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Ontology and the Foundations of Mathematics

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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.

Author: Rush Penelope
Publisher: CAMBRIDGE UNIVERSITY PRESS
Pages: 46
ISBN: 9781108716932
Cover: Paperback
Edition Number: 1
Release Year: 2022

1. What are we Talking about?
2. Inter-translatability
3. Two Access Problems
4. Independence
5. Justification.

Penelope RushThe University of Notre Dame Australia

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