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Early Readings in the Philosophy of Science

Gottfried Wilhelm Leibniz (1646-1716)

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Portrait of Leibniz

Gottfried Wilhelm Leibniz is one of the greates philosophers, mathematicians, and theologians of the Western tradition. Denis Diderot once wrote of him, "If his ideas had been expressed with the flair of Plato, the philosopher of Leipzig would cede nothing to the philosopher of Athens." Leibniz developed calculus independently of Isaac Newton; contributed significantly to the invention and improvement of mechanical calculators; and was an advocate of an optimistic, rational worldview. Many of his philolsophical arguments continue the scholastic traditions of Plato and Aristotle, applying logic to a series of first principles to support his conclusions, rather than empirical observation.

The selections below come from Leibniz' correspondence with Samuel Clarke, in which Leibniz explains his interpretation of space and time as relative contstructs, as opposed to Clarke's support of Newton's arguments in favor of absolute space. In these letters, he repeated appeals to his fundamental principles, especially the Principle of Sufficient Reason, that nothing happens without a cause.

Letters to Samuel Clarke, from The Philosophical Works of Leibniz (1890) 238-286

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Samuel Clarke and Gottfried Leibniz

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Mr. Leibnitz's First Paper: Being an Extract of a Letter Written in November, 1715.

1. Natural religion itself seems to decay [in England] very much. Many will have human souls to be material: others make God himself a corporeal Being.

2. Mr. Locke, and his followers, are uncertain at least, whether the soul be not material, and naturally perishable.

3. Sir Isaac Newton says, that space is an organ, which God makes use of to perceive things by. But if God stands in need of any organ to perceive things by, it will follow, that they do not depend altogether upon him, nor were produced by him.

4. Sir Isaac Newton, and his followers, have also a very odd opinion concerning the work of God. According to their doctrine, God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God's making, is so imperfect, according to these gentlemen; that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it, as a clockmaker mends his work; who must consequently be so much the more unskillful a workman, as he is oftener obliged to mend his work and to set it right. According to my opinion, the same force and vigor remains always in the world, and only passes from one part of matter to another, agreeably to the laws of nature, and the beautiful pre-established order. And I hold, that when God works miracles, he does not do it in order to supply the wants of nature, but those of grace. Whoever thinks otherwise, must needs have a very mean notion of the wisdom and power of God.

Mr. Leibnitz's Second Paper: Being an Answer to Dr. Clarke's First Reply.

1. It is rightly observed in the paper delivered to the Princess of Wales, which her Royal Highness has been pleased to communicate to me, that, next to corruption of manners, the principles of the materialists do very much contribute to keep up impiety. But I believe the author had no reason to add, that the mathematical principles of philosophy are opposite to those of the materialists. On the contrary, they are the same; only with this difference, that the materialists, in imitation of Democritus, Epicurus, and Hobbes, confine themselves altogether to mathematical principles, and admit only bodies, whereas the Christian mathematicians admit also immaterial substances. Wherefore, not mathematical principles (according to the usual sense of that word) but metaphysical principles ought to be opposed to those of the materialists. Pythagoras, Plato, and Aristotle in some measure, had a knowledge of these principles; but I pretend to have established them demonstratively in my Theodicæa, though I have done it in a popular manner. The great foundation of mathematics, is the principle of contradiction or identity, that is, that a proposition cannot be true and false at the same time; and that therefore A is A, and cannot be not A. This single principle is sufficient to demonstrate every part of arithmetic and geometry, that is, all mathematical principles. But in order to proceed from mathematics to natural philosophy, another principle is requisite, as I have observed in my Theodicæa: I mean, the principle of a sufficient reason, viz: that nothing happens without a reason why it should be so, rather than otherwise. And therefore Archimedes being desirous to proceed from mathematics to natural philosophy, in his book De Æquilibria, was obliged to make use of a particular case of the great principle of a sufficient reason. He takes it for granted, that if there be a balance, in which every thing is alike on both sides, and if equal weights are hung on the two ends of that balance, the whole will be at rest. 'Tis because no reason can be given, why one side should weigh down, rather than the other. Now, by that single principle, viz: that there ought to be a sufficient reason why things should be so, and not otherwise, one may demonstrate the being of a God, and all the other parts of metaphysics or natural theology; and even, in some measure, those principles of natural philosophy, that are independent upon mathematics: I mean, the dynamic principles, or the principles of force.

2. The author proceeds and says, that according to the mathematical principles, that is, according to Sir Isaac Newton's philosophy (for mathematical principles determine nothing in the present case,) matter is the most inconsiderable part of the universe. The reason is, because he admits empty space, besides matter; and because, according to his notions, matter fills up only a very small part of space.But Democritus and Epicurus maintained the same thing: they differed from Sir Isaac Newton, only as to the quantity of matter; and perhaps they believed there was more matter in the world, than Sir Isaac Newton will allow: wherein I think their opinion ought to be preferred; for, the more matter there is, the more God has occasion to exercise his wisdom and power. Which is one reason, among others, why I maintain that there is no vacuum at all.

3. I find, in express words, in the Appendix to Sir Isaac Newton's Optics, that space is the sensorium of God. But the word sensorium hath always signified the organ of sensation. He, and his friends, may now, if they think fit, explain themselves quite otherwise: I shall not be against it.

4. The author supposes that the presence of the soul is sufficient to make it perceive what passes in the brain. But this is the very thing which Father Malebranche, and all the Cartesians deny; and they rightly deny it. More is requisite besides bare presence, to enable one thing to perceive what passes in another. Some communication, that may be explained; some sort of influence, is requisite for this purpose. Space, according to Sir Isaac Newton, is intimately present to the body contained in it and commensurate with it. Does it follow from thence, that space perceives what passes in a body; and remembers it, when that body is gone away? Besides, the soul being indivisible, its immediate presence, which may be imagined in the body, would only be in one point. How then could it perceive what happens out of that point? I pretend to be the first, who has shown how the soul perceives what passes in the body.

