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.
Objectivity and Rigor in Classical Italian Algebraic Geometry / De Toffoli, Silvia; Fontanari, Claudio. - In: NOESIS. - ISSN 1275-7691. - 38:(2022), pp. 195-212. [10.4000/11xmd]
Objectivity and Rigor in Classical Italian Algebraic Geometry
De Toffoli, Silvia;Fontanari, Claudio
2022-01-01
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
Noesis.pdf
Solo gestori archivio
Descrizione: numero completo della rivista contente l'articolo
Tipologia:
Versione editoriale (Publisher’s layout)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
2.14 MB
Formato
Adobe PDF
|
2.14 MB | Adobe PDF | Visualizza/Apri |
noesis-7273.pdf
accesso aperto
Tipologia:
Versione editoriale (Publisher’s layout)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
217.76 kB
Formato
Adobe PDF
|
217.76 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione