EXPLANATORY NOTES
© George MacDonald Ross, 1999
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In his earlier writings, Leibniz usually called his simple substances ‘unities’, or ‘substantial forms’, or ‘entelechies’. He first used the term ‘monad’ in 1690 (when he was 44). I don’t think his adoption of this term has any special significance, except as a sort of trademark for his philosophical system. It is a Greek word for ‘unity’, and it had already been used by Pythagoras and Plato in antiquity, and by some more mystically minded philosophers in the 16th and 17th centuries (e.g. John Dee, Giordano Bruno, and Lady Anne Conway).
The question of how monads are supposed to make up, or ‘enter into’ compounds is a fraught one. Some commentators interpret Leibniz as meaning that they are literally the smallest parts of compound bodies; others, such as myself, interpret him as holding that compound bodies are not fully real, but are constructed out of the perceptions of monads. Consequently, it is only in a metaphorical sense that monads can be spoken of as the basic components of compounds. However, taken by itself, the wording of the Monadology favours the former interpretation, and it is only in other writings that Leibniz describes compound bodies as ‘mere phenomena’.
Leibniz is careful to define ‘simple’ as meaning ‘without parts’. Monads are, as it were, mathematical points. But considered as perceivers, they are infinitely complex.
Leibniz does not yet make the distinction (which will become crucial later) between mere compounds, and organic bodies, which are also compounds, but such that the whole is more than just the sum of its parts. Elsewhere, he describes the former as like flocks of sheep, whereas the latter are like the sheep themselves. So a non-organic body is a mere ‘heap or aggregate’ of parts, like a block of chalk formed from particles of chalk dust.
Leibniz’s argument is that since a (non-organic) compound is the sum of its parts, it is only real in so far as its parts are real. But the same is true of the parts of the parts. So ultimately there must be non-compound or simple entities, which are real in themselves, and not by virtue of parts out of which they are compounded.
The implication is that monads must be mathematical points — which raises the question (not discussed in the Monadology) of how any finite being can be compounded from mathematical points. This is one of the reasons for interpreting Leibniz as saying that monads are not really the ultimate components of matter at all, but that matter is a logical construction out of the perceptions of non-spatial monads.
The point of this paragraph is to stress Leibniz’s difference from atomists (or ‘corpuscularians’), such as Gassendi, Locke, and Newton. Note that, etymologically, ‘atom’ means ‘that which cannot be divided,’ ‘corpuscle’ means ‘tiny body,’ and ‘particle’ means ‘tiny part.’
Atomists used much the same argument as Leibniz in Paragraph 2, to show that there must be smallest parts of matter. However, in order for them to be material, they had to have the defining attributes of matter, which were shape and size (or extension); and in order for them to be the building-blocks of macroscopic objects, they had to have a finite size, however small. The atomists’ problem was to explain why it should be possible to divide a body consisting of two atoms into two, but impossible to divide an atom into a left-hand half and a right-hand half. This looks suspiciously like a miraculous infinite force, which can have no natural explanation.
(One might comment that the 20th century has shown that the force is large, but not infinite — hence the manufacture of nuclear weapons. On the other hand, once the existence of sub-atomic particles has been accepted, there seems no end to the possibility of further sub-division, if the properties of a particle are explicable only in terms of the properties of its parts. The Leibnizian point is that you can escape from this infinite regress only by postulating ultimate entities which do not have the properties of matter. Quantum mechanics comes quite close to this, despite the concept of a smallest possible but finite quantity (which is what ‘quantum’ means), since the characteristics of space, time, motion, and causation at the sub-atomic level are almost unrecognisably different from the macroscopic level. The same goes for relativity theory and very large magnitudes.)
So Leibniz is saying that monads are the genuine atoms of Nature, precisely because they have no parts, and hence are indivisible, and have no extension or shape. No extension can be defined, unless it can be expressed as the sum of smaller extensions. No shape can be defined, unless it has a variety of parts (e.g. the difference between two halves of a sphere, and of a pyramid, or of a cube).
The word ‘naturally’ is crucial here. For Leibniz, as for all the early modern philosophers, a process is natural, if and only if it can be accounted for in accordance with the laws of mechanics. For example, a table can be destroyed naturally, and cease to exist, if it is broken up into component parts — with a saw, or an axe, or by the action of fire, which separates its particles into ash and gases. If a magician could annihilate a table, without remainder, by waving a magic wand, or by uttering incantations, that would not be a natural process. Nor would it be a natural process if God suddenly decided ‘let it not be.’
In the case of a simple substance, which has no parts, there is no conceivable way in which it could be broken up into separate parts in accordance with the laws of mechanics. The only way it could cease to be would be through a miraculous decision by God. But since God has already decided that everything will happen in accordance with the laws of mechanics, there is no question of any simple substance simply disappearing into thin air.
The argument here is strictly parallel to the argument of Paragraph 4. A simple substance cannot naturally come into being through the putting together of parts in accordance with the laws of mechanics, since it has no parts. Leibniz’s conclusion is that the universe has existed from eternity with the same number of monads. No new monads are created, and no existing monads are destroyed. All change throughout the history of the universe consists in the transformation of already existing substances in accordance with the laws of mechanics.
This principle is deeply rooted in the modern world view, and it has rarely been challenged (one notable exception is Fred Hoyle’s opinion that new matter is continually coming into being in an expanding universe, so that its average density remains constant).
This paragraph merely summarises what has already been said. Compounds can come in or out of being naturally, through the coming together or separation of parts in accordance with the laws of mechanics. No such process can explain the creation or annihilation of monads. Consequently, all monads have existed from the beginning of time, through the initial and instantaneous act of creation; and if they ceased to exist, it would be have to be through an instantaneous act of annihilation, against God’s original decree that everything would happen in accordance with the laws of nature. So there are no grounds for supposing that any monad will ever cease to exist. God cannot act against Nature, since Nature is what God has decreed.
There are two separate arguments here.
First, the only type of influence we can conceive of, is when one piece of matter is moved by another piece of matter in accordance with the laws of motion. In some cases there is no discernible internal change to the object (though Leibniz argues elsewhere that there must always be some internal change) — for example, when one billiard ball is set in motion by another. In other cases there is an internal change, and this change will consist in a re-arrangement of the object’s internal parts — for example, if I crush a piece of paper, or fry an egg. This is always possible in the case of compounds, since they have parts which can be re-arranged or made to move differently (e.g. to speed up when the object is heated). But monads have no parts, therefore they cannot be changed by anything else acting in accordance with the laws of motion; and there is no other means by which one thing can change another thing (except God, of course).
The second half of the paragraph is concerned more specifically with perception. One of the ways in which one substance might be influenced by another is by perceiving it. We have already seen the difficulties which Augustine and Descartes got into here. There was no problem over explaining how the physical brain might be influenced by images received through the sense organs — but how could these spatial images get into the soul and influence it, since the soul was a non-extended and essentially active substance? Leibniz flatly denies that this can happen. The brain has windows (the sense organs) through which images can enter; but the soul doesn’t. So not only does the soul not have any parts which can be changed by perceiving something, but there is no way anything can get into the soul so as to change its parts, if it had any.
Furthermore, the whole theory that perception consists of a causal influx (literally ‘flowing in’) of ‘sensible species’ is completely wrong. He probably had Suárez in mind here, since he was the scholastic Leibniz knew best. Not only can substances not enter a monad through its non-existent windows, but it’s absurd to suppose that accidents can become detached from substances and travel through the air. On this Leibniz was in complete agreement with Descartes, Hobbes, and Spinoza, that accidents are modes of substances, and cannot exist independently of them. Moreover, in vision and hearing, nothing physically travels from the object to the sense organ — there is merely a wave motion in the ether.
The first two sentences of this paragraph are reasonably straightforward. Leibniz has already said that monads are not quantitatively different from each other, since they do not have quantitative characteristics, such as size, shape, or motion. But they must have some qualities, otherwise they would be nothing. The concept of pure substance without any characteristics is totally empty. Moreover, if they all had the same qualities, they could not account for the variety and change we observe in the world of experience. And of course, there’s no point in postulating the existence of monads, unless they serve as the ultimate explanation of why the world is as it is.
The rest of the paragraph is rather more obscurely written. I think it makes sense only if ‘without qualities’ is read as ‘without different qualities.’ The significance of the qualification ‘given that there is no empty space’ is that, if there were empty space, it would be possible to generate infinite variety from different configurations of monads and not-monads (or empty space). To give an analogy, all the information in this module ultimately derives from different configurations of electrical discharges, and absences of electrical discharges — and there is no limit to the amount of information it could potentially contain. Although Leibniz didn’t get quite as far as inventing the computer, he believed (with some justification) that he was the first person to have the idea that all the information in the universe could be coded in terms of different combinations of 1 and 0 — or, in his more mystical moments, the different degrees of separation of created things from God (=1, or pure active being in its absolute simplicity) and matter (=0, or absence of being, and passivity or matter).
However, if there is no empty space in the material universe, there is no way of distinguishing one part of space from another, unless monads have distinct qualities which are not merely modifications of extension. It is one thing to imagine (as Descartes and Spinoza did) that discrete physical objects are like blocks of ice floating in an infinite sea of water. But the blocks of ice cannot be discerned from the surrounding water unless they have different qualities (they hold together, they refract light differently, and so on). If this were not so, we would have no means of telling whether a given block of ice had moved or not. The later state would be indistinguishable from the earlier state, like eddies in the air which we cannot see.
But in the world of experience, compounds (i.e. everyday physical objects) are distinct from one another. Since their qualities must derive from the simple substances of which they are compounds, it follows that simple substances must have qualitative differences.
So far, Leibniz has established that monads must have qualities, and that they can’t all have exactly the same qualities. Now he asserts that each monad must have a unique set of qualities, which distinguishes it from every other monad. This is known as the ‘principle of the identity of indiscernibles,’ since it is equivalent to saying that, if everything which is true of A is true of B, than A and B are just different names for one and the same thing (e.g. the ‘morning star’ and the ‘evening star’, or Phosphorus and Hesperus, which are different names of the planet Venus).
I say ‘asserts’, because here he provides only a weak, empirical argument, namely that we can always find intrinsic differences between one thing and another. By ‘intrinsic denomination,’ he means a characteristic which belongs to the thing itself, as contrasted with a characteristic it has in relation to something else. So, for example, he is claiming that, if I have something in my right hand, and something else in my left hand (e.g. two leaves from a box tree), if I examine them closely enough I shall always be able to find some difference, other than the fact that the one is in my right hand, and the other is in my left hand (which are ‘extrinsic denominations’).
It is a weak argument for two reasons. The first is that it is not true that we are never confronted with two things which we cannot distinguish. For example, I can see no difference between the two occurrences of the letter ‘s’ in the word ‘distinguish’ as I see it on the screen. If the one were substituted for the other, I could not tell the difference. It might be that, if I examined them closely through a microscope, I would detect tiny differences — but Leibniz has not established that this is necessarily the case.
The second reason is that it might be the case that no two macroscopic objects happen to be identical (e.g. the well-known claim that no two snowflakes are exactly alike), but that they are constructed out of a small range of elementary particles, each one of which is absolutely identical to other particles of the same kind.
Elsewhere, Leibniz provides two main arguments for the principle of the identity of indiscernibles.
The first depends on the Aristotelian element in Leibniz’s thought. Especially in his earlier writings, Leibniz described monads as ‘forms’ or ‘souls’. As we know, the Aristotelians held that, in living organisms, the soul is the form of the body, or of matter. So it is the form or soul which makes a body an organic unity — in other words, a body which is not merely the sum of its parts, but a genuine unity. From this is follows (as we shall see later) that only living organisms are fully real.
Now, for the Aristotelians, the form was a universal: it was that by virtue of which different individuals were members of the same species. It was detailed differences in their matter which made them distinct individuals (in other words, matter was the ‘principle of individuation’). Consequently, if there are any immaterial beings (and Aquinas believed this of angels), then there cannot be more than one of each species, since they have no matter to distinguish one from another. In other words, an individual is a ‘lowest species’.
As a good modern philosopher, Leibniz rejected the Aristotelian and scholastic idea that there were real species of things. Like everyone else, he held that all the qualities of matter could ultimately be reduced to quantifiable modes of extension and motion. Consequently, you can’t carve up the properties of things into those which belong to form, and those which belong to matter. Leibniz ended up with a sort of double-aspect theory (quite similar to Spinoza’s), according to which there is a one-to-one correspondence between the quantitative properties of organic bodies, and the qualitative properties of their form, or soul, or principle of unity.
However, unlike Spinoza, who held that soul and body were equally real, for Leibniz, only the form is a genuine unity, and therefore fully real. Consequently, its individual existence cannot depend on its body or matter. To this extent, each monad is like one of Aquinas’s angels, and must be a lowest species: i.e. there cannot be two with exactly the same set of properties. On the other hand, Leibniz (unlike Aquinas) believed that, God apart, forms cannot exist without the matter of which they are the form or principle of unity. So every form or soul must always have a body, even though the form is ontologically prior to the body.
The second argument depends on Leibniz’s thesis that space and time are ultimately nothing other than relations. They are not independently existent containers within which material objects exist and change. Consequently, they must be defined in terms of the things they relate (i.e. non-spatial simple substances), not the other way round. In themselves, monads are not spatio-temporal beings, so you can’t distinguish one from another by holding one in your left hand and one in your right hand, like two otherwise identical billiard balls. Monads can be numerically distinct from one another only if they are intrinsically different.
It follows from Leibniz’s thesis that there is a one-to-one correspondence between the qualities of a monad and the quantitative characteristics of its organic body, that no two organic bodies are exactly identical.
To sum up, Leibniz’s principle of the identity of indiscernibles doesn’t follow from the fact that in Nature there are never two perfectly similar beings; rather, this fact about Nature follows from the principle of the identity of indiscernibles. One might add that it is only very recently that scientists have come round to the view that what Leibniz says about organic bodies is largely correct — that each cell is unique to the body from which it came, and can be identified as belonging to that body and none other.
This innocuous-seeming little paragraph has more to it than meets the eye.
When he says that every created being is subject to change, it is evident from what he says elsewhere, that he means, not merely that everything is capable of being changed, but that everything is actually changing all the time. In the case of matter, the only change is motion. Consequently, even if a macroscopic physical object appears to be motionless and unchanging, really the particles of which it is composed are seething with motion. And there is nothing here that modern science would disagree with — for example the thesis that temperature is a measure of the motion of particles, and that absolute zero can never be reached, since particles must always have some motion.
Leibniz’s metaphysical argument rests on his belief (not mentioned in the Monadology) that matter is ultimately a mixture of ‘primitive passive power’ and ‘primitive active power’, or energy. Primitive passive power is the same as ‘antitypy’ (a term Hobbes sometimes used), and it means the power to resist being moved (intertia) or penetrated (solidity). This is what the materiality of an object consists in, by contrast with insubstantial things like ghosts. Primitive active power, or energy, is the power to act on other bodies, in particular kinetic energy (the concept of which was first formulated by Leibniz himself). But energy cannot exist if it is merely potential; so it must be actualised. And the only way energy can express itself is through motion. So, since everything must consist of a combination of active and passive power, it would cease to exist if it were not actually in motion.
Now, since there is a one-to-one correspondence between monads and matter, if matter is constantly changing (i.e. in motion), it follows that monads must also be constantly changing. In other words, not only are the qualities of one monad different from those of every other monad at any given time, but the qualities of the same monad are different from one moment to the next.
The last clause of the paragraph contains an interpretational crux. The French word continuel can mean either ‘continual’ or ‘continuous’. Now, if I am correct in maintaining that ‘subject to change’ means ‘constantly changing’, and not merely ‘capable of changing’ (as I think it must), then there is no point in adding that this change is continual, since it has already been said. So it must mean that all change is continuous as will as continual — and this is indeed a Leibnizian doctrine, which he called the ‘law of continuity.’
The difference is that a thing could be continually changing, but jumping from one state to a completely different state (like traffic lights changing from red to green). Leibniz’s law of continuity states that any change from one state to another goes through all the infinitely many intervening states, however quickly. As Leibniz often puts it, ‘There are no jumps in Nature.’ The reason for this is that all change in matter is in accordance with the mathematical laws of motion, and every state has to be explained as the immediate consequence of the preceding state. If there were a jump from one state to a non-adjacent state, the latter would not be explicable as an immediate consequence of the preceding one. The most obvious example is, say, accelerated motion. You can’t get from 30 mph to 40 mph without going through 35 mph, and you can’t get from A to B without covering the intervening distance. So, since all change in the material realm is continuous, all change in the states of monads must also be continuous.
It does indeed seem to follow that there can be no external cause of natural change (i.e. anything other than divine intervention). When Leibniz says changes come from an internal principle, he means this in the traditional sense of an origin or beginning.
‘Precise specification’ is a translation of the word detail, which crops up a number of times in the Monadology, and is quite difficult to translate. I suspect that in this passage Leibniz is thinking of the sense in which it means the precise marching orders given to troops. Leibniz’s point is that, in addition to the source of change, there must be something which specifies precisely what all those changes are going to be. It is something analogous to a computer programme, which controls the whole course of a monad’s development. Elsewhere Leibniz tells us that this is the complete concept of the monad, which includes all the predicates it will ever have.
In the second half of the sentence, Leibniz adds that it is this precise specification (or complete concept) which makes each monad a unique individual, and different from every other monad.
In this paragraph, Leibniz gives a separate argument why a unitary simple substance must contain multiplicity (i.e. a multiplicity of qualities). Given that monads change, and given that the change is gradual, there must be some continuity between one state and the next. In other words, some aspects must remain the same while others change.
I don’t think this is actually a valid argument, since a monad could have just one quality which changed gradually. But what he seems to have in mind is a changing organic body, which gradually adds and loses parts. The organic body can change in this way because it has parts. But the monad of which it is the body cannot do so, since it has no parts. Instead it has a multiplicity of qualities corresponding to the parts, some of which stay the same, and some of which change.
As with Descartes, Spinoza, and others, ‘affection’ is a vague term meaning a quality, or in the case of sentient beings, a perception or an emotion. For Leibniz, monads express relations, such as distances between things, as well as the things related.
Now Leibniz explains that these affections and relations are perceptions. By definition they are representations of a multiplicity within the unity of a simple substance. They are not to be confused with conscious perceptions such as we have when we are awake. Note that Leibniz hardly ever uses the French word conscience (as he does here), since its normal meaning was still ‘conscience’ as in English (it was only in the 17th century that people started using the word ‘consciousness’ in the modern sense). To fill the gap in the French language, Leibniz coined the term apperception.
Leibniz then criticises Descartes for failing to recognise the existence of unconscious perceptions. This isn’t wholly fair, since Descartes did recognise the existence of images in the brain of which we might not be conscious. But Leibniz’s point is that the soul can have unconscious as well as conscious perceptions.
