Principles of Nature and of Grace,
Founded on Reason

By Gottfried Wilhelm Leibniz

Prefatory Note

The Principles of Nature and of Grace has much in common with the Monadology; and, indeed, it reads like a preliminary study, out of which the Monadology has been elaborated. They seem to have been written about the same time; and Gerhardt holds, against the view of previous editors, that the Principles of Nature and of Grace is the treatise which was written for Prince Eugene. It has been shown by Gerhardt that when Nicholas Remond wrote to Leibniz from Paris in 1714, asking for a condensed statement of his philosophy, Leibniz sent him a copy of the Principles of Nature and of Grace, with a letter in course of which he says:

'I now send you a little discourse on my philosophy, which I have written here for Prince Eugene of Savoy. I hope that this little work will help to make my ideas better understood, when taken in connexion with what I have written in the Journals of Leipzig, Paris and Holland. The Leipzig papers are on the whole in the language of the Scholastics; the others are more in the style of the Cartesians; and in this last writing I have endeavoured to express myself in a way which can be understood by those who are not yet thoroughly accustomed to either of the other styles.' (Letter of Aug. 26, 1714, quoted by Gerhardt, vi. 485; E. p. xxvii and p. 704 a.)

Kirchmann suggests that probably Leibniz wrote the Principles of Nature and of Grace for Prince Eugene, and afterwards, thinking it insufficient, worked it up into the Monadology, which he gave to the Prince. The Principles of Nature and of Grace was first published in the French journal, L'Europe Savante, in November, 1718.

There are three different MSS. of this work. The first of these, which is the shortest, is divided, not into paragraphs, but into two chapters, the point of division being the end of paragraph 6, where transition is made from 'Physics' to 'Metaphysics.' In the other two MSS. the paragraph division appears, and the text from which the translation is made is that of the last and most complete manuscript. In the Principles of Nature and of Grace the arrangement of the matter is much less clear and careful than it is in the Monadology. But, following the lines of the division originally made by Leibniz himself, we may say that paragraphs 1-6 inclusive give an account of the created Monads in themselves and in their relations to one another, so far as these can be considered apart from God; while the remaining paragraphs consider the nature of God as ultimate reason of the universe, and the consequences which follow from His perfection in power, wisdom and goodness. Some of the most important points in the Monadology are either passed over or very slightly treated in the Principles of Nature and of Grace. For instance, in the Principles of Nature and of Grace there is nothing to correspond to the passage in the Monadology regarding the two great principles of knowledge, and while the pre-established harmony is mentioned, it is not dwelt upon. But the connexion between the two writings, both in treatment and expression, is so close that the annotations to the Principles of Nature and of Grace may be comparatively brief.

The Principles of Nature and of Grace will be found in E. 714 sqq.; G. vi. 598 sqq.

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Principles of Nature and of Grace, Founded on Reason

§1. Substance is a being capable of action. It is simple or compound. Simple substance is that which has no parts. Compound substance1 is the combination of simple substances or Monads. Monas is a Greek word, which means unity, or that which is one. Compounds or bodies are pluralities [multitudes]; and simple substances, lives, souls, spirits, are unities. And everywhere there must be simple substances, for without simple substances there would not be compounds; and consequently all nature is full of life.2

§2. The Monads, having no parts, can neither be made [formées] nor unmade. They can neither come into being nor come to an end by natural means, and consequently they last as long as the universe, which will be changed, but which will not be destroyed. They can have no shape [figure]; otherwise they would have parts.3 Consequently any one Monad in itself and at a particular moment can be distinguished from any other only by internal qualities and activities [actions],4 which cannot be other than its perceptions (that is to say, the representations of the compound, or of that which is outside,5 in the simple) and its appetitions (that is to say, its tendencies to pass from one perception to another), which are the principles of change. For the simplicity of substance is by no means inconsistent with the multiplicity of the modifications which are to be found together in that same simple substance, and these modifications must consist in variety of relations to the things which are outside.6 It is as in the case of a centre or point, in which, although it is perfectly simple, there is an infinite number of angles formed by the lines which meet in it.

