Pope said that two plus two doesn't make four. what do you think?

Pope said that two plus two doesn't make four. what do you think?

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I am reading Popper's Conjecture and Refutation, mainly because my understanding of falsificationism is only indirect. Therefore, it is necessary for me to read Conjecture and Refutation. But in the process of reading, some problems bothered me, which made me unable to continue. One of the problems is Popper's doubt that two plus two equals four.

The ninth section of the book is entitled "Why logical calculus and arithmetic calculus can be applied to reality". In this section, Popper wrote: "In this sense,' 2+2 = 4' can be considered to mean that if someone puts two apples in a basket, then puts two in it, and doesn't take any apples out of the basket, then there are four apples in the basket. According to this explanation, the statement' 2+2 = 4' helps us to calculate, that is, to describe some physical facts, while the symbol'+'stands for a physical operation-it stands for physically adding something to another. We see here that it is sometimes possible to describe an obvious logical symbol. However, in this explanation, the statement of' 2+2 = 4' becomes a physical theory, not a logical theory; Therefore, we are not sure whether it is still universally applicable. In fact, it is not universally applicable. It may be true for apples, but it is difficult for rabbits. If you put 2+2 rabbits in a basket, you may soon find 7 or 8 rabbits in this basket. Not suitable for things like water drops. If you drop 2+2 drops into a dry beaker, you can never take 4 drops out of it. In other words, if you are confused about what kind of world' 2+2 = 4' does not apply to, then your curiosity will be easily satisfied. A pair of rabbits of different sexes or a few drops of water can be used as a model of such a world. If you answer that these examples are not so appropriate, because some changes have taken place in these rabbits and water droplets, and because the equation' 2+2 = 4' only applies to those objects that have not changed, then my answer is that if you explain it this way, it does not hold true for' reality' (because in' reality', it always changes), but only for' reality'. Obviously, as long as our real world is similar to such an abstract world, for example, as long as our apples don't rot or just rot slowly, or as long as rabbits or crocodiles happen to be barren, in other words, as long as the physical conditions are similar to pure logic or arithmetic addition, arithmetic is of course applicable. However, this is superficial. It can be seen from this passage that Popper believes that "two plus two equals four" is a physical theory, not a logical theory. It may be true for apples, but it is difficult for rabbits and other things. It does not apply to the real world that is always changing, but only to the abstract world composed of unique objects, in which nothing has changed. Therefore, it is not "universally applicable". "

"Two plus two equals four" and "Don't keep the universal truth", then there must be something to keep the universal truth. Yes, Popper told us that this kind of thing is the rule of reasoning. He wrote: "Inference rules are always statements about statements, or statements about statements (they are metalinguistic)" and "Inference rules are unconditional statements about deductibility". In other words, the inference rules are unconditional. "Logical rules, or more precisely, inference rules, are the rules of the program. This means that they apply to certain procedures, not things or facts. If we say that' reality' refers to things or facts described by scientists and historians, then these rules do not apply to reality. " "Logical rules apply to the procedure of reasoning, which can be compared with the procedure that highway rules apply to riding a bike or driving a car. Logical rules can be observed or violated. Applying logical rules does not mean making them appropriate, but rather observing them and acting on them. " The rule of reasoning is only applicable to the rational world, and it is a rule that reason should follow. Therefore, "logic is fundamentally not a self-evident theory; Mainly about the theory of correct reasoning. " In other words, the inference rules only talk about the correctness of the form, regardless of the authenticity of its content. Inference rules are universal.

Actually, it's not. Just like "two plus two equals four", reasoning rules are not "universally applicable"!

It is precisely because there are roads and cars driving on them in the real world that there are highway laws and regulations that must be observed when driving. It can be seen that highway laws and regulations are not created out of thin air, they just come from the real world. The same is true of reasoning rules, which also come from the real world. In the process of exchanging ideas, people always adopt some argumentation methods in order to make their views, ideas, intentions and opinions known to people. These commonly observed methods are inference rules. Inference rules are produced in the real world where people exchange ideas. Therefore, the real world is the source of inference rules. In the process of reasoning, people should abide by the rules of reasoning, not only because the form is correct, but because it makes our opinions, ideas, intentions, viewpoints and so on. It is in line with the facts. Therefore, inference rules not only come from the real world, but more importantly, they should be applied to the real world. This requires that the inference rules are not only correct in form, but also in line with the facts. If someone says that "the sun used to rise in the east every morning, so the sun will not rise in the east tomorrow morning", it will be laughed at, but its reasoning form is correct. Therefore, the inference rule is not unconditional, but conditional. In fact, when Popper said that "inference rules are unconditional statements about deductibility" and "they apply to certain procedures, not things or facts", he had already stipulated conditions for inference rules. How can we say that inference is unconditional? Inference rules are not only correct in form, but also require content to be consistent with facts, which is restricted by the real world.

