Leibniz
1. The Monadology. A work late in L’s life. Never wrote a master-work, but this is an outline of the system. Discuss Rescher’s notation (p. 14).
· “Monad” = “unit”.
2. Sections 1-2. There are composites, hence there must be simples. The latter are the substances.
· Not obvious. What if science discovers that the elementary particles we have are made of smaller elementary particles, and so on ad infinitum? Leibniz actually thinks it is so—at least for physical particles. But he still thinks that metaphysically it’s all made of simples.
· General principle here: There cannot be ungrounded dependency chains, though there can be infinite dependency chains. The whole depends on its parts. This principle reoccurs in the cosmological argument.
· Tortoises all the way down! No, that won’t do. Nor will it do to have each person pointing to the next for payment.
· When is a regress vicious? When the same problem reappears at each stage. The problem here is: “Whence the composite’s reality?”
· The kind of simplicity at issue here is not the absolute simplicity that a Thomas Aquinas or Moses Maimonides attributes to God, but simply a lack of parts that the whole is dependent on.
· Variant form of the argument: Letter to Arnauld (R, 47). Composites have “unity by accident”, and “depend upon the fiction of our minds”. Mere contiguity or tying together—the pond and sheep examples—just won’t do to produce a real thing.
· Two closely principles of Aristotelian philosophy: “being and one are convertible” and “substances are not composed of other substances”.
· How would we justify the two principles? As for the second, Leibniz thinks that substance is what does not depend on anything else for its existence; but the whole depends on its parts; therefore, substances are not composed of other substances. (Aristotelians might argue the other way around—parts depend on wholes—and arrive at the same conclusion.) Epistemic parallel: Substances can be understood on their own—and there must be things like that if rationalism is true. (Else not even God can understand things.)
· A composite is “a mode of being of its component elements” (R, 48). The component elements are in a certain way—e.g., are armed and together—and therefore the composite is. Thus, the very notion of a composite involves things that are a certain way. Again, we must avoid a regress.
· Reductio: If a composite is a substance, all composites are substances, even a circle of men holding hands (top of R, 49).
· Here are some arguments that Leibniz could have given, though he did not in fact.
o The universe is made of things that are objectively delineated, identifiable and countable. What those things are is a question for further investigation. Maybe they are natural things like human beings, horses, nettles, and their like. Maybe they are solid things like human beings, a rock, the Empire State Building and an oak tree. Maybe they are elementary particles such as electrons, photons and fermions. What is important is that it is not just linguistic convention that settles what the things are, what they are identical with and how many of them there are, but objective reality settles it.
· Now, the Sunalex, which is the composite of me and the sun, is not objectively a thing. The reason it is not a thing is that it is two things. Now, of course one wants to retort: In one way the Sunalex is one thing and in another way it is two things. But saying this misses the objectivity involved in identifying the things. If in one way the Sunalex was one and in other two, then because we are looking for the things that are objectively delineated and objectively countable, we would have to have an objective fact of the matter about which of these it really is. When we talk about “that reality, the Sunalex,” are we talking of one thing or two things? Now, given that we must choose, it is evident that on the scientific grounds of what lends itself better to explanatory purposes it will be objectively better to talk of the Sunalex as two things rather than as one. So there already is something we can say about the things. No objective thing can be a composite sum of other things. A heap of sand, then, is not a thing, for it is nothing but the mereological sum of the grains of sand. Whether the grains of sand are things or not is a more difficult question.
· If composites are always things, there is an infinite number of ways of cutting up reality. Instead of talking of me and you, I could talk of two composite beings: the sum of my left half and your left half, and the sum of my right half and your right half. I could do this dividing up arbitrarily and in many ways. This would mean that the world could be divided up in infinitely many ways, all depending on us. But then there is trouble. For instance, instead of describing a horse in terms of its heart, lungs, cells, etc., I could describe it in terms of other ways of dividing it up. If I worked hard enough at it, I could probably show that a tree and a horse are the same thing, on Leibnizian principles. Certainly, I can make the parts of a tree onto the parts of a horse. Admittedly, they won’t interact exactly like the parts of the horse would, but this could be fixed perhaps—just think of these parts as nameless. Anyway, Leibniz doesn’t buy this at the ultimate level of reality. When we’re talking of that level, there is just one way to think of the universe.
· The monads are not subject to our empirical observation. For, any empirically observable entity is further subdivisible (R, 50). After all, any empirically observable entity occupies a certain amount of space, and we can then consider its parts to the left and to the right of some dividing line.
· What of points? Maybe they are the points that make up the entities. This sounds pretty good, except that Leibniz explicitly tells us that the points in space are not real (R, 52). What is Leibniz thinking of? It may be that he thinks that the basic ingredient of space is region rather than point, and points are simply abstractions from these.