Ontology and the Foundations of Mathematics
Talking Past Each Other
Part of Elements in the Philosophy of Mathematics
- Author: Penelope Rush, The University of Notre Dame Australia
- Date Published: February 2022
- availability: Available
- format: Paperback
- isbn: 9781108716932
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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.
Reviews & endorsements
‘… extremely thought-provoking … Rush’s tenacity in pressing [ontological access problem] questions about the relevance of objecthood and independence is unique, unsettling, unrelenting, and effective.’ Nicholas Danne, Metascience
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×Product details
- Date Published: February 2022
- format: Paperback
- isbn: 9781108716932
- length: 75 pages
- dimensions: 229 x 150 x 4 mm
- weight: 0.09kg
- availability: Available
Table of Contents
1. What are we Talking about?
2. Inter-translatability
3. Two Access Problems
4. Independence
5. Justification.
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