莱布尼茨、计算主义与两个哲学难题

Leibniz,Computationalism and Two Philosophical Puzzles

莱布尼茨的单子是无形的自动机,如果把它看作抽象的图灵机,莱布尼茨单子论式的可能世界就是当下计算主义关心的数字宇宙。在这种抽象的“单子”宇宙中,数学的可应用性“谜题”以“不足道”的方式解决,但另一个哲学难题——世界的可知性“谜题”却凸显出来。借助算法信息论的话语,可以精确界定几类“可知的”可能世界,继而可以严格的探讨它们之间的相互关系。至于具体如何认识的问题,所罗门诺夫的通用归纳模型直接体现了方法论自然主义“假设——验证”的试错过程和诸如“简单性”的先验原则,抛开它不可计算的缺陷不谈,借助它,任何可计算的可能世界都是可以被近似认识的。

Since Leibniz’s monads can be taken as incorporeal automata,if we regard the monad as a Turing machine program,then the possible world composed of monads is the digital universe investigated by the computationalists.According to the framework of computationalism,the applicability puzzle of mathematics is“trivially”solved in such a digital universe.Meanwhile,the other important philosophical puzzle——the knowability puzzle of the world is highlighted.With the help of Algorithmic Information Theory,several layers of“knowable”possible worlds as well as their interrelationships can be rigorously defined and studied.As to how to know the actual world,Solomonoff’s universal induction model agrees with the Methodological Naturalism which emphasizes the“hypothesis-testing”process,and reflects the transcendental principle of“simplicity”.Thanks to Solomonoff’s universal induction model,every computable world can be knowable,except that the model itself is uncomputable.