AI 中文总结
本文提出分级认知算术非多元论，主张在哥德尔不完备产生的算术扩展间选择时，其合理性随语句的集合论强度变化，并依赖于大基数的辩护。
AI 中文摘要
哥德尔不完备性产生算术语句$A$，使得$PA+A$与$PA+\ eg A$均一致。这些扩展是否同样合法？我提出分级认知算术非多元论：选择它们之间的理由随$A$的集合论强度而变化。我捍卫$PA+Con(PA)$，并表明鉴于弗里德曼的具体不完备性，柯尔纳对一阶算术的非多元论是不充分的。解决此类语句的选择问题取决于对大基数的辩护。因此，捍卫分级非多元论涉及哥德尔纲领及非常大基数的辩护。
英文摘要
Gödelian incompleteness yields arithmetical sentences $A$ such that $PA+A$ and $PA+\neg A$ are both consistent. Are such extensions equally legitimate? I propose graded epistemic arithmetical non-pluralism: justification for choosing between them varies with the set-theoretic strength of $A$. I defend $PA+Con(PA)$ and show Koellner's non-pluralism for first-order arithmetic is inadequate given Friedman's concrete incompleteness. Resolving the selection problem for such sentences turns on justifying large cardinals. Defending graded non-pluralism thus engages Gödel's programme and the justification of very large cardinals.
CommentsAccepted and forthcoming in Philosophia Mathematica
