Mathematical refutation examples, what is mathematical refutation

To establish one's own argument by exposing and refuting false, reactionary arguments is refutation. The function of refutation is to "break", that is, to distinguish between right and wrong, refute erroneous views, and at the same time establish correct views.

Argumentation, like argumentation, is a way of arguing and reasoning. In refuting arguments, it is necessary to distinguish between contradictions of different natures and adhere to the principle of convincing people with reason. In an article, arguments and arguments often complement each other.

In order to refute an argument, it is necessary to possess the materials in advance, conduct a thorough analysis of the erroneous remarks, find out the crux of the erroneous remarks, and concentrate on one point, so that we can hit the nail on the head and hit the nail on the head. "It is better to cut off one of its fingers than to hurt its ten fingers." This is the gist of the rebuttal. Only when the wrong arguments are refuted can the correct arguments be established.

To refute the argument, it is also necessary to choose the right angle. Just like in a war, if the angle of attack is not well chosen, you will not be able to deliver a fatal blow to the enemy.

The most basic method of refuting an argument is still to present facts and reasoning, and all kinds of methods for making arguments can be used in refutation.

The general methods of refutation include rebuttal arguments, rebuttal arguments, and rebuttal arguments.

A rebuttal is a support for the essay – an argument is refuted, either directly or by summarizing the fallacies in the argument.

Refutation argument is to refute the argumentation of the article, for the example argument can be to find out the part of the example and the facts, the reason, for the comparative argument, can be pointed out.

The irrational part of the comparison can be refuted by the method of pointing out the errors of the reasoning argument (Marxist principle) with philosophical knowledge.

It's a "mathematical paradox", right?

Paradox is a kind of cognitive contradiction, which includes both logical contradictions, semantic contradictions, and contradictions in thinking and methods.

Mathematical paradox, as a type of paradox, mainly occurs in the study of mathematics. According to the broad definition of paradox, the so-called mathematical paradox refers to the unsolvable cognitive contradiction that occurs in the existing mathematical norms in the field of mathematics, and this cognitive contradiction can be resolved in the new mathematical norms.

For example, there is a barber in a certain city, and his advertising slogan reads: "I am very skilled in barbering, and I am famous all over the city."

I will shave the faces of all those in the city who do not shave their faces, and I will only shave their faces. I extend a warm welcome to all of you! "There is an endless stream of people who come to him to shave their faces, and naturally they are all those who don't shave their faces.

But one day, when the barber saw in the mirror that his beard had grown, he instinctively grabbed the razor, and you see if he could shave his own face? If he doesn't shave himself, he belongs to the "one who doesn't shave himself", he has to shave himself, and what if he shaves himself? He belongs to the "person who shaves his face", so he should not shave his face.

The barber's paradox is equivalent to Russell's paradox:

Because, if you look at each person as a set, the elements of this set are defined as the objects of the person's face. The barber, then, declares that his elements are those collections that do not belong to the village that do not belong to him, and that all the collections of the village that do not belong to him belong to him. So does he belong to himself?

In this way, the barber's paradox brought Chang to Russell's paradox. The reverse transformation is also true.