Stevie asked:

What does Leibniz mean by a ‘world’? What does compossibility mean? How does an adequate view of compossibility help Leibniz respond to Spinoza’s necessitarianism?

Answer by Jürgen Lawrenz

Compossibility denotes that certain things or processes in the universe can or could occur simultaneously. Hence the opposite, incompossibility denotes that, although all some of these things and processes could logically exist side by side, their actual existence may be impeded by the effect which their actions may have on each other. E.g. fire and water can co-exist, but in their interaction one destroys the other. But there will be some things and processes which deny co-existence to other things and processes absolutely. E.g. the universe cannot be rigid and fluid at the same time, though perhaps at different times.

So Leibniz’s understanding of the world is the present actual composition of the universe. It doesn’t mean much to us, as we can’t know the total composition of the universe, but God would know. Where this train of thought is useful, however, is in cosmology and metaphysics, where it can happen that some things and processes are logically possible at any time, but the concept of compossibility overrides logic if some of the compossibles cannot co-exist in actuality.

Accordingly, all phenomena are ruled by contingency. Compossibility implies inter alia that the actual existence of X is contingent on being compossible with Y. It is also contingent on prior conditions P that must have been compossible with Q in order to facilitate the existence of X. And so on.

Apply the full weight of this aspect of actuality and you will see that it rules out necessitarianism. In fact, it is one of Leibniz’ principles (so-called ‘minimax’) that the contingency built into the universe by God renders necessitarianism superfluous. To achieve the greatest conceivable variety by the smallest expenditure of means is tantamount to devastating necessitarianism, which requires infinite foresight and control and is therefore ‘labour intensive’ to a degree that (in Leibniz’ sight) would be demeaning to God.

Consider for comparison that you might write a mathematical formula which hides under its curt symbolism a long rat’s tail separate and very laborious subroutines, each of which may change the result of the symbolism by the insertion of specific integers. Leibniz therefore attributes the same skills of abridging huge cosmic events in a single equation, whose details He does not have to know as the equation will constrain any solution to its preset limits.

Finally, contingency ensures continuing creativity, not only by God, but by his creatures as well. In this respect, Leibniz makes the interesting observation that such an enormous clutter of detail as hard determinism requires, is completely unnecessary in a universe driven by contingency, which needs only the provision of boundaries at a preset minimum and maximum.