DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY
The article surveys the problem of the determinacy of reference in the contemporary philosophy of mathematics focusing on Peano arithmetic. I present the philosophical arguments behind the shift from the problem of the referential determinacy of singular mathematical terms to that of nonalgebraic/u...
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| Format: | Article |
| Language: | deu |
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Babeș-Bolyai University
2018-12-01
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| Series: | Studia Universitatis Babeș-Bolyai. Philosophia |
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| Online Access: | https://studia.reviste.ubbcluj.ro/index.php/subbphilosophia/article/view/3151 |
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| author | Adrian LUDUŞAN |
| author_facet | Adrian LUDUŞAN |
| author_sort | Adrian LUDUŞAN |
| collection | DOAJ |
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The article surveys the problem of the determinacy of reference in the contemporary philosophy of mathematics focusing on Peano arithmetic. I present the philosophical arguments behind the shift from the problem of the referential determinacy of singular mathematical terms to that of nonalgebraic/univocal theories. I examine Shaughan Lavine’s particular solution to this problem based on schematic theories and an internalized version of Dedekind’s categoricity theorem for Peano arithmetic. I will argue that Lavine’s detailed and sophisticated solution is unwarranted. However, some of the arguments that I present are applicable, mutatis mutandis, to all versions of internal categoricity conceived as a philosophical remedy for the problem of referential determinacy of arithmetical theories.
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| format | Article |
| id | doaj-art-4d3501e9a1df4fbcbe90ebddf89c856c |
| institution | DOAJ |
| issn | 2065-9407 |
| language | deu |
| publishDate | 2018-12-01 |
| publisher | Babeș-Bolyai University |
| record_format | Article |
| series | Studia Universitatis Babeș-Bolyai. Philosophia |
| spelling | doaj-art-4d3501e9a1df4fbcbe90ebddf89c856c2025-08-20T03:15:57ZdeuBabeș-Bolyai UniversityStudia Universitatis Babeș-Bolyai. Philosophia2065-94072018-12-0163310.24193/subbphil.2018.3.02DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITYAdrian LUDUŞAN0Department of European Studies and Governance, Faculty of European Studies, Cluj-Napoca, Romania. Email: adiludusan@gmail.com. The article surveys the problem of the determinacy of reference in the contemporary philosophy of mathematics focusing on Peano arithmetic. I present the philosophical arguments behind the shift from the problem of the referential determinacy of singular mathematical terms to that of nonalgebraic/univocal theories. I examine Shaughan Lavine’s particular solution to this problem based on schematic theories and an internalized version of Dedekind’s categoricity theorem for Peano arithmetic. I will argue that Lavine’s detailed and sophisticated solution is unwarranted. However, some of the arguments that I present are applicable, mutatis mutandis, to all versions of internal categoricity conceived as a philosophical remedy for the problem of referential determinacy of arithmetical theories. https://studia.reviste.ubbcluj.ro/index.php/subbphilosophia/article/view/3151Determinacy of reference, Peano arithmetic, permutation argument, structuralism, Dedekind’s categoricity theorem, schematic theories, internal categoricity |
| spellingShingle | Adrian LUDUŞAN DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY Studia Universitatis Babeș-Bolyai. Philosophia Determinacy of reference, Peano arithmetic, permutation argument, structuralism, Dedekind’s categoricity theorem, schematic theories, internal categoricity |
| title | DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY |
| title_full | DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY |
| title_fullStr | DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY |
| title_full_unstemmed | DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY |
| title_short | DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY |
| title_sort | determinacy of reference schematic theories and internal categoricity |
| topic | Determinacy of reference, Peano arithmetic, permutation argument, structuralism, Dedekind’s categoricity theorem, schematic theories, internal categoricity |
| url | https://studia.reviste.ubbcluj.ro/index.php/subbphilosophia/article/view/3151 |
| work_keys_str_mv | AT adrianludusan determinacyofreferenceschematictheoriesandinternalcategoricity |