CORRESPONDENCE WITH SOPHIE
Translation © George MacDonald Ross, 1974–1999
1. Leibniz to the Electress Sophie of Hanover, 31.10.1705 (GP.VII)
[562] . . . . And although each fraction (like each note on the musical scale) always exists realised by the divine understanding in the region of eternal truths, nevertheless a number and a fraction must not be conceived as a mass of other smaller fractions. Likewise points, moments, or the limits of an increase or diminution of qualities continued in accordance with certain mathematical laws, are not parts but extremities of space, time, etc.
To have a better conception of the actual division of matter to infinity, and the exclusion of all perfect and indeterminate continuity, you must bear in mind that God has already produced as much order and variety [563] as it has so far been possible to introduce, and hence that no indeterminacy has remained in it; whereas indeterminacy is of the essence of continuity. This is what the divine perfection teaches our soul, and what even sensory experience confirms. There is no drop of water so pure that one cannot detect some variety in it on a close inspection. A piece of stone is composed of certain granules, and through the microscope these granules appear like boulders containing a thousand quirks of nature. If our visual acuity were continually increased, it would always find something to exercise itself upon. Everywhere there are actual variations, and there is never a perfect uniformity; nor are two pieces of matter ever entirely similar to each other, either on the large scale or on the small.
Your Electoral Highness knew this well when she told the late Mr. D’Alvensleben in the garden of Herrenhausen, [n.1] to see if he could find two leaves which perfectly resembled each other, and he could not find any. So there are always actual divisions and variations in the masses of existing bodies, however small you go. It is our imperfection and the inadequacy of our senses that makes us conceive physical things like mathematical entities, where there is indeterminacy. One can prove that there is no line or shape in nature which reproduces exactly and preserves uniformly for the least space or time the properties of a straight of circular line, or of some other line of which a finite spirit can comprehend the definition. In any body of whatever shape, one’s spirit can conceive and draw across it in imagination any line one wishes to imagine, just as one can join the centres of spheres together by imaginary straight lines, or conceive axes and circles in a sphere when it does not have any actual ones. But nature cannot do this, and the divine wisdom does not will to trace these shapes of limited essence exactly, since they presuppose something determined and hence imperfect in the works of God. However, they do exist in phenomena, i.e. the objects of limited spirits: our senses fail to notice, and our spirit ignores, an infinity of little inequalities, though these do not, however, interfere with the perfect regularity of the work of God, although a finite creature cannot understand it at all. However, eternal truths based on limited mathematical ideas are still useful to us in practice, since it is permissible to abstract inequalities too small to cause significant errors [564] in relation to one’s purpose; just as an engineer marking out a regular polygon on the ground does not worry if one side is longer than another by a few inches.
It is obvious that time is not a substance, since an hour, or any other part of time one might take, never exists in its entirety and in all its parts together. It is only a principle of relations, a basis of the order among things in so far as they are conceived as existing successively, i.e. not existing together. The same must be true of space, which is the basis of the relation of the order of things, but in so far as they are conceived as existing together. Both of these bases are true, even though they are ideal. Uniformly regulated continuity, although it is only a supposition and an abstraction, forms the basis of eternal truths and necessary knowledge. As is the case with all truths, it is an object of the divine understanding, whose rays illuminate our understandings as well. Things that are possible, but only imaginary, participate in these bases of order just as much as actual things, and a novel could be as well organised with respect to places and times as piece of true history. Matter appears to us as a continuum, but it only appears so, and the same is true of actual movement. For example, alabaster power seems to form a continuous fluid when it is made to bubble on the fire; and a toothed wheel seems transparent all over when it revolves quickly, since we cannot distinguish the places where the teeth are from the empty places between them, since our perception runs the separate places and times together. So the conclusion can be drawn that a mass of matter is not really a substance; that its unity is only ideal; and that (leaving the understanding aside) it is only an aggregate, a heap, a multiplicity of an infinity of true substances, or a well-founded phenomenon, which never gives the lie to the rules of pure mathematics, though it always contains something further. The conclusion can also be drawn that the duration of things (the multiplicity of momentary states) is the total of an infinity of lightning flashes [n.2] of the divinity, of which each one at each instant is a creation or reproduction of everything; which strictly speaking leaves no continuous passage from one state to the next.