5. The reason why God perceives every thing, is not his bare presence, but also his operation. 'Tis because he preserves things, by an action, which continually produces whatever is good and perfect in them. But the soul having no immediate influence over the body, nor the body over the soul, their mutual correspondence cannot be explained by their being present to each other.

6. The true and principal reason why we commend a machine, is rather grounded upon the effects of the machine, than upon its cause. We don't enquire so much about the power of the artist, as we do about his skill in his workmanship. And therefore the reason alleged by the author for extolling the machine of God's making, grounded upon his having made it entirely, without wanting any materials to make it of; that reason, I say, is not sufficient. 'Tis a mere shift the author has been forced to have recourse to: and the reason why God exceeds any other artist, is not only because he makes the whole, whereas all other artists must have matter to work upon. This excellency in God, would be only on the account of power. But God's excellency arises also from another cause, viz: wisdom, whereby his machine lasts longer, and moves more regularly, than those of any other artist whatsoever. He who buys a watch, does not mind whether the workman made every part of it himself, or whether he got the several parts made by others, and did only put them together; provided the watch goes right. And if the workman had received from God even the gift of creating the matter of the wheels; yet the buyer of the watch would not be satisfied, unless the workman had also received the gift of putting them well together. In like manner, he who will be pleased with God's workmanship, cannot be so, without some other reason than that which the author has here alleged.

7. Thus the skill of God must not be inferior to that of a workman; nay, it must go infinitely beyond it. The bare production of every thing, would indeed show the power of God; but it would not sufficiently show his wisdom. They who maintain the contrary, will fall exactly into the error of the materialists, and of Spinoza, from whom they profess to differ. They would, in such case, acknowledge power, but not sufficient wisdom, in the principle or cause of all things.

8. I do not say, the material world is a machine, or watch, that goes without God's interposition; and I have sufficiently insisted, that the creation wants to be continually influenced by its Creator. But I maintain it to be a watch, that goes without wanting to be mended by him: otherwise we must say, that God bethinks himself again. No; God has foreseen everything; he has provided a remedy for everything before-hand; there is in his works a harmony, a beauty, already pre-established.

9. This opinion does not exclude God's Providence, or his government of the world: on the contrary, it makes it perfect. A true Providence of God, requires a perfect foresight. But then it requires moreover, not only that he should have foreseen everything; but also that he should have provided for everything beforehand, with proper remedies: otherwise, he must want either wisdom to foresee things, or power to provide against them. He will be like the God of the Socinians, who lives only from day to day, as Mr. Jurieu says. Indeed God, according to the Socinians, does not so much as foresee inconveniences; whereas, the gentlemen I am arguing with, who put him upon mending his work, say only, that he does not provide against them. But this seems to me to be still a very great imperfection. According to this doctrine, God must want either power, or good will.

10. I don't think I can be rightly blamed, for saying that God is intelligentia supramundana. Will they say, that he is intelligentia mundana; that is, the soul of the world, I hope not. However, they will do well to take care not to fall into that notion unawares.

11. The comparison of a king, under whose reign everything should go on without his interposition, is by no means to the present purpose; since God preserves everything continually, and nothing can subsist without him. His kingdom therefore is not a nominal one. 'Tis just as if one should say, that a king, who should originally have taken care to have his subjects so well educated, and should, by his care in providing for their subsistence, preserve them so well in their fitness for their several stations, and in their good affection towards him, as that he should have no occasion ever to be amending anything amongst them; would be only a nominal king.

12. To conclude. If God is obliged to mend the course of nature from time to time, it must be done either supernaturally or naturally. If it be done supernaturally, we must have recourse to miracles, in order to explain natural things: which is reducing an hypothesis ad absurdum: for, everything may easily be accounted for by miracles. But if it be done naturally, then God will not be intelligentia supramundana: he will be comprehended under the nature of things; that is, he will be the soul of the world.

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Image of Leibniz' Correspondence, via Wikimedia Commons

Mr. Leibnitz's Third Paper: Being an Answer to Dr. Clarke's Second Reply.

1. According to the usual way of speaking, mathematical principles concern only mere mathematics, viz: numbers, figures, arithmetic, geometry. But metaphysical principles concern more general notions, such as are cause and effect.

2. The author grants me this important principle; that nothing happens without a sufficient reason, why it should be so, rather than otherwise. But he grants it only in words, and in reality denies it. Which shows that he does not fully perceive the strength of it. And therefore he makes use of an influence, which exactly falls in with one of my demonstrations against real absolute space, which is an idol of some modern Englishmen. I call it an idol, not in a theological sense, but in a philosophical one; as Chancellor Bacon says, that there are idola tribus, idola specus.

3. These gentlemen maintain therefore, that space is a real absolute being. But this involves them in great difficulties; for such a being must needs be eternal and infinite. Hence some have believed it to be God himself, or, one of his attributes, his immensity. But since space consists of parts, it is not a thing which can belong to God.

4. As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is; that I hold it to be an order of coexistences, as time is an order of successions. For space denotes, in terms of possibility, an order of things which exist at the same time, considered as existing together without inquiring into their particular manner of existing. And when many things are seen together, one perceives that order of things among themselves.

5. I have many demonstrations, to confute the fancy of those who take space to be a substance, or at least an absolute being. But I shall only use, at the present, one demonstration which the author here gives me occasion to insist upon. I say then, that if space was an absolute being, there would something happen, for which it would be impossible there should be a sufficient reason. Which is against my Axiom. And I prove it thus. Space is something absolutely uniform; and, without the things placed in it, one point of space does not absolutely differ in any respect whatsoever from another point of space. Now from hence it follows, (supposing space to be something in itself, besides the order of bodies among themselves,) that 'tis impossible there should be a reason, why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner, and not otherwise; why everything was not placed the quite contrary way, for instance, by changing east into west. But if space is nothing else, but that order or relation; and is nothing at all without bodies, but the possibility of placing them; then those two states, the one such as it now is, the other supposed to be the quite contrary way, would not at all differ from one another. Their difference therefore is only to be found in our chimerical supposition of the reality of space in itself. But in truth the one would exactly be the same thing as the other, they being absolutely indiscernible; and consequently there is no room to enquire after a reason of the preference of the one to the other.

