34. The author objects against me the vacuum discovered by Mr. Guerike of Magdeburg, which is made by pumping the air out of a receiver; and he pretends that there is truly a perfect vacuum, or a space without matter (at least in part), in that receiver. The Aristotelians and Cartesians, who do not admit a true vacuum, have said in answer to that experiment of Mr. Guerike, as well as to that of Torricellius of Florence, (who emptied the air out of a glass-tube by the help of quicksilver), that there is no vacuum at all in the tube or in the receiver: since glass has small pores, which the beams of light, the effluvia of the loadstone, and other very thin fluids may go through. I am of their opinion: and I think the receiver may be compared to a box full of holes in the water, having fish or other gross bodies shut up in it; which being taken out, their place would nevertheless be filled up with water. There is only this difference; that though water be fluid and more yielding than those gross bodies, yet it is as heavy and massive, if not more, than they: whereas the matter which gets into the receiver in the room of the air, is much more subtle. The new sticklers for a vacuum allege in answer to this instance, that it is not the grossness of matter, but its mere quantity, that makes resistance; and consequently that there is of necessity more vacuum, where there is less resistance. They add, that the subtileness of matters has nothing to do here; and that the particles of quicksilver are as subtle and fine as those of water;  and yet that quicksilver resists above ten times more. To this I reply, that it is not so much the quantity of matter, as its difficulty of giving place, that makes resistance. For instance; floating timber contains less of heavy matter, than an equal bulk of water does; and yet it makes more resistance to a boat, than the water does.

35. And as for quicksilver; 'tis true, it contains about fourteen times more of heavy matter, than an equal bulk of water does; but it does not follow, that it contains fourteen times more matter absolutely. On the contrary, water contains as much matter; if we include both its own matter, which is heavy; and the extraneous matter void of heaviness, which passes through its pores. For, both quicksilver and water, are masses of heavy matter, full of pores, through which there passes a great deal of matter void of heaviness [and which does not sensibly resist]; such as is probably that of the rays of light, and other insensible fluids; and especially that which is itself the cause of the gravity of gross bodies, by receding from the center towards which it drives those bodies. For, it is a strange imagination to make all matter gravitate, and that towards all other matter, as if each body did equally attract every other body according to their masses and distances; and this by an attraction properly so called, which is not derived from an occult impulse of bodies: whereas the gravity of sensible bodies towards the center of the earth, ought to be produced by the motion of some fluid. And the case must be the same with other gravities, such as is that of the planets towards the sun or towards each other. [A body is never moved naturally except by another body which impels it by touching it; and afterwards it advances until it is stopped by another body which touches it. Every other operation on bodies is either miraculous or imaginary.]

To § 8 and 9.

36. I objected, that space, taken for something real and absolute without bodies, would be a thing eternal, impassible, and independent upon God. The author endeavors to elude this difficulty, by saying that space is a property of God. In answer to this, I have said, in my foregoing paper, that the property of God is immensity; but that space (which is often commensurate with bodies), and God's immensity, are not the same thing.

37. I objected further, that if space be a property, and infinite space be the immensity of God; finite space will be the extension or mensurability of something finite. And therefore the space taken up by a body, will be the extension of that body. Which is an absurdity; since a body can change space, but cannot leave its extension.

38. I asked also: if space is a property, what thing will an empty simited space, (such as that which my adversary imagines in an exhausted receiver), be the property of? It does not appear reasonable to say, that this empty space either round or square, is a property of God. Will it be then perhaps the property of some immaterial, extended, imaginary substances, which the author seems to fancy in the imaginary spaces?

39. If space is the property or affection of the substance, which is in space; the same space will be sometimes the affection of one body, sometimes of another body, sometimes of an immaterial substance, and sometimes perhaps of God himself, when it is void of all other substance material or immaterial. But this is a strange property or affection, which passes from one subject to another. Thus subjects will leave off their accidents, like clothes; that other subjects may put them on. At this rate, how shall we distinguish accidents and substances?

40. And if limited spaces are the affections of limited substances, which are in them; and infinite space be a property of God; a property of God must (which is very strange), be made up of the affections of creatures; for all finite spaces taken together make up infinite space.

41. But if the author denies, that limited space is an affection of limited things; it will not be reasonable neither, that infinite space should be the affection or property of an infinite thing. I have suggested all these difficulties in my foregoing paper; but it does not appear that the author has endeavored to answer them.

42. I have still other reasons against this strange imagination, that space is a property of God. If it be so, space belongs to the essence of God. But space has parts: therefore there would be parts in the essence of God. Spectatum admissi.

43. Moreover, spaces are sometimes empty, and sometimes filled up. Therefore there will be in the essence of God, parts sometimes empty and sometimes full, and consequently liable to a perpetual change. Bodies, filling up space, would fill up part of God's essence, and would be commensurate with it; and in the supposition of a vacuum, part of God's essence will be within the receiver. Such a God having parts, will very much resemble the Stoic's God, which was the whole universe considered as a divine animal.

