The asymmetry of mathematical determinacy: understanding why arithmetic is determinate and set theory indeterminate.

数学确定性的不对称性：理解为什么算术是确定的而集合论是不确定的。

• 批准号: 2586962
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2586962
• 关键词: asymmetry; mathematical; determinacy; understanding; why

Most mathematicians and philosophers implicitly accept that arithmetic, the mathematical investigation of natural numbers and their basic operations, is determinate, i.e. all of its statements are either true or false. Nonetheless, many of them also suspect that some statements of set theory, the part of mathematics that deals with collections of objects as well as infinity, could be indeterminate, i.e. lack a truth value. In my project, I try to ground these intuitions by providing philosophical and technical arguments whose ultimate goal is to support a form of set-theoretic pluralism, that is, the idea that, unlike arithmetic, set theory presents a multiplicity of universes. And, on the way there, I hope to grasp what it means for something to be determinate and, more importantly, to reveal some of the hidden features of our everyday use of mathematics and some of the wonders of the infinite.

大多数数学家和哲学家含蓄地接受算术，即对自然数及其基本运算的数学研究是确定的，即它的所有陈述要么是真的，要么是假的。尽管如此，他们中的许多人也怀疑集合论的一些陈述可能是不确定的，即缺乏真值。集合论是数学中处理对象集合和无穷大的部分。在我的项目中，我试图通过提供哲学和技术论证来证明这些直觉的基础，这些论证的最终目标是支持一种集合论多元化，也就是说，与算术不同的是，集合论呈现出多种宇宙。在去那里的路上，我希望能领会什么是确定的东西，更重要的是，揭示我们日常使用数学的一些隐藏特征和无限的一些奇迹。