A third principle is given equal prominence in Leibniz’s earlier writings:
3. The Predicate-in-Subject Principle. This is stated in various ways, for instance: ‘when a proposition is not an identity, that is, when the predicate is not explicitly contained in the subject, it must be contained in it virtually... Thus the subject term must always contain the predicate term, so that one who understands perfectly the notion of the subject would also know that the predicate belongs to it’ (Discourse on Metaphysics). More succinctly: ‘in every true proposition, necessary or contingent, universal or particular, the concept of the predicate is in a sense included in that of the subject, praedicatum inest subjecto, or I know not what truth is’ (Letter to Arnauld).
This third principle has posed many difficulties to commentators, and Leibniz was himself aware of objections to it: in particular, it seems unable to deal with negative propositions, such as ‘No good person is unhappy’. He had intended the principle as a general theory of truth: the truth of a proposition is supposed to consist in the fact that it attributes to the subject a predicate which is already contained in its concept. Whether or not Leibniz still believed in the principle when he wrote the Monadology is a moot point. But it should be understood in terms of the following.
The complete notion
To every individual substance there corresponds a ‘complete notion’, which is given by the complete list of its predications. This notion identifies the substance as the individual that it is, and is the conception given in God’s mind when he chooses to create it. Since there is no truth about a substance that is not a predication of it, substances must be distinguished by their predications. To enumerate those predications is to give the whole truth about the individual to which they apply. Moreover, anything less than the whole truth will not identify the individual as the thing that it is; a monad can share any of its predications, short of the total list, with another monad. If God is to have a reason to create a given monad, therefore, it is only because he has a complete notion of it. The Principle of Sufficient Reason—which implies that there is a sufficient reason for the existence of each contingent thing— also implies that there is a complete notion for every substance.
If that is so, however, then the Predicate-in-Subject Principle is true, even if we ourselves could not make use of it. For God, at least, the truth of every subject—predicate proposition consists in the fact that the concept of the predicate is contained in the complete notion of the subject. One consequence of this is another famous Leibnizian principle:
4. The Identity of Indiscernibles. If a has all its properties in common with b, then a and b are one and the same. Hence, if a and b are not identical, then there must be some difference between them.
The converse of this principle says that if a and b are identical, then they have all their properties in common. It is sometimes known as Leibniz’s law, and is rarely disputed by modern philosophers. The Identity of Indiscernibles, however, is highly controversial, since it is used by Leibniz to prove the relativity of space and time, and to establish a metaphysical distinction between the world of substances and the world of their appearances.
God
Like the other rationalists, Leibniz accepted a version of the ontological argument for God’s existence. However, the proof works, he argued, only on the assumption that the concept of God contains no contradiction. We are entitled to this assumption, he supposed, since the concept of a being with all perfections (including existence) contains nothing negative which would contradict any of the positive predications.
Leibniz also arrives at the existence of God in a more interesting way, through the Principle of Sufficient Reason. The sufficient reason for the existence of contingent things cannot be found in other contingent things, which always demand an explanation for their existence. This explanation can be found only on the assumption that a necessary being also exists— a being which ‘carries the reason for its existence within itself’. And ‘this ultimate reason for the existence of things is called God’.
God is supremely good, and therefore must have created the best of all possible worlds. This conclusion is sometimes proposed in the form of another principle:
5. Principle of the Best. The actual world is the best of all possible worlds. ‘Best’ means ‘simplest in hypotheses, richest in phenomena’. The best world is an optimal solution to two simultaneous requirements: it contains as much reality (perfection) as possible, while being maximally simple and therefore intelligible.
The concept of a ‘possible world’ entered philosophy for the first time with Leibniz. It enabled him to formulate some of the intuitions about necessity and contingency which had proved fundamental to the arguments of Descartes and Spinoza, but which neither of them had made fully clear.
Contingency
The truth of the proposition that Caesar crossed the Rubicon consists in the fact that the predicate ‘crosses the Rubicon’ is contained in the complete notion of Caesar. But in that case, someone might object, it is true by definition, and therefore necessary, that Caesar crossed the Rubicon. What remains, then, of the distinction between necessary and contingent truth?
There is indeed a sense in which it is necessarily true of Caesar that he crossed the Rubicon: anyone who did not do so would not be Caesar. Still, Leibniz argues, Caesar might not have crossed the Rubicon, for there might have been no such individual. Caesar’s existence is a contingent fact, dependent on the will of God. Another way of saying this is that there are possible worlds in which there is no such person, and in which therefore the event of Caesar’s crossing the Rubicon does not occur. Hence the proposition that Caesar crossed the Rubicon might have been false.
A necessary truth, by contrast, is one that is true in all possible worlds; and the marks of a necessary truth are that it is universal and knowable a priori by finite minds. Only God can know a contingent truth a priori, since only God possesses the complete notion of contingent things. We must know such truths a posteriori, by investigation and experiment, if we are to know them at all.
