G.W. Leibnizís Monadology (1714) is a very concise and condensed presentation of his theory that the universe consists of an infinite number of substances called monads. Leibniz discusses the nature of monadic perception and consciousness, the principles which govern truth and reason, and the relation of the monadic universe to God.
Leibniz defines a monad as a simple substance which cannot be divided into parts. A compound substance may be formed by an aggregation of monads. Thus, a compound substance may be divided into simple parts.
According to Leibniz, monads differ in quality, and no two monads are exactly alike. Each monad has its own individual identity. Each monad has its own internal principle of being. A monad may undergo change, but this change is internally determined. Changes in the properties of any monad are not externally determined by other monads.
Each monad has a plurality of properties and relations, which constitutes its perception. Each monad has its own perceptions which differ from the perceptions of other monads. Perceptual changes are constituted by the internal actions of monads. Leibniz describes three levels of monads, which may be differentiated by their modes of perception A simple or bare monad has unconscious perception, but does not have memory. A simple or ordinary soul is a more highly developed monad, which has distinct perceptions, and which has conscious awareness and memory. A rational soul or spirit is an even more highly developed monad, which has self-consciousness and reason (both of which constitute "apperception").
Leibniz says that necessary and eternal truths may be known by reason. A rational soul may know necessary and permanent truths, in contrast to an ordinary soul which can only connect perceptions by means of memory. A rational soul can know eternal truths about the universe and about the relation of the universe to God. A rational soul thinks of itself as limited, but thinks of God as unlimited.
Leibniz explains that reason is governed by two main principles: the principle of contradiction, and the principle of sufficient reason. According to the principle of contradiction, a proposition must be either true or false. If two propositions are contradictory to each other, then one of the propositions must be true, and the other must be false. According to the principle of sufficient reason, nothing happens without a reason. No proposition can be true without a sufficient reason for its being true and not false.
Leibniz declares that there are two kinds of truth: truths of reason, and truths of fact. Truths of reason are a priori, while truths of fact are a posteriori. Truths of reason are necessary, permanent truths. Truths of fact are contingent, empirical truths. Both kinds of truth must have a sufficient reason. Truths of reason have their sufficient reason in being opposed to the contradictoriness and logical inconsistency of propositions which deny them. Truths of fact have their sufficient reason in being more perfect than propositions which deny them.
Leibniz also claims, however, that the ultimate reason of all things must be found in a necessary and universal substance, which is God. A primary substance is not material, according to Leibniz, because matter is infinitely divisible. Every monad is produced from a primary unity, which is God. Every monad is eternal, and contributes to the unity of all the other monads in the universe.
Leibniz says that there is only one necessary substance, and that this is God. A necessary substance is one whose existence is logically necessary. The existence of a necessary substance cannot be denied without causing some form of self-contradiction. Thus, Godís existence is logically necessary. God is absolutely real, infinite, and perfect. All perfection and all reality comes from God. God, as the supreme monad, is an absolute unity.
Leibniz explains that the perfection of a monad is revealed by its activity. The imperfection of a monad is revealed by its passivity. A monad is perfect insofar as it is active, and is imperfect insofar as it is passive. Actions and reactions are reciprocal relations between monads, and are constantly changing. The actions of some monads are a sufficient reason for the reactions of other monads. The reactions of some monads are given sufficient reason by the actions of other monads. All of the actions and reactions of monads are governed by a principle of harmony, which is established by God.
Leibniz argues that, insofar as the rational soul or spirit can know eternal truths and can act according to reason, it can reflect God. The spiritual world is a moral world, which can guide the natural world. The goodness of God ensures that there is harmony between the spiritual world and the natural world, and establishes harmony between moral laws and natural laws. A perfect harmony of moral and natural law is found in the spiritual world, which Leibniz calls the City of God.
Leibniz also says that there are an infinite number of possible universes in the mind of God, but that God has chosen a single universe whose sufficient reason is that it is the best possible universe (i.e. having the highest possible degree of perfection). This claim may be disputed, however, because it may be misused as an argument for an excessive and unjustifiable form of optimism.
Leibniz argues that God is supremely perfect, and that therefore God has chosen the best possible plan for the universe. Godís plan for the universe necessarily produces the greatest amount of happiness and goodness, because it reflects Godís absolute perfection. But Leibnizís argument may be disputed by the opposing argument that the best of all possible worlds may not necessarily contain both good and evil. The best of all possible worlds may not necessaily contain both happiness and unhappiness. The universe may not necessarily be governed by harmony, but may be governed by disharmony. The universe may not necessarily reveal unity, but may reveal disunity.