Leibniz disagrees with this. One of the reasons is that there is an obvious conflict between his pantheism and biblical theology. Secondly, because his theory failed to solve the dualism from Descartes, there is a fault in the world (although he emphasized that the world is one, he did not explain how the unification of this seemingly binary world is possible).
Leibniz thinks that there are many entities, and they are infinite. Following Aristotle's view of entity, he thinks that entity is the subject of proposition. In the proposition that s is p, s is an entity. Because the entity is self-sufficient, it should contain all possible predicates, that is, "... is p". From this, we can deduce that the entity has four characteristics: indivisibility, closeness, unity and morality.
Indispensable means that anything with universality, that is, something with length, can be divided. Divided things contain all their own possibilities. If they are self-sufficient, they have the content of extensive things, that is, the possibility of attaching to his part.
By analogy, as long as it is extensive, it is not self-sufficient, but is recognized by other things (for Leibniz, real knowledge is the possibility of poverty), so it is not an entity. Therefore, the entity is inseparable and has no extension. In Leibniz's later works (monadic theory), he called it monadic, and the essence of monadic is thought.
This vast world is made up of infinite lists.
Closure means that each list must be self-sufficient, independent of other lists and contain all its own possibilities. It is impossible for an only child to interact with another only child. If one list acts on another list, the latter list may not be included in the list, that is, the list cannot contain all its contents, but depends on other contents.
Because of the definition of entity, this is impossible. So Leibniz said, "There is no window between lists."
Unity means that every child must look at the whole world from a certain angle. Because the world is closely composed of cause and effect, A acts on B, not only on B, but on the whole world. If the content of a list contains all its possibilities, then each list points to the whole world centered on the list itself.
The fact that the world is one does not mean that all the lists are the same, because the same world can be recognized from different angles, but it can be regarded as a unified world.
Finally, the morality of the list is more complicated. There are two reasons for this feature, one is the unity of the world, and the other is the certainty of the world. For the former, all the lists contain the whole world, but from their own point of view, is the unity of the world false?
How to talk about reunification? For the latter, the world is composed of a list, and the list is only a collection of its possibilities, and the world is only a possibility. So is it impossible for us to have a kind of knowledge that is not only possible but also inevitable? In what sense can we say that the knowledge about the world is true and certain?
Leibniz attributed it to a God, the creator of the world. On the one hand, before God created the world, there was no established material, so there was no established limited situation, so creation was pure will creation, and God created the world only by his perfection.
Therefore, as Leibniz famously said, this truly completed world is "the best of many possible worlds." This is almost in line with Leibniz's belief requirements. On the other hand, if you want to know something exactly, you should know its reason. To understand this reason, we must also trace the reason.
By analogy, the deterministic knowledge of the world cannot be an efficient reason within a world, but a metaphysical reason beyond it.
Leibniz said that this theoretically necessary setting is metaphysical attribution to God. Therefore, this world is so because it is the best and possibly the best.
People can't fully understand this kind of God's goodwill, but they can move in this direction, because people's minds have made a special list, which contains memories and can plan their future according to the past. This is the common divinity of human beings, that is, the possibility of morality People can learn about the world created by God and how to become a moral person by opening possibilities.
This moral worldview can be regarded as the pioneer of Kant, that is, Leibniz arbitrarily put forward the perfection of God as morality, and described the possibility as the reality in God's eyes, but did not really regard the possibility of the world as the possibility.
Moreover, Leibniz's criticism of innate ideas is Hegel's criticism of Kant. In this sense, on the one hand, Kant was awakened by Hume from Leibniz's arbitrary dream, but at the same time, he was polluted by Locke's philosophical pathological change-the examination of rational boundary. Leibniz is one step ahead of Kant in this respect.
Other contributions
Although the mathematical concept of function was implied in trigonometric functions and logarithmic tables that existed in his time, Leibniz was the first to explicitly use it in 1692 and 1694 to represent any of several geometric concepts derived from curves, such as abscissa, ordinate, tangent, chord and vertical line (see the history of function concepts).
/kloc-in the 0/8th century, "function" lost these geometric associations. Leibniz also believes that the sum of infinite zeros is equal to half in the metaphor of creating the world from scratch. Leibniz is also one of the pioneers of actuarial science. He calculated the purchase price of life annuity and settled the national debt.
The previous section discussed Leibniz's research on formal logic, which is also related to mathematics. The best summary of Leibniz's calculus works can be found in Bos (1974).
Leibniz, who invented the earliest mechanical calculator, put it this way: "Because for an excellent person, it is not worth losing time like calculating labor, if the machine is used, it may become a slave of others safely." ?
Leibniz arranged the coefficients of linear equations into an array, now called a matrix, in order to find the solution (if any) of the system. This method was later called Gaussian elimination. Leibniz laid the foundation and theory of determinant, although Guan Gao discovered determinant before Leibniz long ago.
His work shows the use of auxiliary factors to calculate determinants. Using cofactor to calculate determinant is named Leibniz formula. It is impractical to find the determinant of matrix by this method, and it is necessary to calculate n! ? The product and the number of n permutations. He also used determinant to solve linear equations, which is now known as Kramer's law.