What Is A Monad? Leibniz’s Monadology
Leibniz’s Monadology is a wild text. Famously in it he argues that everything is monads, more or less. But what does that mean? I want to here trace a line through the text and hopefully make things a bit clearer, and also try to illustrate some of the awesome weirdness that Leibniz courageously dives into. These aims will, understandably, occasionally be at odds with one another.
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First off, Leibniz gives the name ‘monad’ to an absolutely simple substance. These absolutely simple substances must exist, because composite things exist. If we grant the existence of some composite thing — water molecules built of hydrogen and oxygen, for example — then we also grant the existence of the simpler elements of which the composite is composed (hydrogen and oxygen in our example) even if we can doubt that these ‘pieces’ may ever occur in isolation from the composite. Now, when we break a composite into its constituent parts, we can ask of those parts whether they are composite or simple. If composite we repeat the procedure, until we get to something absolutely simple — i.e., possessing no constituent parts. Leibniz calls this simple stuff ‘monads’.
The next step is to see what we can infer about the features of these newly titled monads just based on their absolute simplicity. If we’ve been following the above argument with an image of some fundamental teeny-tiny ‘grain’ of matter at the root of all composite things we’ll be here frustrated, because monads cannot have any shape, and thus have no size, teeny-tiny or otherwise. Why? If a monad had a shape (which it would need to have in order for it to have a relative size to other shaped things) then it would, by rights, have constituent parts — a ‘left half’ and a ‘right half’, for example, or a ‘surface’ and an ‘inside’. The problem is not that a thing with a shape is always in fact divisible into components, because this is not true, but rather that it is de jure divisible into components, and thus we can entertain the idea of ‘half a monad’ which contradicts the idea we started out with: absolute simplicity.
We should get the direction right here. It’s not Leibniz is arguing there are these monad things, and they are all such-and-such, it’s rather that the argument goes ‘there has to be something absolutely simple, otherwise there wouldn’t be anything composite’ and in line with this absolute simplicity we argue that if some fundamental particle is offered up as the most basic constituent of everything, if that particle has some shape, then we can ask that: within the confines of its shape, what’s that stuff that it’s ‘filled up’ with? What’s the ‘particle juice’ the form of the particle encloses? And of this ‘particle juice’, what is its structure such that we can explain its possibilities, of what constituents is it composed? The name ‘monad’ Leibniz gives to wherever this game ends, where no further questions can be raised concerning composition, his wager is this will not happen until we have gone ‘beyond’ any possible talk of shape, and thus size, because as long as we have some shape, we can always ask ‘yeah, but what’s it made of?’.
“Now where there are no parts, neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature and, in a word, the elements of things.” (§3)
Now, from the existence of composites, we get the idea of simplicity, and from that we get ‘shapelessness’. There’s a bit more we can squeeze for free: monads cannot be created or destroyed naturally. The assumption here is that all natural creation and destruction is a putting together, or a falling apart, of parts and pieces. As monads have no parts, they can’t ‘fall apart’ or be ‘put together’. Thus their creation and destruction can only happen ‘super-naturally’, that is, beyond the purview of the natural order. This is a novel phrasing of the cosmological argument for the existence of god, but is not necessarily theological in character. It’s the same argument for why our modern physics can’t backwards infer earlier than the big bang — the entire natural order (space, time, matter, energy, cause and effect) break down, thus to speak of ‘super-natural’ causation can be read as similar. Our ‘natural explanations’ reach a limit when trying explain the very origin of nature itself: what was the cause of causality? What was there before time? Why did space begin where it did? There’s nothing spooky going on here, just the limit of an order of explanation — a misplacing of categories where they don’t belong or work. Likewise with the monads; we cannot think about their origination and destruction in terms native to the explanations of the causal, spatio-temporal, world of composite structures we study under the heading of ‘physics’, because they operate under different rules from classical physical ‘things’ (in not having parts, and thus not being ‘composed’ of anything else).
Because of these considerations, monads cannot affect each other, if by ‘affect’ here is meant a real transfer or exchange of parts, motion, states or properties. This is the first truly odd conclusion, that each monad is closed upon itself, without windows through which anything could come in or out.
“There is also no way of explaining how a monad could be internally altered or changed by any other created thing, since it is not possible to rearrange anything in it or to conceive in it any internal motion that could be started, directed, increased, or diminished within it, as can occur in compounds, where there is change among the parts. Monads have no windows through which anything could enter them or depart from them. Accidents cannot become detached, or wander about outside of substances, as the sensible species of the Scholastics once did. Thus neither substance nor accident can enter a monad from outside.” (§7)
The issue with ‘inter-monadic’ causation is not merely that they do not have parts to be jostled or transferred, but is also a deeper rejection of a certain view of causation generally. The Scholastic position Leibniz mentions here held that if I was to take a hot object, like a glowing piece of iron, and plunge it into cold water, the particular heat (this ‘right here and now’ instantiation of heat) in the metal would be transferred to the water. But this would mean that there was a moment, no matter how miniscule in terms of space and time, where there was a particular property ‘heat’ that had no bearer. To be transferred or transmitted is to be a moment in limbo between one’s origin and destination. Leibniz argues its absurd to say that a naked property can be in such a limbo: heat without anything being hot.
And this raises a problem: if each monad is partless, and cannot enter causal relations with any other, but needs to remain independent, then how are they differentiated? Leibniz maintains the principle of ‘the identity of indiscernibles’ — if there are two things between which not a single difference exists, then they are not two things at all, but one thing. This is an application of the principle of sufficient reason to difference itself: if there is a difference between two monads, then there must be a reason for this difference that sufficiently accounts for why they are different and not otherwise. But if monads do not have parts or shapes, in which way can they be differentiated? Or is there just one monad — a single simple substance that is twisted this way and that?
Leibniz solution is to bring in the order of ‘quality’ — each and every monad has, at each moment, a unique set of qualities that define a unique state that it is in. No two monads share the identical set of qualities at the same instant. Their qualities transform and change continually (piece by piece) such that each monad is defined from the past to the future by a sequence of qualitative transformations that make the monad what it is, and such that it is, in its differentiatedness, from all other monads. And since this collection of qualities, the moment by moment state the monad is in, cannot be explained in terms of real causal interaction, then each monad must have a ‘script’ of states that it runs through that have been ‘divinely coordinated’ such that it seems as if they are causally interacting; that is, there is a rational structure to their transformations that references things outside of it. Every monad at every moment has a unique collection of qualities forming a present state of that monad. However, it is not a chaotic or random flux — for each individual quality we can track its emergence and disappearance in relation to all the others and find a rational account — basically what we would call a ‘causal account’ except making no metaphysical assumptions about an actual causality, merely an as though causality.
So, monads are absolutely simple substances that nonetheless possess a unique combination, or multiplicity, and sequence of qualities that are constantly shifting.
Nice. But what does this mean? Leibniz does a pause here, and circles back. So, how are we supposed to think of a simple substance, without parts, that nonetheless has a near infinitely transforming set of qualities that make up a sequence of successive states? Aren’t these qualities just reintroducing parthood into the simplicity? And what does it even mean for a partless substance to be overflowing in transforming qualities?
“We ourselves experience a plurality within a simple substance when we find that the least thought which we apperceive encompasses a variety in its object. So all those who acknowledge that the soul is a simple substance must acknowledge this plurality within the monad…” (§16)
Well, we all know intimately exactly what this is like, because it’s what we are as minds. The mind is a simple substance that is filled with qualities, endlessly changing piece by piece in successive states. We generally call it ‘perception’ or ‘consciousness’. That the mind is ‘partless’ is demonstrated by the difficulty we have in parsing the question ‘if you divided your mind in two, what would be one half and what the other?’ — I can easily think about dividing my mind if that merely meant dividing my perceptions into a left half and a right half, but that is not dividing my mind itself, merely ‘grouping’ the qualities (colors and shapes and feelings and sounds) that currently populate my mind into two regions that I associate relative to more qualities that represent to my mind a body sitting in a chair that I have come to call ‘me’. The mind itself, despite always and everywhere being full of qualities (perceptions), which can be divided and grouped, is itself indivisible and completely simple. In fact, Leibniz very quickly drops the term ‘quality’ and begins using ‘perception’ instead (§14), which radically expands the meaning of that term, while at the same time giving us our concrete reference to the one monad we are intimately acquainted with: our own minds. More on this below.