§3. All nature is a plenum. There are simple substances everywhere,7 which are actually separated from one another by activities of their own,8 and which continually change their relations; and each specially important [distinguée]9 simple substance or Monad, which forms the centre of a compound substance (e.g. of an animal) and the principle of its oneness, is surrounded by a mass composed of an infinity of other Monads, which constitute the particular body of this central Monad, and according to the affections of its body10 the Monad represents, as in a kind of centre, the things which are outside of it. This body is organic, though it forms a kind of automaton or natural machine, which is a machine not only as a whole, but also in the smallest parts of it that can come into observation.11 Since the world is a plenum all things are connected together and each body acts upon every other, more or less, according to their distance, and each, through reaction, is affected by every other. Hence it follows that each Monad is a living mirror, or a mirror endowed with inner activity,12 representative of the universe, according to its point of view, and as subject to rule as is the universe itself. And the perceptions in the Monad are produced one from another according to the laws of desires [appétits] or of the final causes of good and evil which consist in observable perceptions, regular or irregular, as, on the other hand, the changes of bodies and external phenomena are produced one from another according to the laws of efficient causes, that is to say, of motions.13 Thus there is a perfect harmony between the perceptions of the Monad and the motions of bodies, a harmony pre-established from the beginning between the system of efficient causes and that of final causes. And it is in this way that soul and body are in agreement and are physically united, while it is not possible for the one to change the laws of the other.14

§4. Each Monad, with a particular body, forms a living substance. Thus not only is there everywhere life, accompanied with members or organs, but there is also an infinity of degrees in the Monads, one dominating more or less over another. But when the Monad has organs so arranged that they give prominence and sharpness [du relief et du distingué] to the impressions they receive, and consequently to the perceptions which represent these (as, for instance, when, by means of the form of the eye's humours, the rays of light are concentrated and act with more force), this may lead to feeling [sentiment],15 that is to say, to a perception accompanied by memory, in other words, a perception of which a certain echo long remains, so as to make itself heard16 on occasion. Such a living being is called an animal, as its Monad is called a soul. And when this soul is raised to reason, it is something more sublime and is reckoned among spirits [esprits], as will presently be explained. It is true that animals are sometimes in the condition of mere [simple] living beings and their souls in the condition of mere Monads,17 namely when their perceptions are not sufficiently sharp [distingué] to be remembered, as happens in a deep dreamless sleep or in a swoon. But perceptions which have become completely confused are sure to be developed again in animals,18 for reasons which I shall presently mention (§12). Thus it is well to make distinction between perception, which is the inner state of the Monad representing outer things, and apperception, which is consciousness or the reflective knowledge of this inner state, and which is not given to all souls nor to the same soul at all times. It is for lack of this distinction that the Cartesians have made the mistake of ignoring perceptions of which we are not conscious,19 as ordinary people ignore imperceptible [insensible] bodies.20 It is this also that has led these same Cartesians to believe that only minds [esprits] are Monads, that the lower animals have no soul, and that still less are there other principles of life21 And as they came into too great conflict with the common opinion of men in denying feeling [sentiment] to the lower animals, so on the other hand they conformed too much to the prejudices of the crowd in confounding a prolonged unconsciousness, which comes from a great confusion of perceptions, with absolute death, in which all perception would cease. This has confirmed the ill-founded opinion that some souls are destroyed, and the bad ideas of some who call themselves free-thinkers [esprits forts] and who have disputed the immortality of our soul.22

§5. There is a connexion among the perceptions of animals which has some likeness to reason; but it is based only on the memory of facts or effects,23 and not at all on the knowledge of causes. Thus a dog avoids the stick with which it has been beaten, because memory represents to it the pain which this stick has caused it. And men, in so far as they are empirics, that is to say in three-fourths of their actions, do not act otherwise than the lower animals. For instance, we expect that there will be daylight tomorrow because our experience has always been so: it is only the astronomer who rationally foresees it, and even his prediction will ultimately fail when the cause of daylight, which is not eternal, ceases.24 But genuine reasoning depends upon necessary or eternal truths, such as those of logic, of number, of geometry, which produce an indubitable connexion of ideas and infallible inferences. The animals in which these inferences do not appear are called the lower animals [bêtes]; but those which know these necessary truths are properly those which are called rational animals, and their souls are called minds [esprits]. These souls have the power to perform acts of reflexion and to observe that which is called ego, substance,25 soul, mind [esprit], in a word, immaterial things and truths. And this it is which makes science or demonstrative knowledge possible to us.26