In the next sentence, what I have translated as ‘rational beings’ is esprits, or spirits. Leibniz uses the term ‘spirit’ for human souls, and those of beings superior to humans, such as angels. When he says that Descartes didn’t believe in other monads, he is of course using his own rather than Cartesian terminology. What he means is that, for Descartes, the only souls were human and angelic. Here, as elsewhere, he preserves a sharp distinction between:
Leibniz explains the word ‘entelechy’ in Paragraph 18.
The final sentence should also become clearer later. His point is that Descartes (and ordinary folk) were wrong to think of death as a complete separation of the immaterial soul from the body, since it is not separable from the body. In fact what we call ‘death’ is a prolonged period of unconsciousness in a smaller body.
It is slightly odd to attribute to the scholastics the ‘prejudice’ that the soul can be entirely separate from the body, since they usually held that the soul required a ‘spiritual’ body after death, since it needed something to be the form of. As for reinforcing some people’s belief that souls are mortal, he presumably means that, if the only alternatives are belief in an immaterial soul and belief in human mortality, some might opt for the latter. Leibniz is offering a middle way, whereby the soul can survive as the form of a body, but in a state of unconsciousness.
Leibniz now introduces the term appetition or appetite for the action of the internal principle in bringing about change from one perception to another. Again, it is not to be confused with conscious, human appetite or volition; but it is analogous in that it is a directedness towards greater perfection. As we shall see, no individual monad can ever actually attain perfection, since it is in competition with all others; but every appetition makes some progress, and results in a new set of perceptions.
Leibniz comes back to perception again, and says that we should have no difficulty over the concept of multiplicity within a simple substance (i.e. despite the fact that it has no parts), since every time we have a thought, we are conscious of variegation in what we are thinking about, and our souls are simple substances.
Pierre Bayle (1647–1706) published his Dictionnaire historique et critique in 1695–1697. One of the articles was on Rorarius (1485–1556), who held that animals had rational souls. Bayle used the article as a peg for an extensive footnote criticising Leibniz’s philosophy (added to in the second edition, of 1702). This gave rise to an extended change of views between the two philosophers, much of which is included in Francks and Woolhouse, pp.191–257.
Leibniz has already asserted that changed perceptual states are caused by appetition in the internal principle of change. He now gives an argument why they cannot be caused by mechanical causation in matter. Suppose (though this is impossible) a machine designed to produce sensations. Presumably he is thinking of a brain with sense organs. You can imagine it enlarged, so that you can walk inside (or, he might have said, you could imagine inspecting it with a very powerful microscope). All you will see is one part pushing another, and you will never see a perception being produced. Consequently, perceptions cannot be produced by machines, but only by simple substances (as the only alternative).
Leibniz then adds the assertion that there is nothing else in simple substances apart from perceptions and the action of changing them.
Leibniz now explains the meaning of the word entelechy as an alternative for ‘monad’. It comes from the Greek meaning ‘they have perfection’ or ‘completeness’, in the sense of ‘self-sufficiency’. They only have a certain perfection, otherwise they would be God. But leaving aside their dependence on God, they are self-sufficient in that they act entirely independently of all other beings. Just as mechanical automata (e.g. clockwork toys) can move without being pushed, so entelechies are the incorporeal (and hence non-mechanical) source of all their ‘internal actions’ — i.e. all the changes in their perceptual states.
It should be noted that, although Aristotle did use the word ‘entelechy’ to refer to the soul, he meant it in a rather different sense from Leibniz’s.
Here Leibniz amplifies the distinction he made in Paragraph 14, between animal souls and bare monads. All monads (i.e. spirits, animal souls, and bare monads) can be called ‘souls’ in that they all have perception and appetite. But it is less misleading to distinguish between bare monads, which have ‘simple’ perceptions, and animal souls which have ‘sensations.’ The difference is that the latter are ‘more distinct’, and accompanied by memory. He will explain this in greater detail later (Paragraphs 25–27), but the main idea is that sensations are focussed, so that objects are distinguished from the confused perceptual background.
Now Leibniz comes back to the topic of unconscious perception, and he argues that it is something known by experience. Obviously he isn’t saying that we literally experience a state in which our perceptions are completely confused and we don’t remember them. What he means is that it is within our experience that there have been periods of time when have not had a distinct perception of anything, and have not remembered anything. In such a state, the soul differs from a bare monad only in that it has the potential to recover from it (and note that it is in an inferior state to a waking animal). Leibniz’s purpose is to explain how we can conceive of what bare perception is like, by analogy with our conscious experience.
The first part of this paragraph is a recapitulation of what has gone before: simple substances must have a continued existence; but they cannot exist unless they are characterised by some affections, i.e. perceptions.
Leibniz then introduces, without explanation, the expression ‘little perceptions.’ It is a standard Leibnizian expression for perceptions of which we are unconscious. He says that we are unconscious if there are many little perceptions in which nothing is distinguished from anything else. This is not quite as tautologous as it might seem. He is saying that unconsciousness is, by definition, a state in which everything is confused. For us to be conscious, we have to be conscious of something; but if everything is confused, we are not conscious of one thing rather than another.
I should point out that here the word ‘unconsciousness’ is not in the original French, which is étourdi, or ‘stunned’. Leibniz is not talking about human consciousness in particular, but about the state of perceptual awareness which is common to all sentient beings. So in the last sentence he says that animals can be temporarily put in this state by death (implying that animal as well as human souls are immortal).
‘In the natural course of events’ is Leibniz’s usual proviso, meaning that God could always intervene miraculously.
Since monads cannot be influenced by other monads, their whole history must be determined by their internal law of change. At any given time, their present state is completely determined by their immediately preceding state, and any future state can be deduced from it. Monads being ‘pregnant’ with the future is one of Leibniz’s favourite metaphors. The future is already there inside the monad, waiting to come out. To put it another way, since the whole history of each monad is contained within its timeless complete concept, the present moment has no special significance — it is like the particular bit of a recording tape which happens to be passing the playback head.
Now the word for ‘conscious’ is the cognate of the noun apperception, so Leibniz is thinking of humans.
He is providing an additional argument for the existence of unconscious perceptions. When you wake up from a stupor, it is not that you start having perceptions again, but that you start being conscious of them again. The reason (familiar from Spinoza) is that things can be caused only by things of the same category: just as motions can be caused only by motions, so perceptions can be caused only by perceptions, and not by motions. So the first conscious perception on waking up cannot be caused by a motion (such as a motion of particles n the brain), but only by an immediately preceding perception, which must have been an unconscious one, since you were still unconscious at the time. Elsewhere, Leibniz makes the perfectly sensible point that you can’t be woken up by something, unless you perceive it before you wake up. Consequently, it must have been perceived unconsciously.
Here we are back again to the word ‘stunned’, so Leibniz is thinking of animals as well as humans.
He is merely recapitulating the point that bare monads have no sensations, since nothing is distinguished from anything else.
Now (at long last) Leibniz explains how the perceptual state of animals differs from that of bare monads. The function of sense organs is to concentrate information, so that one object becomes highlighted, and distinguished from the confused background. It’s like the difference between simply exposing photographic film to the light, and exposing it to the light through the lens of a camera.
In an aside, Leibniz makes the suggestion that there may be senses of which we are unaware. Perhaps this is an echo of Spinoza’s doctrine that God has infinitely many attributes of which we are unaware, even though they must be present in us, as modes of God’s attributes. However, it follows equally from Leibniz’s own (original) theory of unconscious perception. If there are infinitely many perceptions of which we are unconscious, who is to say that they would all be of the same kind as the ones we are conscious of? For example, we know that there are forces such as magnetism, which we cannot perceive directly. But if we have unconscious perceptions of everything which happens in the universe, we must at least have a confused perception of magnetism. It just so happens that we have no sense organ for detecting magnetism. If we did, we would have distinct perceptions of magnetic fields (in some way we cannot even conceive), such that it would add to the richness of our perceptions, in the way that we have a richer perception of a head of garlic if we can smell it, as well as see it and touch it.
In addition to sensation, animals have something analogous to reasoning in humans. Basically it is the association of ideas, as originally outlined by Hobbes, and later taken up by Hume.
This paragraph makes the simple point that associations are established more quickly if the images make more of an impression.
Leibniz claims that, most of the time, our reasoning is like that of animals. His allusion to the empirical school of medicine is probably to Sextus Empiricus. Sextus did indeed believe that it was better to rely on past experience than to risk the lives of one’s patients by applying untested theories. Although Leibniz is rude about the empiricists, it is fair to point out that his own personal motto was ‘theory with practice.’ In other words, the best way of getting at the truth is to combine theoretical reasoning with practical experience, rather than relying on theory alone.
Leibniz’s grounds for distinguishing between humans and animals are utterly conventional.
This paragraph is important, but somewhat obscure, since it misses out a crucial stage in the argument. It is not said why knowledge of necessary truths gives rise to acts of reflection.
As we have seen, Descartes didn’t really distinguish reason from self-consciousness. The self of which he is directly aware in the act of thinking cogito ergo sum turns out to be pure thought or abstract reason; and Descartes didn’t even have a separate word for self-consciounsness. As with Plato’s nous or intellect, it is that part of the human being which contains abstract and universal ideas, and it does not concern itself with individual existences.
Leibniz, on the other hand, makes a clear distinction between knowledge of eternal truths on the one hand, and self-consciousness on the other (and remember that he had to invent the word ‘apperception’ for this purpose). In this paragraph, he is talking about the order of discovery. For Descartes, we first had to strip away our preconceptions till we arrived at pure knowledge of the thinking self, and then build everything up in the order: self, God, eternal truths, the material world. Leibniz, on the other hand, sees no need to doubt that we perceive individual things (even if they are not as they seem), and that we have knowledge of eternal truths.
Leibniz even seems to imply that we could get by without self-consciousness at all: we could navigate round the world of experience using our senses, and we could do mathematics, by concentrating our whole attention on eternal truths, and what can be deduced from them. Our sense experience doesn’t make us think about ourselves as subjects, since all our awareness is projected outwards to the object. In this respect, we are just like animals, which are not self-aware.
The difference lies in our knowledge of eternal truths. They are not derived from sense experience, and it is only when we think about their origin and justification that our thinking is reflected back into ourselves. They depend on universal, unlimited, and hence infinite concepts, which we find within ourselves. This is the origin of our awareness of our own existence and nature as rational beings. The very last stage of the process is to form a conception of God, by conceiving him as containing what is limited in us to an unlimited degree.
Some commentators (e.g. R. Latta, Leibniz: The Monadology (Oxford, 1898), 234n) see this as containing the germ of Kantianism, on the grounds that he is shifting the focus from substance to the subject. I personally consider this rather far-fetched. More Kantian is Leibniz’s throw-away remark that reflection makes us ‘consider that this or that is in us’ — in other words, it is through reflection that we attribute some of our mental contents to external objects, and some to the conscious subject.
This paragraph is rather awkwardly positioned. Leibniz is about to distinguish between ‘truths of reasoning’ and ‘truths of fact’; but before he has explained the distinction, he introduces the two great principles by which we establish them. The principle of contradiction is what we use to establish truths of reasoning.
His definition of the Principle of Contradiction is also rather awkward, since he is running together two distinct principles. One is what is still called the principle of contradiction (or, confusingly, non-contradiction), namely that ‘p and not-p’ is false. The other is the so-called ‘law of excluded middle,’ according to which, if p is true, then not-p is false (i.e. there is no half-way house between truth and falsehood).
The principle of sufficient reason is what we use to establish truths of fact. Remember that there was still a strong tendency (as in Spinoza) to conflate the concepts of reason and of cause. So what Leibniz means here is that an event cannot occur unless there is a sufficient cause; and by ‘sufficient’ he means a complete and fully determinate set of preconditions, such that if they are present, it is inconceivable that the event should not occur. In this, Leibniz is in full agreement with Hobbes and Spinoza.
When Leibniz says that we usually cannot know the sufficient reason for an event, this is a serious understatement. Since everything is interconnected with everything else, the complete sufficient reason would involve knowledge of the whole universe.
Leibniz’s definitions of truths of reasoning and truths of fact may seem pretty obvious, but you have to remember that the distinction had been obliterated by Hobbes and Spinoza. For both of them, whatever happens, happens necessarily; and the only meaning of ‘possible’ is for an event which is not actual at the moment, but which has either necessarily happened in the past, or will necessarily happen in the future. Leibniz’s definitions open the door for unactualised possibilities, and hence for God’s choice between different possible and contingent universes.
Next, he says that a necessary truth is proved by analysing it into simpler and simpler concepts, until you arrive at ‘primary’ ones, which cannot be further analysed or defined. An example of the process is one familiar from Hobbes: you prove ‘Humans are rational’ by analysing ‘human’ into ‘rational animal’; and it is a visible tautology that a rational animal is rational. One of Leibniz’s big projects (called the ‘universal characteristic’) was to list all the primary concepts, and devise a notation for all complex concepts which would make explicit how they were derived from the primary ones. Once that had been achieved, all reasoning would become a matter of straight calculation, which could be done by a machine.
This paragraph is rather disingenuous. He is in effect claiming that the geometrical method of Euclid is the same as the process of analysis he has just described. But if so, axioms and postulates would not be necessary.
Assuming there are simple (primary) ideas, and we know what they are, it is difficult to see what role there can be for primary principles, or axioms. If they are explicit assertions of identity, they will all be of the form A=A, where A is any primary idea. As before, once everything is defined in terms of primary ideas, there is no need for any primary principles at all.
Leibniz now turns to truths of fact, which are proved by the principle of sufficient reason. He assumes that the reasoning process is also one of analysis. What he doesn’t say here (though he does elsewhere), is that what is being analysed is the complete concept of the individual. The complete concept is infinite, because of the infinite subdivisions of the body, and the infinite number of influences from the whole of the rest of the universe. So the difference between necessary truths and truths of fact is that the former can be proved by a finite process of analysis, whereas the process of analysing a complete concept is infinite — you can never arrive at the totality of simple concept which it contains.
This is what is meant by Leibniz’s doctrine (not mentioned in the Monadology) that all truth is analytic, and that in every true proposition, the concept of the predicate is contained in the concept of the subject. It may seem paradoxical to claim that all contingent truths as well as necessary ones are analytically true; but what Leibniz means is that if we had the complete concept of an individual, then every truth about that individual would be analytically true — which is no more than to say that if we already knew everything, we would have nothing new to learn. Only a tiny proportion of possible complete concepts have been actualised, and it cannot be proved, even by an infinite analysis, whether a concept has been actualised or not. That ultimately depends on the free choice of God in choosing the best possible combination of complete concepts to actualise.
In the last sentence of the paragraph, Leibniz anticipates the point he will make later, that every event has a double explanation; in terms of efficient causes (motions of matter) and of final causes (dispositions of the soul).
Leibniz now moves to the topic of God. Since the sequence of contingent things (or the following of one thing from another) is infinite, it is never possible to arrive at the sufficient reason for anything within this sequence. However far you go, you still have infinitely further to go.
So the ultimate (sufficient) reason for the whole sequence of contingent things must lie outside the sequence, in a necessary substance, or God. A ‘necessary’ substance means one whose existence is not contingent upon anything else. This is generally known as the ‘cosmological’ argument for the existence of God.
There is some obscurity in the phrase ‘in which the detail of changes exists only eminently, as in their source.’ The word ‘detail’ is what I translated as ‘precise specification’ in Paragraph 12. It is that in the monad which provides the sufficient reason for (or is the complete determining cause of) all its changes. The word ‘eminently’ is a scholastic term meaning ‘in a superior form’, and it is normally used for a cause which is different in kind from its effect. For example, when something is set on fire by an electric current rather than by a lighted match. Leibniz’s point is that the sufficient reason for the changes in a created monad lies in the monad itself, and not in God; but there is something different and superior in God, which is the source of the principle of change within the monad. Leibniz is carefully distancing himself from Spinoza, for whom the cause of change was within God himself.
Here I think ‘detail’ means the totality of all changes in the created universe, rather than the principle of change within an individual monad. So, since the universe is an interconnected whole, and the sufficient reason for everything that happens in it is to be found in God (at least eminently), this shows that there is only one God, and that a single God is sufficient to account for everything.
Having shown that God is unique, Leibniz now shows that he is infinite. Note the contrast with Spinoza, who argued the other way round (God must be unique because he is infinite). Leibniz has rather more of a problem, since he can’t argue straightforwardly that God is unlimited, and therefore infinite, because nothing else exists to limit him. There is, after all, the whole of the created universe. So Leibniz has to say that anything other than himself is dependent on him, and therefore presumably cannot impose any restriction on him.
The reference to God’s being the simple consequence of possible being is jumping the gun a bit, since it is not until Paragraph 44 that Leibniz introduces the ontological argument.
I’m not sure that it follows directly from God’s infinity, that he contains as much reality as possible. I think Leibniz needs to add the metaphysical assumption (which he certainly did believe in) that possibility has a positive striving towards existence, so that it will become actual unless something prevents it.
All this paragraph seems to be saying is that God is absolutely perfect, because perfection is the same as infinite positive reality.
This and the next paragraph are concerned with the relationship between God and created things. God gives created things such perfection (= reality) as they have, and their imperfection (= lack of reality) comes from their own nature as created things. If they didn’t have any imperfections, they would be God. As I have already said, what makes things distinct from God is their varying mixtures of being and nothingness.
The last sentence was omitted from the final versions of the text. Leibniz regards the inertia of bodies as an example of an imperfection, because it is a passive rather than an active power. Kinetic energy, on the other hand, would count as a perfection, since it as an active power.
Like Spinoza, Leibniz regards God as the source of essences (ideas, concepts, possibilities) as well as of existences. However, he qualifies this by saying ‘in so far as they are real.’ What he means is that, of course the concept of something possible isn’t real in the way that something which actually exists is real; nevertheless, it must have some sort of reality, otherwise there would be no possibility of the thing. Similarly, there can’t be any eternal truths unless the concepts they involve have some reality. Therefore these possibilities/essences/concepts/ideas must exist in God’s understanding.
Leibniz now gives an argument why they must exist specifically in God. If essences have any reality, this reality must be grounded in something which actually exists (it goes without saying that an essence or a possibility is not a self-subsistent entity, or substance). But in the case of contingent beings, their actual existence depends on the realisation of their essence or possibility — so essences are logically prior to their actual existence. Consequently, essences cannot be grounded in any contingent being, but must be grounded in a necessary being.
Now Leibniz is gearing up for his own formulation of the ontological argument (which he explains in greater detail in other writings). A necessary being is one whose essence includes existence. But essence and possibility are the same. So a necessary being is (by definition) one such that, if it is possible, it actually exists. So God necessary exists if this concept is possible — i.e. if it is not a self-contradictory concept.
