I think conceptual logic and dialectical logic are not the same thing.

Formal logic, dialectical logic and mathematical logic are all produced from conceptual logic. The reason is that dialectical logic, formal logic and mathematical logic are all produced from the abstract operation of conceptual model. Conceptual logic is the general framework of conceptual abstract operation, while formal logic, dialectical logic and mathematical logic are the special frameworks of conceptual abstract operation.

First, formal logic

Formal logic has been inherited and perfected in the history of western philosophy for more than two thousand years, and has been used and annotated since Aristotle.

Formal logic is a kind of logic with a fixed framework, which Aristotle called the first principle of thinking.

People's conscious activities are in the constant change of the relationship between subject and object. Without the freezing of formal logic, that is, the reference, definition and control of freezing, people's conscious activities will not be settled, and the thinking movement of ideas, thoughts, knowledge and self-awareness, as well as the practical creation of conceptual things, will have no place.

Abstract operation of formal logic;

The first is the stipulation of reference. Formal logic requires that all objects have the stipulation of name, that is, the stipulation of reference. For example, horses have the name of "horse" and deer have the name of "deer". In formal logic, everything has its own name, which is fixed, definite, absolute and inherent. A horse is a horse and a deer is a deer. It is absolutely not allowed to "refer to a deer as a horse".

Secondly, it is the definition. Formal logic requires that all concepts have their connotation and extension boundaries, that is, definitions. For example, what is a "weapon"? Searching on Baidu, we get such a definition of connotation and extension: "Weapons, also known as weapons, are tools used for attack, so they are used for deterrence and defense. Anything that can cause harm (even psychological harm) can be called a weapon. As long as it is used for attack, the weapon can be a simple wooden stick or a nuclear warhead. "

With the provisions of reference and definition, formal logic has a basis for judging "yes or no", such as this is a "teacup", not a "pen"; This is a Toyota, not a general-purpose car. This is a "good thing", not a "bad thing"; This is a "public domain", not a "private domain"; This is a "market economy" rather than a "planned economy"; This is "western culture", not "oriental culture", and so on. The identity of formal logic, the law of contradiction, law of excluded middle and the sufficiency of reasons are all ways to judge "yes" or "no". Thus, the human brain can obtain the abstract judgment ability of "yes or no".

Third, it is the rule of unified control. When the human brain controls everything abstractly and reflectively with the provisions of reference and definition, it obtains a control rule, from which the logical reasoning, logical necessity and logical judgment of the control rule are launched.

The syllogism of formal logic is a unified reasoning structure composed of major terms, minor terms and conclusions.

For example:

People always die;

Zhang San is a person;

Zhang San will also die.

Another example is:

The sun rises in the east every morning;

Tomorrow morning;

The sun will also rise in the east.

Wait a minute.

In the reasoning structure of these two syllogisms, the major term of "everyone will die" is of guiding significance, and it is the minor term of "Zhang San is a human being", from which the logical necessity and logical judgment of "Zhang San will die" are drawn. Similarly, the event "the sun rises in the east every morning" is dominated by the event "tomorrow morning", which leads to the logical necessity and logical judgment that "the sun rises in the east tomorrow morning".

The reasoning structure of syllogism is the abstract operation of conceptual model and the most basic logical model, which enables the human brain to obtain the judgment ability of unified reasoning.

An important question involved in discussing the syllogism structure of formal logic is, where does the major term of syllogism, that is, the major premise, come from? This involves the problem of induction.

Induction is the premise of syllogism and reasoning. For example, in the syllogism reasoning that "the sun rises in the east every morning and will rise in the east tomorrow", the premise of "the sun rises in the east every morning" is a constant induction of experience. This kind of induction, at first glance, seems natural and self-absolute, but careful analysis is subject to experience and conceptual abstraction of experience. Such conceptual abstraction cannot transcend experience. The solar system will be destroyed, and such destruction will eventually happen at some time in the future. At that intuitive moment in the future, the reasoning and logic of "the sun will rise in the east tomorrow morning" will inevitably fail completely.

