending are equal. And if equal Bodies liberate upon the Arm of a Balance, at various Distances from the Axis of the Balance; the Forces of the Bodies will be in Proportion as the Arches described by them in librating, because they librate in the same Time. And if two equal Globes lying upon an Horizontal Plain, be impelled by unequal Forces, they will in equal Times describe Spaces proportional to the Forces impelling them. Or if unequal Globes be impelled with equal Forces, they will in equal Times describe Spaces reciprocally proportional to their Masses. And in all these Cases, if equal Bodies be impelled by Unequal Forces, the Forces impressed the Velocities generated, and the Spaces described in equal Times, will be proportional to one another. And if the Bodies be unequal, the Velocity of the bigger Bodies will be so much less, as the Bodies are bigger; And therefore the Motion (arising from the Mass and Velocity together) will he <333> in all these Cases, and in all Other Cases consequently, proportional to the Force imprest. [From whence, by the way, it plainly follows, that if there be always the same impulsive Force in the World, as Mr. Leibnitz affirms; there must be always the same Motion in the World, contrary to what he affirms.]

But Mr. Leibnitz confounds these Cases where the Times are equal, with the Cases where the Times are unequal: And chiefly That of Bodies rising and falling at the Ends of the unequal Arms of a Balance [Acta Erudit. ad Ann. 1686, Pag. 162; & ad Ann. 1690, Pag. 234; & ad Ann. 1691, Pag. 439; & ad Ann. 1695, Pag. 155;] is by him confounded with That of Bodies falling downwards and thrown upwards, without allowing for the Inequality of the Time. For a Body with one and the same Force, and one and the same Velocity, will in a longer Time describe a greater Space; and therefore the Time is to be considered; and the Forces are not to be reckoned proportional to the Spaces, unless where the Times are equal. Where the Times are unequal, the Forces of equal Bodies are as the Spaces applied to the Times. And in This, the Cartesians and other Philosophers and Mathematicians agree; all of them making the impulsive Forces of Bodies proportional to their Motions, and measuring their Motions by their Masses and Velocities together, and their Velocities by the Spaces which they describe, applied to the Times in which they describe them. If a Body thrown upwards does, by doubling its Velocity, ascend four Times higher in twice the Time; its impulsive Force will be increased, not in the proportion of the Space described by its Ascent, but in the Proportion of that Space applied to the Time; that is, in the Proportion of 42 to 11 or 2 to 1. For if, in this Case, the Force should be increased in the Proportion of 4 to 1; and, in oscillating in a Cycloid, the same Body, with the same Velocity doubled, describes only a doubled Arch, and its Force is therefore only doubled; this Body, with one and the same Degree of Velocity, would have twice as <235> much Force when thrown upwards, as when thrown horizontally: Which is a plain Contradiction. And there is the same Contradiction in affirming, that although a Body at the end of the unequal Arms of a Balance, by doubling its Velocity, acquires only a double impulsive Force, yet, by being thrown upwards with the same doubled Velocity, it acquires a quadruple impulsive Force; in this Assertion, I say, there is the same Contradiction: For equal Bodies with equal Velocities, cannot have unequal impulsive Forces.

Upon the Supposition of Gravity being Uniform, Galilæo demonstrated the Motion of Projectiles in Mediums void of Resistance; and his Propositions are allowed by all Mathematicians, not excepting Mr. Leibnitz himself. Now, supposing the Time of a falling Body to be divided into equal Parts; since Gravity is uniform, and, by being so, acts equally in equal Parts of Time, it must by its Action impress and communicate to the falling Body, equal impulsive Forces, Velocities, and Motions, in equal Times. And therefore the impulsive Force, the Velocity, and the Motion of the falling Body, will increase in Proportion to the Time of falling. But the Space described by the falling Body, arises partly from the Velocity of the Body, and partly from the Time of its falling; and so is in a compound ratio of them Both, or as the Square of either of them; and consequently as the Square of the impulsive Force. And by the same way of arguing, it may be proved, that when a Body is thrown upwards with any impulsive Force, the Height to which it will ascend, will be as the Square of that Force: And that the Force requisite to make the Body B, of four Pound Weight, rise up one Yard, will make the Body A, of One Pound Weight, rise up (not four Yards, as Mr. Leibnitz represents but) sixteen Yards, in quadruple the Time. For the Gravity of <337> four Pounds Weight in One part of Time, acts as much as the Gravity of one Pound Weight in Four Parts of Time.

