XIII—Categoricity and Indefinite Extensibility

Author: Walmsley J.

Source: Proceedings of the Aristotelian Society, Volume 102, Number 3, April 2002 , pp. 217-235(19)

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Abstract:

Structure is central to the realist view of mathematical disciplines with intended interpretations and categoricity is a model-theoretic notion that captures the idea of the determination of structure by theory. By considering the cases of arithmetic and (pure) set theory, I investigate how categoricity results might offer support from within to the realist view. I argue, amongst other things, that second-order quantification is essential to the support the categoricity results provide. I also note how the findings on categoricity relate to a fundamental feature of the realist position.

Language: English

Document Type: Research article

Affiliations: 1: All Souls College, Oxford

Publication date: 2002-04-01