Ontology and the Foundations of Mathematics

Ontology and the Foundations of Mathematics

by Penelope Rush
Epub (Kobo), Epub (Adobe)
Publication Date: 31/01/2022

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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.

ISBN:
9781108626569
9781108626569
Category:
Philosophy of science
Format:
Epub (Kobo), Epub (Adobe)
Publication Date:
31-01-2022
Language:
English
Publisher:
Cambridge University Press

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