Is abstract thinking in philosophy the same as in mathematics?

I think it's different.

Mathematics is the study of quantity, while philosophy is the study of quality.

As far as mathematical abstraction is concerned, it mainly embodies the quantitative relationship between the thing itself and other things, and for this reason, it extracts the quality of things and specializes in the quantity of things. Philosophy is different, the ultimate purpose of philosophical abstraction is to study what the essence of the world is, which is precisely what mathematics abstracts away.

But the study of mathematics is indispensable to the ultimate goal of philosophical research, because quality and quantity are indispensable, and quality and quantity can influence each other.

How well did you learn philosophy? Memorizing the dogmas of Marxist philosophy well cannot be regarded as a good study of philosophy.

All subtle philosophical systems, such as Aristotle, Hegel, Buddhist philosophy, etc., all require deep abstract speculation, so in the Western philosophical tradition represented by the first two, philosophical and mathematical masters such as Descartes and Leibniz naturally emerged, and the latter also emerged such logic masters as Chen Na and Xuanzang (logic and mathematics are very similar).

Of course, if the questioner is indeed philosophical, it is probably a matter of interest if he is not good at mathematics

Mathematics focuses on calculation, reasoning, argumentation, and the ability to imagine the graphical space, and is a pure theory of abstraction.

Philosophy is dialectic, a ** of truth, not a purely theoretical **.

There are similarities, and there are differences.

I think there are aspects of philosophy and mathematics that are connected, like:"Logic", there is a lot of research in philosophy, and logical thinking is also very important for mathematics!

First, the nature is different:

Abstract. Usually more emotional, and logical thinking.

More rational. Second, the meaning is different:

Abstract thinking: It is a form of thinking in which people use concepts, judgments, reasoning, etc. in cognitive activities.

The process of indirect, generalizing the reflection of objective reality.

Logical thinking: In the process of understanding things, people actively reflect the rational cognitive process of objective reality with the help of concepts, judgments, reasoning and other forms of thinking.

3. Thinking differently:

Abstract thinking is characterized by abstraction, through the analysis and thinking of perceptual materials, leaving aside the specific images and individual attributes of things, revealing the essential characteristics of matter, forming concepts, and using concepts to judge and reason to reflect reality in generally and indirectly.

Social. It is the basis for the formation and development of logical thinking, and the needs of social practice determine from which aspect people grasp the essence of things, and determine the task and direction of logical thinking.

Ways of thinking

Abstract thinking methods in metaphysics.

In the initial stage, I only know how to use concepts to represent real things, and I only know how to use different concepts to represent different real things, and to use concepts and deductive relationships between concepts to represent the actual connections between real things. It remains to say to what extent this approach deviates from the realities of the real world.

The things that the concept encapsulates are not identical in themselves from a static point of view, but there are differences and differences; From a dynamic point of view, there are still changes, some major changes and some small changes.

The above content reference: Encyclopedia - Abstract Thinking.

Thinking concretely and thinking abstractly is a relatively basic concept in philosophy, and they are mentioned in philosophical works that are not noisy.

For example, the German philosopher Immanuel Kant, in his Critique of Pure Reason, referred to the role of concepts (both abstract and concrete) in the process of recognition and awareness.

In addition, the English philosopher Hume also introduced abstract and concrete concepts in his "Natural History of Human Understanding".

In Chinese philosophy, for example, in Zhou Yi, there are also concepts of concrete and abstract thinking such as "the universe is infinite, and the carrier is invisible".

In conclusion, thinking concretely and thinking abstract are relatively basic concepts in philosophy, which are covered in different philosophical works.

<> learning mathematics requires the ability to think abstractly, but it doesn't have to rely entirely on abstract thinking. The following points can be referred to:

1.Abstract thinking is important for learning math. Mathematics itself is an abstract subject, and many mathematical concepts and theorems are relatively abstract. To understand these abstract concepts and relationships, it is necessary to develop the abstract thinking skills of mathematics.