The characteristic of induction is that its content is empirical and its form is conceptual. Induction is an abstract concept with unchangeable experience, which can't go beyond experience and be self-absolutized. In this way, all the major items provided by induction have their boundaries, that is, they are subject to experience and cannot be surpassed. The characteristics of induction determine that syllogism reasoning based on induction is an abstract operation after induction, which provides the logical inevitability and logical judgment of abstract operation. The logical inevitability and judgment of this abstract operation are not self-absolute, nor can they become the constraints and boundaries beyond the abstract operation, but they need the proof of empirical evidence to obtain the reality, authenticity and effectiveness of its abstraction and empirical unity.

The advantage of formal logic lies in that it provides a fixed foundation for ideas, thoughts, knowledge and self-awareness through reference, definition and control. Formal logic holds that everything should be in its place, which is very consistent with the common sense of daily life within its own framework.

The disadvantages of formal logic are:

1, which is paranoid about freeze-frame and ignores variation. All human conceptual cognition and images are the generation of the relationship between subject and object. In the constant change of the relationship between subject and object, it is necessary not only to freeze the stipulation of things, but also to change the insight and stipulation, so as to grasp the overall, change, process and development of things in the investigation of changes.

2. It is paranoid about the self-absoluteness of conceptual abstraction, and fails to realize that any kind of conceptual abstraction is localized and has its boundaries. In the reasoning and judgment of formal logic, the premise of syllogism is provided by the abstract concept of induction, which is fundamentally subject to experience and cannot be surpassed. Even the induction of "people always die" is subject to experience, which is an abstract concept that is constantly experienced and will change because of the emergence of new experiences. The development of modern science and technology is revealing that with the emergence and development of electronic life and electronic consciousness, the physical death of life and consciousness will be changed and a new empirical and constant conceptual abstraction will be obtained.

Second, dialectical logic-

The core of dialectical logic is variability, and its essence is:

1, unity of opposites.

All conceptual abstractions are in the unity of opposites between "I" and "non-I". Such as infinity and finiteness, up and down, action and reaction, etc.

Neither side of the unity of opposites is absolute and advanced. In the unity of opposites between infinity and finiteness, up and down, action and reaction, infinity does not precede finiteness, and finiteness does not precede infinity; The top is not before the bottom, and the bottom is not before the top; Positive does not precede negative, and negative does not precede positive. The two ends of the unity of opposites cannot exist in isolation. Only with you can I have you, and only with me can I have you. The two are interdependent and reflect each other.

2. More advanced.

The essence of unity of opposites is the construction of things to a higher level and the unity of opposites. For example, the unity of opposites between "topic" and "duality" moves towards a higher and higher combination of topics, while the unity of opposites between "single" and "complex" moves towards a higher and higher whole, and so on.

Dialectical logic endows things with variability, connection, process, historicity and development with unity of opposites and higher-level abstract operation. Examine the whole thing from the aspects of variability, connection, process, historicity and development.

The boundary between dialectical logic and formal logic is that formal logic is a fixed and closed-loop abstract operation, while dialectical logic is a variable and open abstract operation.

There are two different logical ways for the abstract operation of human brain: frozen logical way and changed logical way.

In the fixed framework of formal logic, things have a fixed framework, and the mind can distinguish and reason things in the fixed framework.

In the change of dialectical logic, nothing is absolute and eternal, but is in a higher and more advanced process of unity of opposites.

How to treat the relationship between formal logic and dialectical logic?

1. Both have their own advantages. For human thinking and practice, they complement each other, and cannot be neglected or missing.

2. Without formal logic, the abstract operation of thinking cannot be used to define and judge things; Without dialectical logic, the abstract operation of thinking cannot grasp the process of change and the general appearance of the process.

3. The abstract operation of formal logic and dialectical logic is conceptual, which is the appearance of conceptual logic. We can neither admire dialectical logic but belittle formal logic, nor stay in formal logic to the exclusion of dialectical logic. We should also understand them as an effective way of abstract operation of human thinking.

Third, mathematical logic-

General textbooks always tell us that mathematical logic uses mathematical methods to study logic or formal logic, and uses computational methods to replace the logical reasoning process in people's thinking. /kloc-Leibniz in the 0 th/7 th century once imagined whether a "universal scientific language" could be created, and the reasoning process could be calculated by formulas like mathematics, so as to draw correct conclusions.

It can be seen that the core of mathematical logic is to mathematize logic and transform logical operation into mathematical operation.

Grasp two key points of mathematical logic:

One is what mathematics is. Any mathematics is based on the abstract operation of numerical symbols, algebraic symbols and operational symbols, that is, on the establishment of various specific numerical symbols, algebraic symbols and operational symbols and the establishment of operational rules. Different numerical symbols, algebraic symbols, operation symbols and operation rules are created, and different mathematical categories are produced.

Take four decimal operations as an example:

1+ 1=2;

2- 1= 1;

2×2=4;

6÷3=2。

Here, we can see that the four decimal operations all have their specific number symbols, operation symbols and operation rules. Based on such digital symbols, operation symbols and operation rules, abstract operations are carried out on them, and the logical necessity of abstract operations is obtained.

Take the algebraic binary linear equation as an example:

Four baskets of apples, three baskets of pears weigh 3 10kg, and three baskets of apples and five baskets of pears weigh 370kg. How many kilograms do apples and pears weigh respectively?

Analysis and solution: suppose that each basket of apples is x kg and each basket of pears is y kg. According to the weight of 4 baskets of apples and 3 baskets of pears, the equation 4x+3y = 3 10 is listed. Then, according to the weight of 370kg for 3 baskets of apples and 5 baskets of pears, the equation 3x+5y=370 is listed.

4x+3y=3 10①

3x+5y=370 ②

① Multiply both sides of the formula by 3 to get 12x+9y=930③.

② Multiply both sides of the formula by 4 to get 12x+20y= 1480④.

④ Subtract ③ to get 1 1y=550.

y=50

(3 10-50×3)÷4

= 160÷4

=40 kg

A: Each basket of apples weighs 40 kilograms and each basket of pears weighs 50 kilograms.

It can be seen here that algebraic equation operation also has its specific numerical symbols, operation symbols and operation rules. Based on such digital symbols, operation symbols and operation rules, abstract operation is carried out, and the logical necessity of abstract operation is obtained.

This situation shows that the establishment and application of any mathematics discipline involves not only the establishment of its numerical symbols, algebraic symbols and operational symbols, but also the establishment of its operational rules. The development and establishment of mathematics is essentially the establishment of various new numerical symbols, algebraic symbols and operational symbols, as well as operational rules, which is the soul of mathematics. The key to a country's mathematical innovation lies in whether it can create new numerical symbols, algebraic symbols, operational symbols and operational rules, and then find its application fields in the process of seeking the unity of abstraction and experience.

The second is what logic is. The object of logic is thinking, and the essence of human thinking movement is the abstract operation of concepts, that is, the abstract operation mediated by symbols, which generates human cognition and image, human thought and self-awareness, human practice and spirit. Therefore, the so-called logic, in the final analysis, is an abstract operation with symbols as the intermediary, and it is a structural way of conceptual abstract operation.

Therefore, the so-called mathematical logic is to substitute the abstract operation of concepts mediated by symbols into the abstract operation of mathematical symbols, so that the abstract operation of conceptual methods becomes the operation of mathematical symbols.

For hundreds of years, the development of western logic has been gradual. With the development of limit seeking, graphics seeking, computer-controlled instruction programs, characters, languages, colors, images, music, observation, search and mathematization of various physical, chemical and economic states and characteristics, the technical combination of logic and mathematics has been more and more widely promoted.

With the development of modern electronic intelligence technology, people are eager to create a robot logic device through the combination of mathematical logic and electronic technology. The logic device of this robot can not only replace the human brain for calculation, but also replace the human brain for thinking and autonomous action.

In this way, the essence of the development of contemporary mathematical logic lies in creating a robot logic device with the support of electronic technology. Like the human brain, this logic device can independently generate thoughts, self-awareness and practical creativity on a larger scale, faster and more efficiently, thus creating future electronic life, electronic consciousness and electronic intelligence.

It can be seen that the essence of mathematical logic is not only the mathematical physics of formal logic and dialectical logic, but also an absolute method to provide standards for human language and thinking. Its higher development is to realize the mathematical operation of conceptual logic and provide logic devices for manufacturing human intelligent robots.

To realize the higher development of mathematical logic, it is necessary to deeply investigate the abstract operation of concepts in the structure of human consciousness and find out the logical mode and logical framework of abstract operation of concepts. Only in this way can we truly realize the pursuit of mathematical logic.