Yablo’s Paradox in Second-Order Languages: Consistency and Unsatisfiability
Yablo’s Paradox in Second-Order Languages: Consistency and Unsatisfiability
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二阶语言中的 Yablo 悖论：一致性和不可满足性
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发表时间：
2013
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通讯作者：
L. Picollo
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作者：
L. Picollo
Stephen Yablo[23，24]引入了一个新的非正式悖论，它由一个无限的半形式化句子列表构成。已经证明，用一阶语言形式化的Yablo的推理是无效的，因为主要由于紧致性定理，不可能从序列中推导出Falsum。这一结果让人对这份句子清单的悖论性质产生了怀疑。由于二阶语言不是紧凑的，在确定了一个或一组表达式被认为是悖论的两个常见意义之后，我研究了这些语言中Yablo列表的悖论。虽然在第一种意义上不是悖论，但第二种意义上的清单是一个悖论。我的结论是，这足以认为亚布罗最初的名单自相矛盾，他的非正式论点是有效的。
Stephen Yablo [23,24] introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo’s piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be paradoxical, since second-order languages are not compact, I study the paradoxicality of Yablo’s list within these languages. While non-paradoxical in the first sense, the second-order version of the list is a paradox in our second sense. I conclude that this suffices for regarding Yablo’s original list as paradoxical and his informal argument as valid.