This account of necessity and a priori knowledge indicates a radical division between God’s view of the world and our view. God knows everything a priori, and it is this a priori aspect of things that is captured by the controversial Predicate-in-Subject Principle. In creating contingent things, God is also creating the possible world that contains them, and therefore so ordering them as to form a consistent and harmonious totality. Indeed, Leibniz argues, each individual monad is like a mirror of the universe that contains it, and the universe itself is contained implicitly in all its parts.
Freedom and necessity
What place is there, in Leibniz’s system, for human freedom? In the Discourse on Metaphysics he writes as follows:
We must distinguish between what is certain and what is necessary. Everyone grants that future contingents are certain, since God foresees: them, but we do not concede that they are necessary on that account. But (someone will say) if a conclusion can be deduced infallibly from a definition or notion, it is necessary. And it is true that we are maintaining that everything that must happen to a person is already contained virtually in his nature or notion, just as the properties of a circle are contained in its definition.
Yet, he argues, human freedom is a reality, since although it is necessary in this sense that Caesar should cross the Rubicon, it is still not impossible that the event should not happen. God chose the best possible world, and in that world Caesar crosses the Rubicon; but there is no contradiction in supposing that God had chosen otherwise.
But surely God, being supremely good, must choose the best of all possible worlds—any other choice is incompatible with the nature of God. And in what sense am I, created according to God’s complete notion of me, free to do other than I do, when what I do is contained in my notion from the start? Leibniz seems to say that there are two kinds of reason. In a mathematical proof reasoning necessitates the conclusion. In reasoning ab
out what is best to do, however, our reasons ‘incline without necessitating’. Such are God’s reasons for creating the actual world; and such are our own reasons for behaving as we do. It is in this sense that both we and God are free.
Most commentators have found Leibniz’s treatment of free will obscure at best; part of the problem is that Leibniz has two contrasting ways of envisaging the individuality of monads.
Activity and vis viva
Monads are individuated in God’s mind by their complete notions. But the complete notion merely lists the predicates of a monad and says nothing about the link between them. Looked at in another way, each monad can be seen as a centre of activity, whose perceptions are generated successively by a living force, or vis viva. Like Spinoza, Leibniz was impressed by the substantial unity of organic beings, and believed that we observe in them, from another perspective, the individuality that is revealed in a timeless way to God. He sometimes writes of the conatus of individual substances and defended a theory of dynamics which gave pride of place to the living force in things, as opposed to the ‘dead force’ or momentum that features in Cartesian physics. In defending this idea, Leibniz introduced the concept of kinetic energy into mechanics, and thereby set physics on a new path.
The active principle enables us to individuate monads, even though we do not possess their complete notions. I can identify the individual substance that is Caesar in terms of the living force that propels him, without already predicating of him that he will cross the Rubicon. The active principle binds Caesar’s predicates together, and inclines him from the outset towards the decision that he will one day make, to cross the Rubicon—inclines, but does not necessitate.
Leibniz also refers to the activity of monads in another sense, familiar from Spinoza: a monad is active to the extent that its ideas are ‘distinct’, passive to the extent that they are ‘confused’. To understand this aspect of Leibniz we must turn to the theory of aggregates.
Aggregates of monads
In speaking of organic things we are not, as a rule, talking of individual monads. Every living organism is an aggregate of many monads. What binds them together, and what enables us to speak of one organism, when we have a plurality of simple individuals? It seems that the original problem that motivated Leibniz—the problem of accounting for the actual individuals in our world—remains with him.
Leibniz has recourse to the theory of ideas, which he inherited from Descartes. Each monad has perceptions or knowledge, which may be more or less clear and distinct, and more or less adequate.
When I can recognise a thing from among others without being able to say what its differences or properties consist in, the knowledge is confused. It is in this way that we sometimes know something clearly, without being in any doubt whether a poem or a picture is done well or badly, simply because it has a certain something, I know not what, that satisfies or offends us. But when I can explain the marks which I have, the knowledge is called distinct. And such is the knowledge of the assayer, who discerns the true from the false by means of certain tests or marks which make up the definition of gold.
Distinctness, so defined, admits of degrees, since the notions that enter into the definition of something themselves stand in need of definition. Only when everything that enters into the definition of a thing is known distinctly, can the knowledge of the thing be called adequate.
What then is the relation between an idea and its object? For example, what happens when I perceive something? Nothing is passed to me from the thing perceived; yet there is a sense in which all my perceptions represent the world around me. They do this because the predicates of other monads unfold in harmony with mine: each of my perceptions corresponds to perceptions in surrounding monads and enables me to infer, with a greater or less amount of confusion, what is going on in them. This is guaranteed by another Leibnizian principle:
6. The Principle of Pre-established Harmony. Each monad has a ‘point of view’ on the world, defined by the totality of its perceptions; and because our perceptions evolve in harmony with each other, my perceptions can be treated as representations of the objective order.
