AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA PHILOSOPHIA - Ediţia nr.3 din 2018 | |||||||
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DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY. Autori: ADRIAN LUDUȘAN. |
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Rezumat: 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. Keywords: Determinacy of reference, Peano arithmetic, permutation argument, structuralism, Dedekind’s categoricity theorem, schematic theories, internal categoricity |
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