When people say, "Sentence A can be obtained from the statement B.，or "Sentence A is the logic of the statement B."，or "The reason for the conclusion of the conclusion A as the premise of the sentence is effective"，What do they mean? How to portray the relationship between "logic afterward"、The concept of "logical" relationship or "effective reasoning" is undoubtedly one of the core tasks of logical philosophy。Although the development of logic has a history of more than 2,000 years，But until 1936，Taski in the article "On the Concept of Logic"，Only gives a profoundly influential model of a model theory that affects intuitive logic.。

An attempt described by the relationship after logic is to prove the nature: statement A is the logic of statement set B, and only there are some simple guarantee rules， A can be deduced from B repeatedly from B。From the perspective of Taski，This portrayal is unsuccessful。First，According to Gothic theorem，Given a proper arithmetic axiom，There is a real axiom system that is true but unable to proof。Next，The second -order logic is incomplete compared to standard semantics，There must be a second -order theory.，Then use the concept of "proof" and "deduced" to portray the concept of "(intuitive) logic after logic" is too narrow。

In the book "Logic Structure bet365 Play online games of Language" published in 1934, Calnap gave the "logical post -logo" relationship. Sentence set B and non -A's statement collection is contradictory。Taski improved Calnap's portrayal，Point out that a sufficient definition of "statement A is the logic of statement set B" must meet two conditions: first，Impossible conditions or inevitability conditions -cannot be true in the statement of B and A as a fake。"Must and the truth" should be the core described after any logic。2，Forms -only because of the logical forms of statements A and B, the statement is impossible to be true and A is false，The experience content of the statement is the non -logic constant in the statement, such as the name and the predicate which refers to the specific object、Which specific nature or relationship has nothing to do with。

For example，The statement "There is an object is a logicist" as the logic of the statement "Taski is a logicist"。This is because no matter what individual objects we interpret the name "Tasky"，May wish to be interpreted as Plato; no matter what kind of nature of the predicate of the "logicist"，May wish to be interpreted as the nature of a philosopher，It is impossible to undergo this explanation，The statement "The existence of an object is logicist" is fake，and the sentence "Tasky is a logicist" is true。Because under this explanation，"Tasky is a logicist" means that Plato is a philosopher，and "existing a logicist" means that bet365 best casino games there is a philosopher，It is impossible "Plato is a philosopher" and "existing a philosopher" as a fake。The statement "All birds fly" is the logic of the statement "Everyone who won't fly is not a bird"，Because the non -logical symbol "Bird" and "Flying" are explained to what kind of nature，If it is interpreted as "odd number" and "cannot be divided by two", respectively，Not "all odd numbers cannot be divided by two" are real and "all that can be divided by two is not odd numbers" is false。An non -logic symbol in a logic after logical relationship or effective reasoning is explained by the corresponding type objects，No premise is true and concluded as fake。Form logic is "form" logic，It is because of abandoning "content"，It's like arithmetic equivalent (A2-B2) = (A+B) × (A-B) is the truth of mathematics，No matter what specific numbers are interpreted as "A" and "B"，Any special case of this form of arithmetic is true。Similarly，All A is a logic equivalent to all non -B.，No matter what the nature of "A" and B "refers to，Neither will appear on one side that is true on the other side。

To depict the above inevitable conditions and form conditions，Taski gave logical depicts with the concept of mathematical models: statement A is the logic of statement set B, and only as any of the model is arbitrarily.，Any Non -logical constant (special name、Function symbol、Sign symbol) explanation，All the sentences in the statement of statement Bet365 lotto review b。In other words，B models are all models of A。A model can be regarded as a possible world，In the premise, it is possible to the world，The conclusion is also true。This is the meaning of "inevitable"。

Taski found that the above -mentioned portrayal dependence on logic constant and non -logical constant is divided，This division determines the logical form of the statement，Logic constant, such as "not", "or", "and", "equal", "Dang", "all", "all", "existence" and other words cannot be explained at will，"Plato", "Is a logicist", "Bird", "Flying", or the predicate of the word is not logical constant，It can be explained by the appropriate type of object。How to distinguish logic constant and non -logic constant，Taski gave an interesting answer in the 1966 speech "Logic constant": the object that remains unchanged under any transformation is logical constant or logical object。Ghostists call the dual -shooting function as a transformation，The function definition domain and the value domain are points on the plane or space graphics，They usually study the invariant variables under certain types of transformation，If it translates、Rotating、Axial reflection or flipping orthogonal transformations keep the distance of two points on the plane unchanged。What objects are there to remain unchanged under arbitrary transformation?

Consider the standard model of the following simple types of theory: Bet365 app download the bottom layer of the model is a type of individual object，This type of individual object is the most basic type; the second layer of the model is all possible classes composed of the first layer of individual objects; the third layer is a class composed of all individual objects，and so on。Considering the bottom class of the simple type of standard model to its own one pair of shooting transformation，This transformation naturally seduces or expands to all types of transformations，You can check it under such a double -shooting transformation，Which layer of objects remain unchanged under arbitrary transformation。It is not difficult to see，The minimum individual object is more than one，No variable，Because one object can always be mapped as another; on the second layer，The complete set of empty sets and the complete works is the only invariant variable，Because the empty set was reflected as a empty set，Complete works mapping is the complete works; on the third layer，The class that happens to have a class of n elements is invariable，The image of the collection of n elements also has a collection of n elements。If according to the way of Kuratovsky, define or orderly pair，Then define the dual relationship as an orderly pair of collection，On the fourth floor, you can consider the orderly pair of collection，In it，equal relationship、Full relationship、empty relationship、Not waiting bet365 best casino games for the relationship is not the variable，For example, equal object mapping is equal object。On the fourth floor，The containing relationship between the two categories、The intersection is not empty、No intersection、The relationship between the complement is logical and uninvited。Taski recommends that the object that does not change under any transformation is logical constant。The interesting thing is，If the above Russell type type theory model is used as the background model of the transformation，It belongs to the relationship is logical non -variable，Due to the relationship between the objects of the adjacent level, the image will also maintain the relationship under any transformation。In the context of the collection of the collection of "Tingpu"，The relationship is not logic constant。

Tasky's logic theory has become the basic tool for modern logic research，Dedicated acceptance。In recent years，mcgee、SHER and MacFarlane and other logicians are discussing how to use or modify Tasky's unable variable ideas，to depict the common authentic function connection words、Logic constants represented by quantitative words and various modular vocabulary，Discuss the impact of the corresponding portrayal on the concept of logic。

(Author Unit: Department of Philosophy of Wuhan University of Technology)