Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom
The article examines the common interpretation of the axiom of reducibility in Principia Mathematica according to which the axiom cannot be considered as logical, which casts doubt on the success of the program of logicism. In particular, the ad hoc character attributed to the reducibility axiom...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonomous Educational Institution of Higher Education
2022-05-01
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| Series: | Омский научный вестник: Серия "Общество. История. Современность" |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%D0%A2.%207,%20%E2%84%96%202%20(%D0%9E%D0%98%D0%A1)/102-107%20%D0%A6%D0%B5%D0%BB%D0%B8%D1%89%D0%B5%D0%B2%20%D0%92.%20%D0%92.,%20%D0%A5%D0%BB%D0%B5%D0%B1%D0%B0%D0%BB%D0%B8%D0%BD%20%D0%90.%20%D0%92..pdf |
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| _version_ | 1832570171129069568 |
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| author | V. V. Tselishchev A. V. Khlebalin |
| author_facet | V. V. Tselishchev A. V. Khlebalin |
| author_sort | V. V. Tselishchev |
| collection | DOAJ |
| description | The article examines the common interpretation of the axiom of reducibility in
Principia Mathematica according to which the axiom cannot be considered as logical,
which casts doubt on the success of the program of logicism. In particular, the ad
hoc character attributed to the reducibility axiom is refuted and its explanatory role
in substantiating Russell’s uniform approach to resolving set-theoretic and semantic
paradoxes is affirmed. The key emphasis in the explanatory nature of the axiom of
reducibility is placed on the intensional interpretation of mathematical discourse. |
| format | Article |
| id | doaj-art-de3d180c1f734a28a869fe7f31323c27 |
| institution | Kabale University |
| issn | 2542-0488 2541-7983 |
| language | English |
| publishDate | 2022-05-01 |
| publisher | Omsk State Technical University, Federal State Autonomous Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник: Серия "Общество. История. Современность" |
| spelling | doaj-art-de3d180c1f734a28a869fe7f31323c272025-02-02T16:31:27ZengOmsk State Technical University, Federal State Autonomous Educational Institution of Higher EducationОмский научный вестник: Серия "Общество. История. Современность"2542-04882541-79832022-05-017210210710.25206/2542-0488-2022-7-2-102-107Understanding and ad hoc Explanation: A Case of Russell’s Reducibility AxiomV. V. Tselishchev0A. V. Khlebalin1https://orcid.org/0000-0002-3536-3974Institute of Philosophy and Law of the Siberian Branch of the Russian Academy of SciencesInstitute of Philosophy and Law of the Siberian Branch of the Russian Academy of SciencesThe article examines the common interpretation of the axiom of reducibility in Principia Mathematica according to which the axiom cannot be considered as logical, which casts doubt on the success of the program of logicism. In particular, the ad hoc character attributed to the reducibility axiom is refuted and its explanatory role in substantiating Russell’s uniform approach to resolving set-theoretic and semantic paradoxes is affirmed. The key emphasis in the explanatory nature of the axiom of reducibility is placed on the intensional interpretation of mathematical discourse.https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%D0%A2.%207,%20%E2%84%96%202%20(%D0%9E%D0%98%D0%A1)/102-107%20%D0%A6%D0%B5%D0%BB%D0%B8%D1%89%D0%B5%D0%B2%20%D0%92.%20%D0%92.,%20%D0%A5%D0%BB%D0%B5%D0%B1%D0%B0%D0%BB%D0%B8%D0%BD%20%D0%90.%20%D0%92..pdfbranched type theoryaxiom of reducibilityexplanatory schemeunderstandingintensionality of mathematics |
| spellingShingle | V. V. Tselishchev A. V. Khlebalin Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom Омский научный вестник: Серия "Общество. История. Современность" branched type theory axiom of reducibility explanatory scheme understanding intensionality of mathematics |
| title | Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom |
| title_full | Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom |
| title_fullStr | Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom |
| title_full_unstemmed | Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom |
| title_short | Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom |
| title_sort | understanding and ad hoc explanation a case of russell s reducibility axiom |
| topic | branched type theory axiom of reducibility explanatory scheme understanding intensionality of mathematics |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2022/%D0%A2.%207,%20%E2%84%96%202%20(%D0%9E%D0%98%D0%A1)/102-107%20%D0%A6%D0%B5%D0%BB%D0%B8%D1%89%D0%B5%D0%B2%20%D0%92.%20%D0%92.,%20%D0%A5%D0%BB%D0%B5%D0%B1%D0%B0%D0%BB%D0%B8%D0%BD%20%D0%90.%20%D0%92..pdf |
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