44. If infinite space is God's immensity, infinite time will be God's eternity; and therefore we must say, that what is in space, is in God's immensity, and consequently in his essence; and that what is in time, is also in the essence of God. Strange expressions; which plainly show, that the author makes a wrong use of terms.

45. I shall give another instance of this. God's immensity makes him actually present in all spaces. But now if God is in space, how can it be said that space is in God, or that it is a property of God? We have often heard, that a property is in its subject; but we never heard, that a subject is in its property. In like manner, God exists in all time. How then can time be in God; and how can it be a property of God? These are perpetual alloglossies.

46. It appears that the author confounds immensity, or the extension of things, with the space according to which that extension is taken. Infinite space is not the immensity of God; finite space is not the extension of bodies: as time is not their duration. Things keep their extension, but they do not always keep their space. Everything has its own extension, its own duration; but it has not its own time, and does not keep its own space.

47. I will here show, how men come to form to themselves, the notion of space. They consider that many things exist at once, and they observe in them a certain order of co-existence, according to which the relation of one thing to another is more or less simple. This order is their situation or distance. When it happens that one of those co-existent things changes its relation to a multitude of others, which do not change their relation among themselves; and that another thing, newly come, acquires the same relation to the others, as the former had; we then say it is come into the place of the former; and this change, we call a motion in that body, wherein is the immediate cause of the change. And though many, or even all the co-existent things, should change according to certain known rules of direction and swiftness; yet one may always determine the relation of situation, which every co-existent acquires with respect to every other co-existent; and even that relation, which any other co-existent would have to this, or which this would have to any other, if it had not changed, or if it had changed any otherwise. And supposing, or feigning, that among those co-existents, there is a sufficient number of them, which have undergone no change; then we may say, that those which have such a relation to those fixed existents, as others had to them before, have now the same place which those others had. And that which comprehends all those places, is called space. Which shows, that in order to have an idea of place, and consequently of space, it is sufficient to consider these relations, and the rules of their changes, without needing to fancy any absolute reality out of the things whose situation we consider, and, to give a kind of definition: place is that, which we July is the same to A, and to B, when the relation of the co-existence of B, with C, E, F, G, &c., agrees perfectly with the relation of the co-existence, which A had with the same C, E, F, G, &c., supposing there has been no cause of change in C, E, F, G, &c. It might be said also, without entering into any further particularity, that place is that, which is the same in different moments to different existent things, when their relations of co-exsistence with certain other existents, which are supposed to continue fixed from one of those moments to the other, agree entirely together. And fixed existents are those, in which there has been no cause of any change of the order of their co-existence with others; or (which is the same thing), in which there has been no motion. Lastly, space is that which results from places taken together. And here it may not be amiss to consider the difference between place, and the relation of situation, which is in the body that fills up the place. For, the place of A and B, is the same; whereas the relation of A to fixed bodies, is not precisely and individually the same, as the relation which B (that comes into its place) will have to the same fixed bodies; but these relations agree only. For two different subjects, as A and B, cannot have precisely the same individual affection; it being impossible, that the same individual accident should be in two subjects, or pass from one subject to another. But the mind not contented with an agreement, looks for an identity, for something that should be truly the same; and conceives it as being extrinsic to the subject: and this is what we here call place and space. But this can only be an ideal thing; containing a certain order, wherein the mind conceives the application of relations. In like manner, as the mind can fancy to itself an order made up of genealogical lines, whose bigness would consist only in the number of generations, wherein every person would have his place: and if to this one should add the fiction of a metempsychosis, and bring in the same human souls again; the persons in those lines might change place; he who was a father, or a grand-father, might become a son, or a grand-son, &c. And yet those genealogical places, lines, and spaces, though they should express real truths, would only be ideal things. I shall allege another example, to show how the mind uses, upon occasion of accidents which are in subjects, to fancy to itself something answerable to those accidents, out of the subjects. The ratio or proportion between two lines L and M, may be conceived three several ways; as a ratio of the greater L to the lesser M; as a ratio of the lesser M to the greater L; and lastly, as something abstracted from both, that is, as the ratio between L and M, without considering which is the antecedent, or which the consequent; which the subject, and which the object. And thus it is, that proportions are considered in music. In the first way of considering them, L the greater; in the second, M the lesser, is the subject of that accident, which philosophers call relation. But, which of them will be the subject, in the third way of considering them?It cannot be said that both of them, L and M together, are the subject of such an accident; for if so, we should have an accident in two subjects, with one leg in one, and the other in the other; which is contrary to the notion of accidents. Therefore we must say that this relation, in this third way of considering it, is indeed out of the subjects; but being neither a substance, nor an accident, it must be a mere ideal thing, the consideration of which is nevertheless useful. To conclude: I have here done much like Euclid, who not being able to make his readers well understand what ratio is absolutely in the sense of geometricians; defines what are the same ratios. Thus, in like manner, in order to explain what place is, I have been content to define what is the same place. Lastly; I observe, that the traces of movable bodies, which they leave sometimes upon the immovable ones on which they are moved; have given men occasion to form in their imagination such an idea, as if some trace did still remain, even when there is nothing unmoved. But this is a mere ideal thing, and imports only, that if there was any unmoved thing there, the trace might be marked out upon it. And 'tis this analogy, which makes men fancy places, traces and spaces; though those things consist only in the truth of relations, and not at all in any absolute reality.

