# Fitch’s Paradox of Knowability

> 【EN】Fitch’s paradox of knowability (aka the knowability paradox or Church-Fitch Paradox) concerns any theory committed to the thesis that all truths are knowable. Historical examples of such theories arguably include Michael Dummett’s semantic antirealism (i.e., the view that any truth is verifiable), mathematical constructivism (i.e., the view that the truth of a mathematical formula depends on the mental constructions mathematicians use to prove those formulas), Hilary Putnam’s internal realism (i.e., the view that truth is what we would believe in ideal epistemic circumstances), Charles Sanders Peirce’s pragmatic theory of truth (i.e., that truth is what we would agree to at the limit of inquiry), logical positivism (i.e., the view that meaning is giving by verification conditions), Kant’s transcendental idealism (i.e., that all knowledge is knowledge of appearances), and George Berkeley’ … 【中】词条简述其历史，指出持可知性论题的历史例证包括达米特的语义反实在论、数学构造主义、普特南的内在实在论与皮尔士的实用主义真理论；随后给出悖论本身，并考察两类出路：逻辑上的修订（认知的、直觉主义的、弗协调的）与语义上的限制（情境与严格运算），还讨论相关的未决性悖论。

- ID: m13211
- Category: structure
- Domain: 逻辑学

## Definition

费奇的可知性悖论（又称可知性悖论或丘奇—费奇悖论）针对任何承诺“所有真理都是可知的”这一论题的理论：从这一看似温和的论题，似乎可以推出所有真理都已被知道，从而反实在论陷入困境。 脚手架作用：- 检验可知性：对凡真皆可被人知道这类口号做形式推演，暴露其隐含的代价。 - 识别自指陷阱：留意把知道写入被知内容时产生的自我反驳，防止循环论证。

## How it works

设想存在一个尚未被知道的真理 p，那么“p 且 p 不被知道”本身为真；按可知性论题，这个合取也是可知的，可在知道它的情形中 p 就被知道了，与合取的内容相矛盾，于是“存在未知真理”被排除。

## Practice

1) 明确所考察的理论是否承诺“所有真理可知”；2) 构造“p 且 p 未被知道”这类自指式命题；3) 对之应用可知性原则；4) 检查是否推出矛盾；5) 在限制原则、修改逻辑与放弃论题之间做出选择并说明代价。

## Use

- 检验可知性：对凡真皆可被人知道这类口号做形式推演，暴露其隐含的代价。 - 识别自指陷阱：留意把知道写入被知内容时产生的自我反驳，防止循环论证。

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