意见收敛定理与休谟问题

The Theorem of Convergence of Opinions and Hume's Problem

意见收敛定理是主观主义概率论的一条重要定理,它表明随着证据的增加,验前概率的主观性将被验后概率的客观性所代替。意见收敛定理被看作主观概率的动态合理性原则,因而被用来解决休谟问题,即归纳合理性问题。然而,哈金有说服力地表明,意见收敛定理证明的是条件概率Pr(h/e)的收敛,而不是验后概率Pre(h)的收敛。主观主义概率论暗中接受的一个等式是:Pre(h)=Pr(h/e),通常称之为"条件化规则"。这样,归纳法的合理性问题变成条件化规则的合理性问题。为此,本文提出一个新的合理性原则,即"最少初始概率原则",将它同"局部合理性"观念结合起来便可为条件化规则的合理性加以辩护。

The theorem of convergence of opinions is an important theorem in the subjective theory of probability. It demonstrates that the subjectivity of a prior probability will be substituted with the objectivity of a posterior probability as evidences increase. The theorem of convergence of opinions is regarded as the dynamic principle of rationality concerning the subjective probability, and therefore is used to resolve Hume＇s problem, i. e. , the problem of inductive rationality. However, Hacking convincingly argues that the theorem of convergence of opinions is not about the convergence of a posterior probability Pre（h）, but about the convergence of a conditional probability Pr（h/e）. The subjective theory of probability implies a tacit acceptance of an equation that is Pre（h） = Pr（ h/ e）, usually called ＂the rule of conditionalisation＂. Thus, the problem of rationality of induction is converted into one concerning the rule of conditionalisation. In this paper a new principle of rationality （the principle of minimum number of initial probabilities） is put forward, which, in combination with the concept of ＂local rationality＂, offers a justification for the rule of conditionalisation.