Gottfried Wilhelm Leibniz (1646-1716)

To § 14.

54. I am not sensible of any objection, but what I think I have sufficiently answered. As for the objection that space and time are quantities, or rather things endowed with quantity; and that situation and order are not so: I answer, that order also has its quantity; there is in it, that which goes before, and that which follows; there is distance or interval. Relative things have their quantity, as well as absolute ones. For instance, ratios or proportions in mathematics, have their quantity, and are measured by logarithms;and yet they are relations. And therefore though time and space consist in relations, yet they have their quantity.

To § 15.

55. As to the question, whether God could have created the world sooner; 'tis necessary here to understand each other rightly. Since I have demonstrated, that time, without things, is nothing else but a mere ideal possibility; 'tis manifest, if any one should say that this same world, which has been actually created, might have been created sooner, without any other change; he would say nothing that is intelligible. For there is no mark or difference, whereby it would be possible to know, that this world was created sooner. And therefore, (as I have already said), to suppose that God created the same world sooner, is supposing a chimerical thing. 'Tis making time a thing absolute, independent upon God; whereas time must co-exist with creatures, and is only conceived by the order and quantity of their changes.

Gottfried Wilhelm Leibniz (1646-1716)

Leibniz Diagram of Time

56. But yet absolutely speaking, one may conceive that an universe began sooner, than it actually did. Let us suppose our universe, or any other, to be represented by the figure A F; and that the ordinate A B represents its first state; and the ordinates G D, E F, its following states: I say, one may conceive that such a world began sooner, by conceiving the figure prolonged backwards, and by adding to it S R A B S. For thus, things being increased, time will be also increased. But whether such an augmentation be reasonable and agreeable to God's wisdom, is another question, to which we answer in the negative; otherwise God would have made such an augmentation. It would be like as

Humano capiti cervicem pictor equinam
Jungere si velit.

The case is the same with respect to the destruction [duration—Ger.] of the universe. As one might conceive something added to the beginning, so one might also conceive something taken off towards the end. But such a retrenching from it, would be also unreasonable.

57. Thus it appears how we are to understand, that God created things, at what time he pleased; for this depends upon the things, which he resolved to create. But things being once resolved upon, together with their relations; there remains no longer any choice about the time and the place, which of themselves have nothing in them real, nothing that can distinguish them, nothing that is at all discernible.

58. One cannot therefore say, as the author does here, that the wisdom of God may have good reasons to create this world at such or such a particular time: that particular time, considered without the things, being an impossible fiction; and good reasons for a choice, being not to be found, where everything is indiscernible.

59. When I speak of this world, I mean the whole universe of material and immaterial creatures taken together, from the beginning of things. But if any one mean only the beginning of the material world, and suppose immaterial creatures before it; he would have somewhat more reason for his supposition. For time then being marked by things that existed already, it would be no longer indifferent; and there might be room for choice. And yet indeed, this would be only putting off the difficulty. For, supposeing the whole universe of immaterial and material creatures together, to have a beginning; there is no longer any choice about the time, in which God would place that beginning.

60. And therefore one must not say, as the author does here, that God created things in what particular space, and at what particular time he pleased. For, all time and all spaces being in themselves perfectly uniform and indiscernible from each other, one of them cannot please more than another.

61. I shall not enlarge here upon my opinion explained elsewhere, that there are no created substances wholly destitute of matter. For I hold with the ancients, and according to reason, that angels or intelligences, and souls separated from a gross body, have always subtile bodies, though they themselves be incorporeal. The vulgar philosophy easily admits all sorts of fictions: mine is more strict.

62. I don't say that matter and space are the same thing. I only say, there is no space, where there is no matter; and that space in itself is not an absolute reality. Space and matter differ, as time and motion. However, these things, though different, are inseparable.

63. But yet it does not at all follow, that matter is eternal and necessary; unless we suppose space to be eternal and necessary; a supposition ill-grounded in all respects.

To § 16 and 17.

64. I think I have answered everything; and I have particularly replied to that objection, that space and time have quantity, and that order has none. See above, Number 54.

65. I have clearly shown that the contradiction lies in the hypothesis of the opposite opinion, which looks for a difference where there is none. And it would be a manifest iniquity to infer from thence, that I have acknowledged a contradiction in my own opinion.

