In Leibniz's ontology, real things are substances. A substance is a being which is capable of acting on its own. Each substance has any number of qualities. God is the one and only infinite substance, and through the act of creation, God brought into existence infinitely many other substances (entelechies). God's existence can be proved in several ways, including by the ontological argument.
"God alone, or the necessary being, has the privilege of necessarily existing if he is possible. And since nothing can prevent the possibility of that which is without any limits, without any negation, and consequently, without any contradiction, this fact alone suffices to know the existence of God a priori" ("Monadology," Section 45). Kant's Criticism
God created the best of all possible worlds. That is, God considered all possible combinations of substances and chose to create the best one. The choice of the best above all others is in accordance with God's nature.
Simple substances, those which are not composites of other substances, are called monads. Creation is the only way in which one substance may act upon another, and only God is a creator. All change in a monad comes from a source internal to the monad itself. So finite substances do not interact with one another.
There is . . . no way of explaining how a monad can be altered or changed internally by any other creature, since nothing can be transposed in it, and we cannot conceive in it, as we can in composite things among whose parts there may be changes, that any internal motion can be excited, directed, increased, or diminished from without. Monads have no windows through which anything could enter or depart. ("Monadology," Section 7)
Since they do not interact with one another, the changes in each monad in the world must be harmonious with those in each other monad in the world. This is possible only if at the creation, the principle of change in each monad is properly calibrated, a task seen to by God. One the analogies Leibniz used to illustrate this notion of a pre-established harmony is that of a chorus, each individual member of which occupies a different room. They attain a harmony by singing from the same score, beginning at the same time. But this harmony seems to require that each of the actions of the monads be pre-determined, since any deviation from the original script would produce disharmony.
The realm of possible worlds is in the mind of God; only the actual world has any existence on its own, according to Leibniz. Creation is the result of God's decree, and this decree flows from God's nature. God is free in this respect: that the other worlds are options which were available for God to choose.
The constituents of each possible world are distinct from those of any other world. In contemporary terms, there is no "cross-world" or "trans-world" identity. Although different worlds could contain an individual meeting the description "the first man," only one world, ours, contains Adam. In the other worlds, the first man is someone else.
What makes an individual possible is that its concept contains no contradiction. For Leibniz, an individual is fully described by an individual concept; anyone grasping the concept in its entirety would know everything there is to know about that individual, save whether it exists. To put it another way, the representation of the individual is "given" through its individual concept.
A contradiction is harbored by a concept just in case the analysis of that concept yields a property and its negation. For example, the concept of a square circle contains the concepts "having angles" and "not having angles," A and not-A. Thus a contradictory concept C is one which upon analysis can be found to have a property and the absence of that property. There is no guarantee that a concept is not contradictory, unless it can be analyzed into its simplest components.
In fact, this is how Leibniz tried to show that God is possible, i.e., that the concept of God contains no contradiction. God is a being whose concept contains only positive predicates. There is no not-A among the characteristics of God, so there can be no contradiction in the concept of God. As quoted eariler from the 'Monadology,' Leibniz held that God "is without limits, without negation, and consequently without contradiction" (Section 45).
Kant noted that Leibniz's followers took this idea a step further. "His disciples consider it not only possible, but even natural, to combine all reality in one being, without fear of any conflict. For the only conflict which they recognize is that of contradiction, whereby the concept of a thing is itself removed" (A273-4/B329-30). We will discuss this notion further when considering Kant's claim that there is no metaphysical proof for the existence of God.
The doctrine that the possibility of a thing requires nothing more than the absence of contradiction from its concept was rejected by Kant. We will discuss it in detail later, but for now it is enough to say that the problem lies in the claim that we understand individuals through concepts alone. Kant held that for human knowledge, it is required that objects be given in a non-conceptual way, through what he called sensible intuition The understanding thinks through general concepts, while sensibility represents particular things which affect it. Thus for a thing to be possible, it must either be given or be capable of being given to sensibility. This theme will be developed more fully as we continue.
The doctrine that an individual can be an object for the understanding through the use of concepts alone also supports the claim that the substances making up the world have properties which are purely internal. These internal peoperties "must be something which is either itself a thinking or analogous to thinking. For this reason Leibniz, regarding substances as noumena, took away from them by the manner in which he conceived them, whatever might signify outer relation, including also, therefor, composition, and so made them all, even the constituents of matter, simple subjects with the power of representation -- in a word, MONADS" (A266/B321-2).
Kant notes that this forced Leibniz into his doctrine of the pre-established harmony, discussed in the last lecture. Another consequence of the purely internal status of the property of things is Leibniz's famous principle of the Identity of Indiscernibles. Two individual concepts can represent different things only if there is some difference in the internal properties they represent. Suppose we try to entertain the concepts of two raindrops whose size is exactly the same and whose micro-structure is identical. There would be no basis for difference, on Leibniz's principle. If it be objected that they can be located in different places, Leibniz would respond that being in different places is not an internal, but an external property, and hence is no basis for difference. "There are never two beings in nature that are perfectly alike, two beings in which it is not possible to discover an internal difference, that is, one founded on an intrinsic denomination" ("Monadology," Section 9).
What, then, can be said with respect to "external" properties, such as spatial or temporal properties? Leibniz could only conclude that such properties are derivative from or parasitic upon the internal property. "Leibniz conceived space as a certain order in the community of substances, and time as the dynamical sequence of their states. That which space and time seem to possess as proper to themselves, in independence of things, he ascribed to the confusion in their concepts" (A276/B332).
This characterization of the concepts of space and time as confused gets us to the heart of Kant's criticisms of Leibniz. Confused concepts, according to Kant's interpretation of Leibniz, are those which are the product of sensibility. Unlike Kant's own view, according to which sensibility is given objects of its own by being affected, Leibnizian sensibility is a faculty which only confuses and distorts the concepts that are found in the understanding.
In Kant's terms, objects of sensibility are appearances, things which are given in sensible intuition which represents them as individuals. Through concepts, on the other hand, we think things in general, apart from the way they are given to the sensibility. On the Leibnizian view, the objects of sensibility are just a distorted version of the objects of the understanding ("noumena"). So, again in Kant's terms, Leibniz has taken appearances for things in themselves. That is, Leibniz thought that the same principles (e.g., the Identity of Indiscernibles) which apply to objects of the understanding apart from sensibility also apply to those objects of which we are sensible, since there is no intrinsic difference between the two.
For Kant, the two separate faculties of sensibility and understanding must work together for human knowledge to be possible. Each must make its own distinctive contributions: concepts on the part of the understanding and intuitions on the part of sensibility. "To neither of these powers may a preference be given over the other. Without sensibility, no object would be given to us, without understanding no object would be thought. Thoughts without content are empty, intuitions without concepts are blind. It is, therefore, just as necessary to make our concepts sensible, that is, to add the object to them in intuition, as to make our intuitions intelligible, that is, to bring them under concepts" (A51/B75).