客观世界的n元关系——兼谈传统形式逻辑和数理逻辑

N-ary Relations of Objective World——Also a Discussion on Traditional Formal Logic and Mathematical Logic Being at Most 1/x of Logic

当代形式逻辑对客观世界n元关系的研究,其视野是传统形式逻辑和数理逻辑无法相比的。从主导思想上看,传统形式逻辑是真正的名副其实的逻辑科学,但它只研究1元关系,不研究多元关系和真正普遍有效的关系推理,因此,传统形式逻辑顶多只能算n分之1的逻辑。数理逻辑虽然把1元或多元关系作为自己的研究对象之一,但它没有从内涵的角度去区分关于同一外延的k个尽管相当然而并不相同的n元关系,从量上说至少是"挂1漏k-1"的,即只从外延的角度研究一种关系而漏掉(k-1)种关系,因此,纯外延的数理逻辑顶多只能算k分之1的逻辑。当代形式逻辑从研究论域上的n目组和n目组集入手,亦即通过确定论域上的个体的所有不同序列,对论域上n个个体(n≥1)之间的所有关系进行了逻辑科学应有的全方位研究。

The prospect of the study on n-ary relations of objective world by contemporary formal logic is incomparable that traditional formal logic and mathematical logic can do. To view the dominant ide- as, traditional formal logic is a veritable science of logic, which just studies on 1-ary relations, but not on multivariate relations and generally effective relation inference. Therefore, traditional formal logic is at most one n-th of logic. From connotation angle, mathematical logic doesn＇ t distinguish the equivalent but different k n-ary relations of denotation, though 1-ary or multivariate relations is one of the study objects of mathematical logic. It is at least having 1 but losing k-1, that＇ s to say, mathe- matical logic just studies one relationship from denotation angle but loses k-1 relationship. Therefore, mathematical logic of pure denotation is at most one k-th logic. Contemporary formal logic begins to study with n-item and n-item set of universe of discourse, i.e. it does thorough study, including every field of science of logic, on all the relations among n individuals （ n ≥1 ） by confirming the different sequences of individuals in universe of discourse.