To § 18.

66. Here I find again an argument, which I have overthrown above, Number 17. The author says, God may have good reasons to make two cubes perfectly equal and alike: and then (says he) God must needs assign them their places, though every other respect be perfectly equal. But things ought not to be separated from their circumstances. This argument consists in incomplete notions. God's resolutions are never abstract and imperfect: as if God decreed, first, to create the two cubes; and then, made another decree where to place them. Men, being such limited creatures as they are, may act in this manner. They may resolve upon a thing, and then find themselves perplexed about means, ways, places, and circumstances. But God never takes a resolution about the ends, without resolving at the same time about the means, and all the circumstances. Nay, I have shown in my Theodicæa, that properly speaking, there is but one decree for the whole universe, whereby God resolved to bring it out of possibility into existence. And therefore God will not choose a cube, without choosing its place at the same time; and he will never choose among indiscernibles.

67. The parts of space are not determined and distinguished, but by the things which are in it: and the diversity of things in space, determines God to act differently upon different parts of space. But space without things, has nothing whereby it may be distinguished; and indeed not anything actual.

68. If God is resolved to place a certain cube of matter at all, he is also resolved in which particular place to put it. But 'tis with respect to other parts of matter; and not with respect to bare space itself, in which there is nothing to distinguish it.

69. But wisdom does not allow God to place at the same time two cubes perfectly equal and alike; because there is no way to find any reason for assigning them different places. At this rate, there would be a will without a motive.

70. A will without motive (such as superficial reasoners suppose to be in God), I compared to Epicurus's chance. The author answers; Epicurus's chance is a blind necessity, and not a choice of will. I reply, that Epicurus's chance is not a necessity, but something indifferent. Epicurus brought it in on purpose to avoid necessity. 'Tis true, chance is blind; but a will without motive would be no less blind, and no less owing to mere chance.

To § 19.

71. The author repeats here, what has been already confuted above, Number 21; that matter cannot be created, without God's choosing among indiscernibles. He would be in the right, if matter consisted of atoms, similar particles, or other the like fictions of superficial philosophy. But that great principle, which proves there is no choice among indiscernibles, destroys also these ill-contrived fictions.

To § 20.

72. The author objected against me in his third paper (Numbers 7and 8); that God would not have in himself a principle of acting, if he was determined by things external. I answered, that the ideas of external things are in him: and that therefore he is determined by internal reasons, that is, by his wisdom. But the author here will not understand, to what end I said it.

To § 21.

73. He frequently confounds, in his objections against me, what God will not do, with what he cannot do. See above, Number 9 [and below, Number 76]. For example; God can do everything that is possible, but he will do only what is best. And therefore I don't say, as the author here will have it, that God cannot limit the extension of matter; but 'tis likely he will not do it, and that he has thought it better to set no bounds to matter.

74. From extension to duration, non valet consequentia. Though the extension of matter were unlimited, yet it would not follow that its duration would be also unlimited; nay even à parte ante, it would not follow, that it had no beginning. If it is the nature of things in the whole, to grow uniformly in perfection; the universe of creatures must have had a beginning. And therefore, there will be reasons to limit the duration of things, even though there were none to limit their extension. Besides, the world's having a beginning, does not derogate from the infinity of its duration à parte post; but bounds of the universe would derogate from the infinity of its extension. And therefore it is more reasonable to admit a beginning of the world, than to admit any bounds of it; that the character of its infinite author, may be in both respects preserved.

75. However, those who have admitted the eternity of the world, or, at least, (as some famous divines have done), the possibility of its eternity; did not, for all that, deny its dependence upon God; as the author here lays to their charge, without any ground.

To § 22, 23.

76. He here further objects, without any reason, that, according to my opinion, whatever God can do, he must needs have done. As if he was ignorant, that I have solidly confuted this notion in my Theodicæa; and that I have overthrown the opinion of those, who maintain that there is nothing possible but what really happens; as some ancient philosophers did, and among others Diodorus in Cicero. The author confounds moral necessity, which proceeds from the choice of what is best with absolute necessity: he confounds the will of God, with his power. God can produce everything that is possible, or whatever does not imply a contradiction; but he wills only to produce what is the best among things possible. See what has been said above, Number 9 [and Number 74.]

77. God is not therefore a necessary agent in producing creatures, since he acts with choice. However, what the author adds here, is ill-grounded, viz. that a necessary agent would not be an agent at all. He frequently affirms things boldly, and without any ground; advancing [against me] notions which cannot be proved.

To § 24-28.

78. The author alleges, it was not affirmed that space is God's sensorium, but only as it were his sensorium. The latter seems to be as improper, and as little intelligible, as the former.

To § 29.

79. Space is not the place of all things; for it is not the place of God. Otherwise there would be a thing co-eternal with God, and independent upon him; nay, he himself would depend upon it, if he has need of place.

