Paradox refers to the premise of obviously，Through obvious and effective reasoning，Referred to inference processes or phenomena for obvious contradictions。Semantic paradox involves true、Fake、Indications、Meeting、Definition and other semantic concept paradox。As the oldest semantic paradox，"Paradox of the Lie" dates back to the 6th century BC ancient Greek philosopher Ipimonad。The original form is: Ispmenid, who is the Crete, claims that "all the Cretels are lying"。Later，This paradox has been simplified as: a person claims "I am lying"。"Lie" paradox is the most basic、The most typical semantic paradox，Because of its form is the simplest and clearer，And most of the semantic paradoxes have a structure similar to the paradox of the "Lie"。solved the problem related to the paradox of the "Lie"，It also solves most problems about semantic paradox。

In logical history，The semantic paradox represented by the "Lie" paradox is full of controversy，Also highly valued by logicians。To solve it，Logic scientists are based on their respective positions，Put forward many different solutions。But to this day，We still haven't found a solution that can be universally accepted。Fortunately,，At the end of 19th to the beginning of the 20th century，Modern logic and mathematical basic theoretical research has made significant progress，This makes people more stringent、Discuss more scientific semantic paradox issues。Important achievements according to modern logic，Especially the "diagonal theory" used in the process of prove its "first incomplete Bet365 app download theorem"，and Talski's "(arithmetic truth) irrefutable theorem"，We have the ability to find the root cause of semantic paradox。Based on this，We think，Grammar rich、The combination of simplicity theory and classic logic will cause inconsistency。This means，At least one of these three is a problem with problems，It must be given up or modified。Any solution to try to really solve semantic paradox，All need to face this conclusion to make a choice，and give the corresponding answer。

Classic liar sentence refers to a self -finger sentence with the following forms: "L: L is fake"，That is, the statement l claims that it is fake。If you want to consider L's authenticity，It will fall into dilemma: if L is true，So the phrase "l is fake" is true，So L is fake，Contradiction; if L is fake，The phrase "L is fake" is true，So L is true，Contradiction。We really launched L from L really launched L is fake;。In the classic logic，According to the rhythm，Each statement is true or false; and according to the principle of explosion (the contradiction is launched everything)，Each statement cannot be true and false，Because of the "Contradiction Laipan Everything"。But according to the above reasoning，Regardless of the value of l or false，We will all launch L is both true and false，Obvious contradictions。

Except the situation of direct self -finger，"Lie" paradox also has a form of cycle refers。For example，Plato: "Aristotle's assertion is true。"Aristotle:" Plato's assertion is fake。"We assume that Plato's assertion is true，and Plato breaks out "Aristotle's assertion is true"，So，Aristotle's assertion is true; but Aristotle breaks out "Plato's assertion is fake"，So，Plato's assertion is fake。We have launched "Plato's assertion is Bet365 app download fake" by "Plato's assertion is true"，Contradiction。Converse，We launched "Plato's assertion is true" by "Plato's assertion is fake"，Contradiction。Dialogue like this，Usually called the Lie Cycle，This refers to the chain can be long enough，Finally form a closed cycle。

Because semantic paradox is usually related to self -finger and cycle,，If there is a point of view, it is considered，To avoid paradox，It must be fully prohibited from the use of self -finger and cycle indication。We think，This idea is too simplified，It cannot fundamentally solve the problem of semantic paradox。First，self -finger and cycle indication is a common phenomenon in our language，Not all of the sentences containing self -finger or cycle indication will cause contradictions。For example，Someone guarantees others，"I am talking about it"; or the two parties in the debate accusing each other，"Your point of view is wrong"。Another，Self -finger words like "This article" and "Book"，Normally in our language。If the self -finger and cycle index are completely prohibited，It will cause our language to be too poor。Next，Some sentences become self -finger sentences that may depend on some accidental experience and facts。For example，Teacher let everyone in the classroom say a word，Then judge the authenticity of the statement。One of them said: "The person with the lowest IQ in this classroom is fake。"" But unfortunate is，This speaker happened to be the lowest IQ in the classroom。That is to say，He asserted that what he said was fake。For this type of statement，We seem to have no reason to prohibit it，Because this statement can be a normal statement under other context。again，The formation of some paradox does not involve self -finger or cycle index，The most typical example bet365 best casino games is ABlo Paradox，The sentence that constitutes this paradox does not directly or indirectly talk about itself。Last，It is also the most important，Even if we fully ban the self -finger and cycle index in the language，But as long as our language is rich enough to talk about primary arithmetic，Through the Gothic Code，We can still construct a sentence similar to the paradox of the "Lie"。

