So this sentence can be true, but it cannot be applied to the sentence itself.
There are many paradoxes similar to this sentence, such as:
1. liar paradox
In the 6th century BC, the philosopher epimenides said, "All Celts are lying, and so did one of their poets." This is the origin of this famous paradox.
People will ask: Is Epiminides lying?
A standard form of this paradox is that if event A occurs, non-A is deduced, and if non-A occurs, A is deduced.
This is a self-contradictory infinite logic cycle. One-sided body in topology is the expression of image.
The philosopher Russell once seriously thought about this paradox and tried to find a solution. He said in the seventh chapter "Mathematical Principles" of "The Development of My Philosophy": "Since Aristotle, logicians of any school seem to be able to deduce some contradictions from their recognized premises. This shows that there is a problem, but it cannot point out the way to correct it. In the spring of 1903, one of the contradictory discoveries interrupted the logical honeymoon I was enjoying. "
He said: The liar paradox simply sums up the contradiction he found: "The liar said,' Everything I said is false'. In fact, this is what he said, but this sentence refers to all he said. Only by including this sentence in that crowd will there be a paradox. "
Russell tried to solve the problem through hierarchical propositions: "The first-level propositions can be said to be those that do not involve the whole proposition; Second-level propositions are those that involve the whole first-level proposition; The rest is like this, even infinite. " But this method has not achieved results. "During the whole period of 1903 and 1904, I almost devoted myself to this matter, but it was completely unsuccessful."
Mathematical principles try to deduce the whole pure mathematics on the premise of pure logic, explain concepts in logical terms, and avoid the ambiguity of natural language. But in the preface of this book, he called it "publishing a book that contains so many unresolved disputes." It can be seen that it is not easy to completely solve this paradox from the logic of mathematical basis.
Then he pointed out that in all logical paradoxes, there is a kind of "reflexive self-reference", that is, "it contains something about that whole, and this kind of thing is a part of the whole." This view is easy to understand. If this paradox is said by someone Park Jung-soo thinks, it will be automatically eliminated. But in set theory, the problem is not so simple.
2. The 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".
3. 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.
4. Bibliographic paradox
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.
5. 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. In prout, Golas was expelled and his books were burned.
Twelve years later, Socrates was also sentenced to death, 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.