Classes, why and how
Classes, why and how
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课程、原因和方式
DOI：
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发表时间：
2019
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通讯作者：
T. Schindler
中科院分区：
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作者：
T. Schindler
本文提出了一种新的方法来解决类理论的悖论。在本文的第一部分，我将区分类和集合，描述类对话的功能，并提出假设无类型类的几个理由。这涉及到应用的问题，不受限制的量化，减少属性，自然语言语义，和数学的认识论。在论文的第二部分，我将给出一些无类型类的公理。我的方法是松散的基础上哥德尔-罗素的有限范围的意义的想法。它示出了如何在该理论中推导出二阶Dedekind-Peano公理。最后，我讨论的理论是否可以作为一个解决方案的问题，无限制量化。在附录中，我证明了类理论相对于Zermelo-Fraenkel集理论的一致性。
This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory.