can be derived from it. But does itt not seem that in this way the difference between contingent and necessary truths will be destroyed, that there will be no place for human liberty, and that an absolute fatality will rule as well over all our actions as over all the rest of the events of the world? To this I reply that a distinction must be made between that which is certain and that which is necessary. Every one grants that future contingencies are assured since God foresees them, but we do not say just because of that that they are necessary. But it will be objected, that if any conclusion can be deduced infallibly from some definition or concept, it is necessary; and now since we have maintained that everything which is to happen to anyone is already virtually included in his nature or concept, as all the properties are contained in the definition of a circle, therefore, the difficulty still remains. In order to meet the objection completely, I say that the connection or sequence is of two kinds; the one, absolutely necessary, whose contrary im- plies contradiction, occurs in the eternal verities like the truths of geometry; the other is necessary only ex hypothest, and so to speak by accident, and in itself it is contingent since the contrary is not implied. This latter sequence is not founded upon ideas wholly pure and upon the pure under- standing of God, but upon his free decrees and upon the: processes of ‘the untverse>”) Let vus igive tan example. Since Julius Caesar will become perpet- ual Dictator and master of the Republic and will overthrow the liberty of Rome, this action is con- tained in his concept, for we have supposed that it is the nature of such a perfect concept of a subject DISCOURSE ON METAPHYSICS. 21 to involve everything, in fact so that the predicate may be included in the subject wt posstt inesse sub- jecto. We may say that it is not in virtue of this concept or idea that he is obliged to perform this action, since it pertains to him only because God knows everything. But it will be insisted in reply that his nature or form responds to this concept, and since God imposes upon him this personality, he as. compelled henceforth to live up to it. _ I could reply by instancing the similar case of the future contingencies which as yet have no reality save in the understanding and will of God,and which, because God has given them in advance this form, must needs correspond to it. But I prefer to over- come a difficulty rather than to excuse it by instanc- ing other difficulties, and what I am about to say will serve to clear up the one as well as the other. It is here that must be applied the distinction in the kind of relation, and I say that that which hap- pens conformably to these decrees is assured, but that it is not therefore necessary, and if anyone did the contrary, he would do nothing impossible in itself, although it is impossible ex hypothesi that that other happen. For if anyone were capable of carry- ing out acomplete demonstration by virtue of which he could prove this connection of the subject, which is Caesar, with the predicate, which is his successful enterprise, he would bring us to see in fact that the future dictatorship of Caesar had its basis in his concept or nature, so that one would see there a reason why he resolved to cross the Rubicon rather than to stop, and why he gained instead of losing the day at Pharsalus, and that it was reasonable and by consequence assured that this would occur, but 22 LEIBNIZ, one would not prove that it was necessary in itself, nor that the contrary implied a contradiction, almost in the same way in which it is reasonable and assured that God will always do what is best although that which is less perfect is not thereby implied. For it would be found that this demon- stration of this predicate as belonging to Caesar ts not as absolute as are those of numbers or of geom- etry, but that this predicate supposes a sequence of things which God has shown by his free will. This Sequence 1s based *on the first free decree of God which was to do always that which is the most perfect and upon the decree which God made fol- lowing the first one, regarding human nature, which is that men should always do, although freely, that which appears to be the best. Now every truth which is founded upon this kind of decree is ccn- tingent, although certain, for the decrees of God do not change the possibilities of things and, as I have already said, although God assuredly chooses the best, this does not prevent that which is less per- fect from being possible in itelf. Although it will never happen, it is not its Impossibility but its imperfection which causes him to reject it. Now nothing is necessitated -whose opposite is possible. One will then be in a position to satisfy these kinds of difficulties, however great they may appear (and in fact they have not been less vexing to all other thinkers who have ever treated this matter), provided that he considers well that all contingent propositions have reasons why they are thus, rather than otherwise, or indeed (what is the same thing) that they have proof @ priort of their truth, which render them certain and show that the connection DISCOURSE ON METAPHYSICS. 23 of the subject and predicate in these propositions has its basis in the nature of the one and of the other, but he must further remember that such con- tingent propositions have not the demonstrations of necessity, since their reasons are founded only on the principle of contingency or of the existence of things, that is to say, upon that which is, or which appears to be the best among several things equally possible. Necessary truths, on the other hand, are founded upon the principle of contradiction, and upon the possibility or impossibility of the essences themselves, without regard here to the free will of God or of creatures.
XIV. God produces different substances according to the different views which he has of the world, and by the intervention of God, the appropriate nature of each substance brings it about that what happens to one corresponds to what happens to all the others, without, however, their acting upon one another directly.
