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在数学证明中,学员常常出现循环论证的错误,可怕的是学员往往意识不到自己的证明是错误的,对此教者必须引起注意。循环论证是用某个命题的自身来证明这个命题。主要有两仲形式,其一是在论证时,间接隐蔽地或直接明显地以待证命题作论据,来论证待证命题。其二是以待证命题的等价命题,来论证待证命题。产生循环论证的根源在于,学员缺乏逻辑知识,不掌握论证所应遵循的逻辑规则。因此数学教员应给学员补上这一课,使他们掌握在论证时必须遵循: 1.论题必须明确;2.在论证的全过程中保持同一论题,不许转变;3.论据必须是真实的;4.论据对于论题具有充足的理由,不孤单无力;5.不许循环论证。同时叫学员明确论证的结构:论题——论据——论断。论题是真实性要求证明的判断或命题,论据是论证论题正确而引用的一些判断,论断是借助论据说明论题真实性的议论。逻辑中的论证,是引用其它已知的正确判
In mathematical proofs, students often make the mistake of circular argument. What is horrible is that students often fail to realize that their proofs are wrong, and that the disciples must pay attention. The circular argument is to prove this proposition by a certain proposition itself. There are mainly two forms of the two forms. One is to prove the propositions to be testified indirectly in the demonstration, indirectly or indirectly, directly or indirectly based on the propositions to be examined. The second is to prove the equivalence proposition of the proposition to prove. The origin of circular argument is that students lack of logical knowledge, do not grasp the logic of the argument should be followed. Therefore, the maths teacher should make up the class to the students so that they should grasp the following points in argumentation: 1. the thesis must be clear; 2. the same thesis should be kept in the whole process of argumentation and the change is not allowed; 3. the argument must be true; 4. arguments for the topic with sufficient reason, not alone and weakness; At the same time, it is necessary to call the student a clear demonstration of the structure: thesis - argument - conclusion. The argument is the judgment or proposition of the authenticity requirement proof. The argument is the correct quotation of the argumentation argument. The conclusion is the argumentation of the authenticity of the argument by means of arguments. The argument in logic is to cite other known and correct judgments