The first great German philosopher (1646-1716).
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)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).
Leibniz regarded the physical world as the world of the senses, and thus as "phenomenon." Sense presents the world in a confused way, as in space and time. Since things in space (extended things) are infinitely divisible, nothing in space can be a true unity, a substance. Space and time are merely idealized orders of substances.
Kant attacked Leibniz's view in three places:
Leibniz's view is found in his correspondence with Clarke, Third Paper.
"I hold space to be something merely relative, as time is; . . . I hold it to be an order of coexistences, as time is an order of successions. For space denotes, in terms of possibility, an order of things which exist at the same time, considered as existing together; without enquiring into their manner of existing. And when many things are seen together, one perceives that order of things among themselves" (Section 4). Space "out of the world" or "empty space within the world" is "imaginary" (Fifth Paper, Section 33). "Instants, considered without the things, are nothing at all" (Third Paper, Section 6).
Kant denied that space (as well as time) is relative to things. "We can never represent to ourselves the absence of space, though we can quite well think it as smpty of objects. It must therefore be regarded as the condition of the possibilitiy of appearances, and not as a determination dependent upon them" (A24/B38-9).
Space and time are ideal rather than real. "The reality of space in itself" is only a "chimerical supposition" (Section 5). Cf. the Fifth Paper: "Space in itself is an ideal thing, like time" (Third Paper, Section 33). With respect to space, what is real is a relational property of a body, that of its place relative to other bodies. Suppose body C is fixed, and body A is one foot to its left. Now replace body A with body B, also one foot to the left of body C. Then B is in the same place or position relative to C. There is "entire agreement" between the relation of coexistence between A and C and the relation between B and C. But although they agree, their relations are not identical; it is the space which is supposed to be the same in both cases. "For two different subjects, as A and B, cannot have precisely the same individual affection; it being impossible, that the same individual accident should be in two subjects, or pass from one subject to another. But the mind not contented with an agreement, looks for an indentity, for something that should be truly the same; and conceives it as being extrinsic to the subjects: and this is what we call place and space. But this can only be an ideal thing; containing a certain order, wherein the mind conceives the application of relations" (Section 47).
Kant's agreed that in a sense, space and time are ideal. But it is not Leibniz's sense, i.e., that of a fanciful or imaginary thing which is not an absolute reality. In Kant's terms, this kind of ideality is just a species of confusion. For Kant, space and time are not confused representations at all, but forms of intuition. They are ideal in that they are conditions of human representation and do not apply to things considered apart from the manner in which they are represented.
Leibniz, Kant claimed, used "logical reflection" to determine which of the two items in each pair things fall into. He looked at the concepts themselves, without regard to the way in which the things falling under them are represented. This is opposed to "transcendental reflection," in which one considers the faculty of cognition which represent the things. On Kant's construal, Leibniz's metaphysics was based on four sets of distinctions
Identity and Difference: Leibniz's principle was the identity of indiscernible, according to which if A and B have the same non-relational properties they are identical. Kant's criticism was that objects of sensibility, which are given in space and time, can be internally indiscernible but numerically distinct, because they may be located in different parts of space.
"Certainly, if I know a drop of water in all its internal determinations as a thing in itself, and if the whole concept of any one drop is identical with that of any other, I cannot allow that any drop is different from any other. But if the drop is an appearance in space, it has its location not only in the understanding (under concepts) but in sensible outer intuition (in space) and the physical locations are there quite indifferent to the inner determinations of the things" (A272/B328).
Agreement and opposition Leibniz subscribed to the principle of non-contradiction, according to which no thing can have a property and its negation at once. If a thing is human, it is not non-human: to be human and non-human at once is impossible. According to Kant, the only opposition Leibniz acknowledged is negation. So the concept of God as a being with all non-negative properties is the concept of a possible thing, since there is no negation in the concept. However, Kant held, for an object of sensibility, there can be opposition without negation, as when two forces acting at right angles to each other produce a single movement on the diagonal.
Inner and outer: Leibniz claimed that the substances which make up the world are monads, simple substances whose properties are non-relational states of representation. Kant claimed that the objects of sensiblity, which are in space, have only relational properties, i.e., attraction and repulsion.
Matter and form: Leibniz was held to claim that matter is prior to form. The essential properties are the matter, and the manner of their combination the form. Thus space and time, as modes of combination of things, are dependent on monads. But as objects of sensibility, Kant claimed, form is prior to matter, i.e., space and time are conditions for the existence of senisble things.
"There must be simple substances, since there are compounds, for the compounded is but a collection or an aggregate of things. But where there are no parts, it is impossible to have either extension, or figure, or divisibility" (Sections 2 and 3).
Kant claimed what Leibniz himself recognized, that any limit to the decomposition of a sensible object would be arbitrary. Extended things are infinitely divisible. However, they do not have infinitely many parts.