斯塔尔内克的条件句逻辑问题是不可解的
Stalnaker's logical problem of conditionals is unsolvable
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中文总结 AI 辅助
该研究证明，斯塔尔内克的条件句语义的一阶扩充形式不可递归公理化，即其条件句逻辑问题在含一阶量词的语言中不可解，并探讨了该结果对条件句逻辑研究的意义。
中文摘要 AI 辅助
斯塔尔内克所构想的条件句逻辑问题，相当于对公理进行公理化，该公理采用以命题（即可能世界集合）为自变量的选择函数作为条件句的特定语义。尽管该语义的语句形式可递归公理化，但我们证明其添加一阶量词后的扩充形式不可公理化——即我们表明，在含一阶量词的语言中，斯塔尔内克的条件句逻辑问题不可解。我们通过展示如何在该逻辑中解释算术来证明这一点。结论部分，我们讨论了该结果对条件句逻辑研究的意义。
英文摘要
The logical problem of conditionals, as conceived by Stalnaker, amounts to axiomatizing a particular semantics for conditionals which utilizes selection functions that take propositions (i.e., sets of worlds) as arguments. While the sentential form of this semantics is recursively axiomatizable, we prove that its enrichment with first-order quantifiers is not---that is, we show that Stalnaker's logical problem of conditionals is unsolvable in the language with first-order quantifiers. We demonstrate this by showing how to interpret arithmetic in the logic. In the conclusion, we discuss the implications of this result for the study of conditional logic.
