The Research On The Logical Thought Of "Jiuzhang Suanshu" And Liu Hui's Annotation

"Jiuzhang Suanshu" and Liu Hui's annotation is composed of "Jiuzhang Suanshu,and the annotation which Liu Hui written for "Jiuzhang Suanshu".It is a classie work in the history of ancient Chinese mathematics,and it is rich in logical thought,especially Liu Hui's annotation which is more obvious.The former experts' research methods of the work about the logical thought of "Jiuzhang Suanshu,and Liu Hui's annotation,mainly are the use of formal logic method and cultural comparative analysis method,and so on.For example,using formal logic method which consists of definition,reasoning,logical law and theoretical system,etc,to study the logical thought of "Jiuzhang Suanshu" and Liu Hui's annotation;From the perspective of comparison between Chinese and western culture or ancient Chinese logic to study "Jiuzhang Suanshu" and Liu Hui's annotation.Based on the research achievements of the former experts,this paper will continue to use formal logic method to study "Jiuzhang Suanshu" and Liu Hui's annotation;And using informal logic argumentation theory and general argument to analyze the characteristics of argument of Liu Hui's annotation;Finally,it is to apply mathematical methodology to clarify the uniqueness in terms of mathematical method of Liu Hui's annotation.Formal logic,informal logic and mathematics methodology,they are the research method in three different dimensions or fields of vision.The combination of these three research methods can ensure relatively overall the analysis of the logical thought of "Jiuzhang Suanshu" and Liu Hui's annotation.Because of the close contact between mathematics and logic,it is reasonable to use the method of formal logic to study the logieal thought of "Jiuzhang Suanshu" and Liu Hui's annotation.In the field of vision of formal logic,this paper briefly introduces "Jiuzhang Suanshu",Liu Hui and related background,and simply discusses the logic of choreography of "Jiuzhang Suanshu";And then,the logical characteristics of Liu Hui's annotation are analyzed more comprehensively by the method of concept defining,logic reasoning,and theoretical system;Then,the dealing with the problem of PI and Pythagoras theorem by Euclidean geometry and "Jiuzhang Suanshu" and Liu Hui's annotation is further analyzed to show their similarities and differences for distinguishing different characteristics between the Euclidean geometry and "Jiuzhang Suanshu,and Liu Hui's annotation in logical reasoning and mathematical proof.As Liu Hui's annotation is mainly the argument with the particular cultural factors,it is reasonable to adopt the argument theory of informal logic to study its characteristics.Specifically,this paper uses Toulmin's layout which can represent Liu Hul's argument model and analyze the effect of argument in the method of informal logic.Given to demonstrate the influence of cultural factors,this paper introduces the theory of generalized argument which contains the five elements of cultural generalized argument that are added to Toulmin's layout to reveal the cultural logical features of Liu Hui's argument.The former two fields of vision are targeted at specific mathematical content,but the third one,it is to apply mathematical methodology to study "Jiuzhang Suanshu" and Liu Hui's annotation,from a deeper level to reveal the logical characteristics of Liu Hui's annotation in mathematical methods.In this level,Liu Hui used abstract analysis method and the transformation method more frequently,especially the transformation method of relation-mapping-inversion principle.It is helpful for solving a class of difficult mathematical problems in Liu Hui's annotation.Above three dimensions or fields of vision are relatively independent and significant connection.It is emphasized on the logical content which "Jiuzhang Suanshu" and Liu Hui's annotation has in the field of vision of formal logic.However,it is emphasized on the features of argument of "Jiuzhang Suanshu" and Liu Hui's annotation in the field of vision of informal logic.Although it has the same researching content of the argument between formal logic and informal logic,the portion of informal logic highlights the cultural features of argument of Liu Hui,s annotation.However,since the content of these two aspects don't involve the methodology level,it is necessary to analyze the characteristics of mathematical methods of "Jiuzhang Suanshu" and Liu Hui's annotation in the field of vision of the mathematical methodology,and study the logical thought of it in a more depth level.So,it is fully and sufficiently to study the logical thought of"Jiuzhang Suanshu" and Liu Hui's annotation from the above three dimensions or fields of vision for research,and this is an advance on previous work.