The paradox of baldness holds that if a person with X hairs is called bald, then a person with X+/kloc-0 hairs is also bald. So (X+ 1)+ 1 the hair is still bald. By analogy, no matter how many hairs you have, you are bald.

An analysis of the paradox of bald people

Obviously, this conclusion is wrong. When a conclusion is wrong, its reasoning or at least one premise is wrong. So, what is wrong?

The analysis is as follows:

This kind of mistake is not easy to be clearly pointed out. Because this is an error caused by structural dislocation. To put it simply, idioms of one word are not suitable in different structures. In daily life, we judge whether a person is bald or not, not by a certain amount of hair, but by a general feeling. So the structure of the concept of baldness is different from the concept that can be clearly quantified. Therefore, when we want to care about whether a person is bald one by one, the problem arises. You can blame the concept of baldness for being unscientific, or you can blame science for not being applicable to this concept.

Not all concepts can be clearly defined by science, and the structure of the concept of daily life is also different from that of scientific concepts. But such a problem is not easy to be clearly pointed out because we seldom pay attention to the so-called conceptual structure.

The Solution of Baldness Paradox

Regarding the paradox of baldness, some people say that we can take the average person's 5000 hairs as the boundary, and stipulate that there is baldness below and not baldness above. If so, is 4999 bald? There are 5,000 hairs. If she (he) combs off one while dressing up, will she immediately become "bald"? Obviously ridiculous! How to solve it?

Fuzzy mathematics, namely fuzzy set theory, was founded in 1965 by an American cybernetic expert (Lotfi A. Zadeh), and its key concept is "membership degree", that is, the degree to which an element belongs to a set. Mathematicians stipulate that when an element completely belongs to a set, the degree of membership is 1, and vice versa; When an element belongs to a set to some extent, its membership degree is a value between 0 and 1 (this value range is similar to probability). So for the paradox of baldness, we can agree that people with less than 500 hairs are completely bald, and its membership degree to the {baldness} set is 1, while people with more than 5000 hairs like Meng are not bald at all, and his membership degree to the {baldness} set is 0. In this way, people with hair numbers of 50 1-4999 belong to the {baldy} set to some extent. For example, 50 1 root has a membership degree of 0.998, while 4999 root has a membership degree of 0.002. That is to say, the root pair {baldy} set of 50 1 ~ 49999 is in a state of "both ownership and no ownership". In this way, using fuzzy mathematics, we have solved the paradox of baldness well.