§6. Modern research has taught us, and reason confirms it, that the living beings whose organs are known to us,27 that is to say, plants and animals, do not come from putrefaction or chaos, as the ancients thought, but from preformed seeds, and consequently from the transformation of pre-existing living beings. In the seed of large animals there are animalcules which by means of conception obtain a new outward form, which they make their own and which enables them to grow and become larger so as to pass to a greater theatre and to propagate the large animal.28 It is true that the souls of human spermatic animals are not rational, and that they become so only when conception gives to these animals human nature.29 And as in general animals are not entirely born in conception or generation, no more do they entirely perish in what we call death; for it is reasonable that what does not come into being by natural means should not any more come to an end in the course of nature. Thus, throwing off their mask or their tattered covering, they merely return to a more minute theatre, where they may nevertheless be as sensitive [sensible] and as well ordered as in the larger theatre.30 And what has just been said about the large animals applies also to the generation and death31 of spermatic animals themselves, that is to say, they are growths of other smaller spermatic animals, in comparison with which they in turn may be counted large, for everything in nature proceeds ad infinitum.32 Thus not only souls but also animals are ingenerable and imperishable: they are only developed, enveloped, clothed, unclothed,33 transformed. Souls never put off the whole of their body, and do not pass from one body into another body which is entirely new to them. Accordingly there is no metempsychosis, but there is metamorphosis. Animals change, take on and put off, parts only.34 In nutrition this takes place gradually and by little imperceptible [insensible] portions, but continually; and on the other hand, in conception or in death, when much35 is gained or lost all at once, it takes place suddenly and in a way that can be noticed [notablement], but rarely.

§7. Thus far we have spoken merely as mere physicists:36 now we must rise to metaphysics, making use of the great principle, usually little employed, which affirms that nothing takes place without sufficient reason, that is to say, that nothing happens without its being possible for one who should know things sufficiently, to give a reason which is sufficient to determine why things are so and not otherwise. This principle being laid down, the first question we are entitled to put will be — Why does something exist rather than nothing? For 'nothing' is simpler and easier37 than 'something.' Further, granting that things must exist, we must be able to give a reason why they should exist thus and not otherwise.38

§8. Now this sufficient reason of the existence of the universe cannot be found in the sequence of contingent things, that is to say, of bodies and their representations in souls: because, matter being in itself indifferent to motion and to rest and to one or another particular motion, we cannot find in it the reason of motion and still less the reason of one particular motion.39 And although the motion which is at present in matter comes from the preceding motion, and that again from another preceding motion, we are no farther forward, however far we go; for the same question always remains. Thus the sufficient reason, which has no need of any other reason, must needs be outside of this sequence of contingent things and must be in a substance which is the cause of this sequence, or which is a necessary being, bearing in itself the reason of its own existence, otherwise we should not yet have a sufficient reason with which we could stop. And this ultimate reason of things is called God.40

§9. This primary simple substance must include eminently41 the perfections contained in the derivative substances which are its effects. Thus it will have power, knowledge and will in perfection, that is to say, it will have supreme [souveraine] omnipotence, omniscience and goodness. And as justice, taken very42 generally, is nothing but goodness in conformity with wisdom, there must also be in God supreme justice.43 The reason which has led to the existence of things through Him makes them also depend upon Him for their continued existence and working; and they continually receive from Him that which makes them have any perfection; but any imperfection that remains in them comes from the essential and original limitation of the created thing.44

§10. It follows from the supreme perfection of God that in producing the universe He has chosen the best possible plan, in which there is the greatest variety along with the greatest order; ground, place, time being as well arranged as possible;45 the greatest effect produced by the simplest ways; the most power, knowledge, happiness and goodness in created things that the universe allowed.46 For as all possible things in the understanding of God claim existence in proportion to their perfections, the result of all these claims must be the most perfect actual world that is possible. And apart from this it would not be possible to give a reason why things have gone thus rather than otherwise.47

§11. The supreme wisdom of God led Him to choose specially the laws of motion which are most fitting and which are most in conformity with abstract or metaphysical reasons. There is conserved the same quantity of total and absolute force, or of activity [action], also the same quantity of relative force or of reaction, and finally the same quantity of force of direction.48 Further, action is always equal to reaction, and the whole effect is always equivalent to its full cause. And it is remarkable [surprenant] that by the sole consideration of efficient causes or of matter it was impossible to explain these laws of motion which have been discovered in our time and of which a part has been discovered by myself. For I have found that we must have recourse to final causes, and that these laws are dependent not upon the principle of necessity, like the truths of logic, arithmetic, and geometry, but upon the principle of fitness [convenance], that is to say, upon the choice of wisdom. And this is one of the most effective and remarkable proofs of the existence of God for those who can go deeply into these things.49

§12. Again, it follows from the perfection of the Supreme Author not only that the order of the whole universe is the most perfect that can be, but also that each living mirror representing the universe according to its point of view, that is to say, each Monad, each substantial centre, must have its perceptions and its desires [appetits] as thoroughly well-ordered as is compatible with all the rest. Whence it also follows that souls, that is to say, the most dominant Monads, or rather animals themselves50 cannot fail to awake again from the condition of stupor into which death or some other accident may put them.51