This provides a perfect proof of that famous truth of Christian theologians and philosophers, that the conservation of things is a continual creation; and it gives a very special way of verifying the dependence [565] of every changeable thing on the unchangeable divinity, which is the primitive and absolutely necessary substance without which nothing could exist or last. So this seems the best use one could make of the labyrinth of the composition of the continuum, so notorious among philosophers. The analysis of the actual duration of things in time leads us demonstratively to the existence of God, just as the analysis of the matter which actually exists in space leads us demonstratively to unities of substance — substances that are simple, indivisible, and imperishable — and consequently to souls, or principles of life which can only be immortal, which are spread throughout nature. It is obvious that entelechies (primitive forces), together with the passive element in each unity (for creatures are simultaneously both active and passive), are the source of everything. From this you can see what unities consists in. I have shown elsewhere how souls always retain some sort of body, and that hence even animals continue to exist. I have also given a distinct explanation of the interaction between the soul and the body. Finally, I have shown that rational souls (spirits) are of a higher order, and that God is concerned for them not simply as a supreme architect, but also as a perfectly good monarch.
2. Leibniz to the Electress Sophie of Hanover, 6.2.1706 (GP.VII)
[566] . . . Your Electoral Highness asks me what a simple substance is. I reply that its nature is to have perception, and consequently to represent composite things.
It will be asked how the composite can be represented in the simple, or multiplicity in unity. My reply is that it is rather like when an infinity of radii converge and make angles at a centre, even though this centre is absolutely simple and indivisible.
The radii do not consist merely in lines, but also in tendencies and efforts along the lines, which intersect without interfering with each other, as we can see from the way fluids move.
Thus, if we throw a number of stones into still water at the same time, we see that each one makes circles on the surface of the water; and these cross each other without any interference, each set of circles advancing as if it were the only one. We also see that rays of light interpenetrate without mixing. Finally, it is known that one and the same body can register an infinity of impressions simultaneously, each one having its effect. Again, even the tiniest part of a mass which is under pressure and full of efforts resists the efforts of all the other parts, and this cannot happen without its registering impressions from them. This makes me believe that the unities from which the remainder results must also be modified in relation to everything that surrounds them; and it is this which constitutes the representation I attribute to them.
God is himself a simple substance, but as he is the original and universal centre which includes and produces everything, he is on a different plane. The other simple substances are what I call souls, and nature is full of them.
Each soul is a world in miniature, representing the things [567] outside according to its point of view, and confusedly or distinctly according to the organs which accompany it; whereas God includes everything distinctly and as a more perfect being.
Thus, using souls as so many mirrors, the author of things has found a way of multiplying the very universe, so to speak, i.e. of varying the views of it — just as one and the same town presents different appearances according to the different places from which it is observed.
And since every soul is a mirror of the universe after its fashion, it is easy to see that each soul is as imperishable and incorruptible as the universe itself.
Furthermore, it is evident that since the soul is a simple substance or unity, and has no parts, it could not be formed by the composition of any parts or destroyed by their dissolution. Souls are unities, and bodies are multiplicities.
Since the universe is a sort of fluid, all of one piece and like an unlimited ocean, all motions in it are conserved and propagated to infinity, though insensibly — just as the circles I was just talking about, which were set up in water by a stone thrown into it, are propagated visibly for a certain distance; and although they ultimately become invisible, the impression does not stop extending to infinity, as is clear from the laws of motion.
This communication of motions means that everything is related to and affected by everything else, though distant things usually have no detectable influence.
However, light, sound, the magnet, and various other examples show that there are sometimes detectable actions over a distance.
Thus, since our organs are affected by neighbouring bodies, and those in turn by others next to them, we are affected mediately by all other bodies — and our souls too, since they represent bodies in a way which depends on their organs.
It can also be inferred that the soul is never entirely deprived of an organic body. For the order of the universe requires that every substance is always related to everything else; and this can even be proved.
It follows from this that not only the soul but also the animal always continues to exist. Besides, nature never proceeds by jumps, and all changes are changes [of degree] not of kind.
[568] It is clear from recent observations that the apparent generation of a new plant or animal is only a growth and transformation of a plant or animal already existing in seed.
