Authors
Alexander Paseau
Oxford University
Abstract
James Walmsley in “Categoricity and Indefinite Extensibility” argues that a realist about some branch of mathematics X (e.g. arithmetic) apparently cannot use the categoricity of an axiomatisation of X to justify her belief that every sentence of the language of X has a truth-value. My discussion note first corrects Walmsley’s formulation of his claim. It then shows that his argument for it hinges on the implausible idea that grasping that there is some model of the axioms amounts to grasping that there is a unique such model.
Keywords logic  philosophy of logic  categorical  categoricity  second-order logic
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DOI 10.1111/j.0066-7373.2004.00122.x
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Categoricity and Indefinite Extensibility.James Walmsley - 2002 - Proceedings of the Aristotelian Society 102 (3):217–235.

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