The reception of incompleteness results within the mathematical community was very slow. One reason for the large underestimation of gödelians’ results in part of the community of mathematicians, which helped to brake their assimilation, was linked to the metamathematical character of the statement “I am not provable” used in the constructive proof. The perceived distance from the concrete mathematical work is perhaps behind the most striking case of the silence in this regard: that of the the French group ‘Bourbaki’ of formalists mathematicians. For this reason, in an attempt to address these objections, some scholars have devoted themselves to the search for independent statements of mathematical content, with proofs that did not rely on the typical Gödelian toolbox.
University of Siena, Italy - ORCID: 0000-0001-9441-7226
Chapter Title
Independent sentences of mathematical character
Authors
Duccio Pianigiani
Language
English
DOI
10.36253/979-12-215-0778-2.11
Peer Reviewed
Publication Year
2025
Copyright Information
© 2025 Author(s)
Content License
Metadata License
Book Title
Lectures in Proof Theory and Complexity
Authors
Duccio Pianigiani
Peer Reviewed
Publication Year
2025
Copyright Information
© 2025 Author(s)
Content License
Metadata License
Publisher Name
Firenze University Press, USiena Press
DOI
10.36253/979-12-215-0778-2
eISBN (pdf)
979-12-215-0778-2
eISBN (xml)
979-12-215-0779-9
Series Title
UNIverSI. Ricerca e Didattica all’Università di Siena
Series ISSN
3035-5915
Series E-ISSN
3035-5931