6. The case is the same with respect to time. Supposing any one should ask, why God did not create everything a year sooner; and the same person should infer from thence, that God has done something, concerning which 'tis not possible there should be a reason, why he did it so, and not otherwise: the answer is, that his inference would be right, if time was any thing distinct from things existing in time. For it would be impossible there should be any reason, why things should be applied to such particular instants, rather than to others, their succession continuing the same. But then the same argument proves, that instants, considered without the things, are nothing at all; and that they consist only in the successive order of things: which order remaining the same, one of the two states, viz. that of a supposed anticipation, would not at all differ, nor could be discerned from, the other which now is.

7. It appears from what I have said, that my axiom has not been well understood; and that the author denies it, tho' he seems to grant it. 'Tis true, says he, that there is nothing without a sufficient reason why it is, and why it is thus, rather than otherwise: but he adds, that this sufficient reason, is often the simple or mere will of God: as, when it is asked why matter was not placed otherwise in space; the same situations of bodies among themselves being preserved. But this is plainly maintaining, that God wills something, without any sufficient reason for his will: against the axiom, or the general rule of whatever happens. This is falling back into the loose indifference, which I have confuted at large, and showed to be absolutely chimerical even in creatures, and contrary to the wisdom of God, as if he could operate without acting by reason.

8. The author objects against me, that if we don't admit this simple and mere will, we take away from God the power of choosing, and bring in a fatality. But the quite contrary is true. I maintain that God has the power of choosing, since I ground that power upon the reason of a choice agreeable to his wisdom. And 'tis not this fatality, (which is only the wisest order of Providence) but a blind fatality or necessity, void of all wisdom and choice, which we ought to avoid.

9. I had observed, that by lessening the quantity of matter, the quantity of objects, upon which God may exercise his goodness, will be lessened. The author answers, that instead of matter, there are other things in the void space, on which God may exercise his goodness. Be it so: tho' I don't grant it; for I hold that every created substance is attended with matter. However, let it be so: I answer, that more matter was consistent with those same things; and consequently the said objects will be still lessened. The instance of a greater number of men, or animals, is not to the purpose; for they would fill up place, in exclusion of other things.

10. It will be difficult to make me believe, that sensorium does not, in its usual meaning, signify an organ of sensation. See the words of Rudolphus Goclenius, in his Dictionarium Philosophicum; v. sensiterium. Barbarum Scholasticorum, says he, qui interdum sunt Simiæ Græcorum. Hi dicunt 'Αωητηρων. Ex quo illi fecerunt sensiteriumpro sensorio, id est, organo sensationis.

11. The mere presence of a substance, even an animated one, is not sufficient for perception. A blind man, and even a man whose thoughts are wandering, does not see. The author must explain, how the soul perceives what is without itself.

12. God is not present to things by situation, but by essence: his presence is manifested by his immediate operation. The presence of the soul is quite of another nature. To say that it is diffused all over the body, is to make it extended and divisible. To say it is, the whole of it, in every part of the body, is to make it divided from itself. To fix it to a point, to diffuse it all over many points, are only abusive expressions, idola tribus.

13. If active force should diminish in the universe, by the natural laws which God has established; so that there should be need for him to give a new impression in order to restore that force, like an artist's mending the imperfections of his machine; the disorder would not only be with respect to us, but also with respect to God himself. He might have prevented it, and taken better measures to avoid such an inconvenience: and therefore, indeed, he has actually done it.

14. When I said that God has provided remedies beforehand against such disorders, I did not say that God suffers disorders to happen, and then finds remedies for them; but that he has found a way beforehand to prevent any disorders happening.

15. The author strives in vain to criticize my expression, that God is intelligentia supramundana. To say that God is above the world, is not denying that he is in the world.

16. I never gave any occasion to doubt, but that God's conservation is an actual preservation and continuation of the beings, powers, orders, dispositions, and motions of all things: and I think I have perhaps explained it better than many others. But, says the author, this is all that I contended for. To this I answer; your humble servant for that, sir. Our dispute consists in many other things. The question is, whether God does not act in the most regular and most perfect manner? whether his machine is liable to disorder, which he is obliged to mend by extraordinary means? whether the will of God can act without reason? whether space is an absolute being?also concerning the nature of miracles; and many such things, which make a wide difference between us.

17. Divines will not grant the author's position against me, viz. that there is no difference, with respect to God, between natural and supernatural: and it will be still less approved by most philosophers. There is a vast difference between these two things; but it plainly appears, it has not been duly considered. That which is supernatural exceeds all the powers of creatures. I shall give an instance, which I have often made use of with good success. If God would cause a body to move free in the æther round about a certain fixed center, without any other creature acting upon it: I say, it could not be done without a miracle; since it cannot be explained by the nature of bodies. For, a free body does naturally recede from a curve in the tangent. And therefore I maintain, that the attraction of bodies, properly so called, is a miraculous thing, since it cannot be explained by the nature of bodies.

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Mr. Leibnitz's Fourth Paper; Being an Answer to Dr. Clarke's Third Reply.

1. In things absolutely indifferent, there is no [foundation for] choice; and consequently no election, nor will; since choice must be founded on some reason, or principle.

2. A mere will without any motive, is a fiction, not only contrary to God's perfection, but also chimerical and contradictory; inconsistent with the definition of the will, and sufficiently confuted in my Theodicæa.

3. 'Tis a thing indifferent, to place three bodies, equal and perfectly alike, in any order whatsoever; and consequently they will never be placed in any order, by him who does nothing without wisdom. But then, he being the author of things, no such things will be produced by him at all; and consequently there are no such things in nature.