Another way of putting this is to say that each monad ‘mirrors’ the universe from its own point of view. As Leibniz writes in the Monadology: ‘the interconnection or accommodation of all created things to each other, and each to all the others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual living mirror of the universe.’
How then are monads related? Such influence as there is between monads is only ‘ideal’, an effect of God’s ceaseless intervention. Nevertheless, monads can have a more or less clear idea of each other and of their situation—as I have a clear idea of my body, even though I do not know how it is composed, and therefore even though my idea of my body is not distinct. The varying clarity and distinctness of our perceptions can be understood as defining the ‘distance’ between us and surrounding things. And we can speak of being ‘affected’ by those things, to the extent that our perceptions give us a clear idea of them.
In each organism there is a ‘dominant monad’, distinguished by the clarity of its perceptions of all the others; and this dominant monad is the source of the organism’s unity. Leibniz, following Aristotle, describes this dominant monad as the form or ‘entelechy’ of the body; it is the animating principle or soul. In some way that Leibniz does not succeed in explaining, it binds the aggregate of monads into a quasi-substantial unity: it provides a vinculum substantiale—a ‘substantial chain’—making a new quasi-individual from the simple individuals of the human body.
The appearance of monads
That is confusing enough. But matters are made worse by Leibniz’s growing conviction that the appearance of the world is organised and understood in ways that do not represent the underlying reality. The familiar world around us appears ordered in space and time; it contains extended and durable things, which interact and obey causal laws. Yet monads are not extended—perhaps they are not ‘in time’ in the way that physical objects are. Moreover, they do not interact in the way that physical objects appear to interact, according to causal laws which are established a posteriori, by observation of the physical world. Such laws do not describe the activities of monads, but only the regular connections in the world of appearance, which are the by-product of transformations most of which we do not observe.
Thus, if I see a car passing my window my perception constitutes a state of this monad; this state mirrors the states of the monads which collectively constitute the car, as they are then disposed, in such a way that, to my confused perception, a car is represented in a state of motion. The perceptions of individual monads harmonise, and the phenomenal world which they ‘perceive’ obtains coherence because of the preestablished harmony, according to which the histories of individual monads proceed according to successive ‘mirrorings’ of the whole of things. God established this harmony at the creation, monads then proceeding according to their own individual inner momentum, yet in such a way as to share the collective illusion of a common physical world, in which they participate and of which they have experiential knowledge. Once established, the harmony proceeds forever: it no more needs the intervention of God to see that the laws of the universe appear to be obeyed from any particular point of view, than it needs the intervention of the watchmaker to ensure that two perfectly made watches, once wound up, will go on keeping time.
Leibniz also argued against Newton (through Newton’s representative Samuel Clarke), in favour of a relative as opposed to an absolute view of space. If space is absolute, and possessed of reality over and above the spatial relations between individuals, then the whole universe might be moved through space without discernible change. But then consider the position of the universe as a whole. Why should it be situated in one area rather than another? This question can have no answer. By the postulated nature of space, there will be no discer
nible difference between the two arrangements. Hence there is no explanation of the actuality of either; which violates the Principle of Sufficient Reason. Hence space must consist in the totality of spatial relations between objects. And if one asks for a definition of a point in space, Leibniz says, he can provide it by showing what it is for two objects to occupy the same point. Two objects occupy the same point in space if they stand in the same spatial relation to all other things.
But now what of spatial relations? What we perceive as a relation between A and B consists in fact of particular modifications of A and of B. To take an example: John’s being taller than Henry consists in two facts; first that John measures six feet, secondly that Henry measures five. Thus what we perceive as spatial relations are really certain modifications of monads. These could be called their ‘space-generating’ properties; Leibniz referred to them as their individual ‘points of view’. The familiar world that surrounds us appears spatial, even though monads have no extension and indeed, strictly speaking, no spatial properties at all. Space, as a system of relations, can only be an appearance; however, is not just any kind of appearance. Although when we perceive things as spatially organised, we do not perceive them as they really are, space is still to be distinguished from a mere hallucination. This is what Leibniz meant by describing space as a ‘well-founded phenomenon’.
With this phrase Leibniz introduced one of the crucial concepts underlying the philosophy of Kant. The physical world was described as ‘systematic appearance’. On the Leibnizian system, the whole physical world turns out to be a well-founded phenomenon. Which is to say that the dynamic and static properties of matter, its spatial and even its temporal organisation, and finally the causal laws which govern its behaviour, are assigned by Leibniz to the world of appearance.
A Short History of Modern Philosophy: From Descartes to Wittgenstein, Second Edition Page 9