从分析命题到逻辑真理——论弗雷格对康德分析命题的拓展

From Analytic Statements to Logical Truths——On Frege’s Extension of Kant’s Analytic Statements

本文揭示了弗雷格逻辑主义的核心问题 :如果拓展康德的分析真理到范围更广的逻辑真理 ,能否涵盖某一范围的数学真理 ?弗雷格相信通过对逻辑真理范围的扩展 ,有可能对算术真理进行重新定位。弗雷格是从证明论的角度拓展康德的分析命题的。此外 ,本文通过对函数连续性概念的详尽分析 ,例示了弗雷格的概念词的析出法 ,指出康德概念论的局限在于如下一个简单的事实 :如果约束变元的值域是无限的 ,我们不可能把包含量词的表达式改写成合取范式或析取范式。

The essay reveals the core question of Frege’s logicism: Could we extend Kant’s analytic truths to more general logical truths so as to cover some mathematical truths in certain fields? Frege believes that by extending the scope of logical truths, we mightbe able to relocate arithmetic truth in our system of knowledge. Frege extends Kant’s analytic truths from proof-theoretic point of view. In the last part of the paper, I exemplifies Frege’s method of extraction of concept-words by an analysis of the concept of the continuity of functions, and point out that the limitation of Kant’s doctrine of concept lies in the simple fact that the quantifier expressions cannot be transformed into conjunctive of disjunctive normal forms if the range of the bounded variable is infinite.