The Integrated Structure of Language and Language Behavior with A Psychological Path
Authors: Yang Yingrui 
Published: January 2025

This article discusses language and language behavior. It follows three threads. The first vein we follow is the Structuralism of the Bourbaki School. In this we introduce the syntactic/semantic two-legged structures in language, especially scientific language, covering logic, decision theory, game theory, set theory and gauge field theory. We introduce the various fine formal structures and meta-mathematical structures created by Gödel and Tarski theorems. In the investigation of language games, we introduce the cone structure and the proper cone structure of language games, the algebraic structure of non-commutative relations, the gauge structure of algebraic space, the wave function and Dirac’s delta function structure, the local frame structure of Riemann geometry, and the fiber bundle structure of gauge transformation. Of particular importance is the two-level, two-stage, four-lattice structure of gauge field theory. The second context is the application of theoretical physics to the modeling of language and language behavior. First, we find the global nature of language and the local nature of language behavior, and thus establish a unified gauge field theoretic model for both. Second, on the assumption that language can be treated as contentless, we constructed geometric cones of language and language behavior respectively, thus establishing the special relativity model of language and language behavior. Third, we discovered the non-commutative relation of language behavior, the nature of wave function of language game, and the Dirac delta structure of common observations of language behavior. On this basis, we introduce the quantization model of language and language behavior. Fourth, it introduces the concept of language advantage as a scarce resource and pays attention to the inequality of language society, thus bending the language society. By introducing competition and Pareto efficiency into language games, the curvature and gravity of a curved language society are defined. Therefore, it is necessary to introduce local frame and connection in Riemann geometry. This is the general relativity model of the language society. The third vein is the change and development of Wittgenstein's philosophy of language. Firstly, we noticed Wittgenstein's early pursuit and training of language, especially formal language regularizations. Second, we also paid attention to Wittgenstein's struggle and search in the middle period. He found that Language behavior can be distilled into the concept of language game. From the Gödel incompleteness theorem for formal language, he realized the incompleteness principle of language games. Furthermore, we paid attention to Wittgenstein's return to subjective certainty and his pursuit and belief in the regularization of language games. Finally, he found an indispensable place for psychological games in his world schema during the conceptual transformation between language games and life forms. In this way, Wittgenstein sets out for us a psychological path of language and language behavior.