Inference rules are not "universally applicable" like "two plus two equals four", but only correct within a certain range.

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Two plus two equals four but not five, just as seven plus five equals twelve but not thirteen. This is common sense that even primary school students know, and it is a truth that everyone knows. But Popper pointed out that two drops of water and two drops of water are not equal to four drops of water, and two rabbits and two rabbits are not necessarily equal to four rabbits, but may be seven or eight. Pope was right. In fact, two plus two equals four, which is just a decimal statement. In decimal system, 2+2 = 4, in binary system, 2+2 = 100, and in quaternary system, 2+2 = 10. In other words, not in any case, two plus two equals four; It is conditional that two plus two equals four. Two plus two equals four, only within a certain range, only within a certain range is correct!

However, what attracts our attention is not that two plus two equals four, but that it is not "universal" and only within a certain range, not just that two plus two equals four.

Let's look at another example, such as classical physics.

By the end of19th century, classical physics had made brilliant achievements. In the eyes of most scientists, the development of classical physics is close to the peak, and it is impossible to move forward. However, at this time, the appearance of the three major discoveries has had an unprecedented violent impact on the basic concepts such as mass, energy and motion in classical physics, and classical physics also has its unexplained phenomena. In other words, classical physics, like two plus two equals four, is not "universal" and is only correct within a certain range.

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Only within a certain range is it correct. What is the reason for this phenomenon?

The reason for this phenomenon lies in the observation range!

Most philosophers after Hume disdained observation. Think about it, too Isn't observation just a look? Who can't look at people with normal eyes and who doesn't?

However, it is these dismissive phenomena that make us overconfident, and even our philosophers often show this confidence. Hume, Kant and Popper all think that there is something "universally applicable".

In fact, it is these dismissive phenomena that limit our observation and make "universal truth" impossible.

This is because the human eye can only see a certain range of things.

The formation of conclusions, including theories, is restricted by both subject and object.

According to the system theory, everything in the world is a whole composed of parts and has integrity. We see only a part, but not the whole. What we observe is only a certain range of things. This observation feature is called observation range.

There is a certain range of observation, and the decisive evidence is Heisenberg's uncertainty principle. The essence of Heisenberg's uncertainty principle is that our observation has a certain range.

An object is not a plane, but a three-dimensional one, which is a whole composed of parts and has integrity. This overall feature of the object limits our observation. In addition, the structural characteristics of the human eye also restrict our observation. The dual constraints of subject and object enable us to observe only a certain range of things. Since we only observe things within a certain range, the conclusions drawn from it must also have the characteristics of range.

In fact, whether it is 2+2 = 4 or inference rules, whether it is classical physics or quantum mechanics, whether it is confirmationism or falsificationism, in short, in the process of understanding and transforming the world, we have known all the fields involved, whether it is science, philosophy, culture, politics or any other field, and we have found out what is regular and what reflects the essential characteristics of things, that is, the truth we often say.

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Ignoring the object of observation and dismissing the integrity of the object is the limitation of traditional philosophy, and Popper is naturally influenced by this limitation. This is to treat the object we observe as a plane! It is an important feature of traditional philosophy to regard the object we observe as a plane. Pursuing "universal truth" is one of the main tasks of philosophers. Their thinking mode is concentrated as follows: I am right and others must be wrong. This is the inevitable result of taking the object we observe as a plane.

Everything we can see with our eyes is a whole composed of parts, which has integrity; We can only observe parts, but not the whole. This is normal, familiar and simple. However, the seemingly ordinary and simple phenomenon, from avenue to Jane, or Jane Avenue, implies something regular. For example, it is normal for an apple to fall to the ground, but Newton studied it and discovered the law of gravity.

Violation of the law will be punished by law. Hume's and Popper's questioning of induction is a concrete manifestation of treating the object as a plane. As a result, it leads to doubts about scientific rationality. Not only that, the solution of Hume's problem has put many philosophers into a dilemma that they have tried their best to solve. Similarly, the same is true of Popper's query that "two plus two equals four". He correctly pointed out that "two plus two equals four" does not "maintain universal truth", but he can't explain "two plus two equals four" to a certain extent.

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Although "two plus two equals four" does not "maintain universal truth", it has this characteristic within a certain range. Within a certain range, "two plus two equals four" is a rule that we generally abide by. You bought four rabbits at the farmer's market. According to Pope, you must pay the businessman seven or eight rabbits. That's true. You won't like it, especially in market transactions. It is true that two male rabbits and two female rabbits gave birth to seven or eight rabbits through childbirth, but it takes time and a process. We can only see the status quo of rabbits. There are four rabbits. We can only see the state that has become a reality. As for the future development of rabbits, we can only predict but can't be sure before the fact is formed, so we can't observe it.

