Symbol and Number


This paper explores the view that numbers are symbolically constituted, that numbers just are meaningful symbols. Such a view is what results if we take the conception of number spelled out by Husserl in the second part of his Philosophy of Arithmetic to be self-standing rather than supported by the conception of numbers as abstracted from sets. It will be argued that this latter conception is problematic in itself and, moreover, that it cannot be regarded as providing a foundation for the former.

Keywords: philosophy of arithmetic, Husserl, meaningful formalism, calculation, mathematical ontology

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