Understanding of logic

smartkey

201August 08 1 1 Member of Chinese Poetry Society

I. Origin and definition of logic

There are three sources of logic: formal logic in ancient Greece, Xue Ming in pre-Qin China and Yin Ming in Indian Buddhism.

Logic is a science that studies the forms and laws of thinking. Formerly known as "Xue Ming", "Bian Xue" and "On Xue".

The word logic has three main application fields, and there is potential conceptual unity between them. First of all, it is the field of language and language, including speech, speech, description, statement, demonstration (expressed in language) and so on; Secondly, thinking field and thinking process, including thinking, reasoning, explanation, explanation, etc. The third is the world, that is, the object we speak and think about, including structural principles, formulas, natural laws and so on.

Second, the logic branch

Logic is a very large discipline group, and its branches mainly include the following aspects:

Traditional logic: Aristotle's syllogism.

Classical logic: binary propositional calculus and predicate calculus.

Extended logic: modal logic, sequential logic, deontic logic, epistemological logic, optimization logic, command logic and problem logic.

Abnormal logic: multi-valued logic, intuitive logic, quantum logic and free logic.

inductive logic

Speculative logic.

Third, the evolution of logic

1. The cognitive method of "similarities and differences" refers to the reasoning method from understanding the * * * nature of a class of things to understanding the differences between a class of things or individual particularity, which is a deductive thinking form.

2. "Good analogy" is actually a deductive reasoning method from known to unknown. The knower knows the * * * of two things, while the unknown only knows A but not B, so it is possible for the known to describe the unknown B with the known A, so that the unknown can also know B, which is a form of reasoning proof commonly used by ancient scholars in China.

3. "Dilemma reasoning" is a method that often appears in debates, which is characterized by using various forms of dilemma reasoning as a tool to establish one's own views and refute others' claims.

4. "Kill a thief, not a murderer". Thieves are human beings, so why not kill them? The form of reasoning, "or, false, effective, innovative, beneficial, push" and so on. There are five kinds of reasoning situations, that is, there is but nature, there is but unnatural, there is no but nature, one week is not complete, and one is right and wrong. These five situations are analyzed respectively. "Killing thieves without killing people" belongs to "having but not having".

5. The "theory of contradiction" is mainly aimed at two contradictory propositions, which cannot be true, not that two contradictory propositions can only be true and false.

6. The liar paradox is that epimenides said that "Cretans are liars". However, epimenides himself is a Crete, so the truth of this sentence becomes a problem. Because if we judge according to the rules of formal logic, we will draw contradictory conclusions at the same time. Finally, we don't know whether this sentence is true or false, because if it is true, it is only false, and if it is false, it is true. So formal logic can't judge whether this sentence is true or not. Here, the laws of identity, contradiction and law of excluded middle have all failed. The liar paradox exposes the self-contradiction of human thinking and language in the simplest, most typical and most prominent form. This contradiction can only be solved by dialectical thinking (dialectical logic) rather than formal logic.

7. "The running champion can't catch up with the tortoise" means "Achilles is the legendary Shen Xing Pacific Insurance in ancient Greece, and he runs very well. But he will never catch up with the tortoise running with him. Because Achilles must reach the starting point of the tortoise before he can catch up with it. By the time the pursuers arrived here, the tortoise had climbed forward for some distance. Even if the tortoise climbs slowly, it always climbs forward a little, because it doesn't stop there. This proves that Achilles will never catch up with the tortoise. " Discontinuity and infinite separability of space-time motion are inseparable from continuity and inseparability, and are based on this. Movement is the contradictory unity of continuity and discontinuity, and the contradictory unity of finiteness and infinity.

8. The "half-fee lawsuit" is a method that protagoras used to collect money twice in order to show that his fees were reasonable. He believes that the students he teaches will become lawyers after studying and they will win the case in court for the first time. Violation of identity will inevitably lead to confusion of concepts and propositions, non-standard inconsistency, and thus lead to sophistry.

9. "Spiritual midwifery" is to express ideas, so we must respect logic. What is morality, what is goodness and what is beauty. The concept contains truth, and the essence of truth lies in the concept.

10. Three important contributions of Megara School: research on paradox, propositional logic and modal logic.

Fourth, the basic principles of logic.

1. Identity

Any concept or proposition has its definite content. In the process of thinking and argumentation, it is necessary to maintain the definition and identity of the concept or proposition. Stealing concepts is stealing some seemingly identical concepts. In fact, the scope of application, specific objects, modifiers and specific connotations of the concept have changed. Stealing a topic refers to moving the center of the problem to other aspects when discussing the problem, so that the process of discussing the problem is not on the same platform. Stealing a proposition means distorting, tampering and misinterpreting a proposition. In the discussion, consciously or unconsciously replacing the previously used topic, concept and proposition with a different (or seemingly identical but actually different) topic, concept and proposition is against the law of identity.

2. Law of contradiction

The law of contradiction means that two contradictory views cannot be true at the same time. In any process of thinking and argumentation, thinking must be consistent, not contradictory. The law of contradiction only requires that there can be no "logical contradiction", that is, there can be no contradictory thoughts; The contradiction recognized by dialectics refers to the understanding of the internal contradiction of objective things, which is beyond the scope of logic discussion. "There is a barber in a village. He stipulated that I only shave those who don't shave themselves. Excuse me, does this barber shave himself? " This is the Russell paradox. Paradox is a logical contradiction that ordinary logical methods cannot eliminate.

