Naturalism, notation, and the metaphysics of mathematics

Philosophia Mathematica 7 (2):178-199 (1999)
Abstract
The instability inherent in the historical inventory of mathematical objects challenges philosophers. Naturalism suggests we can construct enduring answers to ontological questions through an investigation of the processes whereby mathematical objects come into existence. Patterns of historical development suggest that mathematical objects undergo an intelligible process of reification in tandem with notational innovation. Investigating changes in mathematical languages is a necessary first step towards a viable ontology. For this reason, scholars should not modernize historical texts without caution, as the use of anachronistic notation tends to impede, rather than enhance, our ability to recognize the emergent nature of mathematical objects.
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