客观世界的集——兼对悖论之王“罗素悖论”的剖析  

Set in Objective World ——simultaneous analysis on the Paradox of Bertrand Russell

作　　者：龚启荣[1] 

机构地区：[1]贵州大学,贵阳550025

出　　处：《重庆理工大学学报（社会科学）》2011年第9期9-14,共6页Journal of Chongqing University of Technology（Social Science）

基　　金：教育部人文社会科学研究项目"当代形式逻辑及其在人工智能中的应用理论研究"(07JA720006)成果

摘　　要：对象就是可以对之思考的一切。在思考时不对之进行分解的单个对象称为个体。集就是由有限或无限个个体组成的组合、总和或整体。为集P的任意元所共有且只为集P的元所仅有的属性称为集P的共仅属性。集由其全部元唯一地确定,这称为集的外延原则。康托尔的集合论"概括原则"说认为,对于任意给出的一项性质p,必定存在一个以p为共仅属性的集P,这显然不能成立。客观世界不存在P∈P,而只存在eP,这称为集的排己性。e∈P和eP不能并存、至少有一存在、是且只能是二者之一,依次称为属于关系的不矛盾律、排中律、选一律。罗素犯了康托尔"概括原则"的唯心论错误,凭空想出个根本就找不到的违反幂集原理的所谓集R,于是虚构了自欺欺人的根本就不可能出现矛盾互推的所谓"矛盾互推"的"悖论"。The object is all that can be thought.Single object that we don＇t split can be termed as unit.Set is a group,aggregate or entirety which is composed of limited or infinite units.The sym-and-only attribute of the set P refers to the one which is common to an arbitrary element of the set P and belongs to the all elements of it alone.The set is defined uniquely,which is called the denotation principle of set.In the set theory of Moritz Benedikt Cantor,namely,the theory of generalization principle,there must exist the set P,which be characterized by the sym-and-only attribute of p,for any given nature p.This argument isn＇t obviously tenable.There isn＇t P∈P in the objective world,but merely exists e∈P,which is considered as the exclusiveness of set itself.The case is that e∈P 和 e∈P cannot coexist,and there is one at least,or only one of the both,which can be called the non-contradiction law,the law of excluded middle,and the selective-one law of the belong-to relation respectively.Bertrand Russell committed an idealism error of the Cantor＇s theory of generalization principle,and he put forward the so-called and groundless set R that cannot be found in the objective world and disobeys the theory of power set,therefore making up the so-called paradox of the so-called contradictory mutual deduction,which cannot appear.

关 键 词：集的共仅属性 集的排己性 属于关系∈的选一律 幂集 罗素集合论悖论 

分 类 号：B81[哲学宗教—逻辑学]