The significance of resolving the paradox

Although it cannot be said that logical type theory has completely solved the above-mentioned paradox, it can be said that it has greatly promoted the development of logic. Because in a certain sense, it correctly reflects the infinite diversity of the objective external world. This diversity can be reflected in people's thinking in the form of a multi-layered nature. As an external manifestation of human thinking, language is bound to indirectly reflect this objective diversity or multi-layering to some extent. When people's language level or thinking level is incompatible with the level of the objective external world, paradoxes may occur. Through the level analysis of language and thinking, we can help us understand the various regulations of things. Of course, we should point out that the so-called "multi-layered nature" of the objective world is by no means as clear-cut as Russell's logical levels, but presents an extremely complex state. Moreover, the level of propositions is only in terms of the form and structure of thinking. To be honest, it is still a hypothesis that needs further testing.

So, what is the significance of people’s efforts to solve the paradox? To sum up, there are roughly the following three aspects: (1) From a mathematical point of view, paradox forces people to conduct a comprehensive and in-depth study of basic mathematical issues from a logical and philosophical perspective. This effort is an attempt to give mathematics a Relatively more solid foundation; (2) From a logical point of view, in terms of binary logic alone, its value must be either true or false, that is, it cannot be both true and false. However, logical paradoxes destroy the law of contradiction and the law of excluded middle, Making the value of a proposition both true and false cannot be determined, and efforts to solve paradoxes can be said to be an attempt to maintain the basic laws of formal logic; (3) From a philosophical point of view, people's efforts to solve paradoxes continue to deepen their understanding. , thus further analyzing the relatively static forms and structures of thinking, as well as the intricate levels and relationships between them. In addition, the above-mentioned efforts also have certain significance in combating sophistry and relativism.