# 连锁悖论（谷堆悖论）

> 【EN】The sorites paradox originated in an ancient puzzle that appears to be generated by vague terms, viz. , terms with unclear (“blurred” or “fuzzy”) boundaries of application. ‘Bald’, ‘heap’, ‘tall’, ‘old’, and ‘blue’ are prime examples of vague terms: no clear line divides people who are bald from people who are not, or blue objects from green (hence not blue), or old people from middle-aged (hence not old). Because the predicate ‘heap’ has unclear boundaries, it seems that no single grain of wheat can make the difference between a number of grains that does, and a number that does not, make a heap. Therefore, since one grain of wheat does not make a heap, it follows that two grains do not; and if two do not, then three do not; and so on. This reasoning leads to the absurd conclusion that no number of grains of wheat make a heap. The same form of reasoning is familiar in everyday life. … 【中】词条追溯连锁悖论从古代到当代的演变，梳理其多种表述形式，并系统评述各类回应方案：理想语言进路、认知主义（认为存在但不可知的精确界限）、超赋值主义及其变体、度理论与多值逻辑、语境主义等。核心议题是如何解释“秃头”“谷堆”“高”“老”“蓝”等模糊谓词的行为。

- ID: m13318
- 分类: structure
- 领域: 逻辑学

## 定义

由含混词项引发的悖论：一粒麦子不能使非谷堆变成谷堆，则逐粒增加也永远不成堆；但常识认为麦粒足够多时确实成堆。它揭示了模糊词项缺乏明确适用边界所导致的逻辑困境。 脚手架作用：- 边界追问：追问模糊词项究竟在哪一点上切换真假。 - 前提拆解：定位应拒绝的是基础前提还是递推前提。 - 语境校准：判断适用边界是否随语境与比较类移动。

## 机制

悖论由两个前提推出矛盾：一粒不成堆，且若n粒不成堆则n+1粒也不成堆。因模糊谓词无清晰边界，后者在直觉上成立，反复应用却推出任何数量都不成堆。各派解法分别通过拒绝某一前提、引入第三值或让边界随语境移动来消解。

## 练习

1) 找出论证所依赖的模糊词项；2) 检查它在边界附近是否允许“微小差异不改变归属”的推理；3) 判断此处能否接受多值、超赋值或语境敏感的处理，再决定是否修正前提。

## 脚手架用法

- 边界追问：追问模糊词项究竟在哪一点上切换真假。 - 前提拆解：定位应拒绝的是基础前提还是递推前提。 - 语境校准：判断适用边界是否随语境与比较类移动。

[阅读网页](https://thinkingmodels.site/entries/detail/m13318)