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本文讨论环绕着真理的概念,主要问题是给予这个概念以满意的定义。真理概念也就是“真理的语义学概念”。[因为]语义学是一门研究语言词语和这些词语所“述及”的对象(或“事件情况”)之间某种关系的学科。而最简单、最自然的获得正确真理定义的方法,包含了运用其它语义学概念的方法,如满足的概念等。同时为真理下定义问题,证明是跟建立理论语义学基础的一般问题有密切联系。只有依靠具有准确地说明了的结构的语言,真理定义问题才能获得确切意义,并可能严肃地解决。但问题的解决有时是肯定的,有时又是否定的。这决定于对象语言和它的元语言之间的形式关系。或者更明确地说,决定于元语言的逻辑部分是否比对象语言“本质上更丰富”。若只限于讨论以逻辑的类型理论为基础的语言,则元语言“本质上更丰富”于对象语言的条件就是前者比后者包含更高的逻辑类型中的变数。元语言满足了上述条件,真理概念就可以在其中得到说明。对于一个句子来说,如果它满足于一切对象,那就是真实的,否则就是错误的。真理定义的结论是:首先,这一定义不仅是形式上正确,而且是实质上适合。其次,可以从定义演绎出各种一般性的规律。第三,将真理原理应用于某种数学的表示广泛类属的形式化语言,则在这一类属学科里,真理的概念同可证实性概念从来不一致。每一种这样的学科是首尾一贯的,但并非完整的,即在任何两个互相矛盾的句子之间,最多只能有一个可被证实,或者虽是互相矛盾的一双句子,但其中没有人造何一个可被证实。
This article discusses the concept of the truth that surrounds the truth. The main problem is to give it a satisfactory definition. The concept of truth is also the concept of truth in semantics. [Because] semantics is a discipline that studies the relationship between language terms and the objects (or “event situations”) that are “addressed” by these terms. The simplest and most natural way to get the definition of the correct truth involves the use of other semantic concepts, such as the concept of satisfaction. At the same time, defining the problem for the truth proves to be closely linked to the general problem of establishing the basis of theoretical semantics. Only by relying on a language that has an accurately illustrated structure, the question of the definition of truth can obtain its exact meaning and may be seriously addressed. However, the solution to the problem is sometimes affirmative and sometimes negative. This depends on the formal relationship between the object language and its metalanguage. Or more specifically, whether the logical part of the metalanguage is “inherently richer” than the object language. If it is limited to discussing languages based on logical type theory, the meta-language is “inherently richer” in the target language if the former contains more variables than the latter. The metalanguage satisfies the above conditions, in which the notion of truth can be explained. For a sentence, if it is satisfied with all objects, it is true, otherwise it is wrong. The conclusion of the definition of truth is: First of all, this definition is not only formally correct but also essentially suitable. Second, you can deduce a variety of general laws from the definition. Thirdly, applying the principle of truth to a formal language of a type of mathematics that represents a wide range of genres, the concept of truth is never consistent with the concept of demonstrableness in this category of subject. Each of these disciplines is consistent but not complete, that is, there can be at most one verifiable or contradictory pair of sentences between any two contradictory sentences, but none of them are man-made One can be confirmed.