To: Yasuko S.
From: Geoffrey Klempner
Subject: Reasons for Leibniz's theory of monads
Date: 2 May 2007 10:30

Dear Yasuko,

Thank you for your email of 30 April, with your essay in response to the University of London question, 'What is a Leibnizian monad? What reasons does Leibniz provide for his claim that such monads exist?'

You have given a clear account of the theory of monads, indicating the main reasons why Leibniz holds this theory.

I have some thoughts about the question itself, and would also like to suggest some additional aspects of the monad question which are worth considering.

As you know, Leibniz published very little. The 'Monadology' presents his views in a simplified form, suitable for amusing the courtiers of Hanover but unsatisfying to the more inquisitive philosopher. Additional arguments are to be found in his scattered letters. For example, the Oxford Companion to Philosophy article on Leibniz quotes from his correspondence with de Volder. There is no way a student can study more than a fraction of Leibniz's voluminous correspondence so you have to rely to some extent on secondary literature to point out the most significant statements.

It is notable that the essay question asks 'What reasons does Leibniz provide...?' rather than the usual formula, 'What arguments does Leibniz give...?' There is no place where Leibniz laid out all his arguments for monads. The wording of the question gives you a bit more license to give 'Leibniz's reasons' even though there may be no particular passage where he explicitly states these reasons. In other words, what you are being asked to do is articulate the monad theory, and explain why Leibniz believed it.

One additional point to make about the question is that Leibniz does not merely claim that 'monads exist', but that nothing exists apart from monads. Monads are the only thing that exist.

Your explanation of the argument about simplicity and complexity is nice and clear. A point that I would make is that it looks at first as though Leibniz is relying on a blatant fallacy: 'There must be simples because there are complexes.' This fallacious because in stating that there are 'complexes' Leibniz is simply assuming what he has set out to prove, that it is not the case that existing things can be divided ad infinitum. In other words, the retort would be, 'There are no "complexes" in your sense.'

In his defence Leibniz would argue that in order to exist, an entity must exhibit 'true unity'. True unity cannot be found in infinitely divisible matter. So this is the real core of the argument. (I am only repeating what you say, but showing the 'logic' of the argument more clearly.')

What other reasons can be found for the monad theory?

The fact that monads provide a solution to the problem of mind-body interaction is important. It is incomprehensible how a Cartesian soul can interact with matter. Leibniz was not the first to consider that the apparent causal interaction between mental and physical can be explained by the theory of 'occasionalism' put forward by Malebranche. However, the monad theory is a significant advance on Malebranche's view because it explains how the states of a monad are a causal consequence of its previous states.

This brings us to the most significant way in which Leibniz departed from Descartes' view of physics. Leibniz criticized Descartes account of material substance on the grounds that it fails to explain the phenomena of force and inpenetrability. Cartesian physics is based on motions of volumes defined in geometric terms. As a result, Descartes was led to the idea that an impulse from a non-material soul can alter the direction of motion of 'animal spirits' without applying any physical force. However, this is impossible in Newtonian physics, which is based on the conservation of energy rather than the conservation of momentum. Leibniz believed that his monad theory was able to account for the aspect of 'force' which is not visible, but necessary in order to account for the phenomena which we observe.

When we observe the motions of material objects, we do not see the forces that are at work. Yet there must be such forces, in order to account for the observed laws of motion. You can't do this, as Descartes tried to do, by means of geometry alone. The actions of monads, each unfolding according to its individual concept, seem to provide the crucial explanation which is missing from Descartes' account of the interactions of material objects. I think that this was a very important consideration for Leibniz.

There are two further reasons which should be mentioned.

Russell, in his book on Leibniz, argued that the monad theory followed from Leibniz's PIS (predicate in subject) principle. Leibniz held this principle, Russell believed, because he wasn't able to grasp the idea of a 'relation' between objects, as something which logically cannot be reduced to predicates of the two objects. However, it is one thing to show that a particular theory can be deduced from a given premise, and quite another thing to claim that this IS the reason why the theory is held. It could equally be argued, in the case of Leibniz, that he held the PIS principle because he had independent reasons for holding the monad theory. So Russell is wrong in his simple characterization of the motivation for Leibniz's theory. Or, at least, the case hasn't been proved.

There is another reason for the monad theory which I think is significant. We can see this if we compare Leibniz's theory of monads with Berkeley's immaterialism. Berkeley's dates are later than Leibniz, but it is arguable that Leibniz's theory is the more sophisticated.

In Berkeley's theory, to exist is to 'perceive or be perceived'. All that exists are God, finite spirits (ourselves) and the perceptions in God's mind which we share. Why didn't Leibniz consider this possibility? On Berkeley's theory, just as on Leibniz's theory, physical objects are merely 'phenomena' or appearances. What is real are souls. The crucial defect in Berkeley's theory, from Leibniz's point of view, would be that phenomena are pure objects of perception which do not correspond to any subject. They are, in effect, merely a show which God puts on for our benefit. Whereas in Leibniz's theory, every observable phenomenon corresponds to an existing entity with its own point of view, as indeed we are ourselves.

As it stands, your essay provides a clear and straightforward answer to the question. The additional points I have mentioned are merely to give you something to think about, which might or might not be useful depending on what questions come up in the exam paper.

All the best,

Geoffrey