论文标题
古典意大利代数几何形状的客观性和严格性
Objectivity and Rigor in Classical Italian Algebraic Geometry
论文作者
论文摘要
意大利代数几何学学院对代数表面的分类被普遍认为是20世纪数学的突破。但是，实现的方法不能符合现代的严谨标准，因此从当代角度看来是可疑的。在本文中，我们瞥见了意大利代数几何学学院三个领先指数的数学实践：Castelnuovo，Enriques和Severi。然后，我们集中于他们对严格和直觉的独特概念。从当今通常假设的角度来看，从他们的角度来看，严谨既不反对直觉，也不理解为统一现象，可以区分小规模的严格和大规模的严格和大规模的严格，而Severi则在正式的严格和实质严格的严格性和实质性严格之间。最后，我们转向数学客观性的概念。我们从案例研究中汲取灵感，以提高客观性的多维分析。具体而言，我们建议各种严格的严格性可能与不同的客观性概念相关联：客观性是对事实和客观性作为主体间性的忠诚。
The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon - Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely objectivity as faithfulness to facts and objectivity as intersubjectivity.