Quite apart from the observations made in relation to this question by Messrs Swammerdam, Leewenhoek and Dodard, [n.3] it can be said to be proved by reason as much as by experience, since there is no mechanism which could generate out of a uniform mass a body endowed with an infinite number of organs, such as is that of an animal. Thus, miracles apart, there must necessarily be a preformation, that is to say a formation in advance. But since it has been realised that the animal comes into being only at the creation of the world, and that generation brings about only change and development, I am surprised that it has not also been realised that it must also survive as long as the world does, and that death is only a diminution and infolding of the animal.
It also appears from all this that since each soul is a mirror of the universe, it must pursue its course just like the universe itself which it represents and that this regular course of a soul can never be completely interrupted by death. Indeed, death is only a sleep, that is to say a state in which perceptions are more confused, and which lasts until such time as they unfold themselves again.
And just as there is reason to suppose that the universe itself develops more and more, and that everything is tending towards some end (since everything comes from an author whose wisdom is perfect), it is also to be believed that souls, which last as long as the universe, also proceed from better to better (physically, at least), and that their perfections go on growing, even if that happens only insensibly for the most part, and sometimes after large backward deviations.
It is often necessary to step back in order to jump better: death and sufferings would never exist in the universe if they were not necessary for great changes for the better. Just as a grain of corn seems to perish in the earth in order to be able to push up a new shoot.
And just as there are two sorts of perception, those that are simple, and those that are accompanied by reflections which bring about the birth of the sciences and of reasoning, so there are two sorts of souls, namely ordinary souls, whose perception is devoid of reflection, and rational souls, which are conscious of what they are doing. The first are simply mirrors of the universe; but the second are also imitations of the divinity.
[569] Ordinary souls are governed merely by particular instances provided by the sense, like empirics; but rational ones use their reason (when they can) to see if past instances are applicable to any given case. Consequently, the souls of animals can never arrive at necessary and general truths; just as an empiric can never be sure whether what he has often found successful without knowing the reason for it will still be successful for him in the future.
It is likely that there are rational souls more perfect than us (one could call these ‘genies’), and one day we could well be of their number. The order of the universe seems to require this.
And as the rational soul is endowed with reflection, that is, it thinks about itself and knows itself at any given time, it is appropriate that it should always know itself, at least when waking from sleep or coming out of some other distraction which could interrupt its attention.
Thus the soul does not preserve its identity merely as a constituent of the realm of nature, but it also retains its moral identity as a person, even after death: this is what makes it susceptible of punishments and rewards under the most perfect government, which is that of God.
So the best conclusion that can be drawn from the true knowledge of principles is the importance of the practice of virtue.
It is true that souls which are born good, or become accustomed to it at an early age, practise it without thinking, and find pleasure in it. But since not everyone has this advantage, and the dictates of fashion and the passions often lead elsewhere, it is important that good principles should be established, which those who have succumbed to contrary inclinations can gradually take up into themselves, and, if they are willing to take the trouble, make themselves as if born to them by deliberate and well organised practice. For one can change even one’s character.
Besides, if reason is joined to good inclination, it makes an action more noble and more constant; for it is good and satisfying to know that one is acting in conformity with reason: nothing does more to raise one above the animal state, and nothing comes nearer to divinity. The divine rays of goodness and wisdom shine with such pre-eminence in certain distinguished persons with whom I have and have had the honour to be associated (among whom I am only prevented from naming you, [570] Madam, by the fear of seeming to be a flatterer), that they can serve as an example to the human race.
P.S. I forgot to add that in fact only nature registers all impressions and makes one of them; but since it has no soul, the order of the impressions matter has received cannot be disentangled, and the impressions are only confused ones. Each specifiable part of matter has a different motion from every other part that can be specified in matter, and its motion is composed of all preceding impressions; but this impression is as simple as those which compose it, and no composition can be discerned in it. However, since the entire effect must always express its cause, there must exist something other than matter. And where the preceding impressions are distinguished and preserved, that is where there is a soul; hence there is soul everywhere. It is true and very noteworthy that, by considering the matter surrounding the point [where the soul is] as well as the soul itself, there is a way of disentangling the past. For all the impressions [in a soul] can be traced, so to speak, in the infinite varieties of shapes and motions existing in the surrounding matter; and these preserve something of all preceding effects. And this is yet another reason why every soul is accompanied by an organic body which corresponds to it.
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