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: | German |
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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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| Summary: | 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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| ISSN: | 2065-9407 |