80. Nor do I see, how it can be said, that space is the place of ideas; for ideas are in the understanding.

81. 'Tis also very strange to say, that the soul of man is the soul of the images it perceives. The images, which are in the understanding, are in the mind: but if the mind was the soul of the images, they would then be extrinsic to it. And if the author means corporeal images, how then will he have a human mind to be the soul of those images, they being only transient impressions in a body belonging to that soul?

82. If 'tis by means of a sensorium, that God perceives what passes in the world; it seems that things act upon him; and that therefore he is what we mean by a soul of the world. The author charges me with repeating objections, without taking notice of the answers; but I don't see that he has answered this difficulty. They had better wholly lay aside this pretended sensorium.

To § 30.

83. The author speaks, as if he did not understand, how, according to my opinion, the soul is a representative principle. Which is, as if he had never heard of my pre-established harmony.

84. I don't assent to the vulgar notions, that the images of things are conveyed by the organs [of sense] to the soul. For, it is not conceivable by what passage, or by what means of conveyance, these images can be carried from the organ to the soul. This vulgar notion in philosophy is not intelligible, as the new Cartesians have sufficiently shown. It cannot be explained, how immaterial substance is affected by matter: and to maintain an unintelligible notion thereupon, is having recourse to the scholastic chimerical notion of I know not what inexplicable species intentionales, passing from the organs to the soul. Those Cartesians saw the difficulty; but they could not explain it. They had recourse to a [certain wholly special] concourse of God, which would really be miraculous. But, I think, I have given the true solution of that enigma.

85. To say that God perceives what passes in the world, because he is present to the things, and not by [the dependence which the continuation of their existence has upon him and which may be said to involve] a continual production of them; is saying something unintelligible. A mere presence or proximity of co-existence, is not sufficient to make us understand, how that which passes in one being, should answer to what passes in another.

86. Besides; this is exactly falling into that opinion, which makes God to be the soul of the world; seeing it supposes God to perceive things, not by their dependence upon him, that is, by a continual production of what is good and perfect in them; but by a kind of perception, such as that by which men fancy our soul perceives what passes in the body. This is a degrading of God's knowledge very much.

87. In truth and reality, this way of perception is wholly chimerical, and has no place even in human souls. They perceive what passes without them, by what passes within them, answering to the things without; in virtue of the harmony, which God has preestablished by the most beautiful and the most admirable of all his productions; whereby every simple substance is by its nature (if one may so say), a concentration, and a living mirror of the whole universe, according to its point of view. Which is likewise one of the most beautiful and most undeniable proofs of the existence of God; since none but God, viz. the universal cause, can produce such a harmony of things. But God himself cannot perceive things by the same means whereby he makes other beings perceive them. He perceives them, because he is able to produce that means. And other beings would not be caused to perceive them, if he himself did not produce them all harmonious, and had not therefore in himself a representation of them; not as if that representation came from the things, but because the things proceed from him, and because he is the efficient and exemplary cause of them. He perceives them, because they proceed from him; if one may be allowed to say, that he perceives them: which ought not to be said, unless we divest that word of its imperfection; for else it seems to signify, that things act upon him. They exist, and are known to him, because he understands and wills them; and because what he wills, is the same, as what exists. Which appears so much the more, because he makes them to be perceived by one another; and makes them perceive one another in consequence of the natures which he has given them once for all, and which he keeps up only according to the laws of every one of them severally; which, though different one from another, yet terminate in an exact correspondence of the results of the whole. This surpasses all the ideas, which men have generally framed concerning the divine perfections, and the works of God; and raises [our notion of] them, to the highest degree; as Mr. Bayle has acknowledged, though he believed, without any ground, that it exceeded possibility.

88. To infer from that passage of Holy Scripture, wherein God is said to have rested from his works, that there is no longer a continual production of them; would be to make a very ill use of that text. 'Tis true, there is no production of new simple substances: but it would be wrong to infer from thence, that God is now in the world, only as the soul is conceived to be in the body, governing it merely by his presence, without any concourse being necessary to continue its existence.

To § 31.

89. The harmony, or correspondence between the soul and the body, is not a perpetual miracle; but the effect or consequence of an original miracle worked at the creation of things; as all natural things are. Though indeed it is a perpetual wonder, as many natural things are.

90. The word, pre-established harmony, is a term of art, I confess; but 'tis not a term that explains nothing, since it is made out very intelligibly; and the author alleges nothing, that shows there is any difficulty in it.

91. The nature of every simple substance, soul, or true monad, being such, that its following state is a consequence of the preceding one; here now is the cause of the harmony found out. For God needs only to make a simple substance become once and from the beginning, a representation of the universe, according to its point of view; since from thence alone it follows, that it will be so perpetually; and that all simple substances will always have a harmony among themselves, because they always represent the same universe.

To § 32.