§13. For all is regulated in things, once for all, with as much order and mutual connexion as possible, since supreme wisdom and goodness can act only with perfect harmony. The present is big with the future, the future might be read in the past, the distant is expressed in the near. We might get to know the beauty of the universe in each soul, if we could unfold all that is enfolded in it and that is perceptibly developed only through time. But as each distinct perception of the soul includes an infinite number of confused perceptions, which involve the whole universe, the soul itself knows the things of which it has perception, only in so far as it has distinct and heightened [or unveiled]52 perceptions of them; and it has perfection in proportion to its distinct perceptions. Each soul knows the infinite, knows all, but confusedly; as when I walk on the sea-shore and hear the great noise the sea makes, I hear the particular sounds which come from the particular waves and which make up the total sound, but I do not discriminate them from one another. Our confused perceptions are the result of the impressions which the whole universe makes upon us. It is the same with each Monad.53 God alone has a distinct knowledge of all, for He is the source of all. It has been very well said that as a centre He is everywhere, but His circumference is nowhere,54 for everything is immediately present to Him without any distance from this centre.

§14. As regards the rational soul or mind [l'esprit], there is in it something more than in the Monads or even in mere [simple] souls.55 It is not only a mirror of the universe of created beings, but also an image of the Deity. The mind [l'esprit] has not merely a perception of the works of God, but it is even capable of producing something which resembles them, although in miniature. For, to say nothing of the wonders of dreams, in which we invent without trouble (but also without willing it)56 things which, in our waking hours, we should have to think long in order to hit upon, our soul is architectonic also in its voluntary activities and, discovering the scientific principles in accordance with which God has ordered things (pondere, mensura, numero, etc.),57 it imitates, in its own province and in the little world in which it is allowed to act, what God does in the great world.58

§15. It is for this reason that all spirits [esprits], whether of men or of angels [génies], entering in virtue of reason and of eternal truths into a kind of fellowship with God, are members of the City of God, that is to say, of the most perfect state, formed and governed by the greatest and best of monarchs: in which there is no crime without punishment, no good action without a proportionate reward, and in short as much virtue and happiness as is possible; and this, not by any interference with the course of nature, as if what God prepares for souls were to disturb the laws of bodies, but by the very order of natural things, in virtue of the harmony pre-established from all time between the realms of nature and of grace, between God as Architect and God as Monarch, so that nature itself59 leads to grace, and grace, by the use it makes of nature, brings it to perfection.60

§16. Thus although reason cannot make known to us the details of the great future (which are reserved for revelation), we can be assured by this same reason that things are made in a way which exceeds our desires. Further, as God is the most perfect and most happy and consequently the most lovable of substances, and as genuine pure love61 consists in the state in which we find pleasure in the perfections and the felicity of the beloved, this love is sure to give us the greatest pleasure of which we are capable, when God is its object.

§17. And it is easy to love God as we ought, if we know Him as I have just said.62 For although God cannot be perceived by our external senses. He is none the less very lovable and He gives very great pleasure. We see how much pleasure honours give to men, although they do not consist in anything that appeals to the external senses. Martyrs and fanatics (though the emotion of the latter is ill-governed) show how much influence mental pleasure [le plaisir de l'esprit] can have: and, what is more, even the pleasures of sense are really intellectual pleasures confusedly known.63 Music charms us, although its beauty consists only in the harmonies [convenances] of numbers and in the counting (of which we are unconscious but which nevertheless the soul does make) of the beats or vibrations of sounding bodies, which beats or vibrations come together at definite intervals. The pleasure which sight finds in good proportions is of the same nature; and the pleasures caused by the other senses will be found to amount to much the same thing, although we may not be able to explain it so distinctly.64

§18. It may even be said that from this time forth the love of God enables us to enjoy a foretaste of future felicity. And although this love is disinterested, it constitutes by itself our greatest good and interest, even though we may not seek these in it and though we may consider only the pleasure it gives without regard to the advantage it brings; for it gives us perfect confidence in the goodness of our Author and Master, which produces real tranquillity of mind, not as in the case of the Stoics, who forcibly school themselves to patience, but through a present content which also assures to us a future happiness.65 And besides the present pleasure it affords, nothing can be of more advantage for the future than this love of God, for it fulfils our expectations also and leads us in the way of supreme happiness, because in virtue of the perfect order that is established in the universe, everything is done as well as possible both for the general good and also for the greatest individual good of those who believe in it and who are satisfied with the Divine government. And this belief and satisfaction must inevitably be the characteristic of those who have learned to love the Source of all good.66 It is true that supreme felicity (by whatever beatific vision, or knowledge of God, it may be accompanied) can never be complete, because God, being infinite, cannot be entirely known.67 Thus our happiness will never consist (and it is right that it should not consist) in complete enjoyment, which would leave nothing more to be desired and would make our mind [esprit] stupid; but it must consist in a perpetual progress to new pleasures and new perfections.68


