There is a long-standing gap in the literature as to whether Gödelian incompleteness constitutes a challenge for Neo-Logicism, and if so how serious it is. In this paper, I articulate and address the challenge in detail. The Neo-Logicist project is to demonstrate the analyticity of arithmetic by deriving all its truths from logical principles and suitable definitions. The specific concern raised by Gödel’s first incompleteness theorem is that no single sound system of logic syntactically implies all arithmetical truths. I set out some responses that initially seem appealing and explain why they are not compelling. The upshot is that Neo-Logicism either offers an epistemic route only to some truths of arithmetic; or that it has to move from a syntactic to a semantic notion of logical consequence, which risks undermining its epistemic goals. I conclude by considering Crispin Wright’s recent attempt to address Gödelian incompleteness, which I argue is not satisfactory.

中文翻译：

---

新逻辑主义和哥德尔不完备性

关于哥德尔的不完备性是否构成对新逻辑主义的挑战，以及如果是的话，它有多严重，文献中存在长期的分歧。在本文中，我详细阐述并解决了这一挑战。新逻辑主义者的项目是通过从逻辑原则和适当的定义中推导出算术的所有真理来证明算术的分析性。哥德尔第一个不完备性定理引起的具体关注是，没有一个单一的逻辑健全系统在句法上蕴含所有算术真理。我列出了一些最初看起来很有吸引力的回答，并解释了为什么它们没有说服力。结果是，新逻辑主义要么只提供通向某些算术真理的认识论途径；要么 或者它必须从句法概念转变为逻辑结果的语义概念，这有可能破坏其认知目标。