“After having seen, to a certain extent,in what the nature of substances consists, we must try to explain the dependence they have upon one another and their actions and passions. Now it is first of all very evident that created substances depend upon God who preserves them and can produce them continually by a kind of emanation just as we pro- duce our thoughts, for when God turns, so to say, on all sides and in all fashions, the general system of phenomena which he finds it good to produce for the sake of manifesting his glory, and when he regards all the aspects of the world in all possible manners, since there is no relation which escapes 24 LEIBNIZ.
24 LEIBNIZ.
his omniscience, the result of each view of the uni- verse as seen from a different position is a sub- stance which expresses the universe conformably to this view, provided God sees fit to render his thought effective and to produce the substance, and since God’s vision ts always true, our per- ceptions are always true and that which deceives us are our judgments, which are of us. Now we have said before, and it follows from what we have just said that each substance is a world by itself, independent of everything else excepting God; therefore, all our phenomena that Is all things which are ever able to happen to us, are only con- sequences of our being. Now as the phenomena maintain a certain order conformably to our nature, or so to speak to the world which ts in us (from whence it follows that we can, for the regulation of our conduct, make useful observations which are justified by the outcome of the future phenomena) and as we are thus able often to judge the future by the past without deceiving ourselves, we have suffi- cient grounds for saying that these phenomena are true and we will not be put to the task of inquiring whether they are outside of us, and whether others perceive them also.
Nevertheless it is most true that the perceptions and expressions of all substances intercorrespond, so that each one following independently certain reasons or laws which he has noticed meets others which are doing the same, as when several have agreed to meet together in a certain place on a set day, they are able to carry out the plan if they wish. Now although all express the same phenomena, this does not bring it about that their expressions DISCOURSE ON METAPHYSICS, 25 are exactly alike. It is sufficient if they are pro- portional. As when several spectators think they see the same thing and are agreed about it, although each one sees or speaks according to the measure of his vision. It is God alone, (from whom all individuals emanate continually, and who sees the universe not only as they see it, but besides in a very different way from them) who is the cause of this correspondence in their phenomena and who brings it about that that which is particular to one, is also common to all, otherwise there would be no relation. In a way, then, we might properly say, although it seems strange, that a particular sub- stance never acts upon another particular substance nor is it acted upon by it. That which happens to each one is only the consequence of its complete idea or concept, since this idea already includes all the predicates and expresses the whole universe. In fact nothing can happen to us except thoughts and perceptions, and all our thoughts and percep- tions are but the consequence, contingent it is true, of our precedent thoughts and perceptions, in such a way that were I able to consider directly all that happens or appears to me at the present time, I should be able to see all that will happen to me or that will ever appear to me. This future will not fail me, and will surely appear to me even if all that which is outside of me were destroyed, save only that God and myself were left.
Since, however, we ordinarily attribute to other things an action upon us which brings us to per- ceive things in a certain manner, it is necessary to consider the basis of this judgment and to inquire what there is of truth in it.
26 LEIBNIZ.
XV. The action of one finite substance upon another consists only in the increase in the degrees of tha expression of the first combined with a decrease in that of the second, in so far as God has in advance fashioned them so that they shall act in accord.
Without entering into a long discussion it is suffi- cient for reconciling the language of metaphysics with that of practical life to remark that we pref- erably attribute to ourselves, and with reason, the phenomena which we express the most perfectly, and that we attribute to other substances those phenomena which each one expresses the best. Thus a substance, which is of an infinite extension in so far as it expresses all, becomes limited in pro- portion to its more or less perfect manner of expres- siom. It is thus then that we may conceive of substances as interfering with and limiting one another, and hence we are able to say that in this sense they act upon one another, and that they, so to speak, accommodate themselves to one another. For it can happen that a single change which aug- ments the expression of the one may diminish that of the other. Now the virtue of a particular sub- stance is to express well the glory of God, and the better 1t expresses it, the less is it limited. Every- thing when it expresses its virtue or power, that ts to say, when it acts, changes to better, and expands just in so far as it acts. When therefore a change occurs by which several substances are affected (in fact every change affects them all) I think we may say that those substances, which by this change pass immediately to a greater degree of perfection, or to a more perfect expression, exert power and DISCOURSE ON METAPHYSICS, £7 act, while those which pass to a lesser degres dis- close their weakness and suffer. I also hold that every activity of a substances which has perception implies some pleasure, and every passion some pain, except that it may very well happen that a present advantage will be eventually destroyed by a greater evil, whence it comes that one may sin in acting or exerting his power and in finding pleasure.
- XVI. The extraordinary intervention of God is not excluded in that which our particular essences express, because their expression includes everything. Such intervention, however, goes beyond the power of our natural being or of our distinct expression, because these are finite, and follow certain subordinate regula- tions.