2.However, abstract thinking also requires a certain foundation. Some basic mathematical knowledge and arithmetic experience need to be learned and mastered through specific examples and operations. This foundation lays the foundation for the development of abstract thinking.

3.Abstract thinking needs to be developed in concrete problems. It is difficult to fully understand abstract knowledge from the beginning, and it is necessary to start by solving some concrete problems and examples, and gradually form and develop abstract thinking in the process.

4.Intuitive thinking and visual thinking are also important. Mathematics learning also requires intuitive and visual thinking. Since many abstract concepts can be expressed in a visual way, this facilitates understanding and also makes learning easier.

5.Abstract thinking needs to be developed gradually. Mathematics learning should be from the lower grades to the upper grades, from simple to complex, and gradually introduce abstract concepts and complex problems, so that abstract thinking can be gradually developed and developed in the learning process, so as to avoid excessive use of abstract thinking at one time and cause learning disabilities.

In summary, learning mathematics requires abstract thinking, but it does not rely entirely on abstract thinking. In the early stages of learning, intuitive and visual thinking is more needed. Abstract thinking needs to be generated and improved in the process of solving concrete problems, and abstract knowledge cannot be directly understood.

At the same time, abstract thinking also requires a certain amount of gradual development, and it is not achieved overnight. Therefore, learning mathematics requires abstract thinking, but it also needs to start from concrete, so that abstract thinking can be gradually formed in solving concrete problems. This needs to be progressed step by step, and intuitive thinking, visual thinking and abstract thinking complement each other and work together, which is the key to learning mathematics.

In short, mathematics learning requires abstract thinking, but it should not rely entirely on abstract thinking, nor should it ignore the role of intuitive thinking and visual thinking. Rather, it is necessary to gradually guide students to develop abstract thinking from intuition and figurative to abstract in the solution of specific problems, making it an important tool for understanding mathematics.

Learning math does require abstract thinking, but it doesn't have to be. Abstract thinking refers to the ability to abstract commonalities and extract laws from concrete physical objects or events.

Mathematics is a highly abstract discipline that requires abstract thinking. However, this does not mean that the study of mathematics must always be in a state of abstract thinking.

In the learning of mathematics in junior and senior high schools, teachers should use contextual and interesting teaching methods to stimulate students' interest, and connect mathematical knowledge with real life, so that students can understand and apply mathematical knowledge in specific life situations, and gradually cultivate their abstract thinking ability.

In fact, in the solution of some mathematical problems, methods such as leading by example and linkage can also be used to solve the problem, and these methods are also meaningful.

Therefore, learning mathematics can take into account both concrete and abstract ways of thinking, and provide a comprehensive and interesting learning environment for mathematics learners.

Mathematics is an abstract subject, so it is true that abstract thinking is required when learning mathematics. Abstract thinking refers to the transformation of concrete things or concepts into symbols or formulas for representation in order to better study and derive. In the science of jujubes, many concepts and theories are represented in an abstract way, such as vectors, matrices, sets, functions, and so on.

However, abstraction does not mean detachment from reality, on the contrary, mathematical abstraction is often based on the derivation and practical application of concrete problems. For example, calculus is introduced by the problem of motion in physics, matrices and vectors are introduced by the problem of systems of equations in linear algebra, probability theory is introduced by random events in real life, and so on. Therefore, when learning mathematics, it is necessary to pay attention to both abstract thinking and the connection and application of practical problems.

When learning mathematics, beginners may find it difficult to understand and grasp abstract concepts and symbols, but as they learn more and gradually master abstract thinking, they will be able to understand the nature and application of mathematics more deeply, so as to improve their mathematical literacy and problem-solving skills.

Learning mathematics requires a certain amount of abstract thinking, but not all mathematical knowledge requires abstract thinking to understand. There are many concepts and theorems in mathematics, some of which are more abstract, such as set theory, group theory, etc., which need to be understood and applied through abstract thinking. However, there are also many specific applications in mathematics, such as geometry, algebra, etc., which are more intuitive and require intuitive and logical thinking to understand.

