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Ontology and the Foundations of Mathematics Penelope Rush

Ontology and the Foundations of Mathematics By Penelope Rush

Ontology and the Foundations of Mathematics by Penelope Rush


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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.

Ontology and the Foundations of Mathematics Summary

Ontology and the Foundations of Mathematics: Talking Past Each Other by Penelope Rush

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.

Table of Contents

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

Additional information

NLS9781108716932
9781108716932
1108716938
Ontology and the Foundations of Mathematics: Talking Past Each Other by Penelope Rush
New
Paperback
Cambridge University Press
2022-02-10
75
N/A
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