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The question I want to raise here and explore concerns the countability of monads. For a given system of things, how to determine the amount of monads present? Each monad is perfectly unique, and differentiated by its present set of qualities/perceptions, which should give us everything we need to begin enumerating identities. I am not so much interested in calculating precise quantities, but ask more for the conditions that allow us to establish the principle whereby we can say “here, here is a monad”. We know if there is a person in the system, then there is at least one monad, because that person’s mind is a monad. In fact if there is an animal in the system we can also count one here. The only clear examples Leibniz gives of “here, here is a monad” in the Monadology are things we would perhaps count off as consciousnesses, with all their varying degree (which is indeed an important departure from the Cartesians who held only humans had minds — Leibniz is open to a wide spectrum of degrees of conscious beings).
So, the world appears to a bat just as much as it appears to me. Here are two perception bearing monads. One might be tempted here to think that a monad is some perceiving kernel enclosed in a complex material body — little cogitos driving biological machines. But this overlooks the fact that for Leibniz, everything is animals all the way down. Animals are made of smaller animals (an idea reeling from the invention of the microscope and the discovery of the microscopic organisms and cells swirling around everywhere). Thus, the number of monads in even your fingernail is infinite. Leibniz holds that:
“each portion of matter is not only divisible to infinity, as the ancients recognised, but also actually subdivided without end, each part into further parts, each of which one has some motion of its own”
“the machines of nature, that is, living bodies, are still machines in their smallest parts, to infinity.” (§64–§65)
This is a twist on the infinite divisibility of matter: it’s not just that matter is infinitely divisible, but that once you go beyond a certain point you’re just slicing something like cheese or tofu — some homogenous matter stuff — rather, in addition to being infinitely divisible, it also has heterogenous structure all the way down forever.
Combine this with perhaps the most beautiful passage of the Monadology:
“From this it is evident that there is a world of created things — living things, animals, entelechies, souls — in the least part of matter.
Each portion of matter may be conceived as a garden full of plants, and as a pond full of fish. But each branch of a plant, each limb of an animal, each drop of its humours, is also such a garden or such a pond.
And although the earth and the air interspersed between the plants in the garden, or the water interspersed between the fish in the pond, are not themselves plant or fish, yet they still contain them, though more often than not of a subtlety imperceptible to us.
Thus there is nothing uncultivated, nothing sterile, nothing dead in the universe, no chaos, no confusions, except in appearance. This is somewhat like what is apparent with a pond viewed from a distance, in which we see a confused motion and swarming of the pond’s fish without making out the fish themselves.” (§66–§69)
Down and down, forever and ever. So, in some system or local situation, we can count there being one monad if there is a person there, but that person’s body contain infinities within it, microcosms within microcosms within microcosms within microcosms, populated by ever simpler creatures, each with their own monad, existing in a milieu, and these microcosms are unending. We can subdivide the matter infinitely and keep finding them at ever smaller levels of description. And each and every one of these creatures in these microcosms is perfectly unique — that is, bearing at every moment a unique collection of qualities, or perceptions.
So, just to be clear, it seems that the answer to question of countability is ‘infinite in every direction’. Not only are these microcosms populated by tiny structured things each with a monad, each part of each of these structured things is itself a microcosm. This means that the microcosm itself is a monad, just like all of its constituents, because it ultimately is a part of a higher structured thing — the garden with the pond and the fish is itself a fish in another, larger, garden and pond. Much like how an image representation of a fractal, say, the Mandelbrot set, is composed of pixels on a screen, but each pixel can be ‘zoomed’ into to discover another complex image, itself composed of pixels that can be zoomed into, and so on unto infinity.
