There are many famous paradoxes in ancient and modern China and abroad, which have impacted the foundation of logic and mathematics, stimulated people's knowledge and precise thinking, and attracted the attention of many thinkers and enthusiasts throughout the ages. Solving paradoxes requires creative thinking, and the solution of paradoxes can often bring people new ideas.
According to the causes of paradox, it can be divided into six types, all of which are common paradoxes that are widely circulated. With the rapid development of modern mathematics, logic, physics and astronomy, many new paradoxes have emerged, which people are tirelessly exploring. It is expected that their achievements will greatly change our thinking concept.
Research on solving contradictions;
The philosopher Russell once seriously thought about this paradox and tried to find a solution. In the seventh chapter of Mathematical Principles, the Development of My Philosophy, he said: 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, a contradictory discovery interrupted my logical honeymoon.
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. " (same as above)
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." (same as above)
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 other than Park Jung-soo, it will be automatically eliminated. But in set theory, the problem is not so simple.