3. law of excluded middle

Law of excluded middle means that two contradictory propositions cannot be correct at the same time. Therefore, in the process of thinking, we must admit that one of the two contradictory propositions is true and give a clear affirmation, and we cannot deny both at the same time. The logical mistakes against law of excluded middle are mainly manifested in "riding on the wall", ambiguity, "detour" and not taking a stand between two contradictory propositions.

4. The rule of sufficient reason

The law of sufficient reason means that in the process of thinking and argumentation, any true argument always has sufficient reasons. The basic logical requirements of the rule of sufficient reason are: (1) The proposition (which can be one or a group) as a reason must be true; (2) There must be a logical reasoning relationship between cause and inference. Errors that violate the requirements of Article 1 are called "false reasons" (the reasons are false) or "expected reasons" (the truth of the reasons has not been proved); Errors that violate the requirements of Article 2 are called "errors that cannot be pushed out". The law of sufficient reason holds that any judgment based on truth must have sufficient basis, and any correct judgment must have basis, and this basis must be related to judgment, which is a sufficient condition for judgment to be established.

Five, the basic method of logic

1. Definition

Definition is to clarify what the defined object is with certain words, symbols and structures. Definition is a clear definition of the defined object. The definition consists of three parts: defined item, defined item and related words. Definition items can be concepts about things themselves, concepts that reflect the essence or relationship of things, and words or symbols that express things, attributes and relationships. Definition items are words or symbols that represent things, properties and relationships, and can also be statements. Related words indicate the definition relationship between the defined item and the defined item, and play an indicative role, indicating that the sentence in which they are located is a definition, with the defined item on the left and the defined item on the right. Use definitions to clarify the meaning or reference of concepts and words used in the dialogue; Establish and consolidate new concepts and terms by defining methods. Connotation definition is a definition that reveals the connotation of a concept. Concept is a form of thinking, which reflects the essence or characteristics of things and is the combination of human thinking. This concept has two aspects: connotation and extension. The connotation of a concept is the reflection of its content and object. The extension of the concept is the object that the concept refers to, which can be concrete things or the nature or relationship of things. Defining the concept, defining the concept and revealing the connotation of the concept is called connotation definition. Extension definition is a method to define the concept from the aspect of extension, and the extension of an item is clearly defined by dividing the object referred to by the defined item into several subclasses. Inductive definition, also known as recursive definition, is often used in disciplines with certain structural requirements. For example, in mathematics and logic, this method is often used to define some methods, rules, structures, sets and so on. Another function of definition is to clarify the expression of concepts. In order to avoid ambiguity in communication, it is necessary to clarify the meaning of each word and which concept they express. This definition is the definition of words. There are two types: clear word definition and prescribed word definition. The definition of explanatory words is to clearly give the existing meaning of a word and get social recognition. For example, the explanation of words in dictionaries is basically the definition of explanatory words; The definition of words means that people stipulate the meaning of certain words through agreement. Most of these definitions are used to simplify language expression, and some concise words are used to express other complex words. For example, the "four theories" commonly used in the logic field refer to the four branches of axiomatic set theory, recursion theory, proof theory and model theory in mathematical logic.

break up

Division is a logical method to divide the extension of a generic concept into several concepts according to some properties of things, so as to clarify the extension of concepts. This division consists of three parts, parent, child and foundation. For example, people can be divided into "China people" and "foreigners" according to different nationalities. "People" is the mother item, "China people" and "foreigners" are the child items, and "nationality" is the basis. The rules to be observed in division are as follows: first, the sum of extensions of children must be equal to the extension of parents; Second, the basis of each division must be the same; Third, the expansion of each sub-item after division must be mutually exclusive. Classification is based on division, but compared with division, it requires higher basis. All the general attributes that can distinguish things can be used as the basis for division, while classification requires the essential attributes or salient features of things as the basis. The division of labor is determined by the actual needs of people, and the working hours can be long or short; Classification is widely used in every science and has played a role in the development of science for a long time.

demonstrate

Argumentative writing refers to a logical method to get another proposition (topic or argument) from a certain proposition (argument) through a series of reasoning. The "series of reasoning" used in argumentation is called argumentation process. These inferences can be deductive or inductive. In practice, argumentation is widely used, such as giving speeches, giving lectures, making reports and writing articles. Arguments are put forward by some people, and arguments are for people to see (or listen to). Proof is a thinking process that uses the judgment of known truth to explain the truth of a judgment through reasoning. Proof is the process of giving sufficient reasons for the truth of judgment. Proof consists of three parts: topic, argument and argument: topic is the judgment that authenticity needs to be explained; Argument is the judgment on the truth of the topic, and known facts, theorems, axioms, laws, definitions and some truths that have been mastered can be used as arguments; Argumentative writing is a reasoning process that uses arguments to illustrate the authenticity of a topic. It is a long reasoning, the premise is the basis of proof, and the final conclusion is the topic that has been proved. Proof is divided into direct proof and indirect proof: direct proof is to directly prove the authenticity of the topic from the front; Indirect proof is to prove this point by finding that the other topics restricted by the truth of the same topic are false.