Ontology and the foundations of mathematics : talking past each other
Author(s)
Bibliographic Information
Ontology and the foundations of mathematics : talking past each other
（Cambridge elements, . Elements in philosophy of mathematics）
Cambridge University Press, 2022
- : pbk
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Note
Includes bibliographical references (p. [45]-46)
Description and Table of Contents
Description
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.
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