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Ontology and the Foundations of Mathematics: Talking Past Each Other.

Ontology and the Foundations of Mathematics: Talking Past Each Other.

・ISBN 978-1-108-71693-2 paper GB£ 18.00

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電子版あり 大学・学術機関向け電子ブック(eBook)ISBN 978-1-108-59250-5

著者・編者Rush, Penelope,
シリーズElements in the Philosophy of Mathematics
出版社(Cambridge U. Pr., UK)
出版年月2022.02
ページ数75 pp.
言語ENG
ニュース番号<679-98>

解説

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.