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Curves in Gödel-Space: Towards a Structuralist Ontology of Mathematical Signs

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Abstract

I propose an account of the metaphysics of the expressions of a mathematical language which brings together the structuralist construal of a mathematical object as a place in a structure, the semantic notion of indexicality and Kit Fine’s ontological theory of qua objects. By contrasting this indexical qua objects account with several other accounts of the metaphysics of mathematical expressions, I show that it does justice both to the abstractness that mathematical expressions have because they are mathematical objects and to the element of concreteness that they have because they are also used as signs. In a concluding section, I comment on the pragmatic element that has entered ontology by way of the notion of indexicality and use it to give an answer to a question Stewart Shapiro has recently posed about the status of meta-mathematics in the structuralist philosophy of mathematics.

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  1. Department of Philosophy, University of Münster, Domplatz 23, D-48143, Münster, Germany

    Martin Pleitz

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  1. Martin Pleitz
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Correspondence to Martin Pleitz.

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In memory of Rosemarie Rheinwald (1948–2009)

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Pleitz, M. Curves in Gödel-Space: Towards a Structuralist Ontology of Mathematical Signs. Stud Logica 96, 193–218 (2010). https://doi.org/10.1007/s11225-010-9286-y

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