AssumptionIt is a form language that is rich enough to contain Piano arithmetic，Discuss directly is the number of nature and its related nature。Gothic discovery，If we are rightEach symbol of each symbol is encoded (that is, select a specific natural number to correspond to it)，and then encode the sequence of each symbol string and symbol strings，So the category of our commonly used grammar，as usual items、Change Yuan、Word item、Phacelet、Formula、Formula sequence、Tormented、theorem and proof, etc.，Codes can be performed。After this encoding，We can talk about the original number of natural numbers，It is regarded as a symbol of these natural digits indirectly、symbol string and symbol string sequence。The grammar category listed above，These are encoded symbols、Symbol strings and symbol string sequences。That is to say，In languageMiddle，We can talk about the number of nature and its related nature，Directly talk about the grammar of the language itself。If a formal language is rich enough to contain Piano arithmetic，We call this language "richness of grammar"。In the process of proved the famous "First Incomitated theorem"，Gothic proves the "diagonal theory"。We can intuitively understand this theory as: Given a Properties A，We can construct a statement D，Claim that it has its own nature a，and D and A ([D]) are the equal value。where，[d] is "D Bet365 lotto review of D"，A ([D]) means "D is in nature a"。Shortly after the Gobel's diagonal is proposed，Talski derived the irrefutable theorem of arithmetic truth based on this reason。This must be expressed，Any consistency containing a rich enough arithmetic form language，Cannot contain your own true predicate words。

In the process of deriving this conclusion，You need to use a rule called the "principles of simple truth"。This rule is also used in the process of launching contradictions from the "Lie" statement.。The principle of simple truth has three different ways of expression: the first expression method is Telsky's T-equivalent: (t) "[p] is true" and only P。where，"P" is any statement，"[P]" is the name P's name。The second way of expression is to treat it as the general name of the two reasoning rules of "T-introduction rules" and "T-disappear rules"。"T-Introduction Rules" says: Any statement P，We can launch the statement "[p] is true" from the statement P;，We can launch statement P。The third expression method is about the real "equivalent replacement rules"。This rule is to say，Entertainment P and the statement "P is true" can always be replaced with each other，But it will not affect the true value of the entire statement。

According to the principle of simplicity,，For any statement P，The sentence "[p] is true" and the statement P should be the same value，can be replaced or launched with each other。and Tarsky's irrefutable theorem tells us，Under the above conditions, we cannot unanimously maintain the principle of simple truth.。Goth's diagonal reason and Taski's (arithmetic truth) irrefutable theorem，It is an important result we must face in the process of discussing semantic paradox。According to the above theorem，We observed，Grammar rich、Principles of Simple truth and classic Bet365 lotto review logic，The combination of these three factors will cause inconsistency。Rich grammar，Let us construct a lie in the language L，Meet L satisfaction: L should be when "[l] is not true"。where，"[L]" is the name of the sentence L。This condition is to say，L and "[L] are not true" are the same value。Requirements for the principles of simple truth，For any statement P，It and the statement "[p] are true" to meet the value of the T and can be replaced with each other。Classic logic provides us with reasoning rules required for the launch of contradictions for the launch of the liar sentence，Ruling Law、explosion principles、Analysis principles and additional principles。

Since the grammatical richness、The principle of simple truth and the establishment of the classic logic at the same time will cause inconsistencies，So at least one of them is a problem，You need to give up or modify it。First，We seem to be able to give up the richness of grammar anyway，Because our language should at least be able to talk about the most basic arithmetic。Next，The principle of simplicity is consistent with the intuition of the concept of "true" in natural language，In intuitive, we think it should be established。It is difficult to imagine that "'snow is white' is really real and only when snow is white."。More，Classic logic is a model of logic system，Is the most "orthodox"、The most "standard" logic system，If it is not based on certain specific philosophical stances，or for some special purpose，We should not give up classic logic。

Any solution to try to really solve semantic paradox，All need to face the above conclusions and answer: What is the rich language and grammar we discussed? Do you recognize the principle of simple truth?，These schemes will be divided into different bet365 best casino games factions。Elski、Logicists represented by Berch and Guba advocate retaining classic logic，Modify and limit the principle of simplicity truth，Its solution is called a classic logic solution。Yipipke、Logicists represented by Philde and Prince advocate the preservation of the principle of simple truth，Modify the classic logic，Its scheme is called a non -classic logic solution。

　　bet365 best casino games

(Author Unit: School of Philosophy of Renmin University of China)