92. 'Tis true, that, according to me, the soul does not disturb the laws of the body, nor the body those of the soul; and that the soul and body do only agree together; the one acting freely, according to the rules of final causes; and the other acting mechanically, according to the laws of efficient causes. But this does not derogate from the liberty of our souls, as the author here will have it. For, every agent which acts (with choice—Ger.) according to final causes, is free, though it happens to agree with an agent acting only by efficient causes without knowledge, or mechanically; because God, foreseeing what the free cause would do, did from the beginning regulate the machine in such manner, that it cannot fail to agree with that free cause. Mr. Jaquelot has very well resolved this difficulty, in one of his books against Mr. Bayle; and I have cited the passage, in my Theodicæa, Part I, § 63. I shall speak of it again below, Number 124.

To § 33.

93. I don't admit, that every action gives a new force to the patient. It frequently happens in the concourse of bodies, that each of them preserves its force; as when two equal hard bodies meet directly. Then the direction only is changed, without any change in the force;each of the bodies receiving the direction of the other, and going back with the same swiftness it came.

94. However, I am far from saying that it is supernatural to give a new force to a body; for I acknowledge that one body does frequently receive a new force from another, which loses as much of its own. But I say only, 'tis supernatural that the whole universe of bodies should receive a new force; and consequently that one body should acquire any new force, without the loss of as much in others. And therefore I say likewise, 'tis an indefensible opinion to suppose the soul gives force to the body;for then the whole universe of bodies would receive a new force.

95. The author's dilemma here, is ill-grounded; viz. that according to me, either a man must act supernaturally, or be a mere machine, like a watch. For, man does not act supernaturally: and his body is truly a machine, acting only mechanically; and yet his soul is a free cause.

To § 34 and 35.

96. I here refer to what has been or shall be said in this paper, Number 82, 86, [88] and 111 : concerning the comparison between a God and a soul of the world; and how the opinion contrary to mine, brings the one of these too near to the other.

To § 36.

97. I here also refer to what I have before said, concerning the harmony between the soul and the body, Number 89, &c.

To § 37.

98. The author tells us, that the soul is not in the brain, but in the sensorium; without saying what that sensorium is. But supposing that sensorium to be extended, as I believe the author understands it; the same difficulty still remains, and the question returns, whether the soul be diffused through that whole extension, be it great or small. For, more or less in bigness, is nothing to the purpose here.

To § 38.

99. I don't undertake here to establish my Dynamics, or my doctrine of forces: this would not be a proper place for it. However, I can very well answer the objection here brought against me. I have affirmed that active forces are preserved in the world [without diminution]. The author objects, that two soft or unelastic bodies meeting together, lose some of their force. I answer, no.

'Tis true, their wholes lose it with respect to their total motion; but their parts receive it, being shaken [internally] by the force of the concourse. And therefore that loss of force, is only in appearance. The forces are not destroyed, but scattered among the small parts. The bodies do not lose their forces; but the case here is the same, as when men change great money into small. However, I agree that the quantity of motion does not remain the same; and herein I approve what Sir Isaac Newton says, page 341 of his Optics, which the author here quotes. But I have shown elsewhere, that there is a difference between the quantity of motion, and the quantity of force.

To § 39.

100. The author maintained against me, that force does naturally lessen in the material universe; and that this arises from the dependence of things, (Third Reply, § 13 and 14). In my third answer, I desired him to prove that this imperfection is a consequence of the dependence of things. He avoids answering my demand; by falling upon an incident, and denying this to be an imperfection. But whether it be an imperfection or not, he should have proved that 'tis a consequence of the dependence of things.

101. However; that which would make the machine of the world as imperfect, as that of an unskillful watchmaker; surely must needs be an imperfection.

102. The author says now, that it is a consequence of the inertia of matter. But this also, he will not prove. That inertia, alleged here by him, mentioned by Kepler, repeated by Cartesius [in his letters], and made use of by me in my Theodicæa, in order to give a notion [and at the same time an example] of the natural imperfection of creatures; has no other effect, than to make the velocities diminish, when the quantities of matter are increased: but this is without any diminution of the forces.

To § 40.

103. I maintained, that the dependence of the machine of the world upon its divine author, is rather a reason why there can be no such imperfection in it; and that the work of God does not want to be set right again; that it is not liable to be disordered; and lastly, that it cannot lessen in perfection. Let any one guess now, how the author can hence infer against me, as he does, that, if this be the case, then the material world must be infinite and eternal, without any beginning; and that God must always have created as many men and other kinds of creatures, as can possibly be created.

To § 41.

104. I don't say, that space is an order or situation, which makes things capable of being situated: this would be nonsense. Anyone needs only consider my own words, and add them to what I said above, (Number 47) in order to show how the mind comes to form to itself an idea of space, and yet that there needs not be any real and absolute being answering to that idea, distinct from the mind, and from all relations. I don't say therefore, that space is an order or situation, but an order of situations; or [an order] according to which, situations are disposed; and that abstract space is that order of situations, when they are conceived as being possible. Space is therefore something (merely) ideal. But, it seems, the author will not understand me. I have already, in this paper, (Number 54) answered the objection, that order is not capable of quantity.