But Mr. Herman, in his Phoronomia, Pag. 113, (arguing for Mr. Leibnitz against Those who hold that the Forces acquired by falling Bodies are proportional to the Times of falling, or to the Velocities acquired,) represents that this is founded upon a False Supposition, that Bodies thrown upwards receive from the Gravity which resists them, an equal Number of Impulses in equal Times. Which is as much as to say, that Gravity is not uniform; and, by Consequence, to overthrow the Theory of Galilæo concerning Projectiles, allowed by all Geometers. I suppose, he means that the swifter the Motion of Bodies is upwards, the more numerous are the Impulses; because the Bodies meet the [imaginary] gravitating Particles. And thus the Weight of Bodies will be greater when they move upwards, and less when they move downwards. And yet Mr. Leibnitz and Mr. Herman themselves allow, that Gravity in equal Times generates equal Velocities in descending Bodies, and takes away equal Velocities in ascending Bodies; and therefore is Uniform. In its action upon Bodies for generating Velocity, they allow it to be uniform; in its action upon them for generating impulsive Force, they deny it to be uniform: And so are inconsistent with themselves.

If the Force acquired by a Body in falling, be as the Space described; let the Time be divided into equal parts; and if in the first part of Time it gain One part of Force, in the two first parts of Time it will gain four parts of Force, in the three first parts of Time it will gain nine parts of Force, and so on. And by consequence, in the second part of Time it will gain three parts of Force, in the third part of Time it will gain five parts of Force, in the fourth part of Time it will gain seven parts of Force, and so on. And therefore if the Action of Gravity for generating these Forces, be supposed, in the middle of the first part of Time, to be of One degree; it will, in the middle of the second, third, and fourth parts of Time, be of three, five, and seven degrees, and so on: That is, it will be proportional to <339> the Time and to the Velocity acquired: And, by consequence, in the Beginning of the Time it will be none at all; and so the Body, for want of Gravity, will not fall down. And by the same way of arguing, when a Body is thrown upwards, its gravity will decrease as its velocity decreases, and cease when the Body ceases to ascend; and then, for want of gravity, it will rest in the Air, and fall down no more. So full of Absurdities is the Notion of this Learned Author in this Particular.

To decide this question demonstratively; let two pendulous globes of hardned Steel, be suspended by equal radij or Threads of equal Length: So that when they hang down and touch each other, the Radij or Threads may be parallel. Let One of the Globes be constantly the same, and be drawn aside from the Other to one and the same distance in All the subsequent Trials. Let the Other be of Any Bigness, and be drawn aside the contrary way to a Distance reciprocally proportional to its Weight. Let Both of them then be let go at one and the same Moment of Time, so that they may meet each other at the lowest place of their Descent, where they hung before they were drawn aside: And the first Globe will always rebound alike, from the Other. Wherefore the Force of the Other is always the same, when its Velocity is reciprocally proportional to its Weight. And by consequence, if its Weight remains the same, its Force will be proportional to its Velocity. Q. E. D.

[85] Acta Erudit. ad Ann. 1686, pag. 162.

[86] See above, the Note on my Third Reply. § 13.

[87] See above, the Note on § 93,—95.

[88] § 99.

[89] The Vis inertiæ of Matter, is That Passive Force, by which it always continues of itself in the State 'tis in; and never changes That State, but in proportion to a contrary Power acting upon it. 'Tis That Passive Force, not by which (as Mr. Leibnitz from Kepler understands it, See Appendix, No 7,) Matter resists Motion; but by which it equally resists Any Change from the State 'tis in, either of Rest or Motion: So that the very same Force, which is requisite to give any certain Velocity to any certain Quantity of Matter at Rest, is always exactly requisite to reduce the same Quantity of Matter from the same degree of Velocity to a state of Rest again. This Vis inertiæ is always proportional to the Quantity of Matter; and therefore continues invariably the same, in all possible States of Matter, whether at Rest or in Motion; and is never transferred from One Body to another. Without this Vis, the Least Force would give Any Velocity to the Greatest Quantity of Matter at Rest; and the Greatest Quantity of Matter in Any Velocity of Motion, would be stopped by the Least Force, without any the least shock at all. So that, properly and indeed, All Force in Matter either at Rest or in Motion, all its Action and Reaction, all Impulse and all Resistance, is nothing but this Vis inertiæ in different Circumstances.

[90] That is; proportional to the Quantity of Matter and the Velocity; not (as Mr. Leibnitz affirms, Acta Erudit. ad Ann. 1695, pag. 156,) to the Quantity of Matter and the Square of the Velocity. See above, the Note on § 93,——95.

[91] See above, the Note on § 93——95; & Third Reply, § 13.

[92] Fourth Paper, § 40, 20, 21, 22; and Fifth Paper, § 29.

[93] Fourth Paper, § 40, 20, 21, 22; and Fifth Paper, § 29.

[94] See above, Mr. Leibnitz's Postscript to his Fourth Paper.

[95] Fourth Paper, § 40, 20, 21, 22; and Fifth Paper, § 29.

[96] § 104.

[97] § 105.

[98] § 106.

[99] § 108.

[100] § 110.

[101] § 110:

[102] § 111.