4. There is no such thing as two individuals indiscernible from each other. An ingenious gentleman of my acquaintance, discoursing with me, in the presence of her Electoral Highness the Princess Sophia, in the garden of Herrenhausen, thought he could find two leaves perfectly alike. The princess defied him to do it, and he ran all over the garden a long time to look for some; but it was to no purpose. Two drops of water, or milk, viewed with a microscope, will appear distinguishable from each other. This is an argument against atoms; which are confuted, as well as a vacuum, by the principles of true metaphysics.

5. Those great principles of a sufficient reason, and of the identity of indiscernibles, change the state of metaphysics. That science becomes real and demonstrative by means of these principles; whereas before, it did generally consist in empty words.

6. To suppose two things indiscernible, is to suppose the same thing under two names. And therefore to suppose that the universe could have had at first another position of time and place, than that which it actually had; and yet that all the parts of the universe should have had the same situation among themselves, as that which they actually had; such a supposition, I say, is an impossible fiction.

7. The same reason, which shows that extramundane space is imaginary, proves that all empty space is an imaginary thing; for they differ only as greater and less.

8. If space is a property or attribute, it must be the property of some substance. But what substance will that bounded empty space be an affection or property of, which the persons I am arguing with, suppose to be between two bodies?

9. If infinite space is immensity, finite space will be the opposite to immensity, that is, 'twill be mensurability, or limited extension. Now extension must be the affection of some thing extended. But if that space be empty, it will be an attribute without a subject, an extension without any thing extended. Wherefore by making space a property, the author falls in with my opinion, which makes it an order of things, and not any thing absolute.

10. If space is an absolute reality; far from being a property or an accident opposed to substance, it will have a greater reality than substances themselves. God cannot destroy it, nor even change it in any respect. It will be not only immense in the whole, but also immutable and eternal in every part. There will be an infinite number of eternal things besides God.

11. To say that infinite space has no parts, is to say that it does not consist of finite spaces; and that infinite space might subsist, though all finite space should be reduced to nothing. It would be, as if one should say, in the Cartesian supposition of a material extended unlimited world, that such a world might subsist, though all the bodies of which it consists, should be reduced to nothing.

12. The author ascribes parts to space, p. 19 of the 3d edition of his Defense of the Argument against Mr. Dodwell; and makes them inseparable one from another. But, p. 30 of his Second Defense, he says they are parts improperly so-called: which may be understood in a good sense.

13. To say that God can cause the whole universe to move forward in a right line, or in any other line, without making otherwise any alteration in it, is another chimerical supposition. For, two states indiscernible from each other, are the same state; and consequently, 'tis a change without any change. Besides, there is neither rhyme nor reason in it. But God does nothing without reason; and 'tis impossible there should be any here. Besides, it would be agenda nihil agere, as I have just now said, because of the indiscernibility.

14. These are idola tribûs, mere chimeras, and superficial imaginations. All this is only grounded upon the supposition, that imaginary space is real.

15. It is a like fiction, (that is) an impossible one, to suppose that God might have created the world some millions of years sooner. They who run into such kind of fictions, can give no answer to one that should argue for the eternity of the world. For since God does nothing without reason, and no reason can be given why he did not create the world sooner; it will follow, either that he has created nothing at all, or that he created the world before any assignable time, that is, that the world is eternal. But when once it has been shown, that the beginning, whenever it was, is always the same thing;the question, why it was not otherwise ordered, becomes needless and insignificant.

16. If space and time were anything absolute, that is, if they were anything else, besides certain orders of things; then indeed my assertion would be a contradiction. But since it is not so, the hypothesis [that space and time are anything absolute] is contradictory, that is, 'tis an impossible fiction.

17. And the case is the same as in geometry; where by the very supposition that a figure is greater than it really is, we sometimes prove that it is not greater. This indeed is a contradiction; but it lies in the hypothesis, which appears to be false for that very reason.

18. Space being uniform, there can be neither any external nor internal reason, by which to distinguish its parts, and to make any choice among them. For, any external reason to discern between them, can only be grounded upon some internal one. Otherwise we should discern what is indiscernible, or choose without discerning. A will without reason, would be the chance of the Epicureans. A God, who should act by such a will, would be a God only in name. The cause of these errors proceeds from want of care to avoid what derogates from the divine perfections.

19. When two things which cannot both be together, are equally good; and neither in themselves, nor by their combination with other things, has the one any advantage over the other; God will produce neither of them.

20. God is never determined by external things, but always by what is in himself; that is, by his knowledge of things, before any thing exists without himself.

21. There is no possible reason, that can limit the quantity of matter; and therefore such limitation can have no place.

22. And supposing an arbitrary limitation of the quantity of matter, something might always be added to it without derogating from the perfection of those things which do already exist; and consequently something must always be added, in order to act according to the principle of the perfection of the divine operations.

23. And therefore it cannot be said, that the present quantity of matter is the fittest for the present constitution of things. And supposing it were, it would follow that this present constitution of things would not be the fittest absolutely, if it hinders God from using more matter. It were therefore better to choose another constitution of things, capable of something more.

24. I should be glad to see a passage of any philosopher, who takes sensorium in any other sense than Goclenius does.

25. If Scapula says that sensorium is the place in which the understanding resides, he means by it the organ of internal sensation. And therefore he does not differ from Goclenius.

26. Sensorium has always signified the organ of sensation. The glandula penealis would be, according to Cartesius, the sensorium, in the above-mentioned sense of Scapula.

27. There is hardly any expression less proper upon this subject, than that which makes God to have a sensorium. It seems to make God the soul of the world. And it will be a hard matter to put a justifiable sense upon this word, according to the use Sir Isaac Newton makes of it.

28. Though the question be about the sense put upon that word by Sir Isaac Newton, and not by Goclenius; yet I am not to blame for quoting the philosophical dictionary of that author, because the design of dictionaries is to show the use of words.

29. God perceives things in himself. Space is the place of things, and not the place of God's ideas: unless we look upon space as something that makes an union between God and things, in imitation of the imagined union between the soul and the body; which would still make God the soul of the world.