1^ See Monadology, note 2. Strictly speaking 'compound substance,' according to Leibniz, is not 'substance' at all. It is not substantia but substantiatum. Failure to observe this distinction was to some extent the source of Wolff's misinterpretation of Leibniz.

2^ To say that matter is infinitely divisible is the same as saying that there is compound substance everywhere; for to be divisible is to be compound. But compound substances are made up of simple substances. Consequently there are simple substances or living beings everywhere.

3^ If they had shape, they would be extended or spatial. But everything extended is divisible, and hence they would not be simple but compound, having parts.

4^ Thus we cannot perceive Monads by means of our senses. What the senses give us is not the substance itself, but merely a phenomenon bene fundatum. 'Spirits, souls, and simple substances or Monads in general cannot be known [comprehendi] by the senses and imagination, because they have no parts.' Epistola ad Bierlingium (1711) (E. 678 a; G. vii. 501).

5^ The compound, as compound, consists of partes extra partes; but as compound, it is merely phenomenal.

6^ 'The simplicity of a substance is by no means inconsistent with its having within it several modes at one time. There are successive perceptions; but there are also simultaneous perceptions. For when there is perception of a whole, there are at the same time perceptions of the actual parts, and even each part has more than one modification; and there is perception at the same time not only of each modification, but also of each part. These multiplied perceptions are different from one another, although our attention cannot always distinguish them, and thus we have confused perceptions, an infinity of which is contained in each distinct perception, because of its relation to everything which is outside. In short, that which is combination of parts in the outside world is represented in the Monad only by combination of its modifications; and without this simple beings could not be internally distinguished from one another, and they would have no relation whatever to external things; and in short, as there are everywhere only simple substances, of which compounds are merely the aggregates, there would be no variation or diversity in things, if there were no internal variation or diversity in simple substances.' Lettre à Masson (1716) (G. vi. 628). Of. Monadology, notes 12 and 20.

7^ E. omits partout, 'everywhere.'

8^ The idea is that each Monad is separated from every other inasmuch as it has spontaneity, i.e. an activity entirely its own; for if it had merely an activity like motion, which passes from one thing to another indifferently, it would be united with all other Monads in a continuum and would thus cease to be a real, independent unit.

9^ E. omits distinguée, reading 'each simple substance.'

10^ Of course, this does not mean that the Monads constituting the body are really affected by outside things. Leibniz is here using popular language.

11^ Cf. Monadology, § 64.

12^ 'This "mirror" is a figurative expression; but it is suitable enough and it has already been employed by theologians and philosophers, when they spoke of a mirror infinitely more perfect, namely, the mirror of the Deity, which they made the object of the beatific vision.' Lettre à Masson (1716) (G. vi. 626).

13^ Ultimately, motions and desires (appétits) are different degrees of the same thing, viz. appetition, or the passage from one conscious or unconscious perception to another. The unconscious appetition is motion or efficient cause, not setting before itself an end, while the conscious appetition or desire does set before itself an end of good or evil, i.e. a final cause.

14^ Cf. Monadology, §§78 sqq.

15^ The transition from the unconscious to the conscious perception is not by any means made clear. Leibniz is, of course, using ordinary language; but it is difficult to see how he could translate it into the terms of his system, unless he were to content himself with saying that conscious Monads have less confused perceptions than unconscious Monads and have bodies whose organs are differently arranged. For, in Leibniz's view, the action of any one Monad upon another is purely ideal; and there is nothing in the world but Monads. Cf. Monadology, § 25.

16^ G. reads étendre, which might here be translated 'increase,' for entendre [heard], which is E.'s reading. Entendre seems more natural.

17^ i.e. unconscious living beings and unconscious Monads.

18^ That is, perceptions (in animals) which have passed into the complete confusion of unconsciousness are sure to pass into consciousness again. Confusion in perceptions is the same thing as envelopment or contraction. (Hence the petites perceptions are confused.) On the other hand, clearness in perceptions is the same thing as development or expansion. Cf. note 51 and New Essays, Introduction, note 74.

