Th. [The idea of substance is not so obscure as you think. You can know what it ought to be, and what it knows of itself in other things; and indeed the knowledge of the concrete always precedes that of the abstract; the hot (thing) rather than the heat.]
§ 7. Ph. In regard to substances there are also two kinds of- ideas: the one of single substances, like that of a man, or a sheep; the other of several substances joined together, as of an army of me'n, or a flock of sheep. These collections form also a single idea.
2 Cf. Leibnitz, New Essays, Bk. II., chap. 80, § 4. — TR.
CH. xin] ON HUMAN UNDERSTANDING 149 Tli. [This unity of the idea of aggregates is very true; but ultimately you must admit that this collective unity is only a congruity or relation, whose ground is in that which is found in each of the single substances separately. Thus these beings by aggregation have no other completed unity than the mental; consequently their entity also is in some mental shape or phe nomenon, as that of the rainbow.]
CHAPTER XIII CHAPTER XIII OF SIMPLE MODES, AND FIRST OF THOSE OF SPACE § 3. Ph. Space considered with respect to the length which separates two bodies is called distance; with respect to length, breadth, and depth it may be called capacity.
Tli. [To speak more distinctly, the distance between two fixed things (be they points or extensions) is the length of the shortest possible line that can be drawn from one to the other. This distance may be considered absolutely or in a certain figure which comprises the two distant things. For example, the straight line is absolutely the distance between two points. I5ut these two points, being in the same spherical surface, the distance of these two points in this surface is the length of the shortest great arc of a circle, which may be drawn from one point to the other. It is well also to notice, that distance is not only between bodies, but also between surfaces, lines, points. It may be said that the capacity or rather the interval between two bodies or two other extensions, or between an extension and a point, is the space constituted by all the shortest lines which may be drawn between the points of each. This interval is filled, except when the two fixed things are in the same surface, when the shortest lines between the points of the fixed things must also fall in this surface or must there be expressly formed.]
§ 4. Ph. Besides that which is in nature, men have estab lished in their minds the ideas of certain determinate lengths, as an inch or a foot.
Th. [They cannot do it. For it is impossible to have the 150 LEIBNITZ'S CRITIQUE OF LOCKE [BK. n idea of a precisely determined length. You can neither say nor understand by the mind what an inch or a foot is. And you can preserve the meaning of these terms only by real measures, which you suppose unchanging, by means of which you can always recover them. Thus Mr. Greaves,1 an Eng lish mathematician, desired to make use of the pyramids of Egypt, which have endured a long time and will endure appar ently some time longer, to conserve our measures, by showing posterity the propositions 2 which have been sketched in defi nite lengths in one of these pyramids. It is true that a little after it was discovered that pendulums serve to perpetuate measures (mensuris rerum ad posteros transmittendis), as Huy- gens,3 Mouton,4 and Buratini, formerly maistre de monnoye in Poland, have demonstrated 5 by showing the proportion of our measures of length to that of the pendulum, which beats pre cisely a second (for example), i.e. the 86400th6 part of a revolution of the fixed stars, or of an astronomical day; and Buratini has composed a treatise expressly thereupon, which 1 John Greaves, 1602-1652, Savilian Professor of Astronomy at Oxford, 1643-1648. His Pyrumidographia, or a Discourse on the Pyramids in Egypt, 2 Gerhardt and Erdmann read: "propositions"; Jacques reads: "propor tions"; Schaarschmidt translates " Verhaltnisse." — TR.
