A Study Of Leibniz’s Logic Thoughts

In the development of logic history, Leibniz’s study is tremendous, and his logic thought is outstanding; this is because he did the researches on the shoulders of the greatest men, and he set up the logic thinking based on the analyzing and absorbing the knowledge of the predecessors. Much of Leibniz’s logic thought can be found its origin from the predecessors. However his kindness and generosity, his critical, sensitive and witted characteristic always resulted in truth and reality in logic region from which others ignored.As to mathematical logic, Leibniz is no doubt the founder for his theoretical exposition on universal language. Leibniz did enormous pioneering work and further research on the modern logic system which is now regarded to be established by Frege, Peirce and Russell. Leibniz put forward the idea to guide universal mathematics: firstly, to set up a kind of universal language which is like symbol of mathematics, and in which each symbol stands for a concept; secondly, to establish a better logic calculation system in which calculation is to build the logical rules to do the symbol operation. The two points above are the basic features of mathematical logic. Leibniz created a logic calculation to combine two concepts, and put forward “the Leibniz’s theorem”, this is, “a is b” and “b is a”. This theorem is marvelous through which the true value of possible existing, uncountable propositions can be made sure only by several steps of procedure, and each possible existing syllogism can be proved.Leibniz put forward the first true value law, that is, a conclusion can be drawn from the Presupposed rule by replacing the same symbol. This law can be interpreted as equivalent word definition by natural language: an object can be replaced by another object while the truth of the original proposition can be remained, that means these two objects are the same. This is called the principle of undistinguished identity. Another Leibniz’s main contribution in mathematical logic region is that the form of proposition is expressed as symbol formula. Leibniz had a strong belief that creating the universal language which contained all subjects was rather difficult, but learning to use the universal language was very easy. As is known that this language is ingenious with huge effect, it will soon be accepted by people, and actively worked in the contact of different peoples. That’s why Leibniz is respected as the founder of the world language. He discovered the universal almighty mathematics, and used the calculation to replace thinking. For this he contributed his whole life.As to traditional logic, Leibniz’s main contribution lies in two aspects: one is to improve the syllogism of Aristotle; another is to put forward the principle of sufficient reason, and this principle is later brought into the fundamental law of traditional logic region. Leibniz realized that mathematic method was essential for the following points: to use characters or symbols to replace concepts was simple; the process of calculation was strict; and the result was without ambiguity. He attempted to use line segments, circles, alphabets, numerals, etc in the form of Aristotle’s syllogism. And besides the rules of the syllogism, he created some new natural deductive rules to do the inference and proof on the transforming of 4 grids and 24 moods of syllogism.Leibniz introduced the principle of sufficient reason into philosophy for the first time to distinguish inferential truth and factual truth. The principle of sufficient reason is the foundation of Leibniz’s thought system, which can be used to prove the existing of the God, and also to prove all the other parts of metaphysics and natural theology, or even more or less to prove those natural philosophical principles which are independent and do not rely on mathematics, for example, the principle of dynamics, the principle of force, the relativity of time and space, etc. so as to solve the two maze problems that puzzle the mankind. There are theoretical connotations and practical meaning in Leibniz’s principle of sufficient reason because it reflects the eternal desire of mankind to explore the origin of the world, the adoration of mankind for rationality, and the hardship to pursuit the truth. Leibniz has great effect on social cognition, modern logic, philosophy, and the development of science and technology.As to philosophy of logic, Leibniz put forward two categories of truth theories and the theory of the possible world which was related to them. He is the first one to distinguish inferential truth and factual truth. The truth is expressed by the proposition which can be divided into two kinds, that is, the proposition of character and the existing proposition, and these two propositions correspond to the two truths mentioned above. The logic predicate of the proposition of character is contained in principal term, and this indicates necessary truth or inferential truth which has the criterion of “true or false” judgment according to the principle of contradiction. The existing proposition indicates factual truth which cannot be judged by the criterion of “true or false” judgment of the principle of contradiction because the opposite of the factual proposition is possible, and the truth of the proposition cannot be denied. So Leibniz put forward the principle of sufficient reason as the criterion of “true or false” judgment to the existing proposition.The principle of contradiction is on the essence of the principle, while the principle of sufficient reason is on the existing of the principle. The former is applied to all in the possible world, and the latter is applied to the existing world(the world of phenomenon) and individual object which is implicated in and happens accidentally. The inferential truth and factual truth are related and also distinctive, and this shows dialectical relationship of the unity of opposites of the two. The inferential truth is the premise and base of factual truth, while the factual truth depends on inferential truth finally. However, the inferential truth is about the existing accidental truth, and it has complete difference from the essential necessary truth. Leibniz established the possible world theory in order to make the two truths above clear. This theory thinks that the mode of existence of matters is varied, and as long as it does not contain logic contradiction, the things can constitute a possible world.Later the modal logic semantic theory is gradually developed and improved based on the theories mentioned above. In the 1930 s, the research on the modal logic was brought up greatly, and the possible world semantics had been one of the most influential semantic theories which is now widely used on alethic logic, deontic logic, temporal logic, topological logic, etc. generalized modal logic region. To large degree, this is related with Leibniz’s possible world theory. The possible world semantics has been improved perfectly, but if it is applied in the natural language with even complicated modal thinking reality of mankind, there is still much hard work and many problems. How to fully understand all kinds of symbols in the theoretical frame from the perspective of philosophical ontology and epistemology, that is, how to “reinterpretation” or “unitary interpretation” is in a continual controversy. In order to find practical ways to solve the problems above, this paper believes that the researchers will have to do the further research on Leibniz’s possible world and his related philosophical thoughts to seek for the nutrients of study.