There remains for us at present only to explain how it is possible that God has influence at times upon men or upon other substances by an extraor- dinary or miraculous intervention, since it seems that nothing is able to happen which its extraor- dinary or supernatural in as much as all the events which occur to the other substances are only the consequences of their natures. We must recall what was said above in regard to the miracles in the universe. These always conform to the univer- sal law of the general order, although they may con- travene the subordinate regulations, and since every person or substance is like a little world. which expresses the great world, we can say that this extraordinary action of God upon this substance is nevertheless miraculous, although it is comprised in the general order ot the universe in so far as it 28 LEIBNIZ, is expressed by the individual essence or concept of this substance. This is why, if we understand in our natures all that they express, nothing ts sup- ernatural in them, because they reach out to every- thing, an effect always expressing its cause, and God being the veritable cause of the substances. But as that which our natures express the most per- fectly pertains to them in a particular manner, that being their special power, and since they are limited, as I have just explained, many things there are which surpass the powers of our natures and even of all limited natures Asa consequence, to speak more clearly, I say that the miracles and the extraor- dinary interventions of God have this peculiarity that they cannot be foreseen by any created mind however enlightened. This is because the distinct comprehension of the fundamental order surpasses them all, while on the other hand, that which is called natural depends upon less fundamental reg- ulations which the creatures are able to understand. In order then that my words may be as irreprehen- sible as the meaning I am trying to convey, it will be well to associate certain words with certain sig- nifications. We may call that which includes every- thing that we express and which expresses our union with God himself, nothing going beyond tt, our essence. But that which is limited in us may be designated as our nature or our power and in accor- dance with this terminology that which goes beyond the natures of all created substances is supernatural.
DISCOURSE ON METAPHYSICS, 29 XVII. An example of a subordinate regulation in the law of nature which demonstrates that God always preserves the same amount of force but not the same quantity of motion:—against the Cartesians and many others.
I have frequently spoken of subordinate regula- tions, or of the laws of nature, and it seems that it will be well to give an example. Our new philosophers are unanimous in employing that famous law that God always preserves the same amount of motion in the universe. In fact it is a very plausible law, and in times past I held it for indubitable. But since then I have learned in what its fault consists. Monsieur Descartes and many other clever mathematicians have thought that the quantity of motion, that is to say the velocity mul- tiplied by the mass* of the moving body, is exactly equivalent to the moving force, or to speak in mathematical terms that the force varies as the velocity multiplied by the mass. Now it is rea- sonable that the same force is always preserved in the universe. So also, looking to phenomena, it will be readily seen that a mechanical perpetual motion is impossible, because the force in sucha machine, being always diminished a little by fric- * This term is employed here for the sake of clearness. Leibniz did not possess the concept ‘‘mass,’’ which was enunciated by Newton in the same year in which the present treatise was written, 1686. Leibniz uses the terms ‘‘body,’’ “magnitude of body,’’ etc. The technical expression ‘‘mass” occurs once only in the writings of Leibniz (in a treatise pub- lished in 1695), and was there doubtless borrowed from Newton. For the history of the controversy concerning the Cartesian and Leibnizian measure of force, see Mach's Science of Mechanics, Chicago, 1893, pp. 272 et seq.— 7raus.
30 LEIBNIZ.
30 LEIBNIZ.
tion and so ultimately destined to be entirely spent, would necessarily have to recoup its losses, and-con- sequently would keep on Increasing of itself without any new impulsion from without; and we see further- more that the force of a body is diminished only in proportion as it gives up force, either to a con- tiguous body or to its own parts, in so far as they have aseparate movement. The mathematicians to whom I have referred think that what can be said of force can be said of the quantity of motion. In order, however, to show the difference I make two suppositions: in the first place, that a body falling from a certain height acquires a force enabling it to remount to the same height, provided that its direc- tion is turned that way, or provided that there are no hindrances. For instance, a pendulum will rise exactly to the height from which it has fallen, pro- vided the resistance of the air and of certain other small particles do not di- minish a little its acquired force.