30. And indeed the author is much in the wrong, when he compares God's knowledge and operation, with the knowledge and operation of souls. The soul knows things, because God has put into it a principle representative of things without. But God knows things, because he produces them continually.

31. The soul does not act upon things, according to my opinion, any otherwise than because the body adapts itself to the desires of the soul, by virtue of the harmony, which God has pre-established between them.

32. But they who fancy that the soul can give a new force to the body; and that God does the same in the world, in order to mend the imperfections of his machine; make God too much like the soul, by ascribing too much to the soul, and too little to God.

33. For, none but God can give a new force to nature; and he does it only supernaturally. If there was need for him to do it in the natural course of things; he would have made a very imperfect work. At that rate, he would be with respect to the world, what the soul, in the vulgar notion, is with respect to the body.

34. Those who undertake to defend the vulgar opinion concerning the soul's influence over the body, by instancing in God's operating on things external; make God still too much like a soul of the world. To which I add, that the author's affecting to find fault with the words, intelligentia supramundana, seems also to incline that way.

35. The images, with which the soul is immediately affected, are within itself; but they correspond to those of the body. The presence of the soul is imperfect, and can only be explained by that correspondence. But the presence of God is perfect, and manifested by his operation.

36. The author wrongly supposes against me, that the presence of the soul is connected with its influence over the body; for he knows, I reject that influence.

37. The soul's being diffused through the brain, is no less inexplicable, than its being diffused through the whole body. The difference is only in more and less.alternate text

38. They who fancy that active force lessens of itself in the world, do not well understand the principal laws of nature, and the beauty of the works of God.

39. How will they be able to prove, that this defect is a consequence of the dependence of things?

40. The imperfection of our machines, which is the reason why they want to be mended, proceeds from this very thing, that they do not sufficiently depend upon the workman. And therefore the dependence of nature upon God, far from being the cause of such an imperfection, is rather the reason why there is no such imperfection in nature, because it depends so much upon an artist, who is too perfect to make a work that wants to be mended. 'Tis true that every particular machine of nature, is, in some measure, liable to be disordered; but not the whole universe, which cannot diminish in perfection.

41. The author contends, that space does not depend upon the situation of bodies. I answer: 'Tis true, it does not depend upon such or such a situation of bodies; but it is that order, which renders bodies capable of being situated, and by which they have a situation among themselves when they exist together; as time is that order, with respect to their successive position. But if there were no creatures, space and time would be only in the ideas of God.

42. The author seems to acknowledge here, that his notion of a miracle is not the same with that which divines and philosophers usually have. It is therefore sufficient for my purpose, that my adversaries are obliged to have recourse to what is commonly called a miracle.

43. I am afraid the author, by altering the sense commonly put upon the word miracle, will fall into an inconvenient opinion. The nature of a miracle does not at all consist in usefulness or unusefulness; for then monsters would be miracles.

44. There are miracles of an inferior sort, which an angel can work. He can, for instance, make a man walk upon the water without sinking. But there are miracles, which none but God can work; they exceeding all natural powers. Of which kind, are creating and annihilating.

45. 'Tis also a supernatural thing, that bodies should attract one another at a distance, without any intermediate means; and that a body should move around, without receding in the tangent, though nothing hinder it from so receding. For these effects cannot be explained by the nature of things.

46. Why should it be impossible to explain the motion of animals by natural forces?Though indeed, the beginning of animals is no less inexplicable by natural forces, than the beginning of the world.

P. S.—All those who maintain a vacuum, are more influenced by imagination than by reason. When I was a young man, I also gave in to the notion of a vacuum and atoms; but reason brought me into the right way. It was a pleasing imagination. Men carry their inquiries no farther than those two things: they (as it were) nail down their thoughts to them: they fancy, they have found out the first elements of things, a non plus ultra. We would have nature to go no farther; and to be finite, as our minds are: but this is being ignorant of the greatness and majesty of the author of things. The least corpuscle is actually subdivided in infinitum, and contains a world of other creatures, which would be wanting in the universe, if that corpuscle was an atom, that is, a body of one entire piece without subdivision. In like manner, to admit a vacuum in nature, is ascribing to God a very imperfect work: 'tis violating the grand principle of the necessity of a sufficient reason; which many havetalked of, without understanding its true meaning; as I have lately shown, in proving, by that principle, that space is only an order of things, as time also is, and not at all an absolute being. To omit many other arguments against a vacuum and atoms, I shall here mention those which I ground upon God's perfection, and upon the necessity of a sufficient reason. I lay it down as a principle, that every perfection, which God could impart to things without derogating from their other perfections, has actually been imparted to them. Now, let us fancy a space wholly empty. God could have placed some matter in it, without derogating in any respectfrom all other things: therefore he hath actually placed some matter in that space: therefore, there is no space wholly empty: therefore all is full. The same argument proves that there is no corpuscle, but what is subdivided. I shall add another argument, grounded upon the necessity of a sufficient reason. 'Tis impossible there should be any principle to determine what proportion of matter there ought to be, out of all the possible degrees from a plenum to a vacuum, or from a vacuum to a plenum. Perhaps it will be said, that the one should be equal to the other: but, because matter is more perfect than a vacuum, reason requires that a geometrical proportion should be observed, and that there should be as much more matter than vacuum, as the former deserves to have the preference before the latter. But then there must be no vacuum at all; for the perfection of matter is to that of a vacuum, as something to nothing. And the case is the same with atoms: What reason can any one assign for confining nature in the progression of subdivision? These are fictions merely arbitrary, and unworthy of true philosophy. The reasons alleged for a vacuum, are mere sophisms.

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Sketch of Leibniz Calculator

Mr. Leibnitz's Fifth Paper: Being an answer to Dr. Clarke's Fourth Reply.

To § 1 and 2, of the foregoing paper [Clarke's Fourth Reply.]