8 Christian Huygeus, 1629-1695, a Dutch physicist, geometer, and astronomer. He discovered the laws of douhle refraction, and was the first to establish on a sure foundation the wave theory of light, in his Traite de la lumiere, Leyden, 1690. His researches in physical optics constitute his chief claim to scientific immortality. His application of the pendulum to regulate the move ment of clocks, arising from his felt need of an exact measure of time in astronomical observations, dates from 1(556. He published his Description de I'horloc/e a pendule in 1657, and presented his first " pendulum-clock " to the States-General June 16, 1657. This Description was republished as chap. 1 of his magnum opus, the Horoloyium oscillatorium, sive de motu pcndulorum ad horolot/ia adaptato, dedicated to Louis XIV., March 25, 1673. In chap. 4 of this work he determined the centre of oscillation of a pendulum, and conse quently the length of the simple isochronous pendulum. His works were published in two vols. 4to, Opera varia, Leyden, 1724, and two supplementary vols. 4to, Opera reliqua, Amsterdam, 1728. — TR.
4 Gabriel Monton, 1618-1694, a French mathematician and astronomer, principally known by his Observations diametrorum solis et lunss apparen- tium, Lyons, 1670. His principal title to honorable mention in the history of science is the invention of the method of differences for the calculation of tables of every kind, afterwards reduced to a system by Sir Isaac Newton, 1642-1727, and known by us as our method of interpolation. — TR.
5 Erdmann and Jacques read: " pre'tendu montrer," i.e. claimed to demon strate. — TR.
6 Erdmann and Jacques read: "864,000th," evidently an error. — TR.
CH. XIH] ON HUMAN UNDERSTANDING 151 I have seen in manuscript. But there is, however, this imper fection in this measure of pendulums, which must be limited to certain countries, for pendulums to beat iu the same time need to be shorter at the equator. And it is furthermore necessary to assume the constancy of the really fundamental measure, viz.: the length of a day or of a revolution of the globe of the earth around its axis, and also of the cause of gravitation, not to speak of other circumstances.]
§ 5. Ph. Observing how extremities are terminated either by straight lines which form distinct angles, or by curved lines in which no angle can be perceived, we form the idea of figure.
Tli. [A superficial figure is terminated by a line or by lines: but the figure of a body can be limited without determined lines, as for example that of a sphere. A single straight line or plane surface cannot enclose any space or make any figure. But a single line can enclose a superficial figure, for example the circle, the oval, as also a single curved surface can enclose a solid figure, like the sphere and the spheroid. Yet, not only several straight lines or plane surfaces, but also several curved lines or several curved surfaces, can concur together and form even angles between themselves, when the one is not the tan gent of the other. It is not easy to give the definition of figure in general according to the usage of geometers. To say that it is a limited extension would be too general, for a straight line, for example, although terminated by the two ends, is not a figure and even two straight lines cannot make one. To say that it is an extension limited by an extension is not general enough, for the entire spherical surface is a figure and yet it is not limited by any extension. It may be said, however, that figure is a limited extension, in which there are an infinite num ber of paths from one point to another. This definition com prises limited surfaces without terminating lines which the preceding definition did not comprise, and excludes the lines, because from one point to another in a line there is only one path or a determined number of paths. But it will be still better to say that figure is limited extension, which may admit an extended section, or better which has breadth, a term which hitherto had not been further defined.]
§ 6. Ph. At the least all figures are only simple modes of space.
152 LEIBNITZ'S CRITIQUE OF LOCKE [UK. 11 Th. [According to your view, the simple modes repeat the same idea, but in figures there is not always the repetition of the same mode. Curves differ much from straight lines and between themselves. So I do not know how the definition of the simple mode will be in place here.]
§ 7. Ph. [We need not take our definitions too strictly. But let us pass from figure to £>?ace.] When we find all the pieces upon the same squares of the chess-board where we left them, we say that they are all in the same place, although per haps the chess-board has been moved. We say also that the chess-board is in the same place, if it remains in the same part of the cabin of the vessel, although the vessel has sailed. The vessel is also said to be in the same place supposing it keeps the same distance with reference to the parts of the neighboring countries, although the earth has perhaps turned round.