I suppose in the second place that it will take as 4 B ae much force to lift a body A weighing one pound 7 he eee ES, (B) * to the height CD, four is feet, as to raise a body B (4) (a weighing four pounds to the height EF, one foot. These two suppositions are granted by our new philosophers. It is therefore manifest that the body A falling from the height CD acquires exactly as much force as the body B falling from the height EF, for the body B at F, having by the first suppo- DISCOURSE ON METAPHYSICS, 31 sition sufficient force to return to E, has therefore the force to carry a body of four pounds to the dis- tance of one foot, EF. And likewise the body A at D, having the force to return to C, has also the force required to carry a body weighing one pound, its own weight, back to C, a distance of four feet. Now by the second supposition the force of these two bodies is equal. Let us now see if the quantity of motion is the same in each case. It!s here that we will be surprised to find a very great difference, for it has been proved by Galileo that the velocity acquired by the fall CD is double the velocity acquired by. the fall EF, although the height is four times as great. Multiplying, there- fore, the body A, whose mass is I, by its velocity, which is 2, the product or the quantity of move- ment will be 2, and on the other hand, if we multi- ply the body B, whose mass is 4, by its velocity, which is I, the product or quantity of motion will be 4. Hence the quantity of the motion of the body A at the point Dis half the quantity of motion of the body B at the point F, yet their forces are equal, and there is therefore a great difference between the quantity of motion and the force. This is what we set out to show. We can see therefore how the force ought to be estimated by the quantity of the effect which it is able to produce, for exam- ple by the height to which a body of certain weight can be raised. This is a very different thing from the velocity which can be imparted to it, and in order to impart to it double the velocity we must have double the force. Nothing is simpler than this proof and Monsieur Descartes has fallen into error here, only because he trusted too much to his 32 LEIBNIZ.
thoughts even when they had not been ripened by reflection. But it astonishes me that his disciples have not noticed this error, and I am afraid that they are beginning to imitate little by little certain Peripatetics whom they ridicule, and that they are accustoming themselves to consult rather the books of their master, than reason or nature.
XVIII. The distinction between force and the quan- tity of motion is, among other reasons, important as showing that we must have recourse to metaphysical considerations in addition to discussions of extension if we wish to explain the phenomena of matter.
This consideration of the force, distinguished from the quantity of motion is of importance, not only in physics and mechanics for finding the real laws of nature and the principles of motion, and even for correcting many practical errors which have crept into the writings of certain able mathe- maticians, but also in metaphysics it is of impor- tance for the better understanding of principles. Because motion, if we regard only its exact and formal meaning, that is, change of place, is not something entirely real, and when several bodies change their places reciprocally, it is not possible to determine by considering the bodies alone to which among them movement or repose is to be attributed, as I could demonstrate geometrically, if I wished to stop for it now. But the force, or the proximate cause of these changes is something more real, and there are sufficient grounds for attributing it to one body rather than to another, and it is only through this latter investigation that we can determine to which one the movement must DISCOURSE ON METAPHYSICS. 33 appertain. Now this force is somethtng different from size, from form or from motion, and it can be seen from this consideration that the whole mean- ing of a body is not exhausted in its extension together with its modifications as our moderns per- suade themselves. We are therefore obliged to restore certain beings or forms which they have ban- ished. It appears more and more clear that although all the particular phenomena of nature can be explained mathematically or mechanically by those who understand them, yet nevertheless, the general principles of corporeal nature and even of mechan- ics are metaphysical rather than geometric, and belong rather to certain indivisible forms or natures as the causes of the appearances, than to the cor- poreal mass or to extension. This reflection is able to reconcile the mechanical philosophy of the moderns with the circumspection of those intelli- gent and well-meaning persons who, with a certain justice, fear that we are becoming too far removed from immaterial beings and that we are thus preju- dicing piety.
XIX. The utility of final causes in Physics.
As I do not wish to judge people in ill part I bring no accusation against our new philosophers who pretend to banish final causes from physics, but Iam nevertheless obliged to avow that the conse- quences of such a banishment appear to me danger- ous, especially when joined to that position which I refuted at the beginning of this treatise. That position seemed to go the length of discarding final causes entirely as though God proposed no end and no good in his activity, or as if good were not to be 34 LEIBNIZ.
the object of his will. I hold on the contrary that it is just in this that the principle of all existences and of the laws of nature must be sought, hence God always proposes the best and most perfect. I am quite willing to grant that we are liable to err when we wish to determine the purposes or councils of God, but this is the case only when we try to limit them to some particular design, thinking that he has had in view only a single thing, while in fact he regards everything at once. As for instance, if we think that God has made the world only for us, it is a great blunder, although it may be quite true that he has made it entirely for us, and that there is nothing in the universe which does not touch us and which does not accommodate itself to the regard which he has for us according to the principle laid down above. Therefore when we see some good effect or some perfection which hap- pens or which follows from the works of God we are able to say assuredly that God has purposed it, for he does nothing by chance, and 1s not like us who sometimes fail to do well. Therefore, far from being able to fall into error in this respect as do the extreme statesmen who postulate too much foresight in the designs of Princes, or as do commentators who-seek for too much erudition in their authors, it will be impossible to attribute too much reflection to God’s infinite wisdom, and there is no matter in which error is less to be feared provided we confine