1. I shall at this time make a larger answer; to clear the difficulties; and to try whether the author be willing to hearken to reason, and to show that he is a lover of truth; or whether he will only cavil, without clearing anything.

2. He often endeavors to impute to me necessity and fatality; though perhaps no one has better and more fully explained, than I have done in my Theodicæ, the true difference between liberty, contingency, spontaneity, on the one side; and absolute necessity, chance, coaction, on the other. I know not yet, whether the author does this, because he will do it, whatever I may say; or whether he does it, (supposing him sincere in those imputations,) because he has not yet duly considered my opinions. I shall soon find what I am to think of it, and I shall take my measures accordingly.

3. It is true, that reason in the mind of a wise being, and motives in any mind whatsoever, do that which answers to the effect produced by weights in a balance. The author objects, that this notion leads to necessity and fatality. But he says so, without proving it, and without taking notice of the explications I have formerly given, in order to remove the difficulties that may be raised upon that head.

4. He seems also to play with equivocal terms. There are necessities, which ought to be admitted. For we must distinguish between an absolute and an hypothetical necessity. We must also distinguish between a necessity, which takes place because the opposite implies a contradiction; (which necessity is called logical, metaphysical, or mathematical;) and a necessity which is moral, whereby a wise being chooses the best, and every mind follows the strongest inclination.

5. Hypothetieal necessity is that, which the supposition or hypothesis of God's foresight and pre-ordination lays upon future contingents. And this must needs be admitted, unless we deny, as the Socinians do, God's foreknowledge of future contingents, and his providence which regulates and governs every particular thing.

6. But neither that foreknowledge, nor that pre-ordination, derogate from liberty. For God, being moved by his supreme reason to choose, among many series of things or worlds, possible, that, in which free creatures should take such or such resolutions, though not without his concourse; has thereby rendered every event certain and determined once for all; without derogating thereby from the liberty of those creatures: that simple decree of choice, not at all changing, but only actualizing their free natures, which he saw in his ideas.

7. As for moral necessity, this also does not derogate from liberty. For when a wise being, and especially God, who has supreme wisdom, chooses what is best, he is not the less free upon that account: on the contrary, it is the most perfect liberty, not to be hindered from acting in the best manner. And when any other chooses according to the most apparent and the most strongly inclining good, he imitates therein the liberty of a truly wise being, in proportion to his disposition. Without this, the choice would be a blind chance.

8. But good, either true or apparent; in a word, the motive, inclines without necessitating; that is, without imposing an absolute necessity. For when God (for instance,) chooses the best: what he does not choose, and is inferior in perfection, is nevertheless possible. But if what he chooses, was absolutely necessary; any other way would be impossible: which is against the hypothesis. For God chooses among possibles, that is, among many ways, none of which implies a contradiction.

9. But to say, that God can only choose what is best; and to infer from thence, that what he does not choose, is impossible; this, I say, is confounding of terms: 'tis blending power and will, metaphysical necessity and moral necessity, essences and existences. For what is necessary, is so by its essence, since the opposite implies a contradiction; but a contingent which exists, owes its existence to the principle of what is best, which is a sufficient reason for the existence of things. And therefore I say, that motives incline without necessitating; and that there is a certainty and infallibility, but not an absolute necessity in contingent things. Add to this, what will be said hereafter, Nos. 73 and 76.

10. And I have sufficiently shown in my Theodicæa, that this moral necessity is a good thing, agreeable to the divine perfection; agreeable to the great principle or ground of existence, which is that of the want of a sufficient reason: whereas absolute and metaphysical necessity, depends upon the other great principle of our reasonings, viz. that of essences; that is, the principle of identity or contradiction: for what is absolutely necessary, is the only possible way, and its contrary implies a contradiction.

11. I have also shown, that our will does not always exactly follow the practical understanding; because it may have or find reasons to suspend its resolution till a further examination.

12. To impute to me after this, the notion of an absolute necessity, without having anything to say against the reasons which I have just now alleged, and which go to the bottom of things, perhaps beyond what is to be seen elsewhere; this, I say, will be an unreasonable obstinacy.

13. As to the notion of fatality, which the author lays also to my charge; this is another ambiguity. There is a fatum Mahometanum, a fatum stoicum, and a fatum Christianum. The Turkish fate will have an effect to happen, even though its cause should be avoided; as if there was an absolute necessity. The Stoical fate will have a man to be quiet, because he must have patience whether he will or not, since 'tis impossible to resist the course of things. But 'tis agreed, that there is fatum Christianum, a certain destiny of every thing, regulated by the foreknowledge and providence of God. Fatum is derived from fari; that is to pronounce, to decree; and in its right sense, it signifies the decree of providence. And those who submit to it through a knowledge of the divine perfections, whereof the love of God is a consequence; have not only patience, like the heathen philosophers, but are also contented with what is ordained by God, knowing he does every thing for the best; and not only for the greatest good in general, but also for the greatest particular good of those who love him.

14. I have been obliged to enlarge, in order to remove ill-grounded imputations once for all; as I hope I shall be able to do by these explications, so as to satisfy equitable persons. I shall now come to an objection raised here, against my comparing the weights of a balance with the motives, of the will. 'Tis objected, that a balance is merely passive, and moved by the weights; whereas agents intelligent, and endowed with will, are active. To this I answer, that the principle of the want of a sufficient reason is common both to agents and patients: they want a sufficient reason of their action, as well as of their passion. A balance does not only not act, when it is equally pulled on both sides; but the equal weights likewise do not act when they are in an equilibrium, so that one of them cannot go down without the other's rising up as much.

15. It must also be considered, that, properly speaking, motives do not act upon the mind, as weights do upon a balance; but 'tis rather the mind that acts by virtue of the motives, which are its dispositions to act. And therefore to pretend, as the author does here, that the mind prefers sometimes weak motives to strong ones, and even that it prefers that which is indifferent before motives: this, I say, is to divide the mind from the motives, as if they were without the mind, as the weight is distinct from the balance; and as if the mind had, besides motives, other dispositions to act, by virtue of which it could reject or accept the motives. Whereas, in truth, the motives comprehend all the dispositions, which the mind can have to act voluntarily; for they include not only the reasons, but also the inclinations arising from passions, or other preceding impressions. Wherefore, if the mind should prefer a weak inclination to a strong one, it would act against itself, and otherwise than it is disposed to act. Which shows that the author's notions, contrary to mine, are superficial, and appear to have no solidity in them, when they are well considered.

