1. Traditional logic Traditional logic usually divides propositions into straightforward propositions, selective propositions and hypothetical propositions, and studies the forms and reasoning forms of these propositions. Traditional logic also includes the theory about the law of contradiction and law of excluded middle, and the theory about lexical items.
The founder of European formal logic is Aristotle in ancient Greece. Aristotle established the first logical system, namely syllogism theory. His representative works on formal logic are Metaphysics and Instrumentalism. After Aristotle, the logic of the Megara-Shi Tuoya School revealed some important properties of propositional conjunctions, found some reasoning forms and laws related to propositional conjunctions, and developed deductive logic. Epicurus, another philosopher in ancient Greece, thought induction was the only scientific method. Some logicians in the Middle Ages developed and enriched formal logic. In modern times, Bacon and Johannes Muller further developed induction.
contrast
In China, the emergence of formal logic is basically the same as in Europe. The representative schools are Mohism and famous scholars, as well as Xunzi of Confucianism. Interestingly, Mohist studies logic in order to find the principle of logic, while famous scholars aim to establish a sophistry system. Mohist understanding of logic is embodied in Mo Jing, which systematically discusses logic. For example, distinguish between sufficient conditions and necessary conditions, and put forward that "big reasons (sufficient and necessary conditions) are inevitable, but not inevitable" and "small reasons (necessary conditions) are not inevitable and not inevitable". In order to cancel the boundary of concept, the famous Hui Shi put forward the sophistry principle of "contract difference". Contrary to Hui Shi, Gong Sunlong, who is also a famous scholar, put forward the sophistry principle of "separating from reality and keeping white", thinking that any independent concept has and can only have a single attribute. Famous experts put forward many sophistry propositions, such as "a white horse is not a horse", "a chicken has three legs", "a solitary calf has no mother", "a chain has no buttons", "a white dog is black" and "let the past come from the present".
Obviously, the research method of "backward deduction" by famous artists is unique to China, and the establishment of its sophistry system just shows that the level of logic development at that time was very low and there were a lot of loopholes-so famous artists had an opportunity to take advantage of it. However, this move by famous artists fully exposed these loopholes and provided a stepping stone for future generations' research. If we want to develop logic, we must overcome the sophistry proposition of famous artists. In addition, there are also reasonable factors in the sophistry propositions of famous artists-some really hit the key of formal logic, that is to say, there are other logics besides formal logic. Finally, some famous artists' propositions may contain reasonable knowledge about nature and human cognitive process. For example, a proposition is "the center of the world, and the north of Yan State is the south of Vietnam". If this proposition is to be established, it must be based on the premise that the earth is round. At that time, when the theory of "covering the sky and covering the sun" was dominant, it was not easy for famous artists to have such an understanding. Another proposition is "Birds don't move". If we make a positive solution, famous people should realize that our intuitive concept of "movement" is based on the understanding of two stillness. It was not easy to make these judgments at that time, but unfortunately these understandings all appeared in the form of sophistry.
Since then, the development of formal logic in China has basically come to a standstill.
In ancient India, in the 4th century BC, the Victory School and the Rationalist School started Karma, and in the 6th century, Dignā ga perfected Karma, which was called the New Karma School. Etymology is formal logic.
2. Mathematical logic, that is, modern formal logic. It is called mathematical logic, on the one hand, because artificial symbolic language is widely used in research, and has developed into a formal axiomatic method, and at the same time, some mathematical tools and concrete achievements have been applied; On the other hand, the development of modern formal logic is promoted by the in-depth study of mathematical basic research, especially the logical law of mathematical proof and the logical problems raised in mathematical basic research. Mathematical logic is also called symbolic logic because it uses artificial symbolic language. The founder of mathematical logic is G.W. Leibniz. Leibniz put forward the idea of establishing "universal symbolic language", reasoning calculus and thinking mechanization. Although Leibniz himself did not achieve his goal, the development of mathematical logic gradually (but not completely) realized Leibniz's ideal. G Frege established the first-order logic system in the book Conceptual Language published in 1879. 19 In the 1970s, Cantor founded set theory. Set theory, especially the establishment of first-order logic system, is a sign that formal logic has entered a modern stage.
3. Formal Logic In the 1930s and 1940s in China, the Soviet Union criticized formal logic as metaphysics and regarded dialectics as the only scientific logic. Dialectics must criticize formal logic. Under this influence, at that time, some people in China "sentenced" the formal logic to death. But before 1949, this ideological trend of completely denying formal logic was not the mainstream in China. From 1949 to 1950, this trend of thought has also become the mainstream thought of China.
1950 after Stalin's Marxism and Linguistics was published, China "resumed" formal logic. However, "recovery" is not complete. Like the Soviet Union, formal logic still bears the hat of "elementary logic", while "advanced logic" is naturally dialectical or dialectical logic. Denying and belittling formal logic not only hinders the development of logic science, but also causes the evil consequences of sophistry. Hegel once commented on Leibniz's hypothesis of mathematical logic with great contempt. The mathematical logic that appeared after the emergence of Marxism (the first system of mathematical logic was put forward by Frege in 1879) was regarded as pseudoscience serving the monopoly bourgeoisie in the early 1950s.
It was not until 196 1 year that we began to break through some frames of Soviet logic textbooks in the fifties and sixties and clean up all kinds of common sense mistakes spread by Soviet textbooks.