大基数和结构反射的内在理由

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2025-05-13 DOI:10.1093/philmat/nkaf006

Joan Bagaria, Claudio Ternullo

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引用次数: 0

摘要

我们处理的问题，是否大的基数本质上证明的集合论原则（本质问题）。为此，我们以系统的方式回顾了为激励它们和它们的数学表达式而制定的抽象原则，并评估了它们的内在合理性。一个平行但紧密相关的问题是，是否存在产生所有大基数的数学原则（普遍性问题），我们也测试原则对这个问题的响应能力。最后，我们讨论了结构反射原理及其对内在性和普遍性的回应，并对结构反射原理的一般正当性作了进一步的思考。

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Intrinsic Justification for Large Cardinals and Structural Reflection

We deal with the issue of whether large cardinals are intrinsically justified set-theoretic principles (Intrinsicness Issue). To this end, we review, in a systematic fashion, the abstract principles that have been formulated to motivate them and their mathematical expressions, and assess their intrinsic justifiability. A parallel, but closely linked, issue is whether there exist mathematical principles that yield all large cardinals (Universality Issue), and we also test principles for their ability to respond to this issue. Finally, we discuss Structural Reflection Principles and their responses to Intrinsicness and Universality, and also make some further considerations on their general justifiability.

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来源期刊

Philosophia Mathematica HISTORY & PHILOSOPHY OF SCIENCE-

CiteScore

1.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Philosophia Mathematica is the only journal in the world devoted specifically to philosophy of mathematics. The journal publishes peer-reviewed new work in philosophy of mathematics, the application of mathematics, and computing. In addition to main articles, sometimes grouped on a single theme, there are shorter discussion notes, letters, and book reviews. The journal is published online-only, with three issues published per year.