To: Kathleen C.
From: Geoffrey Klempner
Subject: Leibniz's theory of monads
Date: 22 January 2007 10:05

Dear Kay,

Thank you for your email of 14 January, with your final essay for the Metaphysics program, in response to the question, 'Sketch the main features of Leibniz's theory of monads, with reference to the problems it was meant to solve. How successful is this theory in solving them?'

No doubt frustrated by the brevity of my account of Leibniz, I am pleased to see that you have done some research of your own.

I wish I had said something about the argument that, given that there 'must' be simples (although your riposte, 'Logically, there is no reason why we should ever reach a "smallest" unity' is pretty strong - Leibniz's 'There must be simples because there are complexes' at the beginning of the Monadology is on the face of it a terrible argument) the objects of our perception cannot be composed of 'extended matter' conceived as a substance, since extension is infinitely divisible.

Later, your question, 'If one unit is unextended how can ten or a thousand have extension?' misses the force of this argument. Monads are unextended because there is no such thing as 'spatial extension'. What we see as 'matter in space' is just a representation in the soul, a representation which is relatively clear compared to lesser monads. That is the point of Leibniz's argument.

Why would Leibniz say that there are an infinite number of 'substances', conceived as monads? As you say, according to Descartes, there are three types of substance, God, material substance and mental substance. However, one may regard a Cartesian soul can be regarded as an individual 'substance' in the Aristotelian sense, i.e. a bearer of attributes defined by its accidental and essential properties. What point, if any, would Leibniz be making in opposition to Descartes? Why can't Leibniz equally say that there are two substances, in the sense of types of substance, God and monads?

You say Leibniz chose not to 'incorporate his creation's choices into the universe through the process of selecting compossibles' but surely he would argue that he does. My choice to write to you today is part of my individual concept, and my individual concept is determined by God's choice of this world, amongst all the possible worlds that he might have chosen to create. The idea that monads are 'generated... by continual fulgurations from the divinity' makes sense only insofar as we conceive of the deity in time - i.e. from our limited point of view - whereas in reality god sees the world sub specie aeternitatis. This view, of monads continually depending on God's creative power is in agreement with Descartes' idea that finite material and mental substances exist only so long as God's creative power maintains them in existence. In that sense, as Spinoza observed, Cartesian souls or material objects are not true 'substances' but more like attributes of the infinite divine substance. Logically, monads are in a similar situation to Descartes' finite substances in that they cannot exist independently of a Deity.

It is possible to have another 'take' on Leibniz's 'perception' which downplays the mental aspect. Instead of seeing the universe as made of independent 'bits' assembled together, Leibniz constructs the universe out of perspectives. You can think of a perspective simply as a relational complex. For example, 'the view from the study window' exists independently of whether any conscious being is currently enjoying that view. If you add up the totality of 'views' or 'perspectives' you get the same result as if you add up the totality of bits (the tree on the left, the tree on the right, the house opposite, the window frame, etc. etc.), because in adding up the bits you also have to describe their spatial relations to one another.

Which reminds me that Russell's big point against Leibniz (in his book on Leibniz) was Leibniz's apparent refusal to recognize the 'reality' of relations, as a result of his insistence that every proposition be reducible to subject-predicate form. But from an ontological perspective, is it so clear that Russell's 'external relations' are easier to comprehend than Leibniz's 'perspectives'?

I am glad that you succeeded in finding something attractive about Leibniz's 'dynamic universe'. You might enjoy dipping into A.N. Whitehead, Russell's collaborator on Principia Mathematica, who takes the 'dynamic perspective' idea much further in his magnum opus 'Process and Reality'.

All the best,

Geoffrey