[103] § 112.

[104] § 113.

[105] Quâ causâ efficiente hæ Attractiones peragantur, in id verò hic non inquiro. Quam ego Attractionem appello, fieri sanè potest ut ea efficiatur Impulsu, vel alio aliquo modo nobis ignoto. Hanc vocem Attractionis ita hic accipi velim, ut in universum solummodo vim aliquam significare intelligatur, quâ corpora ad se mutuo tendant; cuicunque demùm causæ attribuenda sit illa vis. Nam ex phænomenis Naturæ illud nos prius edoctos oportet, quænam corpora se invicem Attrahant, & quænam sint Leges & Proprietates istius Attractionis; quàm in id inquirere par sit, quânam Efficiente Causâ peragatur Attractio. Newtoni Optice, Qu. 23, pag. 322. Atque hæc quidem Principia considero, non ut occultas Qualitates, quæ ex Specificis rerum Formis oriri singantur; sed ut universales Naturæ Leges, quibus res ipsæ sunt formatæ. Nam Principia quidem talia revera existere, ostendunt Phænomena Naturæ; licet ipsorum causæ quæ sint, nondum fuerit explicatum. Affirmare singulas rerum species, specificis præditas esse qualitatibus occultis, per quas eæ Vim certam in Agendo habeant; hoc utique est Nihil dicere. At ex phænomenis Naturæ, duo vel tria derivare generalia Motis Principia; & deinde explicare quemadmodum proprietates & actiones rerum corporearum omnium ex Principiis istis consequantur; id verò magnus esset factus in Philosophiâ progressus, etiamsi Principiorum istorum Causæ nondum essent cognitæ: Id. ibid. Pag. 344. Phænomena Cœlorum & maris nostri per Vim Gravitatis exposui, sed causam Gravitatis nondum assignavi. Oritur utique hæc <357> Vis à causa aliqua, quæ penetrat ad usque centra Solis & Planetarum, sine virtutis diminutione; quæque agit non pro quantitate Superficierum particularum in quas agit, (ut solent causæ mechanicæ,) sed pro quantitate materiæ solidæ; & cujus actio in immensas distantias undique extenditur, decrescendo semper in duplicatâ ratione distantiarum. —— Rationem verò harum Gravitatis proprietaum ex Phænomenis nondum potui deducere, & Hypotheses non fingo: Principia Philos. Schol. generale sub finem. i. e. What the efficient Cause of these Attractions is, I do not here inquire. What I call Attraction, may possibly be caused by some Impulse, or some other way unknown to us. I use the Word Attraction, only in general, to signify the Force by which Bodies tend towards each other; whatever be the Cause of that Force. For we must first learn from the Phænomena of Nature, what Bodies attract each other, and what are the Laws and Properties of that Attraction, before 'tis proper to inquire what the efficient Cause of Attraction is. Again: I consider these Principles, not as occult Qualities, imagined to arise from the specifick Forms of Things; but as Universal Laws of Nature, according to which the Things themselves were formed. For, that such Principles do really exist, appears from the Phænomena of Nature; though, what the Causes of them are, be not yet explained. To affirm that every distinct Species of Things, is indued with specifick occult Qualities, by means whereof the Things have certain Active Forces; this indeed is saying Nothing. But to deduce from the Phænomena of Nature, two or three general Principles of Motion; and then to explain how the Properties and Actions of all corporeal Things follow from those Principles; This would be a great Progress in Philosophy, though the Causes of those Principles were not yet discovered. Again: I have explained the Phænomena of the Heavens and the Sea, by the Force of Gravity; but the Cause of Gravity I have not yet assigned. It is a Force arising from some Cause, which reaches to the very Centers of the Sun and Planets, without any diminution of its Force: And it acts, not proportionally to the Surfaces of the Particles it acts upon, as Mechanical Causes use to do; but proportionally to the Quantity of Solid Matter: And its Action reaches every way to immense Distances, decreasing always in a duplicate ratio of the Distances. But the Cause of these Properties of Gravity, I have not yet found deducible from Phænomena: And Hypotheses I make not.

[106] § 109 and 92, and 87, 89, 90.

[107] See Appendix, No 5.

[108] § 92.

[109] See Appendix, No 13.

[110] See Appendix, No 12.

[111] See Sir Isaac Newton's Opticks, Latin Edition, Pag. 224. English Edition, Book 2, Page 65.

[112] § 115, 116.

[113] See Appendix, No 13.

[114] See above, Mr. Leibnitz's Third Paper, § 17.

[115] § 118.

[116] See above, the Note on § 113.

[117] § 112.

[118] § 123.

[119] § 123.

[120] § 124.

[121] § 128.

[122] § 125, &c.

[123] § 125.

[124] See above, on § 1-20, and 21-25.

[125] § 26 & 125, &c.

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