# 说谎者悖论与自指

> 【EN】The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. We (viz., the authors) have said it, and normally things are said with the intention of being believed. Saying something that way when it is untrue is a lie. But then, given what the sentence says, it is true after all! That there is some sort of puzzle to be found with sentences like the first one of this essay has been noted frequently throughout the history of philosophy. It was discussed in classical times, notably by the Megarians, but it was also mentioned by Aristotle and by Cicero. As one of the insolubilia, it was the subject of extensive investigation by medieval logicians such as Buridan. … 【中】词条考察说谎者悖论。像“本句是假的”这样的句子自古代起就被反复注意到：若它为真则为假，若为假又似乎为真。文章梳理简单不真型说谎者、说谎者循环、布尔复合句与无穷序列等变体，分析其构成要素——真谓词与关于真的原则——并讨论说谎者型句子的存在、其他逻辑规律所受的冲击，以及多值逻辑与双面真理论等回应。

- ID: m13236
- 分类: structure
- 领域: 逻辑学

## 定义

“本句为假”这样说有什么古怪，古人早已知道。一切谎话都不真。那么这句话是真的吗？若真，它便是谎话，于是又不真；若不真，则说出它本意是让人相信，即为谎话，于是它又成了真的。 脚手架作用：- 自指排查：检查语句是否指称自身，提前识别悖论风险。 - 语言分层：用对象语言与元语言的区分切断自指回路。 - 真值检验：检验去引号原则的适用范围，防止真谓词失控。

## 机制

悖论源于自指与真谓词的相互作用。只要一种语言能构造出指称自身的句子，并且我们接受“‘p’为真当且仅当 p”这样的去引号原则，就能产生一个与其自身的假相等价的句子，从而在经典逻辑中导出矛盾。

## 练习

1) 找出自指或循环结构，写出它实际断言的内容；2) 明确所依赖的真的原则，如去引号与二值；3) 分别假设其为真与为假，看是否导出矛盾；4) 据此选择对策：限制自指、放弃二值，或承认某些句子既真又假。

## 脚手架用法

- 自指排查：检查语句是否指称自身，提前识别悖论风险。 - 语言分层：用对象语言与元语言的区分切断自指回路。 - 真值检验：检验去引号原则的适用范围，防止真谓词失控。

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