But how does this square with the initial, tangible, image we have been previously given; that our own minds are perfect examples of monads (simple substances with ever shifting qualities)? Is there really consciousness in the parts, of the parts, of the parts, of a grain of dust?
Yes, and no. Leibniz differentiates human consciousness from the kind of monad that may be associated with a potato on a number of grounds, chief among these being both memory, and awareness, or apperception. For us, it is not just the case that we have perceptions, we are additionally aware that we are having them, and this, for Leibniz, makes all of the difference. Every monad is filled with ‘perceptions’, but only what we would traditionally call ‘minds’ are additionally aware of them. This has the consequence that you have as many perceptions when you are unconscious as you do when awake, the only difference is whether or not you are aware that you are having them, and remember them.
‘Perceptions’, then, as a term is being given technical status. However, it doesn’t thereby lose its traditional referent, but instead what perception covers is expanded by the introduction of all manners of degrees. Beyond the extra layer of ‘awareness’, there is also the degree of clarity/distinctness or confusion of perceptions. To be dizzy or fainting is to lose a clarity or distinctness in one’s perceptions, and be greeted by confused sensations and forms (§21). At times this might track the degree of awareness: as we slip into unconsciousness our perceptions become more and more confused, less defined and individuated. But we can also be aware of confused perceptions simply. Elsewhere, Leibniz gives the example of listening to the waves at the beach. The sound of crashing waves is created by billions of individual pieces of water percussively colliding against each other, but for our awareness this chorus of individual sounds is represented as white noise. However, reasons Leibniz, to hear the combined sound is to hear each of its parts. The issue is we perceive the parts ‘confusedly’, and that’s what we call ‘the sound of waves’: the confused perception of billions upon billions of drops of water colliding with each other. If we couldn’t hear all of the drops, then we couldn’t hear the waves that is just their chorus. God, the infinite being, can ‘hear’ every individual, differentiated, drop of water just fine — we must make do with a confused perception of that multitude.
One can continue here: if asked why we can’t perceive atoms, one can reply that we can and do. If it is the case that the objects around us are composed of atoms, well, then, we are always seeing atoms. What we cannot do is differentiate them, one by one, like each individual drop of water in a water fall, but we nonetheless do perceive them, just not distinctly and clearly, but confusedly — as the material objects around us. Likewise looking backwards through time, or at much bigger scales. Want to witness the big bang? Look out the window — you’re in it. When we see buildings and cars and clouds and people and pigeons instead of the ‘sudden’ vast expansion of the universe and space-time, we perceive the latter confusedly in the form of the former. This is the case because everything around us is a direct effect of it, its unfurling realization — we see a figure confusedly in its shadow insofar as the figure is the direct cause of the shadow.
However, we need to remember that even trees or grains of sand have perceptions attributed to them, the shifting qualities of each monad. So, we’re dealing with a term with quite a large extension. Some clue in how we should understand this is given by Leibniz’s explanation of causality. Now, as we’ve seen monads cannot affect one another, they have no true causal connection, but they ‘perceive’ each other (in fact, every monad perceives every other) in greater or less degrees of clarity. I perceive (as well as being aware that I perceive) the plant on the desk clearly enough, but I also perceive, confusedly, the cells from which it is composed and the molecules from which they are composed (the green of the leaf and its shape). I also see confusedly the seed from which it grew, and the plant that formed that seed. My eyes don’t make all of this readily apparent, but my mind can reason through it all. The plant itself perceives all of this, as well as me and the sun and so on, but just not in terms of color (it has no eyes), nor in terms of awareness (it has no cognition or attention). But each of its states ‘picture’ or represent its environment and history at each moment. It is always in some state, and the components of its states (its ‘perceptions’) are rational references, or connections, to all of the other monads in the universe (though only ‘vividly’ the ones in its local situation)— which we can trace out and pick apart with our rational intellects.
