Later Wittgenstein's Criticism of Mathematical Logicism——On the Possibility of New Ways of Mathematical Philosophy Research
Later Wittgenstein's criticism of mathematical logicism is not only the application of his language criti-cism thought in the field of mathematics,but also an important part of his mathematical philosophy.This critique includes three dimensions:(1)redefining the nature of mathematics,and firmly believing that mathematics is nei-ther a knowledge system about abstract objects nor a science centered on logical deduction,but a technology com-posed of a series of concrete practices such as calculation and reasoning;(2)re-examining propositional con-structivism and assert that mathematical propositions are not mechanical replicas formed under fixed logical rules.On the contrary,the construction of mathematical propositions follows the dynamic grammatical rules and shows infinite creativity in the practice of language;(3)re-evaluating the proof method,emphasizing that mathematical proof aims to visually present the propositional transformation process in the form of pictures,rather than to obtain the final result through rigorous logical reasoning.In a sense,the above criticism not only deconstructs mathemati-cal logicism,but also reconstructs the field of mathematical philosophy,which is concretely reflected in Wittgen-stein's pioneering interpretation of mathematics from the perspective of everyday language analysis:mathematics is a language game.To understand mathematics,or to participate in mathematical language games,is to follow the rules of grammar.Grammatical rules,however,are not self-evident absolute truths,but take on meaning through social practice within the community,and consensus is reached in the process.In other words,mathematics is a standardized and rule-governed practice.This not only challenges the traditional concept of mathematics,but also places mathematics in a broader network of social practice,thus opening up the possibility of a new approach to the study of mathematical philosophy.
later Wittgensteinmathematical logicismphilosophy of mathematicsproposition constructionmathematical proof
万方数据
