亚里士多德划分格与亚里士多德逻辑

Aristotle's Division Lattice and Aristotelian Logic

亚里士多德逻辑究竟是什么逻辑,这个问题实际上并没有真正解决。目前的几种主要看法都是基于数理逻辑的理论得到的,虽然略有不同,但都认为亚里士多德逻辑是一阶逻辑的子逻辑。从技术的观点看,这个结论没有错,但是亚里士多德逻辑有自己的思想基础,不能简单地从数理逻辑的视角来看。我们的观点是,亚里士多德逻辑是一种什么逻辑,应该回到亚里士多德的概念理论来考察。亚里士多德概念理论中作为其逻辑基础的是划分理论。亚里士多德划分理论在两个方面对柏拉图二分法加以改造:根据生物学分类得到亚里士多德分类树;改造柏拉图正反二分法提出了正负二分法。分类树和正负二分形成了亚里士多德划分格。按今天的理论看,亚里士多德划分格就是集合代数上的有补分配格。亚里士多德逻辑实际上是亚里士多德划分格上的逻辑。

What is Aristotelian logic?It is a question that has not been settled yet.Although varying from each others,the major views on this problem,based on the theory of mathematical logic,is that Aristotelian logic is a sub-logic of first-order logic.Technically,this result is acceptable.Nevertheless,when its own ideological basis is considered,Aristotelian logic should not simply be investigated from the standpoint of mathematical logic.Our view is that,in order to solve this problem,we are supposed to return to Aristotle’s conception theory,in which the foundation of Aristotelian logic is his theory of division.Aristotle therein modified Plato’s dichotomy in two ways.First,he derived Aristotelian classification tree in the basis of biological taxonomy.Then,he developed contradictory dichotomy by improving Plato’s contrary dichotomy.It is Aristotelian classification tree and contradictory dichotomy that form Aristotle’s division lattice,which is a complemented distributive lattice in set algebra in today’s terminology.As a matter of fact,Aristotelian logic is the logic on Aristotle’s division lattice.