《逻辑哲学论》论概率和归纳

Tractatus on Probability and Induction:a Tentative Reconstruction

《逻辑哲学论》虽然注家甚多,此书对于概率和归纳问题的零星讨论却一直没有受到后人的重视,而本文则试图对这些讨论进行尝试性的重构。本文的写作目的是双重的。首先,本人试图揭示早期维特根斯坦的概率理论与他的整个逻辑原子论架构之间的关系,说明他是如何通过"真值根据"这个概念而将日常语言中的概率表述全部还原为真值函项理论的。在此基础上,笔者将说明为何他的这种概率理论缺乏实际的应用价值。其次,本文将讨论维氏将归纳问题和概率问题相互分离的"分离策略",并尝试重构出他提出该策略的隐蔽动机。在此基础上,笔者将站在认知科学的立场上为这个策略本身提供一些辩护和批评。笔者认为,早期维氏虽然正确地看到了"思维经济原则"对于归纳推理的重要指导意义,并看到了该原则本身是无法被还原为逻辑真理的,却并没有意识到该原则本身可能是一切具有一定智能水准的问题解决系统所必须依赖的问题解决策略。令人遗憾的是,他对"心理学"和"逻辑"所作的简单的二分法阻止了他更为深入地对智能系统的普遍问题解决逻辑作出探究,尽管这种研究的确是可以相容于他的前述"分离策略"的。总而言之,本文认为早期维氏的概率理论的科学价值相当有限;与之相比较,他的归纳观却可能已指出了如何揭示智能系统的普遍认知机制的正确道路,尽管他在《逻辑哲学论》阶段还缺乏对于这条道路的全面自觉。

Early Wittgenstein＇s discussion of the nature of probability and induction, scattered in Tractatus, has seldom attracted enough attention from commentators. This paper will offer a tentative reconstruction of his position on this issue. The purpose of this reconstruction is twofold. First, I want to show the correlation between early Wittgen- stein＇s notion of probability and his entire logical atomistic framework, especially how he, in terms of ＂truth-grounds＂, systematically reduces every ordinary expression involving probability into one explainable by truth-function theory. Thereby I will illustrate why his probability theory is not practically applicable. Second, I will try to reconstruct his implicit motivations to separate induction from probability theory, and further evaluate this ＂separation strategy＂ by resorting to some observations from cognitive science. Overall, I believe that early Wittgenstein is right by separating ＂the principle of economy＂ from pure logic as well as perceiving the significance of this principle in inductive inferences. But by assimilating this principle into empirical psychology, he still fails to see its applicability to any intelligent problem-solving system designed to be adaptive to its environment. In effect, his psychology/logic dichotomy simply prevents him from developing a universal problem-solving logic applicable to every intelligent system, though to develop it doesn＇t seem to go against his ＂separation strategy＂ conceming the irreducibility of induction to probability. In short, I believe that his probability theory is of little scientific value while his notion of induction, although not fully developed, is probably on the right track of doing justice to the nature of human cognitive architecture.