数学真理困境的新弗雷格主义求解  

Neo-Fregean Solution to the Dilemma of Mathematical Truth

作　　者：刘杰[1] 

机构地区：[1]山西大学科学技术哲学研究中心

出　　处：《哲学研究》2010年第6期92-98,114,共8页Philosophical Research

基　　金：教育部人文社会科学研究青年基金项目"数学真理困境及其语境实在论出路"(编号08JC720009);国家社会科学基金项目"语义分析方法与当代科学哲学的发展"(编号08BZX022)资助

摘　　要：The key contradict of the dilemma of mathematical truth is that Platonist ontology could not comply with empiricist epistemology, which was the boundary Frege maintained all the time. Inherited from Frege’s theories, Neo-Fregean take linguistic analysis as the guide of ontology. They insist that mathematics should be reduced to logic, emphasize especially the importance of abstraction principle (on ground of contextual principle) in introducing numerical singular, which offers a linguistic solution to the dilemma of mathematical truth. However, they had no reasonable justification for the legitimate position of abstraction principle, which led them to a double attitude to the nature of logic. As a result,if Neo-Fregan insist on the truth of first order logic, they have to face the problem that choice axiom could not reconcile with first order logic,or if they insist on abstraction principle, they have to answer the Caesar problem.The key contradict of the dilemma of mathematical truth is that Platonist ontology could not comply with empiricist epistemology, which was the boundary Frege maintained all the time. Inherited from Frege’s theories, Neo-Fregean take linguistic analysis as the guide of ontology. They insist that mathematics should be reduced to logic, emphasize especially the importance of abstraction principle (on ground of contextual principle) in introducing numerical singular, which offers a linguistic solution to the dilemma of mathematical truth. However, they had no reasonable justification for the legitimate position of abstraction principle, which led them to a double attitude to the nature of logic. As a result,if Neo-Fregan insist on the truth of first order logic, they have to face the problem that choice axiom could not reconcile with first order logic,or if they insist on abstraction principle, they have to answer the Caesar problem.

关 键 词：数学真理 困境 弗雷格 求解 主义 数学解 学理论 认识论 

分 类 号：B81[哲学宗教—逻辑学]