“Now this interconnection, or this accommodation of all created things to each other and of each to all the rest, means that each simple substance has relations which express all the others, and that consequently it is a perpetual living mirror of the universe.” (§56)
Now, recall every single monad is running through its pre-harmonized, pre-determined script of successive states (collections of perceptions). Despite not having a real causality between them, they have, nonetheless, an ‘ideal causality’ that is based on an asymmetry in these ‘relations’ whereby each monad expresses all of the others. What we generally think of as ‘causal direction’ (a causing b) is that the references, or relations, have a greater degree of clarity when read in one direction rather than the other, this is all. That is to say that in a causal account, we grasp monad A as acting on B insofar as the event is perceived more clearly from the vantage of A and more confusedly from the vantage of B.
“The created thing is said to act outwardly insofar as it has perfection, and to be acted upon by another insofar as it is imperfect. Thus action is attributed to the monad insofar as it has distinct perceptions and passion insofar as it has confused perceptions.
And one created thing is more perfect than another when what is found in it serves to explain a priori what happens in the other; and this is why we say that it acts upon the other.” (§49–§50)
This is a tricky idea to hold in the head. I think the following example can perhaps show what’s going on here:
I decide to go get a glass of water from the kitchen, so I get up, walk over there, pick up a glass, fill it up, carry it back, and sit back down. Now, there are infinite monads involved in this little drama, as the structural complexity reaches down (and up!) to infinity. Billions upon billions of (or, infinite) state changes. However, when we grasp this ‘chunk’ of the universe with its collection of monads and their state changes, from which vantage point is this ‘event’ the most clearly ‘expressible’ for a rational intellect? My elbow is a little biological mechanism, it too has/is a monad. Its qualities and states change with everything else in this story. It runs independently through its script, swinging back and forth in space as I walk, for example. Insofar as my elbow, as a monad, references (perceives) every other monad in the universe, it could be taken as a ‘locus’, and the above story could be told totally from its vantage, taking it as a subject. However, this will become quickly a convoluted story. The elbow will stretch out and retract at seemingly arbitrary points, though of course clearly and rationally ‘effected’ by the nerves and tensions of the muscles and so on (those ‘characters’ in the story are reasonably distinct and clear from this vantage). But as our story goes on and on it becomes clear that we have massively disadvantaged ourselves by not being able to say things like “the elbow stretches out here as the arm reaches forward to allow the hand to grasp the glass”. That is, if we take the vantage of the whole arm, rather than just the elbow, our story begins to be easier to compress into a rational account. And we can compress further still if instead of just an arm, we take the motions of the entire body. But, still, our story is strangely convoluted (overflowing with sentences about brain activity and pulses in the central nervous system). The easiest way of giving a rational account is the one we began with: “I do this and this and this”. That is, of the billions of changes in qualities and states that occur in our story, the most efficient way of grasping it all is to assume the vantage of the mind associated with the body ‘doing’ all the things. When we have this kind of situation, we say that the mind ‘causes’ the body to act, the arm causes the elbow to stretch, etc etc, but not thereby committing to actual causal power of any of these isolated particulars. We are merely saying that if we think as though this is the case, we can grasp the countless changes in the most efficient way. But, in truth, every single ‘point’ is acting independently, and is uninfluenced by every other (my elbow independently begins swinging back and forth moving through space just now) — causality here is purely an exercise for the rational understanding.
This idea has an affinity with Occam’s Razor. The classic example for this latter principle is how the heliocentric hypothesis had the advantage over the geocentric insofar as it did not require ‘epicycles’ in addition to ‘orbits’ to account for the movements of Venus and Mars. In Leibnizian terms, all we have here is a change of vantage on the situation, from the Earth to the Sun, and with this a sudden greater clarity of rational account. But since the orbits of the planets all follow a rational order, any point within the solar system, taken as a vantage, will still draw a regular pattern of orbits, just of varying complexity. The geocentric calculations and charts are still the most efficient way of rationally understanding the position of, say, Venus on a given evening of the year if what we are interested in is its appearance to observers here on the Earth.
