3 Concepts From Leibniz: Monads, Possibility, and Human Understanding

What are some of Leibniz’s most important philosophical theses, and how do they intersect with one another?

Jun 4, 2023By Luke Dunne, BA Philosophy & Theology
leibniz concepts monads possibility understanding


Do all philosophical concepts require a total system to make sense of them? Is philosophy either totally self-sustaining, or a failure? The intellectual zeitgeist is arguably as anti-systematic as it has ever been in many areas of philosophy. This makes Gottfried Leibniz’s work seem especially untimely to the typical modern reader. Leibniz’s philosophical reputation is as a system builder, a philosopher whose intellectual projects are at least meant to integrate one another seamlessly.


Given this, it is difficult to understand certain elements of Leibniz’s thought in isolation. This article aims to expand on several aspects of his philosophy at once. It begins with a discussion of Leibniz’s view of human understanding. It then moves on to consider the monad – perhaps his most distinctive philosophical concept. It concludes with an analysis of possibility and infinity in Leibniz’s thought.


The Intelligibility of Things According to Leibniz

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Portrait of Gottfried Leibniz, Christoph Bernhard Francke, 1695, via Wikimedia Commons


Leibniz believed that the intelligibility of things had to be foundational: it is an indispensable, a priori principle of rationality that “there is nothing without a reason” or “nothing unintelligible happens”. This principle – known as the principle of sufficient reason – is one of the fundamental principles of reason held by Leibniz.


The other is the principle of contradiction, which Leibniz states thus: “nothing can at the same time be and not be, but everything either is or is not”. Beyond the boundary of the second principle – beyond the boundary of consistency – no sense can be made whatsoever. Within the boundary – the realm designated by the first principle – sense is guaranteed.


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Leibniz holds that our striving to make sense within this boundary is good in itself, both as a mark of our humanity and as a way of emulating God. Adrian Moore points out that, because our ability to theorize necessary, eternal truths inheres in the human condition, Leibniz also takes on a certain claim about perspectival knowledge – that knowledge from a certain perspective always reveals something of these truths, and so we ought to draw on past traditions. Leibniz was both by nature and conviction an eclectic.


Yet, this process of drawing on previous traditions has to proceed without losing sight of the grounds of such insights to the claim of eternal and necessary truths – metaphysics involves a priori qualification.


Leibniz’s Break with Descartes and Spinoza 

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Portrait of René Descartes, Frans Hal, 1649, via Wikimedia Commons


While previous philosophers like Descartes and Spinoza take metaphysics to be valuable in its own sake – a ‘mark of humanity’ or of ‘human excellence’, both had a much more fundamental reason for undertaking a metaphysical project. For Descartes, metaphysics was used in aid of science, and for Spinoza it was used in aid of ethics.


Leibniz goes further, claiming knowledge of “necessary, eternal truths” that “this knowledge alone is good in itself…all the rest is mercenary”. This is in tension with the basis of Leibniz’s thought, which is Christian – that is, a reflection of the culture in which he was embedded. There is nothing de-contextualized about Leibniz’s thought – he does not make claims on eternity in this way.


It is for this reason that Leibniz ascribes to God the conventional aspects of omniscience, omnipotence, and omnibenevolence. God is responsible for all that is ‘contingently the case’, which – in Leibniz’s system – meant everything which is the case in this possible world, but not others. For Leibniz, various states of the world are possible, but given God’s omnibenevolence, it follows that this possible world – the one we live in – is the best.


As Moore has it, if Leibniz’s attempt to make sense of things were to be successful, then it would be as successful as any attempt could possibly be – it would show not only how things are, but that things are how they are because there are cosmically forceful reasons why they could not be any other way. However, Leibniz’s system appears to run into a massive problem – the brute fact that the world is improvable.


The Monad

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Portrait of Gottfried Wilhelm Leibniz, anon, 1711, via Wikimedia Commons


Contemporary philosopher Adrian Moore summarizes Leibniz’s system succinctly as follows:


“The ultimate constituents of the world are individual substances, what Leibniz calls monads. These are minds, or mind- like. Each of them represents the world in some way. They include God, you, next-door’s cat, and countless much less sophisticated monads corresponding to various material features of the world. But none of them is itself, strictly speaking, material. […] For neither space nor time is an ultimate feature of reality…rather, space and time are features of how reality appears to certain of these monads. Leibniz is an idealist.”


