DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY
DOI:
https://doi.org/10.24193/subbphil.2018.3.02Keywords:
Determinacy of reference, Peano arithmetic, permutation argument, structuralism, Dedekind’s categoricity theorem, schematic theories, internal categoricityAbstract
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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