19^ See Monadology, § 14.

20^ 'As in body we hold that there is ἀντιτυπία and figure in general, although we do not know what are the figures of imperceptible bodies; so in the soul we hold that there is perception and appetition, although we do not distinctly know the imperceptible elements of the confused perceptions by which the imperceptible parts of bodies are expressed. … You ask whether I believe that there are bodies which do not fall within sight. Why should I not believe it? I think it impossible to doubt it. Through microscopes we see animalculae otherwise imperceptible, and the nerves of these animalculae, and other animalculae, perhaps swimming in the fluid parts of these, cannot be seen. The minuteness [subtilitas] of nature goes ad infinitum.' Epistola ad Bierlingium (1711) (E. 678 a; G. vii. 501).

21^ Leibniz probably means what elsewhere, following Scholastic usage, he calls 'forms.' Cf. Introduction, Part iv. p. 156.

22^ Cf. Monadology, § 13.

23^ G. reads on effects; E. omits this.

24^ Cf. Monadology, §§ 26-28.

25^ E. reads 'Monad' between 'substance' and 'soul'; G. omits it.

26^ Cf. Monadology, §§ 29 and 30. In the Monadology, God is added as an object of the self-conscious soul.

27^ All Monads have organic bodies, and the series of Monads and of organisms extends continuously from the lowest of Monads with the least perceptible of organisms up to the Monad of Monads, God. At both ends of the scale there are beings whose organs are not known to us.

28^ Cf. Monadology, §§ 74, 75.

29^ Cf. Monadology, § 82. It would be inconsistent with Leibniz's general principles to suppose that a spermatic animal could have a rational soul (otherwise than in germ, as all souls may be regarded as potentially rational). For the rationality of a soul is merely a very high degree of clearness and distinctness in its perceptions, which again determines its rank as a dominant Monad. But nothing else than its rank as a dominant Monad determines the nature of the body it has. Consequently a rational soul must always have a human body or a body of some higher kind, spiritual or angelic, and the union of a spermatic animal's body with a rational soul is impossible.

30^ Cf. Monadology, §§ 73, 76, 77.

31^ E. (manifestly by mistake) omits a clause following these words. A translation of his text would be: 'I' he generation and death of the smaller spermatic animals in comparison with which they' [sc. the large animals] 'may be counted large,' etc. This misses the point of the sentence.

32^ 'So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite 'em,
And so proceed ad infinitum.'
— Swift, On Poetry

The idea of 'infinities of infinity' is a favourite one with Leibniz, and it is closely connected with the notions underlying his differential calculus. 'For instance, we must conceive (1) the diameter of a small element in a grain of sand, (2) the diameter of the grain of sand itself, (3) that of the globe of the earth, (4) the distance of a fixed star from us, (5) the magnitude of the whole system of fixed first degree, (3) an ordinary assignable line, (4) an infinite line, (5) an infinitely infinite line.' Lettre à M. d'Angicourt (1716), Dutens, iii. 500, Cf. Monadology, §§ 65-70.

33^ Cf. 2 Corinthians, v. 4.

34^ Cf. Monadology, §§ 71, 72, 77. Aristotle condemns the theory of transmigration of souls in his De Anima, i. 3, 407b 13.

35^ E. omits beaucoup ['much'] and reads, 'all is gained or lost at once.'

36^ i.e. students of nature.

37^ i.e. more easily brought into existence. But if we can say even this of 'nothing,' must not 'nothing' be 'something'? How can we say of that which is not at all, that it is 'simple' and 'easy' in comparison with other things?

38^ Cf. Monadology, § 32.

39^ Motion (which, for Leibniz, is what we should now call an abstraction) is regarded as passing from body to body and as having no definite source in the phenomenal world. The point of view is that which Descartes substituted for the Peripatetic theories, and Leibniz's point is that, while Descartes's view is good so far as it goes, it is insufficient and requires to be supplemented by a deeper explanation.

40^ i.e. in a higher degree. See Monadology, note 61.

41^ Cf. Monadology, §§ 36-38, and Ultimate Origination of Things, p. 338.

42^ E. omits fort [very].

