What is the Bald Man Paradox?
What is the Bald Paradox
The Bald Paradox holds that if a person with X hairs is called bald, then a person with X + 1 hairs is also bald. Therefore, the person with (X + 1) + 1 hair is still bald. By analogy, no matter how many hairs you have, you are bald.
Analysis of the Bald Man Paradox
Obviously, this conclusion is wrong. When a conclusion is wrong, the reasoning or at least one premise is wrong. So, where is the error?
The analysis is as follows:
This kind of error is not easy to point out clearly. Because this is an error caused by structural misplantation. Simply put, an idiomatic usage of a word is inappropriately placed in a different construction. In our daily life, we determine whether a person is bald or not by not measuring a certain number of hairs, but by a general feeling. So the structure of the concept bald is different from that of a concept that can be clearly quantified. Therefore, problems arise when we use each element to calculate whether a person is bald. You can blame the concept of bald man for not being scientific enough, or you can blame science for not being applicable to such concepts.
Not all concepts can be clearly defined by science, and the structure of daily life concepts is different from the structure of scientific concepts. But this kind of problem is not easy to point out clearly, because we rarely pay attention to the so-called conceptual structure.
Solution to the bald paradox
Regarding the bald paradox, some people say that we can use the average 5,000 hairs that an average person has as a boundary, and stipulate that those below are bald and those above are not bald. If it is stipulated in this way, then, does 4999 hairs count as bald? If she or he has 5,000 hairs and one of them falls off while dressing up, will he or she immediately become "bald"? Obviously too ridiculous! How to solve it?
Fuzzy mathematics, also known as fuzzy set theory, was founded by American cybernetics expert Lotfi A. Zadeh in 1965. Its key concept is "degree of membership", that is, an element belongs to an degree of collection. Mathematicians stipulate that when an element completely belongs to a set, its membership degree is 1, otherwise it is 0; when an element belongs to a set to some extent, its membership degree is a value between 0 and 1. (This range of values is similar to probability). So, for the baldness paradox, we can agree that a person with less than 500 sparse hairs is completely bald, and its membership degree to the set {bald} is 1, while a person like Meng with more than 5,000 thick hairs is Not bald at all, his membership degree to the {bald} set is 0. In this way, people with 501-4999 hairs belong to the {bald} set to a certain extent. For example, the one with 501 roots has a membership degree of 0.998, and the one with 4999 roots has a membership degree of 0.002. This means that those with roots 501 to 49999 are in a state of "both belonging and not belonging" to the {bald} set.
In this way, using fuzzy mathematics, we have solved the Bald Man Paradox well