PL EN


2008 | 17 | 3(67) | 49-60
Article title

The Background and Significance of 'Crises' in the Foundations of Mathematics

Authors
Title variants
Languages of publication
EN
Abstracts
EN
The watersheds in the development of mathematics that lay bare the ambiguities and contradictions among its very basic notions and conceptions are commonly described as 'crises' in mathematics. They coincide with periods of intense mathematical research, often inspired by philosophical doctrines which help to clarify the notions and methods with the use of which many fundamental theorems are proved. The paper presents three best known and most widely discussed crises in the foundations of mathematics, reviews the causes of their appearance and discusses the difficulties that they have led to as well as possible ways of their resolution. The three crises arose in connection with the discovery of the incommensurable line segments in the Pythagorean School, in connection with the operations on the infinitesimals by the creators of the differential calculus (17th-18th centuries) and with respect to the foundations of mathematics connected with operations on the actually infinite sets (19th and 20th centuries).
Year
Volume
17
Issue
Pages
49-60
Physical description
Document type
ARTICLE
Contributors
author
  • J. Mrozek, Uniwersytet Gdanski, Instytut Filozofii, Socjologii i Dziennikarstwa, ul. Bielanska 5, 80-851 Gdansk, Poland
References
Document Type
Publication order reference
Identifiers
CEJSH db identifier
09PLAAAA064015
YADDA identifier
bwmeta1.element.de4c390d-5f2e-37a9-adda-53d963667f9d
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.