Paradox is the confusion of facts and values in different levels of thinking, meaning (content) and expression (form), subjectivity and objectivity, subject and object, proposition or reasoning, and the asymmetry of thinking content and thinking form, thinking subject and thinking object, thinking level and thinking object, thinking structure and logical structure.
Paradox is rooted in the limitations of intellectual knowledge, intellectual logic (traditional logic) and contradictory logic. The root cause of paradox is to formalize traditional logic and absolutize the universality of formal logic, that is, to regard formal logic as a way of thinking.
All paradoxes are caused by formal logical thinking mode, which cannot be found, explained or solved. The so-called solution of paradox is to find and correct the logical errors in paradox by using symmetrical logical thinking mode.
Extended data:
Classic solution:
1, barber paradox
In Saville village, the barber put up a sign: "I only cut the hair of those people in the village who don't cut their own hair." Someone asked him, "Do you cut your hair?" The barber was speechless at once.
This is a paradox: a barber who doesn't cut his hair belongs to the kind of person on the signboard. As promised, he should give himself a haircut. On the other hand, if the barber cuts his own hair, according to the brand, he only cuts the hair of people in the village who don't cut their own hair, and he can't cut it himself.
So no matter how the barber answers, he can't rule out the internal contradictions. This paradox was put forward by Russell in 1902, so it is also called "Russell paradox". This is a popular and story-telling expression of the paradox of set theory. Obviously, there is also an unavoidable problem of "self-reference".
2. Paradox of set theory
"R is the set of all sets that do not contain themselves."
People will also ask: "Does R include R itself?" If not, according to the definition of R, R should belong to R. If R contains itself, R does not belong to R..
Kurt G?del (Czech Republic, 193 1) put forward an "incomplete theorem", which broke the ideal that mathematicians thought that all mathematical systems could be deduced by logic at the end of19th century.
This theorem points out that any postulate system is incomplete, and there must be propositions that can neither be affirmed nor denied. For example, the negation of the "axiom of parallel lines" in Euclidean geometry has produced several non-Euclidean geometries; Russell's paradox also shows that the axiomatic system of set theory is incomplete.
3. The paradox of bibliography
A library compiled a dictionary of titles, which listed all the books in the library without their own titles. So will it list its own title?
This paradox is basically consistent with Barber's paradox.
4. Socrates paradox
Socrates (470-399 BC), an Athenian, is known as "Confucius in the West" and a great philosopher in ancient Greece. He was once opposed to the famous sophists Prut Golas and Gogis.
He established a "definition" to deal with the confusing rhetoric of sophists, thus finding out hundreds of miscellaneous theories. But his moral concept was not accepted by the Greeks, and he was regarded as the representative of sophistry when he was seventy years old.
Twelve years after expelling Prut Goras and burning books, Socrates was also executed, but his theory was inherited by Plato and Aristotle.
Socrates famously said, "I only know one thing, and that is nothing."
This is a paradox, and we can't infer from this sentence whether Socrates doesn't know the matter itself.
References:
Baidu encyclopedia-paradox