Gottfried Leibniz on Time, Space, and Monads

What is the relationship between time, space, and the most fundamental elements of reality? This article presents certain elements of Leibniz’s answer to this question. Why only certain elements? One reason is the complexity of the answer Leibniz gives; another is the complexity of the relationship between time and space in itself.

This article begins with an introduction to this general topic before progressing to a discussion of the perspective of Isaac Newton and Samuel Clarke that Leibniz objected to. Leibniz’s own “relational” theory will be reviewed, along with some of the problems this theory presents in light of Leibniz’s mature philosophy, which centers around the concept of the monad.

Before discussing Leibniz’s theory of space and time, it might be useful to say something about the theory of space and time in general.

The concept of time is often developed on a certain analogy or disanalogy with space. The relationship between our experience of being in time and our ability to theorize time is complicated, not least because having a concept of a thing often requires us to conceive of what would happen if the concept changed. We add the concept to the world, then we imagine the world without it. What’s the difference?

It is worth further prefacing this discussion of Leibniz’s views on space and time with a note on his intellectual development.

At the time of his death, the vast majority of Leibniz’s work was unpublished. Why? This was partly due to Leibniz’s concern that his metaphysics would be misunderstood, both due to its incompleteness and its complexity. This was a meaningful risk for him, given that he saw the purpose of his life as lying not just in the successful prosecution of his philosophical investigations, but in a wide program of educational and social reform. To achieve this, he needed to retain the privileged political position of a court intellectual which he held throughout much of his adult life. In other words, reputation mattered a great deal, and it was in Leibniz’s interest not to allow an excessively radical philosophical work to jeopardize it.

Those who have attempted to follow the train of Leibniz’s thought have had to make sense of a large and sometimes incoherent posthumous corpus. The upshot of all this is that making sense of Leibniz’s theory of space and time involves, at certain points, making inferences for him given the overall shape of his philosophy rather than what he explicitly says.

Samuel Clarke, an avid follower of Isaac Newton, developed the theory of time and space that Leibniz was responding to, both directly and indirectly. It is worth noting that Leibniz and Newton were locked in a vicious and highly public spat over who invented calculus (the consensus now being that they made the discovery simultaneously).

What is the Clarke-Newton approach to space and time? First, that tim and space are conceptually and logically prior to the existence of things. Things need space and time to exist — they cannot exist outside of the conceptual space of space and time. Yet the inverse is not true — time and space do not rely on things for their concept or for their meaning. It is possible to conceive of time and space which is empty of objects, of things. Physical objects exist in space and time, not the other way around.

It is possible to delineate or otherwise pick out parts of space and time, but that is all we are doing – we are picking out parts of space and time; we are not finding sections that are already there. Space and time are continuous rather than intrinsically divisible — the parts we identify are our own imposition upon them. Space and time correlate to divine aspects – space correlates to God’s “immensity,” and time to God’s “eternity.”

Leibniz’s Criticisms of the Clarke-Newton Theory of Time

This picture of space and time seems, on the face of it, reasonably plausible, and yet Leibniz had deep misgivings about it. What were they?

The first criticism is concerned with the last point summarized above; that space and time correlate to divine aspects. In a response Leibniz wrote to Clarke himself, he poses the following problem: “if space is a property of God … space belongs to the essence of God. But space has parts: therefore there would be parts in the essence of God”. What exactly is the problem here? Implicitly, it is not in God’s nature to have parts. Associating space with God’s aspects means transferring the properties of space over to God in inadmissible ways.

There are other ways in which this undermines a Christian understanding of God’s nature. As Leibniz has it, “Sir Isaac Newton says, that space is an organ, which God makes use of to perceive things by. But if God stands in need of any organ to perceive things by, it will follow, that they do not depend altogether upon him, nor were produced by him.” This contradicts God’s being the cause of all things.

A second criticism draws on one of Leibniz’s most famous philosophical principles – that of the “Identity of Indiscernibles.” What is this principle? Jeffrey K McDonough, a contemporary philosopher, puts the principle in these terms:

“In the present context we may understand the PII (Principle of Identity of Indiscernibles) as ruling out the possibility of two things being distinct, but not distinct in virtue of some discernible property. It thus suggests that where we cannot identify a recognizable difference between two things or possibilities, those two are in fact only one — that is, as Leibniz puts it, that ‘To suppose two things indiscernible, is to suppose the same thing under two names.’”

Leibniz holds that the concept of absolute space violates the principle of the identity of indiscernibles. Roughly, the reason Leibniz gives for this hinges on the contentless nature of the concept of absolute space. The world “orientated” towards absolute space is no different than if it were not. The concept of absolute space is vacuous, and therefore contradictory. This is one of the surprising consequences of Leibniz’s identity of indiscernibles.

Leibniz offered other criticisms too, but these two are sufficient to illustrate the thrust of Leibniz’s point: absolute space and time are philosophically and theologically incoherent.

What of Leibniz’s own theory of time? First, Leibniz holds, contra Newton and Clarke, that time and space are relations. To illustrate this, he liked to use the analogy of the family tree, which is not itself “real,” but merely plots the relationship between real things (i.e, members of the same family).

Understanding Leibniz’s theory in more depth means understanding it in terms of one of his most notorious and difficult concepts – that of the monad. What is a monad? It is the defining concept of Leibniz’s “mature” metaphysics: that is, the set of philosophical positions which we held later in life. The monad is Leibniz’s answer to the question which arguably defined early modern philosophy from Descartes onwards: “what is (a) substance?” Leibniz’s work on the monad, titled Monadology, begins with the following characterization of the monad’s key features:

“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. And there must be simple substances, because there are composites; for the composite is nothing other than a collection or aggregatum of simples. 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”

Space, Time, and the Monad in Leibniz’s Philosophy: a Complicated Relationship 

The relationship between Leibniz’s theory of space and time and the Leibnizian monad is complicated. We can conclude this article by observing several specific complications.

For one thing, space and time cannot be conceived of relating different monads to one another straightforwardly. Whereas the relationships between monads are fluid and changeable, both time and space plot fixed relations. Moreover, at least by the end of his philosophical career, Leibniz denies that what reality consists in, most fundamentally, are objects. McDonough characterizes the implications of this as follows:

“Relations of relative distance and duration holding between bodies must therefore themselves be a step removed from monadic reality, and thus space and time must be, as it were, a second step removed from the most basic non-relational entities of Leibniz’s most mature metaphysics.”

In other words, Leibniz wants to characterize space and time as wholly relational, and yet space and time do not straightforwardly relate the most fundamental entities that exist.