Confused about Leibniz’s theory of monads

Vicky asked:

I am confused at Leibniz’s concept of matter and monads and their relationship to one another. So from what I have got so far, and is confusing me, is that bodies are the repetition of monads, simple substances, since nothing else exists. Therefore in order to have an extended body, something extended must exist, the repetition of which will give us extension. But this contradicts the properties of monads which are unextended, without size, shape, dimension, virtually out of existence, so how can the repetition of that which has no extension give extension?

On the other hand, the infinite divisibility of matter means we can never arrive at the ultimate unit of our division. How can that which is continuous be made up of discrete parts? If the division were finite we should find that our ultimate unit would be extended entities and not monads.

Hence the concept of the infinite divisibility of extended matter denies the possibility of ultimate units; we can never have monads out of which matter is said to be made.

The unlimited, or the ‘continuous’, cannot be composed of units however small and however many.

So if we begin with monads as unextended units we can never get extension; and conversely if we begin with an extended body we can never arrive by division at the monads which are supposed to constitute the body.

Why is Leibniz called an idealist when he talks of matter?

Any clarification or help would be much appreciated!

Answer by Jürgen Lawrenz

No need to be ashamed on being confused about Leibniz’s monads. There is a long history of confusion about them, even among scholars. In part this problem arose because of the publications history of his works and also because some of Leibniz’s explanations are in (apparent) conflict with each other. Above all the problem lies with acceptance of his ‘Monadology’ as his central statement of the theory, which was not Leibniz’s intention. But for 300 years, we believed it on his posthumous editor’s assurance. Hence all the ambiguities.

So to start with: The monad is not a thing that exists. As Leibniz says, it is a simple substance, which means it cannot be divided. It follows that ‘The Monad’ is a purely theoretical construction. But as a creation by God, it has certain attributes that lend themselves to making monads (important to note the plural!) real existents.

Those attributes are force (two kinds: active and passive), appetition and perception. In modern language, quite permissible, you can think of a monad as a field of force either positive or negative, meaning its force may expand or be inert. Appetition is their desire to exist (in German ‘Daseinstreben’). But since one monad has no existence, it must congregate with other. This is where perception comes, which is the recognition of itself in relation to others. You need not assume this to be consciousness. It means nothing other than that monads, being zero dimensional, cannot intermingle, but they can attach. It is not as outrageous as it sounds. In fundamental physics there is a veritable zoo of particles with zero dimension, zero momentum etc. But in experiments they leave traces of their force that we can detect. Which is why the monad theory seems such a curious premonition of things Leibniz could know nothing about.

Now I’m going to ask you to imagine such particles. For convenience, let them be four kinds of marbles. If a million of inert marbles stick together, they will generate an impression that they are dense, rigid, solid – in a word ‘matter’. If a million active monads stick together, they will generate the impression of being an ethereal thing, such as a ‘mind’. Since there is an infinitude, however, each unique, you never get 100% solid or 100% etherial, but always something between these limits. You are therefore entitled to say that any collection of monads in which a preponderance exhibits inertia, will be perceived as ‘matter’.

Now take notice that ‘perceive’ is the operative word. This is where things become very difficult. Since all this monadic stuff is zero-dimensional, it cannot be hard, solid, rigid etc. in any objective sense. It is hard, solid, rigid etc. to a perceiving agent. The way you need to understand this is as follows: When you start your day in the morning, you are starting motions of your body through a colossal obstacles course: furniture, trees, houses, cars etc. You can’t just walk through them. On the other hand, a dust mite lodged in your clothes might well see nothing to stop it from crawling through most of the material impediments that force you to go around them. A neutrino might go right through all of it in a straight line!

This is the basis of the estimation of Leibniz as an idealist. I propose to you this is wrong.

Although perception is the key, it perceives something real, namely the collective FORCE inherent in all these things. So when the collective monads of your body try to go through a glass door, they are physically repulsed by the inert force of the glass. In other words: Leibniz’s monadic theory is a sort of ‘pointillist’ theory of forces in the world, each point endowed with the aforementioned attributes. In order to actually exist, they must collectivise in their millions to make up a perceivable force.

Infinite dimensions enter the picture as per the example I just gave. Leibniz assumed that in a dimension below the one we live in, another universe could exist. Not the same, but again created by monads. To them we don’t exist, and they don’t exist for us; and we have no means of communicating. In his day, microscopic cells were first discovered, which gave him that idea.

One more step: As monads form collectives, you will understand from the four attributes (or ‘laws’ as Leibniz prefer to style them) that the possibilities for different kinds of things is also infinite. Therefore Leibniz assumes that God played in his mind all these infinite possibilities to see which is the richest of all these possible world, and in the end gave the nod (permission to actualise) to those collectives which now comprise our universe. Logically therefore ours must be the best possible world!

There is much more to it, but I hope this answers at least your most pressing and immediate needs!


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