| As an inseparable part of people's life, people keep deep interest in language from the time we entered the enlightened age and explore many aspects of it. Before any systematic study of language, the following questions must be carefully examined:What is language? Or what is the essence of language?How language relates to the world?What is the meaning of language?What is the rule of language?Various answers to these questions not only reflect people's different views of language but also determine their future studies.The paper aims to explore Wittgenstein's theory of language game and Hintikka'game-theoretical semantics and their application in the study of natural language. On?this basis, it will use independence-friendly first-order logic and game-theoreticalsemantics to investigate the universal quantified structures in natural language.People's understanding of language goes from simple to complex, superficial to in-depth and one-sided to complete. We are getting nearer to the essence of language. In chapter one, this paper first goes over some historical views about language. As far back as in ancient China and Greece, many scholars had penetrated deep into language. Many of their viewpoints are still valuable nowadays. In the middle age, St. Augustine proposed an idea of language that carried weight both at that time and in later years. Early Wittgenstein's view about language was somewhat similar to St. Augustine's. Their theories could be called language schema that thought language was a schema of the world. In his later years, Wittgenstein changed his view and advanced the theory of language game. He took language game as an integral combination of language and activities that relate to the language. He held that language was a part of human being's life. It related to the world in its actualutilization. The meaning of word or expression existed in its actual usage. Language game should follow certain rules. His theory of language game had great influences in philosophy, logic and linguistics and propelled the development of these fields.Chapter two comes to game-theoretical semantics. The theory of game was first created as a mathematical theory. After its birth, people pay much attention to it and apply it in many disciplines that study the behaviors of rational human beings. Language is also an important kind of activity of human beings, so the basic ideas of Wittgenstein's theory of language game and game theory are similar. J. Hintikka applied some cardinal concepts of game theory to language game and thus got game-theoretical semantics. This theory inherits Wittgenstein's ideas about meaning and rules of language. Moreover, it transforms the theory of language game into a systematic and formalized theory with the help of game theory and logic. Hitinkka defines language game as a game of "searching and finding". He also formulates some game rules for the quantifiers. This theory provides us with a new view and method to study linguistic problems.Language and logic are dependent on each other. On the one hand, logic is an important tool for linguistics. On the other hand, the study of language can afford new ideas for logic. Hintikka points out that the theory of first-order logic, which was developed by Frege et al, encounters difficulties that are hard to get over when it tries to describe the dependent and independent relations among quantifiers. So, Hintikka expands it into independence-friendly first-order logic. The combination of it and game-theoretical semantics may give a complete description of the quantified structures in natural language.Quantified structure in natural language is one of the most important and troublesome problems in the field of formal linguistics. All kinds of theories make much account of it. Hintikka and his students also give a preliminary description of this problem with independence-friendly first-order logic and game-theoretical semantics and work out some game rules for them. Based on their research, this paper will try to study more...
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