In a certain time and space, we can only observe the development state that has become a fact by observing things; Things move and develop in a certain time and space, and time and space are also important factors affecting the development of things, but this important factor has been ignored by Popper. The arithmetic theory of "two plus two equals four" draws the conclusion that putting 2+2 rabbits and 2+2 drops of water belong to different ranges, but Popper has mixed the phenomena in different ranges. As Popper said, "two plus two equals four" does not "maintain universal truth", so it does not apply to the real world. Nevertheless, it is applicable to a certain extent in the real world. Within a certain range, "two plus two equals four" and "maintaining universal truth" have some truth, which is a rule that our daily life science research institute must abide by. Because of this, it is the theoretical knowledge that we should learn and master from an early age. Popper's query that "two plus two equals four" is a fundamental denial of arithmetic theory.

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Popper questioned "two plus two equals four" in order to provide evidence for his falsificationism.

The central argument in the book Conjecture and Refutation is that the standard to measure the scientific status of a theory is its falsifiability or refutability or testability. In his view, the so-called knowledge is only a hypothesis, and "two plus two equals four" is also a hypothesis. Because all knowledge can be confirmed by induction. In his view, inductive reasoning is the reasoning from single name judgment to full name judgment, so it is unreasonable and invalid. For example, he said that induction can prove that swans are white, but it cannot prove that all swans are white. Similarly, induction can prove that "two plus two equals four", but it cannot prove that all "two plus two equals four". "Two plus two equals four" and "not keeping universal truth" do not apply to the real world. The reason why he questioned that "two plus two equals four" is a concrete manifestation of the limitations of traditional philosophy, because in the view of traditional philosophy, one theory is correct, then the other theory must be wrong, because there is only one truth. Therefore, in order to prove his falsificationism, he must prove that falsificationism is wrong. However, in practice, Popper inevitably adopted induction while opposing it. Because if you want people to accept falsificationism, induction is a necessary tool.

In fact, Popper questioned "two plus two equals four" only because he stood from different angles and observed in different scopes. If both parties observe a monument at the same time, but A observes the front and B observes the back, they observe the same monument, but the description and conclusion of the monument may be different. The same is true of Popper's questioning of positivism. Although both positivism and falsificationism abide by the boundary between science and non-science, it is the same as the observation of historical sites by both parties ... Our observation objects, whether intuitive or abstract, are all composed of parts and have integrity. The same is true of the demarcation between science and non-science, which is also a whole composed of parts and has integrity. Confirmationism and falsificationism, they both observe the parts that make up the whole. Just as positivism can't observe the falsificationism, falsificationism can't observe the confirmatory side. Therefore, whether positivism or falsificationism, they are only within a certain range. We say positivism is right, or falsificationism is right, only to a certain extent. Whether positivism or falsificationism is correct within a certain range, they all have their own unexplained phenomena. In fact, the demarcation standard between science and non-science is its verifiability and falsifiability, both of which are indispensable. The basic feature of theoretical scientificity is that it must be proved and falsified.

Einstein's theory of relativity is a falsification of Newtonian mechanics, and quantum theory is a falsification of classical physics. But this only points out that the classical physics of Newtonian mechanics is only applicable to the macro world, which reveals the laws of material movement and change in the macro world. It is still the scientific knowledge that we should learn and master, the rules that we must strictly abide by in production practice and scientific experiments, and it is still shining within its scope of application. For example, the application in aerospace is a good example. Falsification does not mean that this theory is wrong and should be overthrown and denied. Falsification only points out the scope and boundary of this theory, that's all! Within its scope of application, this theory still "maintains universal truth" and still has certain truth. We should understand falsificationism in this way!

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However, Popper's doubt that "two plus two equals four" is of great significance, especially for our theoretical circles, because its essence is that any theory can be falsified.

Popper's falsificationism is the greatest contribution to philosophy. The demarcation standard between science and non-science is its falsifiability. How to explain how to be correct, how to apply it everywhere and how to be incorrect is precisely a sign of non-science. Popper takes astrology as an example. Astrologers always say, "The prophecy is so vague that it will never fail. This is a typical soothsayer trick, which makes the prediction irrefutable. " He can explain his divination results in many ways, so he is always right. When a theory is widely publicized, in the face of falsification cases, its followers usually reinterpret the theory to make the case conform to the theory, so that the theory is not refuted, thus ensuring that the theory is always in the right position. Popper criticized that this is a "fortune teller's practice", "so that their theory of rescue will not be refuted; ..... it destroys the scientific status advertised by this theory. " This is not to maintain the theory, but to belittle the theory, which is to belittle the theory from science to non-science like astrology.

Any theory or conclusion is correct only within a certain range! There is no theory or conclusion of "maintaining universal truth" without scope constraints! Popper's falsificationism gives a good answer to this point.

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