What does paradox mean?

A paradox is the implication of two opposing conclusions in apparently the same proposition or inference, both of which are self-evident. The abstract formula for a paradox is: if event A occurs, then non-A is deduced, and if non-A occurs, then A is deduced.

A paradox is the confusion of different levels of thinking, meaning (content) and expression (form), subjectivity and objectivity, subject and object, fact and value, implicit in propositions or reasoning, and the confusion of the content of thinking with the form of thinking, the subject of thinking with the object of thinking, and the hierarchy of thinking with the object of thinking.

A paradox is the asymmetry of thinking structure, logical structure, and logical structure. Asymmetry, is the asymmetry of thinking structure, logical structure.

Paradoxes are rooted in the limitations of intellectual awareness, intellectual logic (traditional logic), and paradoxical logic. The root cause of paradox is the formalization of traditional logic, the absolutization of the universality of formal logic, i.e., formal logic as a way of thinking.

All paradoxes are due to the formal logic way of thinking, the formal logic way of thinking can not find, can not explain, can not solve the logical errors. The so-called paradox solution is to use symmetric logic way of thinking to discover and correct the logical errors in the paradox.

Expanded:

Classic Paradoxes Solved:

1, The Barber's Paradox

In the village of Saville, the barber puts up a sign that says, "I only give haircuts to all those people in the village who don't give their own haircuts." Someone asked him, "Do you cut your own hair?" The barber was speechless.

It was a paradoxical reasoning: if the barber did not cut his own hair, he belonged to the class of people on the sign. There is a word that he should cut his own hair. Conversely, if this barber cuts his own hair, according to what the signboard says, he only cuts the hair of those in the village who don't cut their own hair; he cannot cut his own hair.

Thus, no matter how this barber answers, he cannot rule out the inherent contradiction. This paradox was proposed by Russell in 1902, so it is also called "Russell's paradox". This is the common, storyline expression of the set theory paradox. Obviously, there is also a problem of "self-reference" that cannot be ruled out.

2, The Set Theory Paradox

"R is the set of all sets that do not contain themselves."

One might similarly ask, "Does R contain not contain R itself?" If it does not, by definition R belongs to R. If R contains itself, R does not belong to R.

Following Russell's paradoxes of set theory, which revealed a problem with the foundations of mathematics, in 1931 Kurt Godel (1906-1978, Czechoslovakia) formulated an "incomplete theorem", which broke the 19th century's "Theorem of Completeness". Theorem", which broke the ideal of mathematicians at the end of the nineteenth century that "all mathematical systems can be deduced from logic".

The theorem states that no axiomatic system is complete, and that there must be propositions in it that can neither be affirmed nor denied. For example, the "axiom of parallels" in Euclidean geometry, the negation of which gives rise to several non-Euclidean geometries, and Russell's paradoxes show that the axiomatic system of set theory is incomplete.

3, The Bibliographic Paradox

A library compiles a dictionary of titles, which lists, and only lists, all the books in the library that do not list their own titles. So does it list its own titles?

This paradox is essentially the same as the barber's paradox.

4, Socrates Paradox

Socrates (470-399 BC), the Athenian known as "Confucius of the West", was a great philosopher in ancient Greece, who was opposed to famous sophists such as Protagoras and Gorgias.

He established "definitions" to deal with the confusing rhetoric of the sophists, and thus surveyed the miscellaneous statements of a hundred schools of thought. But his morality was not tolerated by the Greeks, and he was taken as a representative of sophistry at the age of seventy.

Twelve years after the expulsion of Plotegoras and the burning of his books, Socrates was also put to death, but his doctrines were succeeded by Plato and Aristotle.

Socrates famously said, "I know only one thing, and that is nothing."

It is a paradox that we cannot infer from this statement whether Socrates also knew nothing about the matter itself.

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