数学的新基础危机,真的发生了吗?
A new foundational crisis in mathematics, is it really happening?
摘要:
本文在HoTT发现后重新思考了数学数学基础的地位。这一发现在数学家、哲学家和计算机科学家群体中引发的讨论可能预示着数学基础的新危机。通过研究HoTT背后的数学事实及其与现有基础的关系,我们得出结论,目前的危机不是一个。我们重申对数学基础的多元主义观点。本文包含了一个简短的调查的数学和历史背景需要了解的主要原则的基础问题。
英文摘要:
The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。