Til. [Place is either particular when considered with regard to certain bodies, or universal when it relates to all, and with reference to which all the changes possible in relation to any body are taken into account. And if there were nothing fixed in the universe, the place of each thing could still be deter mined by reasoning,1 if there were means of making a record of all the changes, or if the memory of a creature could suffice for them, as they say, the Arabs play chess by memory and on horseback. What we cannot understand, however, is neverthe less determined in the truth of things.]
§ 15. Ph. If any man asks me what space is, I am ready to tell him when he tells me what extension is.
Th. [I wish I could speak of the nature of fever or any other malady with the same certainty with which I believe the nature of space is expounded. Extension is the abstract of the ex tended. Now the extended is a continuum whose parts are coexistent, or exist at the same time.]
§ 17. Ph. If any one asks whether space without body is 1 Schaarschmidt says that the statements here made by Leibnitz have since found their confirmation and accomplishment through Gauss' Theoria motus corporum coelcxtium. The work was published at Hamburg, in 1809, and "gave a powerful impulse to the true methods of astronomical observation." The author, Carl Friedrich Gauss, 1777-1X55, was an eminent German mathe matician. His collected works, edited by E. J. Srhering, have been published by the Royal Society of Gottingen, 7 vols.,4to. Gottingen: 18G3-1871. — TR.
en. xin] ON HUMAN UNDERSTANDING 153 substance or accident, I should reply without hesitation that I know nothing about it.
Tli. [I fear you may think me vain in wishing to determine what you, sir, admit you do not know. But if it is expedient to judge, (I fear) that you know more about the matter than you state or think you do. Some have believed that God is the place of things.1 Lessius and Guericke, if I am not mis taken, were of this opinion, but then place contains something more than what we attribute to the space which we deprive of all activity; and in this way it is no more a substance than time, and if it has parts it cannot be God. It is a relation, an order, not only between existences, but also between possibili ties as they may exist. But its truth and reality, like all eternal truths, is grounded in God.]
Ph. [I am not far from your view, and you know the pas sage of St. Paul, who says that we live and move arid have our being in God.2 Thus, according to different ways of con sidering the matter, it may be said that space is God, and also that it is only an order or a relation.]
Th. [The better statement then will be that space is an order, but that God is its source.]
§ 18. Ph. [Yet to know whether space is a substance, it would be needful to know in what the nature of substance in general consists. But in this there is a difficulty. If God, finite spirits, and bodies participate in common in an identical substantial nature, would it not follow that they differ only as different modifications of this substance?]
1 This doctrine appeared very early. Schaarschmidt refers to the collection of poems of uncertain origin called Orphica, where (Fragt. vi.,p. 457, ed. Her mann, v. 8 and 9) it is poetically expressed thus: " All that has been and here after will he, is formed together in the hosom of Zeus." Again (v. 17-20): "One is the ruling Being, in whom the All moves, fire, water, earth and air, day and night, reason, the first principle and joyful love • — all this lies in the great hosom of Zeus," etc. Malebranche represents a phase of the same view in his doctrine that we see all things in God. Cf. his Ue la Recherche de la Verite, III., ii., (i: "We abide thus in the view that God is the intelligible world or the place of spirits, just as the material world is the place of bodies. From His power they receive all their modifications, in His wisdom they find all their ideas, by His love they are moved in all their moral inclinations. But because His power and His love are nothing else than Himself, we will believe with St. Paul, that He is not far from any one of us, and that in Him we live and move and have our being." Cf. also James Martineau, Types of Ethical Theory, 2d ed.. Vol. 1, p. 170 sq. New York: Macrnillan & Co., 188(>. — Tn.
154 LEIBNITZ'S CRITIQUE OF LOCKE [UK. n Th. [If this result follows, it would follow also, that God, finite spirits, and bodies, participating in common in an iden tical nature of being, would differ only as different modifica tions of this being.]
§ 19. Ph. Those who first thought of regarding accidents as a kind of real beings, which need something in which to inhere, were constrained to invent the word substance to serve as a support to the accidents.