43^ There is a great difference between the way in which men are just and the way in which God is just; but it is merely a difference in degree. For God is perfectly and entirely just, and the justice of men is mingled with injustice, faults, and sins because of the imperfection of human nature. The perfections of God are infinite and ours are limited. ... Justice is nothing but that which is in conformity with wisdom and goodness taken together; the end of goodness is the greatest good, but in order to recognize this there is need of wisdom, which is nothing but the knowledge of the good. In the same way, goodness is nothing but the inclination to do good to all and to prevent evil, unless it be necessary in order to secure a greater good or to prevent a greater evil. Thus wisdom is in the understanding and goodness in the will. And consequently justice is in both. Power is another thing; but if it comes into play, it makes the right become actual and causes what ought to be really to exist, so far as the nature of things allows. This is what God does in the world.' Meditation sur la notion commune de la justice (Mollat, pp. 60, 62). Cf. On the Notions of Right and Justice (1693) p. 283.

44^ Cf. Monadology, § 42. This is a brief statement of the main contention of the Théodicée, in so far as it endeavours to vindicate the goodness of God in face of the evil in the world. God is the source of the perfections of each Monad, because it is through His choice of the best of all possible worlds that each Monad actually exists and continues in existence. But every Monad has some essential, inalienable imperfection; otherwise it would be indistinguishable from God. And God cannot change the essence of any Monad, as it is in the 'region of ideas,' which is His understanding. He can merely create and support, or withhold His creation and preservation.

45^ Cf. Ultimate Origination of Things, pp. 340 sqq.

46^ Cf. Monadology, §§ 55-58.

47^ Cf. Monadology, §§ 53 and 54.

48^ Every system or aggregate of bodies has a total absolute force, i.e. a total force belonging to the system as a completely independent system — a total force calculated on the supposition that there are no other total forces in relation to it, which might increase or diminish it. The whole matter of the universe is such a system, and consequently its total absolute force remains always the same. But total absolute force is always made up of two partial forces, i.e. forces which belong to the parts of the aggregate or system. These partial forces are (i 'relative force' or 'force of reaction,' which is the force involved in the mutual action and reaction of the bodies constituting the system or aggregate, i.e. its internal action, and (2) 'force of direction,' which is the force involved in the external action of the system. Cf, Introduction, Part iii. pp. 89 sqq. See also Explanation of the New System, note 30.

49^ The laws of actual 'concrete' motion cannot be deduced a priori under the law of contradiction; but a knowledge of them involves a reference to experience. As a result of this reference to experience we are compelled to conceive body, not as mere externality of parts, indifferent to motion, but as something which always has a force of its own. Thus bodies are ultimately or really (as distinct from phenomenally) independent forces (Monads), which differ from one another endlessly but are yet in such harmony that they form one perfectly regular system, the laws of which we can discover and state. Such a system could never have come into existence 'of itself,' by a law of blind necessity, indifferent to good and evil, like the principle of contradiction. An all-wise, all-powerful and infinitely good God must have chosen this system as the best among all possible systems. Cf. Monadology, § 51.

50^ E. omits, 'themselves.'

51^ Conscious Monads may for a time fall into unconsciousness; but that they should remain permanently in that condition would be against the general order of things. For the tendency of all created Monads is to advance to higher perceptions. In this advance each Monad is essentially limited to some extent; but apart from this essential limitation, which is independent of the will of God, no other permanent limitation is imposed. Thus, if a Monad has once been conscious, it may be conscious again, for manifestly it is not essentially limited to the unconscious state. And it must some day be conscious again, for the world is the best of all possible worlds, not merely on the whole but as regards each of its parts, which is equivalent to saying that the world is so constructed that each of the Monads constituting it shall rise to the highest point of perfection (i.e. of perception and appetition) which its essential limitations allow. Leibniz elsewhere speaks of the world in terms which, with slight alteration, he would apply to the individual soul. 'You are right in saying that our globe ought to have been a kind of Paradise, and I add that, if that is so, it can quite well become one yet, and it may have drawn back in order to make a better leap forward.' Lettre à Bourguet (1715) (E. 731 a; G. iii. 578J. Cf. Lettre touchant ce qui est indépendant des Sens et de la Matière (1702) (G. vi. 507): 'Always when we penetrate into the depths of any things, we find in them the most beautiful order that could be desired, even beyond what we imagined, as all those who have gone deeply into the sciences are aware; and accordingly we may hold that the same is the case as regards all other things, and that not only do immaterial substances always continue to exist but their lives, their progress and their changes also are regulated so as to attain a certain end, or rather to approach it more and more, as asymptotes do. And although we sometimes fall back, like lines which have bends in them, advance none the less prevails in the end and gets the victory.' Cf, New Essays, Introduction, note 74.

52^ E. reads relevées; G. reads revelées. Revelées (without the usual accents) looks like a slip of the pen and relevées is elsewhere used in a similar connexion. Cf. Monadology, § 25.