It’s worth pausing here for a second, because this image is really insane in a good way. Monads don’t interact, nor do they have shapes, so they are not little atom things flying around in space-time. However, they are ordered: each monad perceives all of the others, which it represents in its states. Some monads perceive some others more distinctly which means they are a ‘good’ vantage upon them when we try to rationally understand their states, both the former and the latter. There is an intellectual structure they are all arranged in. You yourself are one, single monad. Within you you perceive the entire universe, and everything within it. However, you only perceive some of the stuff of the universe clearly, the ‘objecty’ things around you within a certain range of scale (grain of sand, up to a building or mountain, depending on how good your eyesight is). You also perceive the planet at every moment, as well as a particular photon that has zigged its ways to the planet from the sun, as well as the origins of all the ‘objecty’ things around you, the soil the tree grew in from which the wood was taken to make the table, and drops of rain that fell on it, and so on — but all of that is confused for the eyes, you need a sharp intellect (and our collective centuries of intellectual theorizing) to even dimly grasp it. And then, what’s the difference between being the monad that is you, and being the monad that is your wisdom tooth? Or even your whole head? It just means to be in a position, a vantage, among the rational order of all of the monads such that you represent clearly a particular scale and depth of that order in the way we generally do as human minds, and for you to feature in the ‘subject’ position of thoughts that describe events at that scale and depth, in a region. ‘Seeing’ and ‘acting upon’ clusters of things that are roughly the right size. When I pick up a ball, I cause some errant electrons to have some adventure through minor static electricity, or something — but, to be a human mind is to intuitively act on things like the ball itself, taken as aggregate, not its individual atomic constitution, despite the fact that we can’t do one without doing the other, it’s just that an explanation of what is going on with this particular electron is going to be very ‘confused’ and blurry if I insist on including myself and my hand in it. It’s a confused vantage because the scale is all ‘wrong’. Not wrong in the sense of incorrect, but wrong in the sense that it just is a much more convoluted tale for the understanding than it needs to be.
Leibniz ends the Monadology with an ethic concerning human minds, morality, and God’s creation, but here I want to extract another ethic that emerged for me, following Leibniz all the way through this. Monads cannot be naturally created nor destroyed, and, as a monad, that means you have been and will be around forever. But everything we can point to, at any scale, is a monad — a certain perspective or vantage upon the universe in which the ordering of the monads, their relations and references, appears with a certain clarity or confusion. As people, we enjoy a pretty awesome vantage. Not only is a certain scale and depth of all the states of the monads given to us sensually, as colors and shapes and sensations, but we can also ‘clarify’ what initially appears to us as confused, we can rationally understand something of that order. One day I’ll die, which means this entire system of a body which my mind does such a good job of reflecting and explaining will fall apart. Since for Leibniz it’s ‘animals’ all the way down, death is an animal falling apart into millions of smaller animals, just as generation is when a tiny spermatic animal begins to pull structures (smaller animals) into its unfurling developing/organizing activity (§75). My wisdom tooth will sit in the dirt, and reflect, perhaps for another rational intellect, the person I was and every bite of food I’ve had since it began its little ‘pull all of the calcium into a tooth shape’ project in my jaw. The monad I am will still be somewhere, but not apart from the world, but still in it, serving to efficiently explain now a hole in the ground or a tuft of grass or even a small region of a forest or the knee joint of an ant, or the whole leg of a rat, or an entire bee colony, or the wax of the hive, or a layer of clay in the ground, or perhaps just a single carbon atom. I won’t be aware of any of this, because within the ordering of the monads I no longer occupy that very particular position, that particular vantage upon the universe of created things called a human mind which additional apperceives what it perceives. We’ve all been around since the beginning, and we’ll still be somewhere, still will be something until the end — it’s just for this little bit we have, despite all of the odds, managed to sit in this very particular vantage overlooking the universe so clearly. [I pluck out an eyelash, holding it between my fingers] — I could have just as easily been this.
Leibniz, G. and Strickland, L., 2014. Leibniz’s Monadology: A New Translation And Guide. 1st ed. Edinburgh: Edinburgh University Press.