DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY
DETERMINACY OF REFERENCE, SCHEMATIC THEORIES, AND INTERNAL CATEGORICITY

Summary/Abstract: 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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