交错群A_(4)在布尔系统上的不可表示性  

Nonrepresentability of the Alternating Group A_(4)on Boolean Systems

作　　者：曹航杰 熊明 Hangjie Cao;Ming Xiong

机构地区：[1]华南师范大学哲学与社会发展学院

出　　处：《逻辑学研究》2024年第2期56-72,共17页Studies in Logic

摘　　要：非非悖论是一类比较典型的具有对称性的语义悖论,这类悖论的对称性都可用置换群进行刻画。当一个置换群刻画了某个悖论的对称性时,我们称此置换群可由该悖论表示。Hisung(2022)提出如下猜测:任意置换群都可由非非类型的悖论表示。本文通过使用群映射等概念来分析群作用到真值序列集上的轨道和稳定化子,证明了交错群A4不能被任何布尔系统表示。这表明如果把非非类型的悖论限制在布尔悖论的范围内,并不是每个置换群都能由非非类型悖论来表示。本文还通过置换群直和构造给出了其他不能被布尔系统表示的置换群例子。研究表明不可被布尔系统表示的置换群不是孤立的,而是有一定存在基础的。The no-no paradox is a typical type of symmetrical semantic paradox with its sym-metry,which can be characterized by permutation groups.When a pemmutation group characterizes the symmetry of a paradox,we call that the group is represented by this paradox.Hisung(2022)proposed the conjecture that any permutation group can be rep-resented by a no-no type of paradox.In this paper,by using concepts such as group map,we analyze the orbits and stabilizers of group actions on the set of tnuth value sequences,and prove that the alternating group A_(4)cannot be represented by any Boolean system.This indicates that if no-no type paradoxes are restricted within the scope of Boolean paradoxes,not every permutation group can be represented by a no-no type of paradox.This paper also provides examples of permutation groups that cannot be represented by Boolean systems through the construction of direct sum of permutation groups.Our re-search shows that permutation groups that cannot be represented by Boolean systems are not isolated,but have a certain basis for its existence.

关 键 词：非非悖论 布尔系统 对称性 置换群 可表示 

分 类 号：B81[哲学宗教—逻辑学]