Ontology and the Foundations of Mathematics: Talking Past Each Other
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.
Categories:
Year:
2022
Publisher:
Cambridge University Press
Language:
english
Pages:
54
ISBN 10:
1108716938
ISBN 13:
9781108716932
File:
PDF, 1.01 MB
IPFS:
,
english, 2022
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