谓词类和严格的潜在论

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2024-11-12 DOI:10.1093/philmat/nkae020

Øystein Linnebo, Stewart Shapiro

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引用次数: 0

摘要

集合是由元素定义的组合集合，而类则是由成员条件定义的逻辑集合。我们在潜在论的背景下，对（组合）集合的（逻辑）类提出了一种谓词方法。我们有理由采用一种更严格的潜在论形式，这种潜在论不仅坚持认为每个对象都是在不可完成过程的某个阶段产生的，而且坚持认为每个真理都是在这样的某个阶段 "成真 "的。这种严格形式的潜在论的自然逻辑是半直觉主义的：每个集合大小的域是经典的，所有集合或所有类的域是直觉主义的。

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Predicative Classes and Strict Potentialism

While sets are combinatorial collections, defined by their elements, classes are logical collections, defined by their membership conditions. We develop, in a potentialist setting, a predicative approach to (logical) classes of (combinatorial) sets. Some reasons emerge to adopt a stricter form of potentialism, which insists, not only that each object is generated at some stage of an incompletable process, but also that each truth is “made true” at some such stage. The natural logic of this strict form of potentialism is semi-intuitionistic: where each set-sized domain is classical, the domain of all sets or all classes is intuitionistic.

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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.