A Study On Types Of Numeral Structures

Different languages have many universals as well as many differences. As a part of their language systems, different numeral systems also have some similarities and differences. They can give us important insight. A lot of research studied on numeral systems, but just a little was on the classification of numeral systems. Meanwhile, due to the lack of studies on numeral system structure, current research was mainly targeted at basic numerals, while few at multiplicative numerals, fractional numerals, or numerals of estimation. At the same time, some of the typological research on basic numerals is debatable.This dissertation defines numeral system on the basis of distinguishing it from related concepts, and constructs a universal-oriented system of numerals. On the one hand, the dissertation establishes a multilingual library of basic numerals, marks their features, systematically compares numerals of different languages, and summarizes the study on semantic relationship types of their components, formal realization of these relationships, the ordering and semantic restrictions of components, using the method of statistical analysis. On the other hand, by systematically comparing the numerals of relative quantity in Chinese and English, it summarizes their similarities and differences to arrive at some structural types, on which basis it speculates the types of numerals of relative quantity in different languages, in hopes of laying a foundation for further type study.The dissertation consists of six chapters. Each chapter has the following major content:Chapter Ⅰ:Introduction. The reasons of choosing the topic, an academic research overview and research content of this dissertation are introduced in this chapter. The research overview presents an overview of comparative studies and typological studies on numeral systems. It also summarizes existing research results and the room for further research. The introduction of present study tells about research content and scope, research planning and methods, research priorities and difficulties as well as innovations, also about corpus sources, of this research work.Chapter Ⅱ:Numeral system and its structure. This chapter introduces current studies on the structure of numeral system, analyzes their disagreements and the reasons of these disagreements, and solves these problems by the study in the second and the third section of this chapter. Section Ⅱ studies the differences and relationship between numeral system and number awareness, number concept, number expression, scientific number, digit, quantifier, syntax number and numerals. It defines numeral system as language forms and ways in expressing number, and on this basis it introduces the hierarchical structure of numeral system. Section III provides a comparison of Chinese and English numeral system. Based on the structure of number system, it constructs a universal-oriented numeral system, and describes the structure and hierarchy of this system.The main conclusions of this chapter are as follows:The numeral system of different languages all consists of basic numerals and numerals of relative quantity, while the latter include numerals of estimation, fractional numerals and multiplicative numerals. This is the composition of a universal-oriented numeral system. This system does not include expressions inquiring for number, ordinals, atom-base structure or whole-fraction structure, decimals, negative numbers or varia lectios of numerals.Chapter Ⅲ:Types of basic numeral structures. This chapter first defines terminology and reviews related research. At the preparation phase of the study, a library of basic numerals from different languages is constructed, upon which feature annotation and analysis is done and the types of basic numeral structures are concluded. This chapter mainly studies on semantic relationship types of basic numerals and its implicated university, the ordering of components and the formal realization of these relationships, as well as the numerical entry requirements on the components.The main conclusions of this chapter are:1.There are four types of semantic relationship among the components of basic numerals:addition, subtraction, multiplication, and exponentiation; the semantic relationship of division does not exist; overcounting or going-on counting is not a semantic relationship between components, but a counting method; in addition, the dissertation argues that there is exponentiation, but its connotation is different from previous understanding.2. The applying ratio of semantic relationship types can be arranged from high to low as:addition multiplication-subtraction-exponentiation, and addition and multiplication appear in basic numerals of most languages. Their applying ration is much higher than the other two. In terms of the implicated relationship between these relationships and other factors in numeral system, there must be addition if a numeral system has one semantic relationship between components, and there must be multiplication if a numeral system has base. Quite few numeral systems have only simple numerals and thereby have no internal semantic relationship. As for the implication relations between the four types of relationships, there must be addition if there is multiplication, there must be multiplication and addition if there is subtraction, and there must be multiplication and addition if there is exponentiation.Chapter Ⅳ:Pre-type-study on numerals of relative quantity. This chapter has a detailed comparison on numerals of relative quantity in Chinese and English, summarizes the similarities and differences of numerals of estimation, fractional numerals and multiplicative numerals of the two languages, and makes hypothesizes on types of the counterparts in different languages.This chapter holds the following views:The similarities and differences of numerals of estimation, fractional numerals and multiplicative numerals in Chinese and English reflect the structural features of counterparts in different languages to a certain extent. Making hypothesis on different languages based on an in-depth systematic comparison of two well-developed languages which are used in a wide range can be a new attempt of typology research.Chapter Ⅴ:Universals of numeral systems. This chapter summarizes structural features and expression characteristics of different numeral systems based on the comparison and type research in Chapters Ⅲ and Ⅳ.The main conclusions of this chapter are:1.The overall structure of numeral systems are ordered and hierarchical, some special forms and structures-for example, basic numerals of subtraction semantic relationship and those with overcounting-do not affect these two general characteristics.2. Basic numeral structures show that there are two types of counting method:piling-accumulation and filling-accumulation. At the same time, numeral systems use many concepts associated with body, and its usage is reflected in the forms of individual basic numerals and in the numerical value of bases.3. The forms of numeral systems are also hierarchical. First of all, forms of numerals develop from simple to complex, including simple expressions are used to express complex number concepts and words of concrete concepts are used to express abstract relative numerical value. Secondly, numerals of fixed value are used to express fuzzy numerical concept. Finally, different forms of one type of numerals usually range from typical to minor-typical, and then to atypical.Chapter Ⅵ:Conclusion. This chapter summarizes the main points and conclusions, and presents the deficiency of this research as well as questions to be further explored. They are also problems that the author of the dissertation will study and research on.