105. The author objects here, that time cannot be an order of successive things, because the quantity of time may become greater or less, and yet the order of successions continue the same. I answer: this is not so. For if the timeis greater, there will be more successive and like states interposed; and if it be less, there will be fewer; seeing there is no vacuum, nor condensation, nor penetration (if I may so speak), in times, any more than in places.

106. 'Tis true, [I maintain that] the immensity and eternity of God would subsist, though there were no creatures; but those attributes would have no dependence either on times or places. If there were no creatures, there would be neither time nor place, and consequently no actual space. The immensity of God is independent upon space, as his eternity is independent upon time. These attributes signify only [in respect to these two orders of things], that God would be present and co-existent with all the things that should exist. And therefore I don't admit what's here alleged, that if God existed alone, there would be time and space as there is now; whereas then, in my opinion, they would be only in the ideas of God as mere possibilities. The immensity and eternity of God are things more transcendent, than the duration and extension of creatures; not only with respect to the greatness, but also to the nature of the things. Those divine attributes do not imply the supposition of things extrinsic to God, such as are actual places and times. These truths have been sufficiently acknowledged by divines and philosophers.

To § 42.

107. I maintained, that an operation of God, by which he should mend the machine of the material world, tending in its nature (as this author pretends) to lose all its motion, would be a miracle. His answer was; that it would not be a miraculous operation, because it would be usual, and must frequently happen. I replied; that 'tis not usualness or unusualness, that makes a miracle properly so called, or a miracle of the highest sort; but its surpassing the powers of creatures; and that this is the [general] opinion of divines and philosophers: and that therefore the author acknowledges at least, that the thing he introduces, and I disallow, is, according to the received notion, a miracle of the highest sort, that is, one which surpasses all created powers: and that this is the very thing which all men endeavor to avoid in philosophy. He answers now, that this is appealing from reason to vulgar opinion. But I reply again, that this vulgar opinion, according to which we ought in philosophy to avoid, as much as possible, what surpasses the natures of creatures; is a very reasonable opinion. Otherwise nothing will be easier than to account for anything by bringing in the Deity, Deum ex machina, without minding the natures of things.

108. Besides; the common opinion of divines, ought not to be looked upon merely as vulgar opinion. A man should have weighty reasons, before he ventures to contradict it; and I see no such reasons here.

109. The author seems to depart from his own notion, according to which a miracle ought to be unusual; when, in § 31, he objects to me (though without any ground), that the pre-established harmony would be a perpetual miracle. Here, I say, he seems to depart from his own notion; unless he had a mind to argue against me ad hominem.

To § 43.

110. If a miracle differs from what is natural, only in appearance and with respect to us; so that we call that only a miracle, which we seldom see; there will be no internal real difference, between a miracle and what is natural; and at the bottom, every thing will be either equally natural, or equally miraculous. Will divines like the former, or philosophers the latter?

111. Will not this doctrine, moreover, tend to make God the soul of the world; if all his operations are natural, like those of our souls upon our bodies? And so God will be a part of nature.

112. In good philosophy, and sound theology, we ought to distinguish between what is explicable by the natures and powers of creatures, and what is explicable only by the powers of the infinite substance. We ought to make an infinite difference between the operation of God, which goes beyond the extent of natural powers; and the operations of things that follow the law which God has given them, and which he has enabled them to follow by their natural powers, though not without his assistance.

113. This overthrows attractions, properly so called, and other operations inexplicable by the natural powers of creatures; which kinds of operations, the assertors of them must suppose to be effected by miracle;or else have recourse to absurdities, that is, to the occult qualities of the schools; which some men begin to revive under the specious name of forces; but they bring us back again into the kingdom of darkness. This is, inventa fruge, glandibus vesci.

114. In the time of Mr. Boyle, and other excellent men, who flourished in England under Charles the IId, nobody would have ventured to publish such chimerical notions. I hope that happy time will return under so good a government as the present [and that minds a little too much carried away by the misfortune of the times will betake themselves to the better cultivation of sound learning]. Mr. Boyle made it his chief business to inculcate, that everything was done mechanically in natural philosophy. But it is men's misfortune to grow, at last, out of conceit with reason itself, and to be weary of light. Chimeras begin to appear again, and they are pleasing because they have something in them that is wonderful. What has happened in poetry, happens also in the philosophical world. People are grown weary of rational romances, such as were the French Clelia, or the German Aramene; and they are become fond again of the tales of fairies.

115. As for the motions of the celestial bodies, and even the formation of plants and animals; there is nothing in them that looks like a miracle, except their beginning.The organism of animals is a mechanism, which supposes a divine pre-formation. What follows upon it is purely natural, and entirely mechanical.