Th. [Do you then think, sir, that the accidents can subsist apart from the substance? or do you mean that they are not real beings? You seem to multiply difficulties without reason, and I have remarked above that substances or concretes are conceived rather than accidents or abstracts.]
Ph. The words substance and accident are in my view of little use in philosophy.
Th. [I admit that I am of another opinion, and I believe that the consideration of substance l is one of the most important and fruitful points of philosophy.]
§ 21. Ph. [We have now spoken of substance only by the way, while asking if space is a substance. But it is sufficient for us that it is not a body.] No one will dare to make body infinite like space.
Th. [Descartes and his followers have said, nevertheless, that matter has no limits, in making the world indefinite, so that it is not possible for us to conceive of its extremities. And they have changed the term infinite into indefinite with some reason; for there never is an infinite whole in the world, 1 Cf. New Essays, Bk. II., chap. 23, § 2; De primus philosophise emenda- tione et de notione substuntise, 1G94, Gephardt, Vol. 4, pp. 468-470; Erdmann, pp. 121-122; A. Jacques, (Euvres de Leibniz, Vol. 1, pp. 452-454 (in French); translation, Appendix, pp.; Systems nouveau de la nature et de la communication des substances, aussi bien que de I'union qu'il y a entre I'dme et le corps, 1695, §§ 2, 3, Gerhardt, Vol. 4, pp. 477 sq.; Erdmann, pp. 124-128; Jacques, Vol. 1, pp. 469 sq.; translation, Appendix, pp.; De ipsa natura, sire de vi insita actionibusque creaturum, 1G98, Gerhardt, Vol. 4, pp. 504-516; Erdmann, pp. 154-160; Jacques, Vol. 1, pp. 455-468 (in French); trans lation, Appendix, pp.; Considerations sur le principe de vie et sur les natures plastiques, 1705, Gerhardt, Vol. 6, pp. 539-546; Erdmann, pp. 429-432; translation, Duncan, Philos. Works of Leibnitz, pp. 163-169; Prin- cipes de la nature et de la c/race fondes en raison, c. 1714, Gerhardt, Vol. 6, pp. 598-606; Erdmann, pp. 714-718; translation, Duncan, o;). cit., pp. 209-217; La Monadolor/ic, 1714, Gerhardt, Vol.6, pp. 607-623; Erdmann, pp. 705-712; translation, Duncan, op. cit., pp. 218-232; also F. H. Hedge, in " The Jour. Spec. Philos.," Vol. 1, pp. 129-137. — TR.
CH. xiv] ON HUMAN UNDERSTANDING 155 although there are always some wholes greater than others to infinity, and the universe even cannot pass for a whole as I have elsewhere * shown.
Ph. Those who take matter and extension as one and the same thing maintain that the inner sides of a hollow vacuous body would touch. But the space which is between two bodies suffices to prevent their mutual contact.
Th. [I am of your opinion, for although I do not admit a vacuum, I distinguish matter from extension, and I admit that if there were a vacuum in a sphere, the opposite poles in the hollow space would not on that account touch. But I believe that this is a case which the divine perfection does not allow.]
§ 23. Ph. It seems, however, that motion proves a vacuum. When the least part of the divided body is as large as a grain of mustard-seed, a void space equal to the size of a grain of mustard is requisite in order to make room for the parts of this body to move freely; the same condition will hold good when the parts of the matter are one hundred million times smaller.
Th. [It is true, that if the world were full of hard corpus cles, which could neither yield nor divide, as the atoms are depicted, motion would be impossible. But in truth, there is no original hardness; on the contrary, fluidity is the original condition, and bodies are divided as needful, since there is nothing to prevent it. This takes away all the force in the argument for a vacuum drawn from motion.]
CHAPTER XIV OF DURATION AXD ITS SIMPLE MODES § 10. Ph. To extension corresponds duration. And a part of duration in which we remark no successions of ideas we call an instant.
Tli. This definition of an instant ought (I believe) to mean the popular notion, like that which the common people have 1 Cf. ante, pp. 16, 17; also New Essays, Bk. II., chap. 17, § 1. The proof that the universe is not, strictly speaking, a whole, is given in the letter to Des Bosses, March 11, 1706, Gerliardt, Vol. 2, p.304sg.,Erdmann, pp. 435-436. — TR.
156 LEIBNITZ'S CRITIQUE OF LOCKE [BK. n of a point. For strictly the point and the instant are not parts of time or space, neither have they parts. They are extremities only.
§ 16. Ph. It is not motion, but a constant succession of ideas which gives us the idea of duration.
Th. [A succession of perceptions awakes in us the idea of duration, but it does not make it. Our perceptions never have a succession sufficiently constant and regular to correspond to that of time, which is a continuum uniform and simple, like a straight line. Changing perceptions furnish us the occasion for thinking of time, and we measure it by uniform changes. But were there nothing uniform in nature, time could not be determined, as space likewise could not be determined if there were no fixed or immovable body. So that knowing the rules of different motions, we can always refer them to the uniform intelligible motions, and see beforehand by this means what will happen through the different motions taken together. And in this sense time is the measure of motion, i.e. uniform motion is the measure of non-uniform motion.]
§ 21. Ph. No two parts of duration can certainly be known to be equal; [and you must admit that observations can attain only approximate equality.] After exact research the dis covery has been made that there is really an inequality in the diurnal revolutions of the sun, and we do not know but that the annual revolutions are unequal also.
Th. [The pendulum has made us realize and see the in equality of the days from one noon to another: Solem dicere falsum auclet. It is true that men knew this already, and that this inequality has its rules. As for the annual revolution, which makes good the inequalities of solar days, it may change in the course of time. The revolution of the earth about its axis which is commonly attributed to the primum mobile,1 is our best measure up to the present time, and clocks and watches serve to divide it for us. Furthermore this same daily revolu- 1 In Aristotle's philosophy, TO TrpZ>rov KIVOVV, i.e. God, who, himself unmoved, is the necessary first and unceasing source of the eternal movement of the uni verse. Cf. Metaphys., A,' (J-10, 1071 sq.; Phys., VIII., <>, 25S'> 10; also Zeller, Outlines, § 56, 3, and Die Philos. d. Griech., 3d ed., 1879, Vol. 4, p. 358; Wallace, Outlines of the Philos. of Aristotle, 3d ed., § 39; Hegel, Gesch. d. Philos., 2d ed., Vol. 2, p. 289 sq.; Benn, The Greek Philosophers, Vol. 1, pp.
en. xiv] ON HUMAN UNDERSTANDING 157 tion of the earth may also change in the course of time: and if any pyramid could endure long enough, or if we should build new ones we could perceive it by observing there the length of pendulums a known number of whose beats occurs now during this revolution; we could also know in some way the change by comparing this revolution with others, as with those of Jupiter's satellites, for it is not apparent that, if there is any change in one or the other, it will always be proportional.
Ph. Our measure of time would be more exact if we could preserve a past day in order to compare it with the days to come, as we preserve the measures of space.
Tli. [But instead of that we are reduced to preserving and watching bodies which move in nearly equal times. Also we cannot say that a measure of space, as for example, an ell which is preserved in wood or metal remains perfectly the same.]
§ 22. Ph. Now since all men manifestly measure time by the motion of the heavenly bodies, it is very strange that one is not permitted to define time as the measure of motion.
Th. [I just stated (§ 16) how that should be understood. It is true that Aristotle says * that time is the number and not the measure of motion. And in fact, it may be said that duration is known by the number of periodic equal motions of which one begins when another ends, for example, by so many revolu tions of the earth or the stars.]