Moore holds that we can see Leibniz, like Spinoza before him, as reacting to Descartes’ substance dualism – that is, to the division between matter and mind. Their responses are similar in the sense that they believe that whatever can be called ‘substance’ is both without parts and contains within it all the diversity of reality. To quote Leibniz himself, “The monad, about which we shall speak here, is nothing other than a simple substance which enters into compounds, ‘simple’ meaning ‘without parts’.” The concept of substance, on which Leibniz relies, is an old one.


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Bust of Aristotle, Lysippos, 330BC, via Wikimedia Commons


For Aristotle, substance was an answer to the question of ‘what is being’, or – posed somewhat differently – ‘what is truly real’. The Aristotelian criteria of being (which would become common sense in Europe during the medieval period) were twofold.


First, for something to constitute a substance, that something should be the subject of predication, rather than further predication. This is a way of distinguishing a substance from its qualities. Second, it should have the ability to act, not merely be acted upon. To call something a substance is to imply a certain form of activity.


Leibniz progresses from a very Aristotelian understanding of substance to the additional criteria of indivisibility, or unity – substance is really one being. Elsewhere, Leibniz adds other connotations, especially that of force – “I consider it to be somewhere between a power and an action”. Elsewhere still he adds the criterion of perception: “Your Electoral Highness asks me what a simple substance is. I reply that its nature is to have perception, and consequently to represent composite things.”


What is a Possible World? 

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Panorama of Leipzig (where Leibniz lived), 2013, via Wikimedia Commons


God is also a monad. However, God is a monad unlike any other, because God is necessary whereas all other monads are contingent, given that they rely on Him for their existence. God’s work is that of instantiation and the regulation of possibility:


“Given any non-Divine monad that exists in this world, there are therefore other possible worlds in which it does not exist. And there are other possible worlds in which non-Divine monads exist that do not exist in this world. We might put it like this: God’s creative act is to actualize some, but not all, ‘possible monads’”.


What is a possible world? We might assume it to be not merely a collection of possible monads, but an arrangement of some sort. However, there is much to preclude this in Leibniz. Moreover, there is much to preclude the existence of a monad in more than one possible world. Therefore, many sets of possible monads cannot constitute possible worlds, which Leibniz is committed to in any case because acknowledges incompossibility between monads (that is, mutual exclusion).


All monads have two qualities: they are ‘windowless’ and they ‘mirror the whole world’. Windowless means that “neither substance nor accident can enter [it] from without” – this is a kind of imperviousness. Each monad is “a world apart”, “whatever happens to each [monad] would flow from its nature and its notion even if the rest were supposed to be absent”, and “‘it is as if there were as many different universes [sc. as there are monads]’. It would not effect the existence of any given monad if, ‘nothing else existed but only God and itself’. As Moore observes, it follows from this that making sense of anything outside of ourselves relies on our ability to understand a kind of deep transcendence.


Leibniz on God’s Goodness 

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Portrait of René Descartes in a 1656 copy of his “Principia philosophiae.”, 1656, via Wikimedia Commons


For Leibniz (as for Descartes), it is God’s goodness which guarantees the possibility of any understanding. Indeed, this guarantee is located in the second quality of monads – that they ‘mirror the whole world’. Thus Leibniz explains:


“God first created the soul, and every other real unity [i.e. monad], in such a way that everything in it must spring from within itself, by a perfect spontaneity with regard to itself, and yet in a perfect conformity with things outside…. It follows from this that, since each of these substances exactly represents the whole universe in its own way and from a certain point of view, and since the perceptions or expressions of external things reach the soul at the proper time by virtue of its own laws… there will be a perfect agreement between all these substances, producing the same effect as would occur if these communicated with one another by means of a transmission of species or qualities”.


All that distinguishes a monad is its representation of the world – monads are differentiated by the fact that this representation is grounded in a particular point of view.


Comprehension is grounded in the perspectival aspect of representation. As Moore has it: “each representation is more distinct either the closer its subject matter is to the corresponding monad or the larger its subject matter is… If the question concerns something about which your representation is very indistinct, then you will need to apply effort of some appropriate kind to ‘reposition’ yourself and make it more distinct. And this may in practice, if not in principle, be beyond you.” Or, as per Leibniz: “[A] soul can read in itself only what is distinctly represented there; it is unable to develop all at once all the things that are folded within it, for they stretch to infinity”.

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By Luke DunneBA Philosophy & TheologyLuke is a graduate of the University of Oxford's departments of Philosophy and Theology, his main interests include the history of philosophy, the metaphysics of mind, and social theory.