116. Whatever is performed in the body of man, and of every animal, is no less mechanical, than what is performed in a watch. The difference is only such, as ought to be between a machine of divine invention, and the workmanship of such a limited artist as man is.

To § 44.

117. There is no difficulty among divines, about the miracles of angels. The question is only about the use of that word. It may be said that angels work miracles; but less properly so called, or of an inferior order. To dispute about this, would be a mere question about a word. It may be said that the angel, who carried Habakkuk through the air, and he who troubled the water of the pool of Bethesda, worked a miracle. But it was not a miracle of the highest order; for it may be explained by the natural powers of angels, which surpass those of man.

To § 45.

118. I objected, that an attraction, properly so called, or in the scholastic sense, would be an operation at a distance, without any means intervening. The author answers here, that an attraction without any means intervening, would be indeed a contradiction. Very well! But then what does he mean, when he will have the sun to attract the globe of the earth through an empty space? Is it God himself that performs it?But this would be a miracle, if ever there was any. This would surely exceed the powers of creatures.

119. Or, are perhaps some immaterial substances, or some spiritual rays, or some accident without a substance, or some kind of species intentionalis, or some other I know not what, the means by which this is pretended to be performed? Of which sort of things, the author seems to have still a good stock in his head, without explaining himself sufficiently.

120. That means of communication (says he) is invisible, intangible, not mechanical. He might as well have added, inexplicable, unintelligible, precarious, groundless, and unexampled.

121. But it is regular, (says the author), it is constant, and consequently natural. I answer; it cannot be regular, without being reasonable; nor natural, unless it can be explained by the natures of creatures.

122. If the means, which causes an attraction properly so called, be constant, and at the same time inexplicable by the powers of creatures, and yet be true; it must be a perpetual miracle: and if it is not miraculous, it is false. 'Tis a chimerical thing, a scholastic occult quality.

123. The case would be the same, as in a body going round without receding in the tangent, though nothing that can be explained, hindered it from receding. Which is an instance I have already alleged; and the author has not thought fit to answer it, because it shows too clearly the difference between what is truly natural on the one side, and a chimerical occult quality of the schools on the other.

To § 46.

124. All the natural forces of bodies, are subject to mechanical laws; and all the natural powers of spirits, are subject to moral laws. The former follow the order of efficient causes; and the latter follow the order of final causes. The former operate without liberty, like a watch; the latter operate with liberty, though they exactly agree with that machine, which another cause, free and superior, has adapted to them beforehand. I have already spoken of this, above, No. 92.

125. I shall conclude with what the author objected against me at the beginning of this fourth reply: to which I have already given an answer above (Number 18, 19, 20). But I deferred speaking more fully upon that head, to the conclusion of this paper. He pretended, that I have been guilty of a petitio principii. But, of what principle, I beseech you? Would to God, less clear principles had never been laid down. The principle in question, is the principle of the want of a sufficient reason; in order to any thing's existing, in order to any event's happening, in order to any truth's taking place. Is this a principle, that wants to be proved?The author granted it, or pretended to grant it, Number 2, of his third paper; possibly, because the denial of it would have appeared too unreasonable. But either he has done it only in words, or he contradicts himself, or retracts his concession.

126. I dare say, that without this great principle, one cannot prove the existence of God, nor account for many other important truths.

127. Has not everybody made use of this principle, upon a thousand occasions? 'Tis true, it has been neglected, out of carelessness, on many occasions: but that neglect has been the true cause of chimeras; such as are (for instance), an absolute real time or space, a vacuum, atoms, attraction in the scholastic sense, a physical influence of the soul over the body, and a thousand other fictions, either derived from erroneous opinions of the ancients, or lately invented by modern philosophers.

128. Was it not upon account of Epicurus's violating this great principle, that the ancients derided his groundless declination of atoms? And I dare say, the scholastic attraction, revived in our days, and no less derided about thirty years ago, is not at all more reasonable.

129. I have often defied people to allege an instance against that great principle, to bring any one uncontested example wherein it fails. But they have never done it, nor ever will. 'Tis certain, there is an infinite number of instances, wherein it succeeds, [or rather it succeeds] in all the known cases in which it has been made use of. From whence one may reasonably judge, that it will succeed also in unknown cases, or in such cases as can only by its means become known: according to the method of experimental philosophy, which proceeds a posteriori; though the principle were not perhaps otherwise justified by bare reason, or a priori.

130. To deny this great principle, is likewise to do as Epicurus did; who was reduced to deny that other great principle, viz. the principle of contradiction; which is, that every intelligible enunciation must be either true, or false. Chrysippus undertook to prove that principle against Epicurus; but I think I need not imitate him. I have already said, what is sufficient to justify mine: and I might say something more upon it; but perhaps it would be too abstruse for this present dispute. And, I believe, reasonable and impartial men will grant me, that having forced an adversary to deny that principle, is reducing him ad absurdum.