A Short History of Modern Philosophy: From Descartes to Wittgenstein, Second Edition (11 page)

Monads

Every entity is either composite or simple, and simple entities do not contain parts. It is the simple entities that are the true substances, from which all other things are composed. These simple entities cannot be extended in space, since everything extended is also divisible. They are not to be confused, therefore, with the atoms of physical theory, and can best be understood in terms of their one accessible instance—the human soul, which is neither extended nor divisible, and which seems to be self-contained, simple and durable in exactly the way that a substance must be. Such basic individuals Leibniz called ‘monads’; and although the soul is our clearest example, there are and must be other kinds of monads, which do not share our distinguishing attributes of rationality and self-consciousness.

Leibniz’s theory of monads (the ‘monadology’) contains three parts, being the theories of the monad, of the aggregates of monads and of the appearances of monads. These tend in three separate directions, and much ingenuity was needed in order to attempt a reconciliation. The theory of the monad can be briefly summarised in the following six propositions:

1. Monads are not extended in space.
   
2. Monads are distinguished from one another by their properties (their ‘predicates’).
   
3. No monad can come into being or pass away in the natural course of things; a monad is created or annihilated only by a ‘miracle’.
   
4. The predicates of a monad are ‘perceptions’—i.e. mental states— and the objects of these mental states are ideas. Inanimate entities are in fact the appearances of animated things: aggregates of monads, each endowed with perceptions.
   
5. Not all perceptions are conscious. The conscious perceptions, or apperceptions, are characteristic of rational souls, but not of lesser beings. And even rational souls have perceptions of which they are not conscious.
   
6. ‘Monads have no windows’—that is, nothing is passed to them from outside; each of their states is generated from their own inner nature. This does not mean that monads do not interact; but it does mean that certain theories as to
   how
   individual substances interact are untenable.
   

Those propositions follow, Leibniz thinks, from the very idea of an individual substance, once the idea is taken seriously. But they can also be derived independently, from certain metaphysical principles which it would be absurd to question.

Principles

Leibniz’s rationalism is displayed most vividly by his guiding principles, which he held to be at one and the same time laws of rational thinking and deep descriptions of reality. We need only follow these principles in order to arrive at a description of how things are—indeed, of how things
must
be. Naturally, this description of the world must be compatible with natural science. But science can be incorporated into metaphysics, Leibniz believed, once it is seen that scientific discoveries concern the ‘phenomena’ and not the underlying reality. Natural science is the representation of the world as it systematically appears, while the world as it really is can be known only from the self-evident principles of rational thinking.

There are two supreme principles, which Leibniz treated as axiomatic to the end of his philosophical career:

Corresponding to those two principles there are two kinds of truth: truths of reason, which depend upon the first principle, and truths of fact, which depend upon the second. Truths of reason are necessary, and their opposite impossible; truths of fact are contingent, and their opposite possible. Leibniz’s rationalism is reflected in his belief that for every truth of fact there is a sufficient reason, so that there is no
bare
contingency in the world, and the structure of reality conforms to the principles of rational argument.

A third principle is given equal prominence in Leibniz’s earlier writings:

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 about 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.