The inconsistency of paradoxes, the causes of paradoxes

The difference between a fallacy and a paradox is that a fallacy is a non-conformityLogical thinkingis a judgment that needs to be refuted by logic. And the paradox is not, the paradox isLogicThe middle finger uses contradictory hypothetical premises as a choice of arguments to produce conclusions that are impossible in reality.

In the set paradox of mathematics, it arises because a set is too broadly qualified to join contradictory children to the same set. For example: if it is believed to be true, it is false; If it's considered fake, it's true.

Types of paradoxes: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.

According to the reasons for the formation of paradoxes, they are grouped into six types, and they are all common paradoxes that have been widely circulated. With the rapid development of modern mathematics, logic, physics and astronomy, many new paradoxes have emerged.

Causes of paradoxes: Only "logical, philosophical, and linguistic paradoxes" are considered here, and other paradoxes such as the voting paradox, the Fermi paradox, the grandmother paradox, and so on are not discussed here. Because there are so many things involved, and logical, philosophical, and linguistic paradoxes do not require any other intellectual background, and the discussion of them can reveal the nature of paradoxes better.

What is Paradox? A paradox is first and foremost an argument. (Don't talk to me about the liar's paradox is just a sentence, don't you argue to know that it is contradictory?)

A paradox in a broad sense refers to the fact that a premise that is intuitively true is derived from a valid form of argument and leads to a conclusion that is intuitively false. A paradox in the narrow sense refers to the introduction of a paradox.

The definition of paradox 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 non-b is the premise, B can also be deduced. Then proposition b is a paradox.

Of course, non-B is also a paradox. We can judge the incarnation or prove the truth or falsity of a proposition according to certain axiomatic rules made or agreed, but when we judge or prove the truth or falsity of some propositions according to the axiomatic rules established or agreed, sometimes paradoxical problems arise that cannot be solved.

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Problem description: What is the cause of the paradox? Is it just because there's something wrong with that admitted proposition? But there seems to be nothing wrong with many of the paradoxes. It is also nonsense to say that modern numbers still think that paradox and logic are contradictory. I would like to explain it in detail and it would be better to illustrate it with examples.

Analysis: There are many reasons for the paradox. Russell argues that the key lies in the infinite "vicious circle", Poincaré argues that the key is the use of "non-explicit statements" in the definition of concepts, and Weil argues that the root of the difficulty lies in the concept of infinity and infinity used in infinite programs, and that Weil even points to the point that mathematics is inherently about the science of infinity, and so on.

The crux of the real problem, or the crux of the matter, is that the language of mathematics of mankind, and indeed all of humanity's natural language, has so far been based on the logic of duality. This duality of basic logic is the root cause of all so-called paradoxes. It is precisely for this reason that the Logicist school wants to unify all mathematics based on dualistic logic, which is an obvious dream, so in this crisis, the logicians have failed the most, and the * ones are not better, and the only ones who can have a little self-comfort are the intuitionists, but their language, in fact, is also deeply rooted in the soil of dualist logic, and if they do not recognize this, it is still difficult for them to make great progress in mathematics.

The only way to get out of the cloud of this crisis is to completely break the dependence on dualistic logic, and in particular, to completely abandon the imprisonment of the law of exclusion on human thinking. My proposition is to replace the law of exclusion with the law of the three perfections, or simply replace the law of exclusion with Lao Tzu's law of "three beings and all things", which is a later story and will be discussed later.

What is the paradox? To put it simply, the inferences contradict the premises. (There is a more rigorous definition in the treatise on logic, which will not be presented here). There are many classic paradoxes throughout the ages, which will not be explained here.

Classification of paradoxes.

First of all, to classify paradoxes, paradoxes can be divided into set theory paradoxes, semantic paradoxes, pragmatic paradoxes, and so on.

Above** Yu Chen Bo's "Fifteen Lectures on Logic" Lecture 14 A cat biting its own tail and spinning around.

Among them, morphological paradoxes and semantic paradoxes are based on Ramsey's classification of paradoxes. The morphological paradox can also be understood as a set theory paradox, which is what Ramsey calls a "logical-mathematical paradox".

In 1925, the young British mathematician and philosopher Ramsey (in an article entitled "Foundations of Mathematics") was the first to divide the paradoxes known at that time into two categories: logical-mathematical paradoxes and semantic paradoxes.

He argues that there is a paradox that does not involve content, but is only related to mathematical concepts such as elements, classes or sets, belonging and not belonging, cardinal and ordinal numbers, which can be expressed in the language of symbolic logic and appears only in mathematics, and such paradoxes are logical-mathematical paradoxes (morphological paradoxes).

The other paradox is not purely logical and purely mathematical, but related to some psychological or semantic concepts such as meaning, naming, referent, definition, assertion, truth, falsehood, and so on. This type of paradox does not arise in mathematics, and they may not arise from errors in logic and mathematics, but from the ambiguity of concepts of meaning, referent, assertion, etc., in psychology or epistemology. This is the semantic paradox.

A number of new paradoxes have emerged, but it is difficult to classify them into the above two categories, and they can be collectively referred to as "cognitive paradoxes" or "pragmatic paradoxes" because they relate to the context and the cognitive subject and its background knowledge. The epistemological paradoxes of medieval logicians have long been discussed, i.e., the paradoxes associated with epistemological concepts such as knowing, believing, doubting, and hesitating, as well as semantic concepts such as truth and falsehood; and paradoxes related to the words or attitudes that command, promise, promise, or hope, which guide action. ）

Seeing this, I am confused, I can't clearly distinguish between semantic paradox and pragmatic paradox, can anyone answer?

The cause of the paradox.

It is generally believed that paradoxes (especially strictly logical paradoxes) arise in connection with the obscuration of three factors, namely, self-referentiality, negative concepts, and totality and infinity. Although it cannot be said that these three factors necessarily lead to a paradox, they are generally contained in a paradox.

The Ultimate Question: How to Solve the Contradiction?

The understanding of the paradox is still shallow and needs to be continued.