What is reasoning that contains paradoxes The popular understanding of paradoxes

1. If Pinocchio says, "My nose will grow longer soon." "What will be the result?

2. Suppose you pass by a barbershop with a sign that says, "Do you shave your face?" If not, please allow the shop to shave your face!

I only shave the faces of some people in the city who don't shave their own faces, and no one else shaves. "That's enough to get you inside the barbershop, but then you find the question – does the barber shave his face? If he shaves himself, then he is breaking his promise to only shave his own face, and if he doesn't shave himself, then he has to shave himself, because his promise says that he only shaves his own face for people who don't.

Both assumptions make this statement unreasonable.

3. The crocodile paradox. A crocodile grabbed a child and said to the child's mother, "Do you think I will eat him?"

If you guess right, I won't eat him. I guessed wrong and ate it. The child's mother said

I'm guessing you're going to eat my baby. The crocodile said, "Haha, then I'm going to eat it."

The child's mother said, "If I guessed right, then you shouldn't eat him." "The crocodile is confused, if she gives it back to her, then he guessed the wrong I should have eaten it, but if I ate him, she guessed correctly that I shouldn't eat him.

What is "paradox"? A lot of people misunderstand, and that's what it really means.

The paradox is superficially the sameImplicit in a proposition or reasoning are two opposing conclusions, both of which can be justified.

It usually refers to a proposition that, according to the generally accepted method of logical reasoning, can lead to two opposing conclusions in the form of: if event A occurs, then non-A is deduced, and if non-A occurs, A is derived.

There are many famous paradoxes in ancient and modern times, both in China and abroad, which have shaken the foundations of logic and mathematics, stimulated people's curiosity and precise thinking, and attracted the attention of many thinkers and enthusiasts throughout the ages. Solving paradoxical puzzles requires creative thinking, and the solution of paradoxes can often lead to completely new ideas.

Significance and impact of paradox research:

At the end of the 19th century and the beginning of the 20th century, the foundations of logic and mathematics were affected by the discovery of many difficult (so-called paradoxes), especially the contradictory phenomena found in classical set theory, especially Russell's paradox, which shook the foundations of mathematics in a very concise form, which was the "third mathematical crisis".

Paradoxes have acquired a new role in contemporary logic, and they have led to the discovery of new theorems (often negative outcomes, such as unprovability and undecidability). The development of several basic concepts of logic, which has reached its current state, is usually due to various attempts to solve paradoxes.

This is especially true for the emergence of the concepts of sets and collections, the basic syntactic and semantic concepts of standard classical logic (the logical language of a given order, the concept of satisfiability, definability).

A paradox is a statement or proposition that seems logical on the surface, but in fact it is self-contradictory, untenable, and a mistake in thinking. Paradoxes are challenges to logical thinking and are often used in thinking and research in fields such as philosophy, mathematics, physics, linguistics, etc. The existence of paradoxes reveals the limitations of language and logic, highlights the limitations and deficiencies of our thinking and reasoning, and reminds us to pay attention to various premises and starting points when thinking about problems and reasoning.

Paradoxes often show people's logical dilemmas and ideological biases, and some wrong ways of thinking can be broken through paradoxes, so that we can understand the essence of things more clearly. Paradoxes come in many forms, the most famous of which are the following:1

Bertrand's Paradox: If a coin is uniformly random, what is the probability that at least half of the results of 100 tosses will be heads up? Bertrand's paradox is that when you think the probability is 50%, the probability is actually about.

This is due to the fact that in the case of a uniform distribution, the more you throw, the higher the probability, so the 50% probability is a misunderstanding. 2.Achilles and the Tortoise Paradox:

Achilles had to overtake a turtle, but had to start in a queue 10 meters in front of him. First of all, Aki [oo

A paradox is a theory that defies common sense or is absurd, or a contradictory statement or a high-rent proposition. "Paradox" is not only a very catchy word, but it is also a special and proprietary conceptual noun in logic and mathematical reasoning. The so-called "paradox" means that if a proposition A is admitted, it can be inferred as a non-A proposition.

Conversely, if we admit that it is not A, we can deduce A. This contradictory proposition A, then, would be called a "paradox" by Hambi. Definitions:

According to the "paradox" entry in the Stanford Encyclopedia of Philosophy, a paradox is generally a proposition that, according to a generally accepted method of logical reasoning, leads to a conclusion that goes beyond "generally acceptable opinion." Or rather, the conclusion is contradictory. A paradox is when there are two opposing conclusions implied in the ostensibly same hail proposition or reasoning, both of which can be justified.

The abstract formula for the paradox is that if event A occurs, then it is deduced that it is not A, and if it does not occur A, it is deduced.

The first thing to know is that paradox is a term of logic.

Its definition can be expressed as follows: a proposition that is recognized as true is premised, set to b, and after correct logical reasoning, a conclusion that contradicts the premise is not b; Conversely, if it is not b, b. can also be deducedThen proposition b is a paradox.

Of course, non-B is also a paradox.

Paradoxes, of course, contain a wealth of ideological content. This article is not intended to go into details. The easiest reason for misunderstanding paradoxes is that they want to make sense of the text.

When I see that there is a word "theory" in the noun paradox, I think that the form of paradox is a statement or theory; or that a paradox is a form of inference (i.e., a process of reasoning); Or take paradoxes as conclusions as the result of reasoning. Not really. As for the kind of self-righteous people who do not know anything about it, who do not know how to pretend to understand, and who misregard the fallacies of chaotic contradictions and contradictions as paradoxes in logic, then it is not a matter of misunderstanding.

As a paradox, it has the following characteristics:

A paradox is a proposition.

is a true proposition that is recognized as a premise;

Based on the premise of the above true propositions, correct logical reasoning is carried out;

The conclusion is a proposition that contradicts the premise (and it should be admitted that it is a true proposition).

As mentioned above, who does not know that paradox is a logical term; Who does not know that a proposition that is a paradox must be a true proposition to be recognized.