Russell provides another colourful description of the next philosopher, referring to Leibniz as “one of the supreme intellects of all time”, but not admirable as a human being. He created two systems of philosophy: one which he thought would win him the acclaim of powerful and influential people, and another which he thought would make him unpopular, and which he did not publish. Russell believed the latter to be far superior.

Infinite Substances

Regarding his published philosophy, where Spinoza said that everything is really part of one substance, Leibniz said that every object is a separate substance and there is an infinite number of substances, called ‘monads’, and each monad has a soul. Like Descartes’ followers, he also believed that substances cannot interact with each other. He says that monads are ‘windowless’, which I think was intended to mean that they have no awareness of their surroundings. He develops the analogy of the two clocks to be an infinite number of clocks, all designed by a Creator to strike together to give the illusion of interaction.  However, there is a hierarchy of monads. A person can be considered to be a single monad (with a soul or mind) which is dominant and made up of many individual monads. The mind of a person does not directly cause individual monads in the body to behave in a certain way, but the purpose of the individual monads is to enable whatever the purpose of the mind is. Leibniz believed the hierarchy of his system allowed free will. The actions of individual monads are not the inevitable result of logical necessity, but are determined by our minds.

The Existence of God

Leibniz developed the intellectual arguments for the existence of God, which had begun with the ancient Greeks and were formalised by the scholastics. It should be noted that Rousseau and the romantics had an entirely different conception of God and argument for the existence of God which is more common among modern theologians, but that is for another time. The ontological argument, as discussed in a previous post, says that God is the most perfect being and that God would be better if he existed than if he didn’t (because he could then do good things). From those two statements it can be deduced that God exists. There is also the cosmological argument, which is a development of Aristotle’s ‘unmoved mover’ theory (i.e. everything must have an initial cause and that cause is God). Leibniz said that every particular thing in the universe is ‘contingent’, i.e. it doesn’t logically have to exist, but everything that does exist has a reason to exist. These statements can be applied to the universe as a whole. God is outside of the universe and is the reason why it exists, and there can be no other rational reason why it exists. God was not compelled by logical necessity to create the universe, but freely chose to because of His goodness. This argument is strong as long as you believe that everything that exists must have a reason to exist, rather than existing randomly or by chance. Finally, the argument of ‘pre-established harmony’ relates to the theory of the clocks which are all in time without awareness of each other. This theory relies on a Being who created the system in the first place and set it in motion. Leibniz also has an answer for why evil exists even though God is omnipotent and good. God could have created many different universes and chose the best version, with the greatest excess of good over evil. Some evil is required to enable the most goodness. For example, food tastes better when we are hungry. If we were never hungry there is a limit to how good things would taste. To take a more serious example, death is a source of enormous fear and sadness. However, Leibniz would have said that it is fear of death that makes life so precious and drives us to live life to the full. If we were immortal we might find that life would be distinctly boring. This does not explain why God appears to allow the distribution of hunger and death to be so apparently unfair.

A Mathematical Model for All Reality

Russell considered Leibniz’s unpublished work to be a truer reflection of what he thought and far more profound, but a contemporary of Leibniz thought it to be so shocking that it would be universally rejected. Leibniz hoped to discover a generalised logic, such that the answer to any problem, including in ethics, could be calculated in the same way that a mathematical solution can be calculated. He did not achieve this, but according to Russell he invented mathematical logic a century and half before anyone else, but kept the work to himself. He assumed his work was wrong because it contradicted Aristotle’s doctrine of the syllogism. He did believe that it is possible to derive by deductive logic every aspect of a person or object that exists, including everything that is yet to happen. This relies on a belief in determinism such that if I choose to go shopping on Saturday, that event has always and will always be a part of me. God is able to understand the world in this way, and it is theoretically possible for us to do so if we had the intellectual capability. This of course contradicts the Christian doctrine of sin and free will. Leibniz believed that it is better for things to exist, and therefore God created as much as possible. The only limitation on whether something can exist is whether it logically contradicts the existence of something else. To take a simplistic example, consider three objects A, B & C. Suppose that objects A and B can exist with or are compatible with each other, but C is not compatible with A or B. It is easy to determine that if the greatest number of compatible things will exist then A & B will exist but not C. Leibniz believed that in theory a suitably gifted logician could apply this method to life in general and deduce what can and cannot exist. This appears fantastical to the modern mind, but that is partly because we generally don’t accept determinism. Russell does nevertheless applaud it as a very clear and precise attempt to provide a mathematical model to derive truths about existence purely by logical deductive means.