§ 24. Ph. Nevertheless to anticipate these revolutions and say that Abraham was born in the year 2712 of the Julian era, is to speak as unintelligibly, as if you counted from the begin ning of the world, although you suppose that the Julian era commenced several Imndred years before there were any days, nights, or years marked by any revolution of the sun.
Th. [This vacuum which may be conceived in time, indicates, like that of space, that time and space extend to the possible as well as to the actual. Besides, of all the chronological methods, that of reckoning the years since the beginning of the world is the least convenient, although this would be, without touching upon other reasons, only because of the great difference exist ing between the Septuagint and the Hebrew text.]
1 PJu/s., IV., 11, 219i> 1, 219i>8; cf. Wallace, Outlines of the Philos. of Aris totle, 3d ed., § 44. Wallace quotes the Greek of the first passage here referred 158 LEIBNITZ'S CRITIQUE OF LOCKE [BK. H § 26. Ph. One may conceive the beginning of motion, al though he may not comprehend that of duration taken in all its extension. One may give limits to the body, but cannot do it with regard to space.
Tli. [It is as I just said that time and space indicate the possibilities beyond the supposition of existences. Time and space are of the nature of eternal truths which consider equally the possible and the actual.]
§ 27. Ph. In fact the ideas of time and eternity come from the same source, for we can in our thought add certain lengths of duration to one another as often as we please.
Th. [But in order to draw from them the notion of eternity, it is necessary to think besides that the same reason always exists for going farther. It is this rational consideration which achieves the notion of the infinite or the indefinite in possible progress. Thus the senses alone cannot suffice to cause the formation of these notions. And ultimately it may be said that the idea of the absolute1 is anterior in the nature of things to that of the limits which are added, but we notice the former only as we commence with what is limited and strikes our senses.]
CHAPTEE XV OF DURATION AND EXPANSION CONSIDERED TOGETHER § 4. Ph. One admits more easily an infinite duration of time than an infinite expansion of space, because we conceive infinite duration in God, and attribute extension only to matter which is finite, and call the space beyond the universe imaginary. But (§ 2) Solomon seems to have other thoughts when, speak ing of God, he says: the heaven and the heaven of heavens can not contain Thee;2 and for myself I believe that he magnifies too highly the capacity of his own understanding who imag ines he can extend his thoughts farther than the place where God exists.
1 T/ic idea of the absolute belongs to our reason as such, cf. New Essays, Bk. II., chap. 17, § 3, Th., § 16, Th., though we first become aware of it through our consciousness of the particular ideas of the reason as limitations of the idea of the absolute. — TR.
CH. xv J ON HUMAN UNDERSTANDING 159 Tli. If God were extended, he would have parts. But dura tion grants these only to his works. However in relation to space immensity must be attributed to him, which gives also parts and order to the immediate works of God. He is the source of possibilities as of actualities, of the one by his essence, of the other by his will. Thus space like time has its reality only from him, and he can fill the void when it seems to him good. Thus it is that in this respect he is everywhere.1] § 11. Ph. We do not know what relations spirits have with space, nor how they participate therein. But we know that they participate in duration.
Tli. [All finite spirits are always united to some organic body, and they represent to themselves other bodies by means of relations to their own. Thus their relation to space is as evident as that of bodies. For the rest, before leaving this subject, I would add a comparison between time and space to those which you have given; viz.: — if there were a vacuum in space (as, for instance, if a sphere were hollow within), you could determine its size; but if there were a vacuum in time, i.e. a duration without changes, it would be impossible to determine its length. Whence it comes that you may refute the one who would maintain that two bodies, between which there is a vacuum, touch; for geometry defends the proposition that two opposite poles of a hollow sphere would not touch: but you cannot refute the one who would maintain that two worlds, the one of which succeeds the other, touch as to dura tion, so that the one necessarily begins when the other ends, without the possibility of an interval. You could not refute it, I say, because this interval is indeterminable. If space were only a line, and if body were immovable, it would no longer be possible to determine the length of the vacuum between two bodies.