Now Leibniz gives his proof that God must be possible, and therefore necessarily existent. Since he is infinite, he has no limits (‘infinite’ and ‘unlimited’ mean the same). But there can be no negation without some sort of limit (if there is some respect in which God is not, then he is limited in that respect). Consequently his concept can contain no contradiction, since, without negation, it is impossible to derive a proposition of the form ‘A = not-A.’ In other places Leibniz expresses this by saying that God contains nothing but positive predicates (as you would expect of an entity which is nothing but pure being); and it similarly follows that no contradiction can be derived.
The rest of the paragraph reviews the three proofs he has given of God’s existence. The ontological argument is ‘apriori’ in the sense that it runs from cause to effect (it starts from God as the ultimate cause of everything). The cosmological argument (which he gave first) was ‘aposteriori’, in the sense that it runs from effect to cause (given that the created universe exists, it must have been created by God). As for the argument in the middle (from the existence of eternal truths), Leibniz doesn’t actually say whether it is apriori or aposteriori, though he implies that it is the former. As eternal truths, they are co-existent with God’s nature, and therefore belong to the cause rather than to the effect.
Leibniz also implies that an apriori proof is better than an aposteriori one — presumably because an extreme sceptic might query whether or not the created universe does actually exist. On the other hand, the ontological argument would still be valid, even if God had never created anything.
Having proved the existence of God, Leibniz now turns to his nature. First he considers what depends on God’s will, and he takes a position half-way between the extremes of Descartes (who held that everything depends on his will), and Spinoza (who held that nothing depends on his will). Incidentally, Pierre Poiret (1646-1719) was a Calvinist minister, who was a devoted Cartesian for a time, and wrote a book called Rational Thoughts on God, the Soul, and Evil.
Eternal truths depend, not on God’s will, but on his understanding. He cannot arbitrarily will that they be otherwise (e.g. that a triangle has 200 degrees). But this does not mean that he is in any way constrained by anything external to himself, since eternal truths are the internal object of his understanding.
On the other hand, contingent truths do depend on his will, since his understanding can entertain alternative possibilities. But his will to choose the world he has created is not arbitrary, since he chooses the best, or most harmonious possible universe.
Next, God is a unity or simple substance, presumably in the sense that he has no parts. He certainly has different predicates, different aspects, and an infinitely complex range of concepts in his understanding.
Leibniz uses a metaphor to describe how created monads depend on him, namely like flashes of lightening. This is a surprising metaphor, since philosophers in the Platonic tradition (such as Leibniz) usually used the metaphor of light radiating from the sun, which becomes more and more diluted with not-being as it gets further and further away. Leibniz himself does sometimes use this metaphor; but here he wants to emphasise that monads are continually re-created, as if by repeated lightening flashes rather than by the continuous light from the sun. In this he is in complete agreement with Descartes. The point is that the state of the universe at any given instant is not brought into being by the immediately preceding state. The preceding state is the reason for the next state, but God is the only being with the power to make it happen.
Nevertheless, despite the immediate dependence of everything on God, created monads are limited in what they can receive from him, since they are essentially finite.
Finally on God, Leibniz lists the trinity of his faculties: power, knowledge, and will (in the Theodicy, §150, he suggests that they correspond to God the Father, God the Son, and God the Holy Ghost).
Leibniz often says that monads are finite images or imitations of God (Genesis, 1.26: "And God said, Let us make man in our image, after our likeness"). Here he draws a parallel between God’s three faculties, and three aspects of created monads. Perception and appetition are unproblematic; but it is more difficult to see how the ‘subject or basis’ corresponds to power in God, since it looks more like substance than power. Perhaps the point is that created monads do not really have any power at all, since it is God who creates things, and brings about all changes in them.
Now there is a crux, not over how the text is to be translated, but over how it is to be read. The earlier drafts of Leibniz’s MS have limitations, and later versions have imitations. It’s difficult to explain how he could have written limitations, and let it stand through a number of revisions, if that wasn’t what he meant. But if imitations was merely a transcription error by his secretary, it’s equally difficult to explain how Leibniz failed to spot it when making further revisions.
Some translators read it as ‘limitations’ (e.g. Francks and Woolhouse), but I don’t think this makes sense. It is true that created monads and their faculties are limited; but to say that their faculties are limitations of the attributes of God is dangerously close to Spinozistic pantheism, given that a limitation is a determination, or particular instantiation. Moreover, what I have translated as ‘which are closer the more perfection they have,’ is literally ‘in proportion as there is some perfection.’ This makes the wording very odd if they are limitations, since Leibniz would appear to be saying that the more perfect they are, the more limited they are — when it should be the other way round.
It makes much more sense if we read it as ‘imitations’, since we know from many other passages that this is a Leibnizian doctrine, and that the more perfect a monad is, the more god-like it becomes.
Finally, in an aside, Leibniz makes an additional comment about the meaning of the word ‘entelechy’ (which should really have gone in Paragraph 18). Ermolao Barbaro (1454–1493) was an Italian humanist, who tried to rescue the genuine Aristotle from the misinterpretations and accretions of the scholastics. Of course, he himself didn’t use the expression ‘perfection-havers,’ since he was translating Greek into Latin. But the English corresponds exactly to his perfectihabiae (or perfectihabies in Leibniz’s French).
In this and the following three paragraphs, Leibniz explains what he means by causation, given that there is no direct interaction between one monad and another.
Remember that, for Leibniz, created beings are a mixture of primitive passive power (their material aspect), and primitive active power (their spiritual aspect). So here he identifies activity with perfection and distinctness of perception, and passivity with imperfection and confusedness of perception.
To give an example, if I creep up behind someone and hit them over the head with a stick, I have a distinct perception of the sequence of events. If the other person is absorbed in reading a book, the sudden sensation of pain will have no connection with what they were perceiving immediately before, and their perception of it will be confused, and they won’t know what has just happened to them. So, even though monads don’t really interact, on this occasion I am the active party, and the other person is the passive one.
However, it’s not merely that one monad has more distinct perceptions than the other, but that it provides the apriori explanation of what happens in the other. Remember that ‘apriori’ simply means an explanation which runs from cause to effect, and not ‘non-empirical’. So, in the previous example, there is a coherent causal story running from my initial intention to hit someone on the head and the actual blow, whereas, in that other person, there is no causal connection between reading a particular sentence, and the sudden blow to the head.
Note, however, that we are not God. God can cause an effect without suffering any reaction, whereas we can’t. Our state is never perfect; our perceptions are always partly confused; and we are always partly passive as well as active — the difference between activity and passivity is only one of degree. So, for example, when I hit someone on the head, I will have a sudden pain in my hand and arm, which is causally explained by the reactive forces in the matter of which their skull is composed. So there is some passivity in me, and some confused perception, even when I am relatively the more active partner. Every event is not just a one-sided action of one thing on another, but an interaction.
When Leibniz uses the word ‘ideal’, he means ‘not real’. Monads do not really influence one another, and only God can have a real influence on things. Leibniz now explains (rather confusedly) what causal interaction really amounts to.
Remember that, for Leibniz, God doesn’t make things up as he goes along, but executes his original will from the beginning of time. When he was deciding what universe to create, he considered all possible monads (far more than the infinitely many actual ones), and selected the best possible combination. One of the main criteria for what is the best is that all monads should be mutually harmonious: that what happens in one should correspond to, or be accommodated to, what happens in every other. For example, when I perceive myself hitting someone over the head, at the very same time, that person perceives themselves being hit over the head.
Leibniz’s language is very florid here: ‘one monad has reason to demand that [God] pays attention to it when organising the others.’ Obviously he is talking about possible monads, before they are created, and they’re not all shouting at him, clamouring for attention. However, as I said earlier, Leibniz does believe that possibilities have some sort of drive towards existence, so that they will actually exist unless prevented by something else which is incompatible with them; and the mere perfect they are, the more likely they are to succeed. Or sometimes he expresses this (lawyer as he was) in legal terms, by saying that possibilities have the right to exist in proportion to their perfection. Here we have the legal metaphor, with God standing judge over all possible monads, and deciding which have made the best case for existence.
So, given that God has decided to include me in the best possible universe, he pays special attention to my perception of hitting someone over the head, and ‘organises’ the others so that there is a simultaneous perception of being hit on the head.
Now Leibniz says explicitly that interaction is mutual — that is, each partner is partly active and partly passive, and the difference is one of degree, or even of perspective. So one way of looking at what happens when I hit someone over the head, is that the smooth sweep of my arm is rudely interrupted by the intervention of the hard particles of calcium in my victim’s skull; they react with a force equal and opposite to mine, and send shock waves surging through my flesh, bones, and nerves, with consequent turmoil in the grey matter of my brain. Plenty of activity there, and coming from the relatively passive partner in the interaction!
From here until Paragraph 61, Leibniz considers the universe as a whole, and the universal harmony between monads.
As against Descartes, he maintains that God’s choice is rational, not arbitrary; and as against Spinoza, he maintains that God does have a choice between different possible universes. As with other writers of the period, the word ‘determine’ doesn’t mean ‘causally necessitate,’ but to delimit a universal or a range of possibilities to one particular instance. If you like, the formula for the best possible universe, to be created by the best possible God, must have a unique solution, otherwise God wouldn’t be able to make a rational choice. He would be like Buridan’s ass, which starved to death because it couldn’t choose between two equally enticing bundles of hay equidistant from it.
