说谎者悖论:语言学中的一种代数学现象

The Liar Paradox: An Algebraic Phenomenon in Linguistics

从关于说谎者悖论的“句方程”方案中可以提炼出总的看法:说谎者悖论是语言学中一种相当纯粹的代数学现象。这是“句方程”方案的必然结论。实际上,“句方程”方案全面吸收了代数学的思想成果,从基本定义开始,就是参照代数学的思想建立和展开的。而之所以可以把说谎者悖论与代数学做如此深度的连接,根本原因在于三卡悖论的发现。三卡悖论是说谎者悖论与布尔代数深度相关的无可辩驳的证据,是“句方程”方案立论的基础。

In this paper we refine the ideas of the theory of“sentence equation”on the liar paradox.The main statement is that the liar paradox is a quite purely algebraic phenomenon in linguistics.In fact,the whole theory of“sentence equation”is inspired by algebra and developed along the route of algebra,starting with the very basic concepts.The reason it can be done this way is all due to the discovery of a“three cards paradox”.The Three cards paradox is an irrefutable evidence for the link between the liar paradox and Boolean algebra,and serves as the corner stone for the theory of“sentence equations”.