Russell’s Paradox: a historical study about the paradox in Frege’s theories
For over twenty years, Frege tried to find the foundations of arithmetic through logic, and by doing this, he attempted to establish the truth and certainty of the knowledge. However, when he believed his work wasdone, Bertrand Russell sent him a letter pointing out a paradox, known as Russell‟s par...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de História da Matemáticas (SBHMat)
2020-10-01
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| Series: | Revista Brasileira de História da Matemática |
| Subjects: | |
| Online Access: | https://www.rbhm.org.br/index.php/RBHM/article/view/24 |
| _version_ | 1818885272113250304 |
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| author | Aline Germano Fonseca Coury Denise Silva Vilela |
| author_facet | Aline Germano Fonseca Coury Denise Silva Vilela |
| author_sort | Aline Germano Fonseca Coury |
| collection | DOAJ |
| description | For over twenty years, Frege tried to find the foundations of arithmetic through logic, and by doing this, he attempted to establish the truth and certainty of the knowledge. However, when he believed his work wasdone, Bertrand Russell sent him a letter pointing out a paradox, known as Russell‟s paradox. It is often considered that Russell identified the paradox in Frege‟s theories. However, as shown in this paper, Russell, Frege and also George Cantor contributedsignificantly to the identification of the paradox. In 1902, Russell encouraged Frege to reconsider a portion of his work based in a paradox built from Cantor‟s theories. Previously, in 1885, Cantor had warned Frege about taking extensions of concepts in the construction of his system. With these considerations, Frege managed to identify the precise law and definitions that allowed the generation of the paradox in his system. The objective of this paper is to present a historical reconstruction of the paradox in Frege‟s publications and discuss it considering the correspondences exchanged between him and Russell. We shall take special attention to the role played by each of these mathematicians in the identification of the paradox and its developments. We also will show how Frege anticipated the solutions and new theories that would arise when dealing with logico-mathematical paradoxes, including but not limited to Russell‟s paradox. |
| first_indexed | 2024-12-19T16:02:48Z |
| format | Article |
| id | doaj.art-04b6e1515e704521baebd9a6136dd6a8 |
| institution | Directory Open Access Journal |
| issn | 1519-955X 2675-7079 |
| language | English |
| last_indexed | 2024-12-19T16:02:48Z |
| publishDate | 2020-10-01 |
| publisher | Sociedade Brasileira de História da Matemáticas (SBHMat) |
| record_format | Article |
| series | Revista Brasileira de História da Matemática |
| spelling | doaj.art-04b6e1515e704521baebd9a6136dd6a82022-12-21T20:14:54ZengSociedade Brasileira de História da Matemáticas (SBHMat)Revista Brasileira de História da Matemática1519-955X2675-70792020-10-01183510.47976/RBHM2018v18n351-22Russell’s Paradox: a historical study about the paradox in Frege’s theoriesAline Germano Fonseca Coury0Denise Silva Vilela1Universidade Federal de São CarlosUniversidade Federal de São CarlosFor over twenty years, Frege tried to find the foundations of arithmetic through logic, and by doing this, he attempted to establish the truth and certainty of the knowledge. However, when he believed his work wasdone, Bertrand Russell sent him a letter pointing out a paradox, known as Russell‟s paradox. It is often considered that Russell identified the paradox in Frege‟s theories. However, as shown in this paper, Russell, Frege and also George Cantor contributedsignificantly to the identification of the paradox. In 1902, Russell encouraged Frege to reconsider a portion of his work based in a paradox built from Cantor‟s theories. Previously, in 1885, Cantor had warned Frege about taking extensions of concepts in the construction of his system. With these considerations, Frege managed to identify the precise law and definitions that allowed the generation of the paradox in his system. The objective of this paper is to present a historical reconstruction of the paradox in Frege‟s publications and discuss it considering the correspondences exchanged between him and Russell. We shall take special attention to the role played by each of these mathematicians in the identification of the paradox and its developments. We also will show how Frege anticipated the solutions and new theories that would arise when dealing with logico-mathematical paradoxes, including but not limited to Russell‟s paradox.https://www.rbhm.org.br/index.php/RBHM/article/view/24MathematicHistoryRussell‟s ParadoxGottlob Frege |
| spellingShingle | Aline Germano Fonseca Coury Denise Silva Vilela Russell’s Paradox: a historical study about the paradox in Frege’s theories Revista Brasileira de História da Matemática Mathematic History Russell‟s Paradox Gottlob Frege |
| title | Russell’s Paradox: a historical study about the paradox in Frege’s theories |
| title_full | Russell’s Paradox: a historical study about the paradox in Frege’s theories |
| title_fullStr | Russell’s Paradox: a historical study about the paradox in Frege’s theories |
| title_full_unstemmed | Russell’s Paradox: a historical study about the paradox in Frege’s theories |
| title_short | Russell’s Paradox: a historical study about the paradox in Frege’s theories |
| title_sort | russell s paradox a historical study about the paradox in frege s theories |
| topic | Mathematic History Russell‟s Paradox Gottlob Frege |
| url | https://www.rbhm.org.br/index.php/RBHM/article/view/24 |
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