Leibniz’s writing is rather loose here, since harmony and degree of perfection are not the same thing. Degree of perfection is the amount of positive reality, and also the amount of distinct perception; whereas harmony is the accommodation of the perceptions of monads to each other. For example, the universe would have more perfection if the person I hit on the head had a distinct rather than a confused perception of the event; but it would be less harmonious, since their passivity has to be accommodated to my activity. Really Leibniz should be saying that the best possible universe is that which has the optimal compromise between harmony and quantity of reality.
Again, as in Paragraph 51, we have the legal metaphor of possibilities having ‘the right to claim’ existence in proportion to their perfection.
It is only now that Leibniz says explicitly that God must choose the best possible universe because of his goodness. His goodness is the goodness of his will, just as his wisdom is the wisdom of his knowledge, and his power is what brings about the act of creation.
The perceptions of monads are expressions of their relations to every other. They must have relations to every other monad because the harmony of the universe means that they are all accommodated to each other, and are hence interconnected. Although monads don’t really have any causal influence on each other, it is just as if they did. So the expression of relations is not just things like distance, but more dynamic relations, such as the ripple effect throughout the ether of any motion of any physical object. (You might prefer the example of gravitational attraction, whereby every body attracts every other body, with a force which is etc. etc.; but Leibniz didn’t believe in it.)
The metaphor of monads as living mirrors is one of Leibniz’s favourites. Each monad reflects every other monad in the universe; and it is ‘permanent’, since a monad cannot come in or out of being.
By the perspectival multiplication of a town, Leibniz means that there are infinitely many different views of it, even though there is only one town. Similarly, there are infinitely many different perspectives on the universe as a whole, each represented by the perceptions of a monad. If we consider monadic perceptions, it is as if there were infinitely many different universes; but as with the town, they are just different representations of a single universe.
Although Leibniz doesn’t go into this question here, the concept of a monad’s unique point of view is crucial to his account of space. As I said earlier, space is a logical construction out of monadic perceptions — monads are not in space, but space is in them. However, one can talk of monads as if they were in space, since their point of view gives them a unique position in relation to all other monads. To give an analogy, you might have a number of digital images of a town on the hard disk of your computer. On the hard disk, it doesn’t have any meaning to ask where any given image is, or where it is in relation to the others (in effect, it is all but non-spatial). But if you print them out, you can put them in their proper order by virtue of the differences in their points of view (this was taken just to the left of that one, or exactly from the opposite side of the town, and so on).
Now we have a rather tighter definition of ‘perfection’ in the sense of goodness: the maximum variety (which includes quantity of reality as well as differentness), together with the maximum order (or harmony).
Leibniz now claims that his account is the only one which gives due justice to the greatness of God. He probably has in mind the rival accounts of Descartes (too capricious), Spinoza (no goodness or freedom), Malebranche (too much miraculous interference), and Newton (too hands off: he built the clock, but has to wind it up from time to time since he wasn’t clever enough to make it go on for ever).
Leibniz calls his account a ‘hypothesis’, which means an unproved theory which accounts for the facts. That a particular hypothesis is the best is prima facie grounds for supposing it to be true — but somebody could always come up with a better one. So this argument (that it is the only hypothesis to give due recognition to the greatness of God) is no more than supporting evidence. This is why he adds that he thinks he has already succeeded in demonstrating it.
He then defends himself against Bayle’s charge that he has attributed to God more than is possible (which supports his case that he has attributed more to God than other philosophers have). He merely says that Bayle has given no reason why the universal harmony should be impossible — with the implication that, if it is not impossible, then God can do it.
He now gives an apriori argument for the universal harmony — that is to say, an argument which proceeds from cause (God’s creative act) to effect (the created universe), and not from effect to hypothetical cause.
The first bit of fresh argument is that, since monads are by nature representative, nothing can restrict them from representing everything. However, I don’t think the argument is valid as it stands. It needs two further premises. The first is Leibniz’s deep-rooted assumption that whatever exists in essence is actualised unless something prevents it. So since monads are essentially representative, they will represent everything unless stopped.
The second is his thesis that nothing (apart from God) can influence the inside of monad. Consequently, nothing can block a monad’s representations. Presumably God could have limited monads’ representations — but if he had done so, they would have been less perfect, and they couldn’t have provided the sufficient reason for everything that happens in a thoroughly interconnected universe.
However, we are monads, and it is a commonsense observation that we don’t perceive everything. Leibniz’s response is to say that the only perceptions we are aware of are distinct ones, which make up a tiny proportion of the whole. For example, we distinctly perceive things we are in physical contact with, or more distant things, some of whose properties are focussed and highlighted by our sense organs. All the rest is confused or ‘little’ perceptions, which we cannot discern. If we perceived everything distinctly, we would be gods.
(Note, however, that this divine perception would be totally unlike perception as we know it. For example, if we could see molecules of air, we would be in a complete fog, and couldn’t see anything at all, let alone distinctly. The only sense I can give to the concept of distinct perception, is that a limited range of things are perceived distinctly, against a background — and foreground — of things which are not. If God perceives everything distinctly, he is no better off than a bare monad, which perceives everything confusedly.)
Anyway, Leibniz says that, in one sense, we all know everything; but we differ in how we know it. What distinguishes us from God is that only some of our perceptions are distinct; and what distinguishes us from each other is the variations in our distinct perceptions (rather than the infinite backdrop of confused perceptions, such as gravitational influences from the fixed stars).
So far Leibniz has been talking about the perceptions of monads. But there is a one-to-one correspondence between monadic perceptions and compound bodies, so the same must be true of the universe as material.
In the material universe, the interconnectedness of everything is mediated by one piece of matter pushing against its neighbours in accordance with the laws of motion. If there were any gaps, the causal chains would be broken, and the universe wouldn’t be interconnected. Consequently, there cannot be a vacuum. (In fact Leibniz’s argument runs in the opposite direction, but I think this makes more sense, since he hasn’t independently established that there is no vacuum.)
In a plenum (i.e. a universe full of matter), every motion is transmitted in every direction (imagine a bomb exploding deep in the ocean). The force of the shock wave diminishes with distance as it spreads more widely. But given that there are no smallest quantities in Nature, the wave will spread to infinity. As Leibniz has already established, every physical object is in motion, and therefore setting up wave motions in the objects surrounding it. Consequently, every object is transmitting motions to every other object, and every object is receiving motions from every other object. Just as monads are mirrors of the whole universe, an omniscient being would be able to read off from the motions of an individual object what is happening everywhere else, and what has happened in the past, and what will happen in the future.
In his philosophical system, Leibniz makes some pretty strong claims, and this is one of the strongest of them all. He made a major contribution to science by formulating the principle of the conservation of energy. Now he is formulating a much more radical principle of the conservation of information. It is a truism of modern science that the motion of any particle is the resultant of an infinity of forces acting on it. What Leibniz is in effect saying is that, if a particle is to obey the laws of Nature, it must perform an infinitely complex calculation. It must register all the forces acting on it, and feed the information into a mathematical formula which yields the required result — motion in a particular direction, with a particular speed and kinetic energy. If an omniscient being could read off all the information contained in the particle’s computer program, that being could calculate all the forces acting on it from every other particle in the universe, and hence the forces from which they arose, and the forces they would give rise to.
The reason why this seems absurd is because we think of a particle as something simple, which cannot contain infinite complexity, let alone calculate how to obey the laws of Nature.
But for Leibniz, any particle, however small, has infinitely many parts. Consequently, it can contain infinitely more information than any computer constructed by humans. And the same goes for the parts of its parts.
Similarly, every monad has a program which determines the evolution of its perceptual states, and there must be something corresponding to it in the material realm, since there is a one-to-one correspondence between the two.
When it comes to the crunch, what Leibniz is saying is that things cannot obey the laws of Nature, unless they know what the laws are, and have the necessary information for applying them (namely the state of the whole universe). Perhaps he is again thinking too much like a lawyer than like a physicist. But what does the metaphor of a law of Nature mean, unless things in Nature have the means to obey it? The only realistic alternative would seem to be a Spinozistic world, in which everything emanates inexorably from Nature itself. A mechanistic world in which atoms just happen to behave in a law-abiding way explains nothing at all.
However, although we contain all this infinity of information within ourselves, we can read off only what is represented distinctly.
Paragraphs 62–71 are about the relationship between the soul and the body, and more generally the relationship between monads and matter.
The soul is not literally in the body, nor is it (strictly speaking) causally related to it. What makes my body my body is that it is represented more distinctly than surrounding bodies. Presumably he means that, just as our sense organs enable us to have a relatively distinct perception of some external objects, so our nervous system means that we have a distinct perception of the parts of the body, which ends at the outer limits of the body. He doesn’t elaborate, but one can imagine the sort of story he could tell about the various ways in which there is a special harmony between my soul and the parts of my body (I feel its pains, it obeys my will, and so on).
The second sentence is interesting, since it implies that the fact that bodies represent the entire universe is logically prior to the fact that monads also do so. Leibniz says that the soul represents the whole universe only because it represents its body, which represents the whole universe. I’m sure this is inconsistent with what he said earlier about the creation of monads, especially if monads are logically prior to bodies in space. What he should be saying is that the two go hand in hand: that there is a one-to-one correspondence between the distinct and confused representations of the whole universe in the soul, and the infinitely complex motions in the body.
A complete being has to be a combination of monad and body (or form and matter, in Aristotelian terms). Of these there are two types: if the monad is a bare monad, or entelechy, the combination is called a ‘living being’; and if it is a soul such as all sentient creatures have, it is called an ‘animal’. Note that Leibniz is not always consistent about his terminology: he often calls all monads ‘entelechies’ or ‘souls’. Note also that he has defined dead matter out of existence — the only real beings are living beings.
When he says that all these bodies are ‘organic’, I am not 100% certain what he means, since the word has acquired many new meanings since his time (e.g. organic chemistry, or organic farming). He might merely mean that they have bodily organs; but he probably means ‘constituting a systematic and interconnected whole,’ since the reason he gives is that they mirror the universal harmony of the whole universe.
Note that here again he makes the body logically prior to the monad: the monad’s perceptions must be organic, since they ‘follow’ what is in the body.
Machines are human artefacts made out of working parts. Mostly they need to be operated by a human (e.g. a pump or a mill); but even in Leibniz’s day there were machines which could work by themselves for a while, such as clockwork toys. These were called ‘automata’. Here Leibniz elaborates on his remark in Paragraph 18, that entelechies are incorporeal automata.
Organic bodies are divine machines or natural automata, and they differ from human machines in that their parts are also machines down to infinity. We can construct machines with parts which are also machines. For example, an explosive device consisting of a bomb and a timer, in which the timer has distinct components. But eventually there comes a point when the parts have been constructed from raw materials such as metal or wood, which are not themselves machines. By contrast, organic bodies have organs (heart, lungs, etc.), which are themselves organic bodies with organs (e.g. cells); and they in turn have an organic structure (the nucleus, the cell wall etc.), and their parts have an organic structure (e.g. chromosomes). Leibniz didn’t know all this, but his belief was that there could be no arbitrary point at which the process of subdividing into organs of organs of organs could ever stop. It is exactly analogous to the process of splitting the atom into sub-atomic particles, and them into even small particles and so on — except that, for Leibniz, we are dealing with organic matter at every stage.
Certainly some ancients recognised that matter was infinitely divisible, but not all (e.g. the atomists denied it). However, Leibniz understates his own originality. Instead of taking the material world as a homogeneous whole, which is prior to its parts and capable of infinite subdivision (as Descartes and Spinoza did), he states that it is built up out of infinitely small parts. He says this must be the case, otherwise each part of matter couldn’t express the whole universe — it can do so only because it has an infinity of smaller parts, each moving in different ways.
As for how matter can be constructed out of infinitely many parts, it is surprising and significant that Leibniz doesn’t appeal to his own great invention, the concept of an infinitesimal. As we have already seen in the case of Spinoza, matter cannot be constructed out of mathematical points, since infinitely many mathematical points are still at one point. Nor can it be constructed out of finite atoms, since they will have parts. An infinitesimal quantity is one which is greater than zero, but less than any finitely specifiable quantity. If monads were infinitesimals, they would seem to fit the bill.
My personal answer to this conundrum is that Leibniz didn’t believe that monads were parts of matter at all. Monads are not in matter, but matter is in them. Because there are infinitely many monads, there is an inexhaustible supply of them for one to be the entelechy of any given volume of matter, however small.
In the light of the above, I would distinguish the two pairs: living beings and animals, and entelechies and souls. In the smallest part of matter there might be the bodies of living beings and animals, but not literally their entelechies or souls.
‘World’ is a strong word to use, since it is the equivalent of ‘universe’. But it is a logical consequence of the infinite division of matter that there is no mid-point between the infinitely large and the infinitely small. If an atom is like a miniature planetary system, with electrons orbiting round the nucleus as the planets orbit round the sun, then there is no absurdity in supposing that any electron carries the same diversity of life as does planet Earth. Similarly, planet Earth might be an electron relative to some enormous being, of which the solar system is just one atom. Elsewhere, Leibniz makes precisely these speculations.
It may all seem highly fanciful, but, as I have said, it is a logical consequence of the assumption that matter is infinitely divisible, together with the assumption that the laws of nature are the same everywhere. With the notable exception of Galileo (who realised that a scale model of a ship would collapse under its own weightif sufficiently enlarged), most philosophers and scientists accepted Leibniz’s premises, but balked at drawing his conclusions. It was only the twentieth century which saw the development of relativity theory (very large magnitudes behave differently) and quantum mechanics (very small magnitudes behave differently). In a sense, it restored one aspect of the medieval world view, namely that human beings are roughly half-way between two extremes.
Here Leibniz waxes poetical. Each portion of matter consists of living bodies, and intervening matter which is not itself alive. The same is true of each organic part of the living bodies — that they consist of more living bodies, and intervening matter.
Even the intervening matter contains living bodies, though they are imperceptibly small. The implication is that, if you were to probe deep enough, you would find that ultimately there was no intervening dead matter at all, and everything would be full of living bodies.
In other writings, Leibniz refers explicitly to investigations with the recently invented microscope. For example, blood looks like a homogeneous red fluid; but through the microscope you can distinguish the red blood cells from the surrounding transparent fluid. Why shouldn’t a more powerful microscope reveal similar, smaller organisms in the transparent fluid (as in fact it does)? Again, chalk looks like a homogeneous lump of white matter; but through the microscope you can see the shells of tiny sea creatures. And if chalk is full of life, why shouldn’t the same be true of clay, or stone, or any other substance, if only we had powerful enough microscopes?
Things seem inert, because our perception is confused. It is only when we come close enough (e.g. thanks to a microscope) that we can have a distinct perception of the tiny living organisms. Ultimately, the whole of the universe is made up of living organisms.
Here Leibniz introduces the concept of a dominant entelechy, soul, or monad. Each living body is a compound of smaller living bodies, and they all have their own special monad, which is the principle of unity of the organic body. Since there is a one-to-one correspondence between the monadic and the material realms, there must be something in the monadic realm which corresponds to the relation between whole and part in the material realm. Obviously monads cannot be parts of each other. So the relation between them is one of dominance. My soul dominates the monads which are the principles of the unity of the organs of which my body is composed. They in turn dominate the monads which are the principles of the unity of the parts of their bodies; and so on to infinity.
He doesn’t actually say what this dominance consists in; but it must be some sort of control — the perceptions of the dominant monad will be more distinct, and will serve to explain the changes in the perceptions of the subordinate monads, rather than the other way round. In other words, the dominant monad is the more active partner in their interactions.
Leibniz now states that there is no particular piece of matter to which a monad is permanently attached. He accepts the ancient principle of Heraclitus that ‘everything flows,’ like a river, so that bodies (presumably he means both organic and inorganic bodies) are constantly losing and gaining particles.
In the case of organic bodies, it must follow that the hierarchy of subordinate monads over which a dominant monad dominates must also be losing and gaining members, so that there is no one monad, or group of monads, which are permanently in its service.
What Leibniz doesn’t say explicitly here is that, when a subordinate organism joins or leaves a larger organism, it must be somehow transformed (i.e. take on a different form), so that it becomes, or ceases to be, a member of that particular hierarchy. When I digest food, the particles must take on the individual form of my body, so that they become parts of my body. For example, if I swallow a cherry whole, the flesh is transformed into my flesh; and with a sufficiently powerful microscope you could see that it was different from anyone else’s flesh gained by eating a cherry. But although the stone is inside my body for a while, it never becomes part of it. The reverse happens when cells of my body break down, and are excreted.
Paragraphs 72–77 are about immortality.
Leibniz starts by repeating the thesis that souls gradually lose parts of their body, but are never completely deprived of a body. Animals often undergo ‘metamorphosis’ (which is just the Greek for ‘transformation’) — that is to say, they undergo a change of form, or become animals of a different species.
He then denies two theories of immortality. The first is that of Pythagoras and Plato, namely metempsychosis or transmigration, which literally means that the soul is transferred across into another body. In other words, the (immaterial) soul is taken out of one body (leaving it dead), and is put into another, soulless, body, so that it becomes alive.
The other is that of Descartes and others, namely that the immaterial soul can continue to exist without a body after it has left its original body. Nor are there any superior beings (such as angels) which have no bodies at all. Only God himself is wholly immaterial.
Just as death is neither the annihilation of the soul, nor the separation of the soul from the body; similarly, birth is neither the creation of the soul out of nothing, nor its being joined to the body.
‘Generation’ is the process by which a new member of the species comes into being. It obviously involves growth, since even foetuses are much larger than eggs or spermatozoa. It involves ‘unfolding’ in that the form or soul (e.g. of a human) is not added to the matter out of nothing, but pre-existed in it, and is revealed by the process of generation. Death is the opposite process. The body shrinks back to something the size of, say, a spermatozoon, and the form of a human being is packed away inside it.
Leibniz (rightly) points out that there had been many conflicting theories as to the origins of living beings. It was commonly believed that many kinds of living being could emerge spontaneously from certain kinds of material. For example, aquatic insects from stagnant water; flies from dung; or bees from the carcase of a lion (Judges, 14.14, and tins of Lyle’s golden syrup: ‘Out of the strong came forth sweetness.’). It was only thanks to the recent invention of the microscope that people were able to see spermatozoa (literally ‘seed-animals’), and the other ‘seeds’ from which macroscopic organisms sprang. Leibniz takes it for granted that the seed somehow contains the form which will characterise the mature animal, though without manifesting that form itself. This is what he means by ‘preformation.’
So the conclusion is, not merely that there is a seed (the ‘organic body’) before the generation or conception of the new animal, but that the animal itself (body plus soul) pre-existed in it. On conception, the latent or infolded form or soul becomes dominant, and the animal changes species, or is ‘transformed’. The transformation of a caterpillar into a butterfly is a similar process, except that the butterfly sloughs off the skin of the caterpillar, which doesn’t happen in conception.
