Frege's two notions of "extension"
| dc.creator | Velloso, Araceli Rosich Soares | |
| dc.date.accessioned | 2024-01-09T11:33:09Z | |
| dc.date.available | 2024-01-09T11:33:09Z | |
| dc.date.issued | 2023-06-28 | |
| dc.description.abstract | The goal of this paper is to answer a question proposed by Richard Heck in the paper “Formal Arithmetic Before Grundgesetze”. In that paper, Heck inquires as to the reasons why it took almost eight years for Frege to honor his promises of concluding his grandiose project of grounding mathe matics on logic. Although Heck tried to answer his own question, we think that a more adequate philosophical discussion regarding Frege’s delay can still be offered. This paper will try to fill in that gap by presenting what we under stand was the central problem faced by Frege on Die Grundlagen der Arithmetik: the lack of a standard criterion to fix the meaning of identity propositions of mathematics. We believe that Frege’s initial proposal of a dual character for “identity propositions” was the cause of all his problems in fixing his defini tion of numbers in Die Grundlagen. In the aforementioned eight-year period, Frege’s challenge became that of finding a criterion capable of unifying his treatment of identities. In our account, the German philosopher finally de cided to fill in this gap by providing a new construal of “extension”, one which included some important refinements on his previous account of that notion. The new concept thus construed allowed Frege to unify his treatment of iden tity propositions by including in his system a universal and flexible criterion for deciding the truth of any identity proposition. Frege’s new construal of “extension” was supported by his famous basic law V. So, our claim will be that Frege’s resistance and doubts about the inclusion of axiom V as a logical law in his system were the primary cause of that delay. | |
| dc.identifier.citation | VELLOSO, Araceli. Frege's two notions of "extension". Philósophos, Goiânia, v. 28, n. 1, p. 1-34, jan./jun. 2023. DOI: 10.5216/phi.v28i1.75351. Disponível em: https://revistas.ufg.br/philosophos/article/view/75351/39970. Acesso em: 26 dez. 2023. | |
| dc.identifier.doi | 10.5216/phi.v28i1.75351 | |
| dc.identifier.issn | e- 1982-2928 | |
| dc.identifier.uri | http://repositorio.bc.ufg.br//handle/ri/24056 | |
| dc.language.iso | eng | |
| dc.publisher | Universidade Federal de Goiás | |
| dc.publisher.country | Brasil | |
| dc.publisher.department | Faculdade de Filosofia - FAFIL (RMG) | |
| dc.publisher.initials | UFG | |
| dc.rights | Acesso Aberto | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Frege | |
| dc.subject | Extension | |
| dc.subject | Identity | |
| dc.title | Frege's two notions of "extension" | |
| dc.type | Artigo |
Arquivos
Pacote Original
1 - 1 de 1
Nenhuma Miniatura disponível
- Nome:
- Artigo - Araceli Rosich Soares Velloso - 2023.pdf
- Tamanho:
- 414.09 KB
- Formato:
- Adobe Portable Document Format
Licença do Pacote
1 - 1 de 1
Nenhuma Miniatura disponível
- Nome:
- license.txt
- Tamanho:
- 1.71 KB
- Formato:
- Item-specific license agreed upon to submission
- Descrição: