What Are Monads? Leibniz On the Most Fundamental Substance

What is the most basic kind of thing? This article focuses on an attempt to answer this question: the monad. This attempt comes from Gottfried Leibniz, one of the most significant Early Modern philosophers.

This article begins with a discussion of why the monad is philosophically interesting and sets out Leibniz’s purposes for postulating the existence of the monad. It then looks into the monad’s place within the concept of substance more broadly. The article ends by outlining the two central features of monads — simplicity and activity.

Why are monads interesting, besides whatever interest we might have in Leibniz’s work for its own sake? Philosophy often seems to be an attempt to give an explanation of what really is, as opposed to how things appear to be. Arguably, this is the most traditional task of philosophy – the earliest Greek philosophers understood this task in a way not dissimilar to Leibniz, as the pursuit of the most basic substance in the universe.

The impulse here is to take a world that we perceive to be full of diverse, changeable things and to discover what, if anything, is simple and unchanging. The search for that which is unchanging in spite of the daunting force with which change makes itself known in our ordinary lives is a profound one. This tendency to find what is unchanging is so strong that it can manifest as a religious impulse in the proper context.

The monad is interesting because it is an attempt to resolve this desire. Among the various attempts, this one was especially notable for taking place when the natural sciences and mathematics were starting to resemble what they look like today.

The History of Substance

The purpose of the concept of the monad is to create a concept that encapsulates what is metaphysically prior, or basic. Often, this task is paraphrased as the search for simple substances. But what is a substance?

Aristotle first formalized the concept of the substance, which Leibniz took up as what has come to be known as “Aristotelian substance.” The Aristotelian analysis of substance gives it two main components – form and matter.

Form is the “shape” or “structure” of matter. Howard Robinson summarizes three further elements of the Aristotelian conception of substance in the following terms:

“Being objects of predication but not being themselves predicable of anything else (at least, not in the way entities in the other categories are: see the problem about attribution to location above). Being able to receive contraries (4 a10). A substance can go from being hot to being cold, or from being red to being blue, but the instance of blue in an object cannot similarly take on and lose a wide range of attributes. If substance did not exist it would be impossible for things in any of the other categories to exist. There could be no instances of properties if there were no substances to possess them.”

Leibniz takes this Aristotelian idea and augments it. It is fair to say that his conception of substance is not utterly at odds with the Aristotelian notion of a substance. One of the primary claims Leibniz makes is regarding the unity of the monad as a necessary condition of being a basic substance.

The Monadology, a work substantially focused on the idea of the monad, begins in the following way:

“1. The monad, of which we shall speak here, is nothing other than a simple substance which enters into composites; simple, that is to say, without parts. 2. And there must be simple substances, because there are composites; for the composite is nothing other than a collection or aggregatum of simples. 3. Now, where there are no parts, neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature.”

It seems intuitive that the most basic thing should not have any parts – if it did, then those parts would be more basic than it! To put the point another way – if this simple thing had parts, it could be divided even further. It would follow that the thing into which our original substance had been divided was instead itself the most basic substance. The division can continue ad nauseam until we eventually come to something that cannot be divided. In short, the most simple substance will have no parts.

Monads Are Not in Space

The monad, the most simple substance, does not have an extension. What does extension imply? In this context, extension always refers to “extension in space” – something’s capacity to take up some amount of space.

This might seem curious. After all, it was mentioned at the outset that Leibniz’s philosophical project was formed by the scientific climate in which he lived and directly participated. In fact, a large part of Leibniz’s project is focused on developing a metaphysical architecture on which the emerging physical sciences could be based.

The apparent departure from the world of tangible things which characterizes Leibniz’s philosophy should not be understood to run against that. As modern-day Leibniz scholar Maria Rosa Antognazza has it,

“Simple, immaterial, non-extended, indivisible entities are the condition of the existence of composed, material, extended, divisible entities. The world of extended bodies studied by physics is ultimately intelligible only if we postulate metaphysical entities which must exist in order for those extended bodies to exist, at least in the minimal sense of being ‘something’ (whatever that is) as opposed to nothing.”

In The Monadology, the monad is defined around the concept of unity. Elsewhere in Leibniz’s authorship, other elements of the monad are emphasized instead.

Notably, one of these other elements is that the monad should be defined in terms of activity. The element of monadic activity is central to how the monad is defined in Principles of Nature and Grace, along with further papers towards the latter half of Leibniz’s life. Consider the following quote from one of these later works, entitled On Nature Itself:

“The substance of things itself consists in the force of acting and being acted upon…from this one can conclude that there must be found in corporeal substance a primary entelechy, or a first subject of activity, namely a primitive motive force … And it is this substantial principle itself which is called force … And it is this substantial principle itself which is called soul in living beings, and substantial form in other beings, and insofar as it truly constitutes one substance with matter, or a unum per se, it makes what I call a monad.”

There are various elements of the monadic activity that are worth taking a moment to clarify. Evidently, it was important to Leibniz that monads are both active and the recipients of action. Yet, given that monads are created rather than divine, they must have only a limited active power.

Monads and Forces

Monads should be thought of in terms of forces: that is, in terms of focused exertions of influence. Another element of activity needing clarification is that these primitive active and passive powers are not to be conceived of as parts of the monad. For, if the active elements of a monad were parts, then the entire purpose of describing the monads as a simple substance without parts would be fatally undermined.

What are these elements, if not parts? At one point, Leibniz calls them “abstractions,” meaning that they are elements of our analysis but not elements of the monads themselves. In other words, the active and passive elements of the monads cannot be distinguished or simplified from the monads, not even hypothetically. We can focus on them but not conceive of them as detached from the monad.

Lastly, it should be stressed that these forces are not physical forces. To follow Antognazza, “What is ultimately real in the Leibnizian universe is not extended stuff but powers or forces which are manifested derivatively in natural phenomena.”