16. To assert also, that the mind may have good reasons to act, when it has no motives, and when things are absolutely indifferent, as the author explains himself here; this, I say, is a manifest contradiction. For if the mind has good reasons for taking the part it takes, then the things are not indifferent to the mind.

17. And to affirm that the mind will act, when it has reasons to act, even though the ways of acting were absolutely indifferent: this, I say, is to speak again very superficially, and in a manner that cannot be defended. For a man never has a sufficient reason to act, when he has not also a sufficient reason to act in a certain particular manner; every action being individual, and not general, nor abstract from its circumstances, but always needing some particular way of being put in execution. Wherefore, when there is a sufficient reason to do any particular thing, there is also a sufficient reason to do it in a certain particular manner; and consequently, several manners of doing it are not indifferent. As often as a man has sufficient reasons for a single action, he has also sufficient reasons for all its requisites. See also what I shall say below. No. 66.

18. These arguments are very obvious: and 'tis very strange to charge me with advancing my principle of the want of a sufficient reason, without any proof drawn either from the nature of things, or from the divine perfections. For the nature of things requires, that every event should have beforehand its proper conditions, requisites, and dispositions, the existence whereof makes the sufficient reason of such event.

19. And God's perfection requires, that all his actions should be agreeable to his wisdom; and that it may not be said of him, that he has acted without reason; or even that he has preferred a weaker reason before a stronger.

20. But I shall speak more largely at the conclusion of this paper, concerning the solidity and importance of this great principle, of the want of a sufficient reason in order to every event; the overthrowing of which principle, would overthrow the best part of all philosophy. 'Tis therefore very strange that the author should say, I am herein guilty of a petitio principii; and it plainly appears he is desirous to maintain indefensible opinions, since he is reduced to deny that great principle, which is one of the most essential principles of reason.

To § 3 and 4.

21. It must be confessed, that though this great principle has been acknowledged, yet it has not been sufficiently made use of. Which is, in great measure, the reason why the prima philosophia has not been hitherto so fruitful and demonstrative, as it should have been. I infer from that principle, among other consequences, that there are not in nature two real, absolute beings, indiscernible from each other; because if there were, God and nature would act without reason, in ordering the one otherwise than the other; and that therefore God does not produce two pieces of matter perfectly equal, and alike. The author answers this conclusion, without confuting the reason of it; and he answers with a very weak objection. That argument, says he, if it was good, would prove that it would be impossible for God to create any matter at all. For, the perfectly solid parts of matter, if we take them of equal figure and dimensions, (which is always possible in supposition), would be exactly alike. But 'tis a manifest petitio principii to suppose that perfect likeness, which, according to me, cannot be admitted. This supposition of two indiscernibles, such as two pieces of matter perfectly alike, seems indeed to be possible in abstract terms; but it is not consistent with the order of things, nor with the divine wisdom, by which nothing is admitted without reason. The vulgar fancy such things, because they content themselves with incomplete notions. And this is one of the faults of the atomists.

22. Besides; I don't admit in matter, parts perfectly solid, or that are the same throughout, without any variety or particular motion in their parts, as the pretended atoms are imagined to be. To suppose such bodies, is another popular opinion ill-grounded. According to my demonstrations, every part of matter is actually subdivided into parts differently moved, and no one of them is perfectly like another.

23. I said, that in sensible things, two, that are indiscernible from each other, can never be found; that (for instance) two leaves in a garden, or two drops of water, perfectly alike, are not to be found. The author acknowledges it as to leaves, and perhaps as to drops of water. But he might have admitted it, without any hesitation, without a perhaps, (an Italian would say, senzà forse,) as to drops of water likewise.

24. I believe that these general observations in things sensible hold also in proportion in things insensible, and that one may say, in this respect, what harlequin says in the Emperor of the Moon; 'tis there, just as 'tis here. And 'tis a great objection against indiscernibles, that no instance of them is to be found. But the author opposes this consequence, because (says he) sensible bodies are compounded; whereas he maintains there are insensible bodies which are simple. I answer again that I don't admit simple bodies.There is nothing simple, in my opinion, but true monads, which have neither parts nor extension. Simple bodies, and even perfectly similar ones, are a consequence of the false hypothesis of a vacuum and of atoms, or of lazy philosophy, which does not sufficiently carry on the analysis of things, and fancies it can attain to the first material elements of nature, because our imagination would be therewith satisfied.

25. When I deny that there are two drops of water perfectly alike, or any two other bodies indiscernible from each other; I don't say, 'tis absolutely impossible to suppose them; but that 'tis a thing contrary to the divine wisdom, and which consequently does not exist.

To § 5 and 6.

26. I own, that if two things perfectly indiscernible from each other did exist, they would be two; but that supposition is false, and contrary to the grand principle of reason. The vulgar philosophers were mistaken, when they believed that there are things different solo numero, or only because they are two; and from this error have arisen their perplexities about what they called the principle of individuation. Metaphysics have generally been handled like a science of mere words, like a philosophical dictionary, without entering into the discussion of things. Superficial philosophy, such as is that of the atomists and vacuists, forges things, which superior reasons do not admit. I hope my demonstrations will change the face of philosophy, notwithstanding such weak objections as the author raises here against me.

27. The parts of time or place, considered in themselves, are ideal things; and therefore they perfectly resemble one another, like to abstract units. But it is not so with two concrete ones, or with two real times, or two spaces filled up, that is, truly actual.

