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卡尔纳普认为,“确证”只是对现阶段的得到的确定,“概率”是归纳前提(证据)对结论(假说)的确证,可用函数c(h,e)表示。为了计算c的值,卡尔纳普定义了状态描述、结构描述、量程等重要概念和定理,在构建的一阶语言系统Ln中,引入了测度函数m和确证函数c,其中测度函数是确证函数的基础,由语句所满足的状态描述的测度函数m值来确定确证函数c的值,后来又引入了λ参数进一步完善了他的理论。他的这一理论为归纳逻辑的形式化做出了巨大的贡献,对科学的合理性作出了辩护,并没沿概率的方向发展了现代归纳逻辑。
Carnap argues that “corroboration” is only a confirmation of what has been achieved at this stage. “Probability” is a corollary of the precondition (evidence) of the conclusion (hypothesis) that can be expressed by the function c (h, e). In order to calculate the value of c, Carnap defined the important concepts and theorems of state description, structure description, range and so on. In the constructed first-order language system Ln, a measure function m and a corollary function c were introduced, in which the measure function is a corollary function , The value of the confirmatory function c is determined by the value of the measure function m of the state description satisfied by the statement, and then the λ parameter is introduced to further improve his theory. His theory made a great contribution to the formalization of inductive logic, defended the rationality of science, and did not develop the modern inductive logic in the direction of probability.