Therefore, learning mathematics requires flexible use of different ways of thinking according to different knowledge points and difficulty levels. For more abstract mathematical knowledge, abstract thinking can be used to understand and apply; For more specific mathematical knowledge, intuitive and logical thinking can be used to understand and apply. In addition, mathematics learning also needs to have enough practice and practice, and only through continuous practice and application can you truly master the knowledge of mathematics and improve your ability and level.

Abstract thinking is a very important part of mathematics learning, because mathematical concepts are often abstract and symbolic, rather than intuitive. Through abstract thinking, we can better understand mathematical concepts and theorems and be able to apply them to a wider range of fields. However, abstract concepts can be difficult for beginners to understand, so in the process of learning mathematics, we also need to pay attention to concrete examples and graphical representations to help us understand the concepts and principles of mathematics in depth.

Therefore, both abstract thinking and concrete thinking are essential in the study of mathematics.

In fact, learning mathematics also requires one's own accumulated efforts, and people's abstract thinking is also trained by oneself.

Maybe some people are born with a knack for how to learn math; Maybe some people try very hard to learn, but they still can't.

The reason for this phenomenon is actually very simple: how to master the method of learning.

Learning is not rote memorization, it is useless, you memorize it in a few days and forget it. You need to understand what he means, how he works.

So how can you understand it?

It's about to use your thinking ability, and the strength of your thinking ability determines how quickly you understand the problem. Some people think of a question at once, but some people can't think of it, as if their brains are short-circuited.

In fact, people's thinking ability is not born with it. It can be improved through later practice and exercise.

The mathematics I understand is actually to conceive the steps in your head, and before you can conceive these steps, you have to look at the concept and understanding of the formula.

And to improve the ability to conceive in your head, you can do it by writing out the steps when you are doing some of the topics you know. Think of the steps in your head, think of the macro plan, and then write down the steps to see if the answers you conceive and the answers you write are correct. Abbreviation (oral arithmetic, mental arithmetic).

Through oral arithmetic, you can greatly improve your ability to conceive, the most important thing is to act, how can your mathematical ability improve for no reason if you sit there blankly? Therefore, the way to improve ability is actually to practice.

Generally speaking, there are two angles to understand mathematics roughly, one is abstract, the other is concrete, and as for which one is biased, it varies from person to person. Some people are accustomed to understanding abstract concepts through concrete examples.

No. Philosophy is the quest for intuition, putting that statement in words, and then sharing it.

Philosophy is an understanding.

We can understand what is right. We can understand that something went wrong. We can understand what is real. Moreover, we can understand what is untrue.

We do this by thinking, but you have to be very deliberate. The idea of answering a reed at will not make you understand anything.

You also need to think deeply.

Philosophy related to reality will require a lot of physical evidence and first-hand observation of the world.

Philosophy related to psychology will require a high level of devotion in your own psyche and in the behavior of others.

As always, literature helps.

Philosophy is the continuation of thought, and if someone has already thought of it, there is no point in thinking about it again. Just start there.

Is it possible to think without philosophy?

I'm not sure what this question means. Many animals believe that there has been an extraordinary observation of crows in this regard. The team of engineers who design aircraft engines all think about speeding without any philosophy.

There are a lot of bad insights and contrived ideas in philosophy. In my opinion, the Kalam cosmology is a good example. But that's another question.

Should we call it philosophical thinking?

There are many types of thinking, such as creative thinking (problem-solving, innovation), critical thinking (improving our thinking), and many more. Philosophy is about thinking about the purpose and meaning of life, what is right and wrong, and how we know what we know, and so on. It's more of a deep and basic way of thinking.

Therefore, it is best to leave a clear and understandable philosophy in our communication.

What are some examples of biased thinking in philosophy?

Every idea is one-sided, especially. In philosophy! How can one think absolutely or comprehensively in a way that encompasses everything (in one subject)? (One can say "God," but so what?) How could this possibly be of any help? ）