Ontology and the Foundations of Mathematics: Talking Past Each Other

Penelope Rush

doi:10.1017/9781108592505

Series: Elements in the Philosophy of Mathematics

Ontology and the Foundations of Mathematics

Talking Past Each Other

Published online by Cambridge University Press: 17 January 2022

Penelope Rush

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Penelope Rush: Affiliation:
The University of Notre Dame Australia

Summary

This Element looks at the problem of inter-translation between mathematical realism and anti-realism and argues that so far as realism is inter-translatable with anti-realism, there is a burden on the realist to show how her posited reality differs from that of the anti-realist. It also argues that an effective defence of just such a difference needs a commitment to the independence of mathematical reality, which in turn involves a commitment to the ontological access problem – the problem of how knowable mathematical truths are identifiable with a reality independent of us as knowers. Specifically, if the only access problem acknowledged is the epistemological problem – i.e. the problem of how we come to know mathematical truths – then nothing is gained by the realist notion of an independent reality and in effect, nothing distinguishes realism from anti-realism in mathematics.

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realism anti-realism independence inter-translatability truth

Type: Element
Information: Series: Elements in the Philosophy of Mathematics

DOI: https://doi.org/10.1017/9781108592505 [Opens in a new window]

Online ISBN: 9781108592505

Publisher: Cambridge University Press

Print publication: 10 February 2022

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Ontology and the Foundations of Mathematics

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