Leibniz’s idea that ‘seminal animals’ have a life of their own may seem highly fanciful. On the other hand, our bodies do contain billions of bacteria, microbes, germs, and viruses, which do have their own life-cycles; and he wasn’t to know that spermatozoa can’t breed (any more than tadpoles can).
Just as only a tiny proportion of acorns become oaks, so only a tiny proportion of spermatozoa are ‘chosen’ to pass through to a ‘larger theatre.’ In fact the French is ‘elected’; and in the case of humans, I wonder whether there is a hint of Leibniz’s Protestant optimism here — that all humans are numbered among the ‘elect’, and will eventually be saved. As we shall shortly see, the ‘larger theatre’ is not just larger in size, but (again in the case of humans) raises them to a higher status in the scheme of things.
‘This is only half the truth’ — i.e., so far he has only discussed coming into being. Death is the converse of birth, and the animal is transformed back into a seminal animal, or something similar.
These aposteriori arguments (from empirical observations back to their causes) confirm the stronger, apriori arguments (from causes to their effects) which he gave in Paragraphs 71–73.
So, it’s not merely that the soul or monad is immortal (on the apriori grounds that it is a mirror of the indestructible universe), but that the animal is immortal. It always has some body, even if the matter of the body is in permanent flux, and it sometimes loses a lot of organs very rapidly, as at death. The word I have translated as ‘covering’ is depouille, which means skin, clothing, corpse, or a sloughed off snakeskin.
Paragraphs 78–81 are concerned with the relation between souls and bodies. Although he has humans primarily in mind, what he says applies to the relation between any kind of monad and matter.
The relation between soul and body is not strictly a union, in the sense of their being bound together into a compound, but rather a mutual, or one-to-one correspondence between perceptions in the soul, and motions in the body. They follow their own laws, in that the perceptions of a monad follow from preceding perceptions, and the motions of a body follow from preceding motions. There is no causal influence of one upon the other. The reason why they coincide (i.e. the reason why the one-to-one correspondence is maintained) is because of the pre-established harmony between all substances. The harmony is ‘pre-established’, because it was set up in God’s original creative act, and he never changes it. The two systems (that of monadic perceptions and that of bodies in motion), correspond perfectly since they are both representations, though in different ways, of one and the same universe.
Elsewhere, Leibniz gives the analogy of two clocks which keep perfect time. The perfect clockmaker made them so well that neither of them ever goes wrong. They don’t keep in harmony because of any causal interaction (e.g. a rod linking the two pairs of hands); nor because the clockmaker adjusts one of them whenever he sees them beginning to diverge.
Souls act in accordance with the laws of final causes — that is to say, they are constantly striving for, and being drawn towards greater and greater perfection. Bodies act in accordance with the laws of efficient causes — that is to say, they act in accordance with the laws of mechanics, and are pushed from behind by blind forces acting on them. God has brought it about that the two are in perfect harmony.
So, for example, my brain is a natural machine, in which particles of different shapes and sizes are whirring around at different speeds and in different directions. At some given moment, the brain transmits a motion down some nerves, which forces some muscles to contract or relax, and my arm rises. Exactly corresponding to these physical events, there are perceptions and appetitions in my soul, which result in my willing my arm to rise. The pre-established harmony ensures that they both happen at exactly the same time.
In this paragraph, Leibniz gives a very clever explanation of how Descartes might have thought that the soul could influence the body, without contravening the laws of mechanics. Descartes believed in a law of conservation of ‘motion’, so that its quantity in nature could be neither increased nor diminished. If the soul could make a particle of matter in the brain move faster, this would contravene the law. But if it merely deflected the particle, so that it travelled into a different nerve ending, the total quantity of motion would be conserved. What Descartes failed to understand was that what is conserved is motion in a given direction, and that it requires an input of energy to change the direction of motion of a particle.
Leibniz sums up by saying that we can explain physical events without taking souls into account; and we can explain mental events without taking matter into account; and yet the two systems run in parallel, so that it is as if the one were influencing the other.
The remainder of the Monadology is concerned with the special status of human souls.
Existentially, humans are in the same position as other living beings: from the creation of the universe they have existed with body and soul, and they will continue to do so to eternity. During the periods when they are not actual, living human beings, but only seminal animals, they have distinct perceptions, like other animals with sensitive souls (a sensitive soul being one whose body has sense organs). It is only when they become actual human beings through the act of conception that they acquire the rank of reason and the privileges of spirits (i.e. rational souls). Again Leibniz uses the theological term ‘elected’.
Leibniz has already summarised the differences between human and animal capacities in Paragraphs 29–30: we have knowledge of necessary truths; we have self-consciousness; and we have a concept of God. He doesn’t offer any explanation of how these extra capacities can arise naturally, and he sometimes implies that they are a supernatural gift from God.
Leibniz now adds that, whereas all monads are images of the created universe, human souls are also images of God. In fact, he has already said (in Paragraph 48) that all monads are images of God, in so far as they have substance, perception, and appetition. What is special about humans is that they, unlike other animals, are capable of knowing the system of the universe, and of using this knowledge to make machines.
He even goes as far as to say that humans are like minor deities within their own sphere of authority. Marxist commentators have noted how this reflects the feudal structure of Hanoverian society. The Duke himself is God; senior officials like Leibniz are humans, who understand what’s going on and have the power to institute public works; junior officials are like animals, who can carry out menial tasks under orders; and the workers are just bare monads.
Next Leibniz adds another dimension. Since humans are images of God himself, they can have a kind of social or personal relationship with him. He is not just their creator (as an engineer is of his machines), but he enters into a reciprocal (if one-sided) relationship with them — as king (in respect of his power), and as father (in respect of his love).
The metaphor of the City of God is taken straight from St. Augustine.
Now Leibniz introduces a moral dimension for the first time — even if he is concerned with God’s goodness, rather than with what it is to be a good human. He makes two points.
First, God couldn’t be glorious without the City of God, since otherwise there wouldn’t be any creatures capable of glorifying him. Leibniz might just as well have said that you can’t be the greatest conceivable pop star, if you haven’t got any fans. He needs us as much as we need him (well, not quite as much . . .).
Second, the concept of goodness has application only with respect to moral agents. If God had merely created a huge machine of a universe, you could admire his cleverness and power, but the machine would be morally neutral. God needs rational and moral beings in order to manifest goodness (justice, mercy, and so on).
This paragraph is transitional. Leibniz has already established the harmony between the realms of final and of efficient causes. He now points to a harmony between the realm of nature and the realm of grace (or the City of God). It’s important to note that these two contrasts are not the same. Even if there were no humans, there would still be a harmony between final and efficient causes. Here the contrast is between humans and the rest of Nature.
Just as final and efficient causes go hand in hand to produce the same outcome, the same is true of the realms of grace and of nature.
Here I detect a tension between Leibniz’s Christianity and his Platonism. According to Christian doctrine, there will be a single Last Judgment, when the world is overturned, and sinners die a second death. The world will then be restored, and the elect will live in eternal bliss under Christ’s reign. This, for example, is Hobbes’s interpretation of the Bible.
According to Plato, and other ancient philosophers (and indeed Descartes, as far as I can tell), the universe is cyclical, so that there is a succession of holocausts (everything being consumed by fire), followed by a new beginning.
As far as I can make out, Leibniz’s view is an amalgam of the two. The earth will be destroyed periodically (‘as and when it is required by the government of spirits’), but each period will be better than the previous one, because the universe is becoming ever more perfect. If it were ever to become absolutely perfect, it would collapse back into God himself. In other writings, Leibniz suggests that, instead of collapsing back into seminal animals, (good) humans might be elevated to an even higher status, such as that of angels.
At the times when the earth is destroyed, things might seem to be getting worse. But, as Leibniz so often says, one has to take a step back in order to leap forward.
The essential point Leibniz is making here, is that the purely mechanical laws of Nature will bring about a destruction of the earth, exactly when the moral laws of the City of God require some people to be punished, and others rewarded.
So God as creator sets up rewards and punishments as and when they are required by God as legislator. Leibniz could hardly make it more explicit that rewards and punishments will be felt by our living bodies in a continuation of the present universe, and not by disembodied souls in some extra-terrestrial heaven or hell.
Rewards and punishments need not happen immediately, since they will not be properly felt by a human who has infolded back into the status of a seminal animal. Presumably the dead are resurrected, or brought back into the human state, in order to be rewarded or punished.
As with Spinoza, the good life is not measured in terms of one’s relations to other people, but in terms of one’s relations to God. Ultimately, virtue consists in the pure and disinterested love of God.
We then have a little bit of scholastic terminology. The ‘antecedent’ will is the will that everything should be the best for every individual; the consequent will, which results in the creation of the actual universe, is the best possible compromise between what is good for each individual. It is ‘secret’ because we finite beings cannot make the same calculations as God does.
Again like Spinoza, Leibniz is heavily influenced by Stoicism — the view that we should be indifferent to our own sufferings, and see them as contributing to the good of the whole, governed by a divine providence. It we understood things well enough, we would see that this is the best of possible worlds, and rejoice in the fact.
However, there is a Christian twist at the very end. Provided that we align ourselves with the will of God, we will find that this is not only the best possible world in general, but that it is the best possible for ourselves in particular. Less Christian is the implication that our happiness will be fulfilled on earth, not through a one-off second coming of Christ (as Hobbes held), but through a succession of rebirths as humans, each one of which will be better than the last.
Now return to the Index to Unit 5, and complete the questionnaire.