Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know (Rosenkranz Mind, 127 (506), 309–338 2018 ). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is not provable in minimal arithmetic or that the negation of that sentence is not provable in minimal arithmetic. This serves as the formal background for an example that calls into question the correctness of Rosenkranz’s logic of justification.

中文翻译：

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罗森克兰兹的正当性和不可证明性逻辑

Rosenkranz 最近提出了一种命题式、非事实性的、考虑到所有事物的理由的逻辑，该逻辑基于处于能够知道的概念的逻辑 (Rosenkranz Mind, 127 (506), 309–338 2018 ) . 除了罗森克兰兹已经接受的一些核心原则之外，我还从三个相当弱的假设开始，我证明，如果一个人对最小算术公理有积极的内省和模态稳健的知识，那么一个人就能够知道一个句子在最小算术中是不可证明的，或者该句子的否定在最小算术中是不可证明的。这作为一个例子的形式背景，该例子质疑罗森克兰茨的辩护逻辑的正确性。