53^ Cf. Monadology, §§60 and 61.

54^ The world is an infinite sphere, of which the centre is everywhere, the circumference nowhere.' Pascal, Pensées, i. (Havet's ed., p. 1). Havet traces the phrase to Rabelais (bk. iii. ch. 13), thence to Gerson and Bonaventura, and ultimately to Vincent de Beauvais (early in the thirteenth century) who attributes it to Empedocles. It is not in any writing of Empedocles now known. See Havet's Pascal, pp. 17 sqq.

55^ 'The Monads' here means bare or unconscious Monads, while 'mere souls' means conscious souls, which are not self-conscious.

56^ E. reads sans en avoir même la volonté, 'without even willing it.' G. (from whom I translate) has mais aussi sans en avoir la volonté.

57^ Sed omnia in mensura, et numero etpondere disposuistis. A quotation (frequently used in Leibniz's time) from the Vulgate, Book of Wisdom, ch. II, V. 21. 'But by measure and number and weight Thou didst order all things' [R. V. ch. 11, v. 20). The phrase pondere, numero, mensura occurs in the remains of Ulpian, Instit. bk. i, fragment iii.

58^ Cf, Monadology, § 82.

59^ E. omits 'itself.'

60^ Cf. Monadology, §§ 84-89.

61^ i.e. 'disinterested' love. See Monadology, § 90, note 142.

62^ God is love [charitas], which is known by love [amor] and is loved in being known.' Nicholas of Cusa, Excitationes ex Sermonibus, 10, 188 b.

63^ For sense is confused perception. Cf. Introduction, Part iii. p. 125.

64^ Leibniz does not mean, as some of his critics (e.g. Kirchmann) seem to have thought, that the pleasure we have in music or in painting is entirely a matter of the senses. What he wants to show is that even the sense-element in artistic pleasure is really of an intellectual kind, and this he does by showing that it depends upon an unrecognized perception of proportion, measure or rhythm. He elsewhere calls it 'a hidden [occulte] arithmetic' (G. iv. 551).

65^ 'There is as much difference between genuine morality [morale] and that of the Stoics and Epicureans, as there is between joy and patience; for their tranquillity was founded only upon necessity, while ours should be founded upon the perfection and the beauty of things, upon our own felicity.' Théodicée, § 254; E. 580 b; G. vi. 268. 'What is called Fatum Stoicum was not so black as it is painted. It did not keep men from looking after their affairs; but it tended to give them tranquillity as regard; events, through the consideration of their necessity, which makes our anxieties and regrets useless. … The teachings of the Stoics (and perhaps also of some famous philosophers of our own time), being confined to this supposed necessity, can only secure a forced patience; instead of which our Lord inspires us with more sublime thoughts and teaches us even the way to have content, when He assures us that as God is perfectly good and wise and takes all under His care, so as not even to neglect a hair of our heads our confidence in Him ought to be complete; so that we should see, if we were able to comprehend it, that it is impossible even to desire anything better (either absolutely or for ourselves) than what He does. It is as if we were to say to men: " Do your duty and be content with what comes of it, not only because you cannot resist Divine providence or the nature of things (which would be enough to make us tranquil, but not to make us content) but also because you have to do with a good Master." And this might be called Fatum Christianum.' Théodicée, Préface, E. 470 b; G. vi. 30.

66^ 'We ought always to be content with the order of the past, because it is in conformity with the absolute will of God, which we know through what has come to pass; but we must try to make the future, so far as it depends upon us, in conformity with the presumptive will of God or His commandments, to adorn our Sparta and to labor at doing good, yet without vexing ourselves when success does not come to us, in the firm belief that God will be able to find the most fitting season in which to make changes for the better. Those who are not content with the order of things cannot flatter themselves that they love God as they ought.' Lettre à Arnauld (1690) (G. ii. 136; E. 108 a).

67^ According to Leibniz's system, if a Monad were to know God entirely, it would he God and would thus cease to be itself, which is impossible. Yet Leibniz regards the relation of men to God as so close that he calls them 'little gods, subject to the great God.' Lettre à Arnauld (1687) (G. ii. 125). Cf. Nicholas of Cusa, Excitationes ex Sermonibus, x. 188 a: 'To be able always more and more to understand (to conform oneself to the Creator) without end, is the likeness of eternal wisdom.'

68^ 'Felicity is to persons what perfection is to beings.' Paper without a title (1686) (G. iv. 462). Cf. Ultimate Origination of Things, pp. 345, 348.

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