28. I don't say that two points of space are one and the same point, nor that two instants of time are one and the same instant, as the author seems to charge me with saying. But a man may fancy, for want of knowledge, that there are two different instants, where there is but one: in like manner as I observed in the 17th paragraph of the foregoing answer, that frequently in geometry we suppose two, in order to represent the error of a gainsayer, when there is really but one. If any man should suppose that a right line cuts another in two points; it will be found after all, that those two pretended points must coincide, and make but one point.

29. I have demonstrated, that space is nothing else but an order of the existence of things, observed as existing together; and therefore the fiction of a material finite universe, moving forward in an infinite empty space, cannot be admitted. It is altogether unreasonable and impracticable. For, besides that there is no real space out of the material universe; such an action would be without any design in it: it would be working without doing anything, agendo nihil agere. There would happen no change, which could be observed by any person whatsoever. These are imaginations of philosophers who have incomplete notions, who make space an absolute reality. Mere mathematicians, who are only taken up with the concepts of imagination, are apt to forge such notions; but they are destroyed by superior reasons.

30. Absolutely speaking, it appears that God can make the material universe finite in extension; but the contrary appears more agreeable to his wisdom.

31. I don't grant, that every finite is movable. According to the hypothesis of my adversaries themselves, a part of space, though finite, is not movable. What is movable, must be capable of changing its situation with respect to something else, and to be in a new state discernible from the first: otherwise the change is . but a fiction. A movable finite, must therefore make part of another finite, that any change may happen which can be observed.

32. Cartesius maintains, that matter is unlimited; and I don't think he has been sufficiently confuted. And though this be granted him, yet it does not follow that matter would be necessary, nor that it would have existed from all eternity; since that unlimited diffusion of matter, would only be an effect of God's choice, judging that to be the better.

To §7.

33. Since space in itself is an ideal thing, like time; space out of the world must needs be imaginary, as the schoolmen themselves have acknowledged. The case is the same with empty space within the world; which I take also to be imaginary, for the reasons before alleged.

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.

48. To conclude. If the space (which the author fancies) void of all bodies, is not altogether empty; what is it then full of? Is it full of extended spirits perhaps, or immaterial substances, capable of extending and contracting themselves; which move therein, and penetrate each other without any inconveniency, as the shadows of two bodies penetrate one another upon the surface of a wall? Methinks I see the revival of the odd imaginations of Dr. Henry More (otherwise a learned and well-meaning man), and of some others, who fancied that those spirits can make themselves impenetrable whenever they please. Nay, some have fancied, that man in the state of innocency, had also the gift of penetration; and that he became solid, opaque, and impenetrable by his fall. Is it not overthrowing our notions of things, to make God have parts, to make spirits have extension?The principle of the want of a sufficient reason does alone drive away all these spectres of imagination. Men easily run into fictions, for want of making a right use of that great principle.

To § 10.

49. It cannot be said, that [a certain] duration is eternal; but that things, which continue always, are eternal, [by gaining always new duration.] Whatever exists, of time and of duration, [being successive] perishes continually: and how can a thing exist eternally, which (to speak exactly,) does never exist at all? For, how can a thing exist, whereof no part does ever exist? Nothing of time does ever exist, but instants; and an instant is not even itself a part of time. Whoever considers these observations, will easily apprehend that time can only be an ideal thing. And the analogy between time and space, will easily make it appear, that the one is as merely ideal as the other. [However, if by saying that the duration of a thing is eternal, is merely understood that it lasts eternally, I have no objection.]

50. If the reality of space and time, is necessary to the immensity and eternity of God; if God must be in space; if being in space, is a property of God; he will, in some measure, depend upon time and space, and stand in need of them. For I have already prevented that subterfuge, that space and time are [in God and as it were] properties of God. [Could the opinion which should affirm that bodies move about in the parts of the divine essence be maintained ?]

To § 11 and 12.

51. I objected that space cannot be in God, because it has parts. Hereupon the author seeks another subterfuge, by departing from the received sense of words; maintaining that space has no parts, because its parts are not separable, and cannot be removed from one another by discerption. But 'tis sufficient that space has parts, whether those parts be separable or not; and they may be assigned in space, either by the bodies that are in it, or by lines and surfaces that may be drawn and described in it.

To § 13.

52. In order to prove that space, without bodies, is an absolute reality; the author objected, that a finite material universe might move forward in space. I answered, it does not appear reasonable that the material universe should be finite; and, though we should suppose it to be finite; yet 'tis unreasonable it should have motion any otherwise, than as its parts change their situation among themselves; because such a motion would produce no change that could be observed, and would be without design. 'Tis another thing, when its parts change their situation among themselves; for then there is a motion in space; but it consists in the order of relations which are changed. The author replies now, that the reality of motion does not depend upon being observed;and that a ship may go forward, and yet a man, who is in the ship, may not perceive it. I answer, motion does not indeed depend upon being observed; but it does depend upon being possible to be observed. There is no motion, when there is no change that can be observed. And when there is no change that can be observed, there is no change at all. The contrary opinion is grounded upon the supposition of a real absolute space, which I have demonstratively confuted by the principle of the want of a sufficient reason of things.

53. I find nothing in the eighth definition of the Mathematical Principles of Nature, nor in the scholium belonging to it, that proves, or can prove, the reality of space in itself. However, I grant there is a difference between an absolute true motion of a body, and a mere relative change of its situation with respect to any other body. For when the immediate cause of the change is in the body, that body is truly in motion; and then the situation of other bodies, with respect to it, will be changed consequently, though the cause of that change be not in them. 'Tis true that, exactly speaking, there is not any one body, that is perfectly and entirely at rest; but we frame an abstract notion of rest, by considering the thing mathematically. Thus have I left nothing unanswered, of what has been alleged for the absolute reality of space. And I have demonstrated the falsehood of that reality, by a fundamental principle, one of the most certain, both in reason and experience; against which, no exception or instance can be alleged. Upon the whole, one may judge from what has been said, that I ought not to admit a movable universe; nor any place out of the material universe.

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)

alternate text
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.

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