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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.