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.

中文翻译：

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大基数和结构反射的内在理由


我们处理的是大基数是否是内在合理的集合论原则（内在性问题）的问题。为此，我们系统地回顾了为激励它们及其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。一个平行但密切相关的问题是是否存在产生所有大基数的数学原理（普遍性问题），我们还测试了原则对这个问题的回答能力。最后，我们讨论了结构反射原则及其对内在性和普遍性的回应，并进一步考虑了它们的一般合理性。